Factors Analyzed in PIT and TTC Probabilities
\r\n\tThe discovery of Nylon by Wallace Hume Carothers, a Harvard-educated world-renowned organic chemist born in Burlington, IA in 1896, successfully crowned the attempts developed by E.I du Pont de Nemours & Company to investigate the structure of high molecular weight polymers and to synthesize the first synthetic polymeric fibre.
\r\n\tWhen it hit the market, it was in the form of stockings and all the women in the US wanted to get their hands on a pair. Despite the successful launch of Nylon on the synthetic fibre market and the high expectations created by its extraordinary features, the unexpected war events in 1941 diverted the production of the new synthetic fibre almost exclusively on military applications. Parachutes, ropes, bootlaces, fuel tanks, mosquito nets and hammocks absorbed the production of Nylon, which helped to determine the WWII events. When the war ended and production returned to pre-war levels, consumers rushed to the department stores in search of stockings, accessories and high-fashion garments.
\r\n\tEven if the world of high fashion now seems to more appreciate the use of natural fibres, Nylon is one of the most widely used polymers for the production of technical fibres and fabrics, automotive and micromechanical components. The global nylon 6 & 66 market is expected to reach USD 41.13 billion by 2025, by the following growth at 6.1% CAGR owing to the Increasing focus on fuel-efficient and less polluting vehicles.
\r\n\t
\r\n\tThe amazing success story of Nylon still continues. While its wide availability inspired the development of innovative applications, such as the additive manufacturing, on the other hand, proper disposal after use of high amounts of Nylon resin energised the development of efficient recycling methodology, including chemical recycling. Moreover, the production of Nylon precursors from biomass has become desirable due to the depletion of fossil hydrocarbons and to reduce greenhouse gas (GHG) emissions. This unique combination of technical and socio-economic driving forces is one that aims to further promote the development of Nylon as one of the most suitable ""best polymers"" with a low ecological footprint.
\r\n\t
\r\n\tThe aim of this publication is to unveil the relationships between the chemical structure and the outstanding properties of the broad family of polyamides and to describe the most recent use of Nylon in fostering new applications and promoting a culture aware of environmental sustainability.
Fuzzy systems have been applied in a variety of problems with great success. One key factor is that the fuzzy rules database can be easily designed, in order to emulate a human rational decision making process just as experts usually do while facing hard jobs. Thus, in essence any process that requires human judgment can be translated into simple rules in a fuzzy system, provided that variables can be used in fuzzy sets or linguistic terms. One example is the prediction of a customer’s default delay in payment, which seems to be a very simplistic and intuitive process and can be indeed modeled into a set of rules based on an expert’s knowledge. In addition, the facility of implementing a fuzzy system can speed up the analysis of huge customer databases, since the usual manual process of analyzing each customer can be automated by a system which in theory has the same ability to infer as the human mind does.
This chapter shows the whole design of the fuzzy system to predict the customers’ default rate in small and medium-sized businesses, and how this information can be used to provide a better cash flow estimate. The chapter is structured as follows: in section 2 we present the current economy scenario and why the default is a big problem; in section 3 we analyze some tools that are used to mitigate the risks; in section 4 we explain in details how the fuzzy approach can be exploited in this case; in section 5 we show the design of the fuzzy system; in section 6 we show some results from the simulations of this system; and finally in section 7 we discuss the results and conclude this chapter.
The default in the retail sector is a concerning problem in the modern world [1]. According to the formal definition, the default is a broader term. Technically it means any failure of some entity, natural or legal, to meet its legal obligations by not paying invoices of loan, services, bonds or wholesales [2]. The term default also applies to the failure of a government to repay its national debt; in that case it is national or sovereign default. In the case of customer default, the concerns are on rent, mortgage, consumer credits, utility payments or funding. While in the first case, the debt is related to the macroeconomic scenario, that means financial crisis over a whole country or continent, the latter is more related to customer’s profiles and microeconomics. That led to the development of risk and credit analysis [3].
The default has a strong effect in developing companies, as well as in small and medium sized business. Mortgage and interest rates could be strongly affected by the customer default rate. Since the whole economy is tightly linked, the default represents a break in this chain, leading, in large scale, to a national level crisis.
Economic Chain
When the default happens, it starts a shortcoming in a company’s finance, and that means a loss for the provider. Some tools such as financial protection insurance and risk scores may remedy to a certain point, but in most cases they are insufficient to recover from the main problem [4]. However, if one could forecast or predict how many customers would delay payment or how much would be default, the companies would have the chance to prepare itself against a possible low cash flow.
Analysing per sector, it is known that service based industries are usually more affected by defaults.
Defaults per Industry. Source: Serasa, 2013 [5]
In order to better understand this problem, we should take into account the reasons for consumer default. The recent economic growing and integration speeded up the development of many enterprises, and much of this has been accomplished by the mechanisms of credit and financial leasing [6]. The credit offers expanded to small businesses and so have been to ordinary workers, thus increasing the economic activity [7]. In developing countries such as Brazil, many families from lower and middle classes turned out to actively participate in the economy as voracious consumers [4]. Consequently the debt of Brazilian families rose from 15% in 1992 to over 40% in 2012 [5]. Moreover, by analysing the reasons for the debt, it can be easily perceived that this index is not likely to be lowered, but limiting credit seems also not to be a good option [7]. However, the consumer default is correlated to some behaviours that can be detected in risk analysis systems [8]. Therefore by understanding the reasons for default, this problem can be more controllable.
Upon a report issued by Central Bank of Brazil [9], the causes for consumer default vary from bad financial habits (compulsivity, expenses greater than revenue) to financial problems (unemployment, little wages, crises, default from their clients).
Causes for Defaults. Source: Annibal, 2009
Risk Analysis tools take into account as much information as possible from clients in order to evaluate the risk score of a given client. It is known that when a customer faces problems, he or she is more likely to overdue the bills or even not to pay at all. Likewise when customers always pay their bills without delay, it is a good sign they are less likely to delay.
The customer default prediction remains a concern for many enterprises, owners, investors and business men all over the world. Every default implies that some party is losing money, since a good or a service has been offered for free without any compensation. In large scale this leads to economy shrinking and inflation [10]. For small companies the effects may be even more drastic due to its small budget. Every small business is oriented to observe its cash flow, but in fact when a customer fails to pay its debt to the company, the cash flow accuracy is severely affected. So there is a need to estimate a percentage of default from its clients. The first and main consequence for small business is that it may not be able to meet its obligations, although it has a quite good financial planning. A second consequence is that the billing department will be overloaded since many bills remain unpaid and the company itself may fail to operate.
The defaults cannot be prevented, but can be forecasted. Whenever a lender wants to issue credits to a borrower, he may perform an analysis on the financial statements of the borrower in order to assess its capability to comply with its debts [11]. However many aspects may be not considered in traditional risk and credit analysis, since many risk analysis are conducted by means of likelihood and probabilities [2]. On the other hand, there is a call for simpler and quicker risk analysis [12, 13].
Although most of these tools address the credit analysis in the form of a loan, the same procedure applies to any customer that is buying goods/services from a supplier [14], especially if it is in the form of leasing or even contracting. Since we are dealing here with the problem of predicting default, our goal is to forecast when a customer will not pay his/debt causing a default. To that end, the methodologies fall particularly on risk and credit analysis, bankruptcy prediction and probability of default.
In recent decades, a number of objective, quantitative systems for scoring credits have been developed. The risk of credit is assessed by comparison of accounting ratios of potential borrowers with industry or trends in the financial variables. The banks are provided with many of these ratios, since they are the main credit providers, but that information is not always available to enterprises. Traditional credit risk analyses are implemented in expensive expert systems whose development is very time-consuming. On the other hand simpler forms to grant credit may be achieved by the use of reduced models, such as Balanced Scorecard, Jarrow-Turnbull, among others [15].
Balanced Scorecard, also known as BSC, is actually a management technique aimed at assessing an enterprise’s performance from four perspectives: financial, customer, internal processes, and learning. A balanced score of these indicators makes a system that helps the enterprise to select and focus strategies to achieve goals in the near future. The customer and financial perspective of this analysis composes a good index to evaluate the risk of servicing a given client [12]. But unfortunately this is not always enough to define strategy, and there should be also other performance indicators to determine the risk in a more accurate way.
A reduced form of risk model was published by [16] which is an extension of the Merton model [17] to a random interest rates framework. In this model, risk is modeled as a statistical process. The value of risk is evaluated using a continuous probability of default, estimated in two approaches: Deriving Point in Time (PIT) or Through the Cycle (TTC). The main difference between these approaches regards to internal and external factors. The term PIT applies to probabilities of default that are dependent of general credit conditions or external factors, while TTC applies to probabilities of default that are not subjected to external factors [18].
\n\t\t\t\tPIT Factors\n\t\t\t | \n\t\t\t\n\t\t\t\tTTC Factors\n\t\t\t | \n\t\t
GDP Growth Rates | \n\t\t\tRevenue Growth | \n\t\t
House Price Indices | \n\t\t\tNumber of Default Cases | \n\t\t
Unemployment | \n\t\t\tLoad to Value Ratio | \n\t\t
Factors Analyzed in PIT and TTC Probabilities
One benefit of risk analysis is that it allows the prediction of bankruptcy for a given entity. One of the oldest methods for bankruptcy prediction was published in 1968 by Altman. His formula is used to predict the probability of bankruptcy within 2 years by using Z-scores. The Z-score is a linear combination of four or five coefficient-weighted common business ratios.
where:
T1 is the Working Capital / Total Assets
T2 is the Retained Earnings / Total Assets
T3 is the Earnings Before Interest and Taxes / Total Assets
T4 is the Market Value of Equity / Book Value of Liabilities
T5 is the Sales or Revenue / Total Assets
Z is the score which denotes where an entity will face bankruptcy or not. The Bankruptcy threshold varies on the entity’s activity, but in general it is defined as follows
Altman Z-Score [19] model was found to be 72% accurate in predicting bankruptcy two years before the event with only 6% of false negatives. It is still well accepted by auditors, management accountants and financial directors for load evaluation. However, this model is not recommended for use with financial companies such as banks or factoring, because the balance sheets of companies are usually opaque and the model does not address off-balance sheet items. For prediction of default for financial companies, the Merton Model is used.
Although additional methods for bankruptcy prediction have been developed by taking into account more data, their practicability turned out to be expensive, since it depends on a lot of data to be collected [20].
Given that many methods of risk and credit analysis, and bankruptcy prediction are based on stochastic models, we are now focusing on the measures for evaluating the probability of default. Most of methods exploit logistic regression functions as well as inversed probability distribution formulas.
The Probability of Default may be used in two ways: to address the causes of default; to predict and prevent new cases of default. Camargos et al [7] performed a survey to find conditioning factors that lead small business to default, as depicted in figure 4.
Variables that influence the default according to [7]
This survey has been conducted in an important Brazilian Program for encouragement of entrepreneurship among small-sized businesses. The method used to assess the risk of default was the logistic regression:
The equation has only one dependent variable X1, as the variable influencing on defaut. A threshold value of 0.5 is selected to determine whether a case is to be classified as compliant or default. Considering the probability as an input for the binary logistic regression variable Y, and then rearranging the coefficients, we obtain a linear logarithmic model:
where:
P(X) is the probability of default according to the set of variables X
β0 is a model bias constant
βi is coefficient for the variable Xi
Xi variable taken into account in the model
Other models include bivariate probit model by Jacobson and Roszbach [21], to estimate default probabilities and the effects of default-risk-based acceptance rule changes on a bank’s portfolio. Katchova and Barry [6] used the distance-to-default approach to determine the Value at Risk (VaR). All these models use logistic regression functions on multiple variables. By investigating these models amongst others, Odeh et al [22] applied a conceptual model for predicting default in agricultural loans, assuming the expected loss is expressed as a result of three components.
where
EL is the expected loss in monetary units
PD is the probability of default in percentages
LGD is the percentage of loss from the loan volume suffered by the granting institution
EAD is the loan amount plus accrued fees
Usually the Probability of Default is expressed in terms of N customers, so the equation 5 can be rearranged in the form:
where now
ELP is the expected loss on a specific portfolio
PDi is the probability of default for a specific loan
N is the total of granted loans
Combining the logistic regression (eq. 4) with the conceptual model (eq. 6), we can express the maximum likelihood estimation as in the equation:
where
PDi is the probability of default as stated in the equation 6
B is a vector of coefficients
X is a vector of explanatory variables and ε is a stochastic error
The coefficients may be determined empirically and vary from many aspects taken from the enterprise’s assets. Odeh et al [22] evaluated these methods by using data from Farm Credit System, and found that credit default predictions are really sensitive on data.
One of the recent technologies that has evolved and been used are the expert systems. Not only they have been used considerably since the 1980’s in financial institutions for decision making tasks, the prediction of default has also been an issue the experts systems have been used for [23]. In addition, computing intelligence techniques, such as Genetic Algorithms, Fuzzy C-Means, and Mars, have also been exploited [24] due to its capability of learning from an expert. The use of neural networks, neuro-fuzzy and fuzzy logic has also grown in recent decades, because they better handle on imprecise information and there is no pure analytical model of the market [25].
Furthermore, the database containing hundreds of financial operations represent an implicit knowledge that is available for modeling and prediction. By means of data mining [14], many customer behaviors can be analyzed based on past values. Thus, more reliable and developed models can be accomplished by the use of artificial intelligence.
Fuzzy Systems have already been used in a variety of problems, not only regarding risk and credit analysis, but also bankruptcy and default prediction. A Fuzzy approach combines an easy design fully based both on an expert’s opinion and on data history. Zirakja and Samizadeh [8] performed a risk analysis in e-commerce (EC) activities in a more broad vision, including the projects’ risk, by relying on experts’ opinions to build a fuzzy decision support system (FDSS). Martin et al [24] implemented a fuzzy system to predict bankruptcy by using expert knowledge applied in fuzzy rules with a classification rate of 88% in a single model. In a hybrid model, by using neuro-fuzzy and genetic algorithm, the classification rate was 73,6% but with more input variables.
Fuzzy logic arises as a good tool to emulate expert rules since they don’t require too much effort for modeling as other traditional methods do. A fuzzy system can emulate rules of type:
where conditions and consequences are fuzzy propositions built by linguistic expressions:
x is Low
y is NOT Tall
x is Low AND y is Tall
x is Low OR y is Tall
The expressions 1 and 2 define “immediate“ propositions, and the expressions 3 and 4 define combined propositions. Since they operate over fuzzy variables, they need to be defined in linguistic terms or fuzzy sets. Fuzzy sets usually take the form of membership functions.
Example of a membership function plot.
Fuzzy expressions are built using boolean operators such as NOT, OR and AND. These expressions are combined to form relations R. A fuzzy relation is defined against two universes U and V, as U x V being a subset of the Cartesian product of those, so that R: UxV
Therefore, Fuzzy rules can be defined in fuzzy operations as in the equation.
where
R(l) is a Fuzzy rule of index l
xi is an input fuzzy variable of index i
Ail is an input fuzzy set of index i in a rule l
y is an output fuzzy variable
Bl is an output fuzzy set in a rule l
which in turn can be represented by membership functions
where
µR(l)(X) is the membership function of the rule
µA1l(xi) is the membership function of the input variable of index i on fuzzy set Ail
µB(y) is the resulting membership function of the output variable y on fuzzy set B in rule l
min is the minimum operator
max is the maximum operator
sup is the supremum operator
A Fuzzy System usually has:
Input Variables (with their respective Fuzzy datasets);
Output Variables (the diagnostics values);
Rule Base: determines outputs for each combination of input fuzzy values;
Inference Machine: applies fuzzy operations;
Fuzzy Sets: Linguistic Terms for each Variable;
Crisp Values: Numeric values taken from real world.
Figure 6 shows the structure of a basic model of fuzzy system, consisting of four components: Input Fuzzification, Rule Database, Inference Machine and Defuzzification.
Fuzzy System Structure
A Fuzzy system can be defined in the following operations:
Input Fuzzyfication: transform the real world crisp values into fuzzy values.
Fuzzy Operation: Applies Fuzzy Operators Min or Max in input Variables according to available rules if they should be inclusive (AND) or exclusive (OR).
Aggregation: These operators can group several found output values provided that several rules may have triggered.
Defuzzification: transform the output found fuzzy values into real world crisp values.
In this chapter we are dealing with the application of a fuzzy system in predicting the default, so the details on these operations are beyond the scope, and for further information the reader is suggested with the references [26, 27].
Fuzzy systems are relatively simple to create and deploy, and it is fully based on human experts’ evaluation. Fuzzy has been applied in many fields involving decision processes which require some sort of judgment. The human mind abstracts real world variables in an imprecise manner forming semantic networks [28]. These semantic networks define relations that can be expressed with linguistic terms just as experts do. Therefore any activity requiring an expert opinion or judgment can be modeled in fuzzy logic rules without the need of an existing theoretic model to lie upon.
In small and medium-sized companies, the financial/collect department usually takes decisions regarding granting credit or not. Without any supporting tool, the decision is taken purely by an expert’s experience or opinion. The same applies for predicting cash flow based on client’s past financial transactions. Based on a given customer’s history, it can be inferred whether this customer will pay on time or default. This kind of analysis can be performed by an expert, but as a company’s portfolio grows, the task of analyzing becomes more time-consuming and then needs to be automated, and fuzzy systems emerge as a good option to automate this type of analysis [29].
By taking into account all the previous information, we designed a system capable of predicting the default rate based on historical records of customers. The methodology used in this design was the same used in the work of [27], which consisted of the following procedure.
Fuzzy Modelling Procedure
According to literature, the default is influenced by many aspects of the customers, but many of them are unknown to the provider, unless they are declared. However, simple models of probability of default can be able to yield good results using statistical measures. So, to make this system more applicable, we took into account only the minimum amount of information a collection or billing department would have regarding customers’ transactions. Thus in this work, we considered the database consisting only of customer invoices in the form of table.
\n\t\t\t\tId\n\t\t\t | \n\t\t\t\n\t\t\t\tClient\n\t\t\t | \n\t\t\t\n\t\t\t\tDescription\n\t\t\t | \n\t\t\t\n\t\t\t\tValue\n\t\t\t | \n\t\t\t\n\t\t\t\tDue Date\n\t\t\t | \n\t\t\t\n\t\t\t\tPayment\n\t\t\t | \n\t\t
23129 | \n\t\t\tIncs. Co. | \n\t\t\tMaintenance apr/12 | \n\t\t\t99.00 | \n\t\t\t20/04/12 | \n\t\t\t24/04/12 | \n\t\t
23137 | \n\t\t\tSol. Llc. | \n\t\t\tDevelopment apr/12 | \n\t\t\t1342.00 | \n\t\t\t25/04/12 | \n\t\t\t23/04/12 | \n\t\t
23144 | \n\t\t\tWhite Ss. | \n\t\t\tFin. SSAS fee apr/12 | \n\t\t\t49.90 | \n\t\t\t11/04/12 | \n\t\t\t09/06/12 | \n\t\t
... | \n\t\t\t... | \n\t\t\t... | \n\t\t\t... | \n\t\t\t... | \n\t\t\t... | \n\t\t
Accounting Records Database
According to the database depicted in table 2, we defined the following input variables for the fuzzy system.
Average Payment Delay (APD)
Amount Owed (AO)
Maximum Payment Delay (MPD)
Maximum Amount Owed (MAO)
Time as a Client (TC)
Number of Default Cases (NDC)
A formal definition of each variable is outlined in the following equations:
where
PDij is the Payment Date of the Invoice j of the Client i
DDij is the Due Date of the Invoice j of the Client i
N is the number of issued Invoices
t is the current Date
For specific purposes of this work, a default is considered to be when an invoice is not paid before the due date.
Upon consultation with experts in the collect department, we found the following terms for each of the input variables.
\n\t\t\t\tInput Variables\n\t\t\t | \n\t\t\t\n\t\t\t\tLinguistic terms\n\t\t\t | \n\t\t|
APD | \n\t\t\tAverage Payment Delay | \n\t\t\tShort, Middle, Long | \n\t\t
AO | \n\t\t\tAmount Owed | \n\t\t\tLow, Middle, High | \n\t\t
MPD | \n\t\t\tMaximum Payment Delay | \n\t\t\tShort, Middle, Long | \n\t\t
MAO | \n\t\t\tMaximum Amount Owed | \n\t\t\tLow, Middle, High | \n\t\t
TC | \n\t\t\tTime as a Client | \n\t\t\tNew, Known, Old Known | \n\t\t
NDC | \n\t\t\tNumber of Default Cases | \n\t\t\tLow, Middle, High | \n\t\t
Fuzzy Input Variables and their Linguistic Terms
The output variables are the values we want to predict, namely when and how much is customer going to pay. That can be express in two ways: Expected Amount/Date of receipt; Probability of Receiving a certain amount within a period of time. Since here we are considering only internal factors, this kind of prediction is through the cycle (TTC). According to Basel II Parameters [10], the simplest approach to estimate the probability of default is logistic regression, taking historical database as a basis for estimation.
Thus, given a date, the probability distribution of payment can be expressed by the following equation:
where
PDR is the Probability of Receipt or Payment
EDR is the Expected Date of Receipt (in days)
EAR is the Expected Amount to Receive (in monetary units)
NDC is the Number of Default Cases
A, B, C and D are coefficients
Upon experiments and linear regression we found the coefficients to be.
It can be seen that there is a relation between the next payment date and the probability. So the output variables were chosen to be the next payment and expected amount to be paid.
\n\t\t\t\tOutput Variables\n\t\t\t | \n\t\t\t\n\t\t\t\tLinguistic terms\n\t\t\t | \n\t\t|
EAR | \n\t\t\tExpected Amount to Receive | \n\t\t\tNone, Little, Enough, Integral | \n\t\t
EDR | \n\t\t\tExpected Date of Receipt | \n\t\t\tNear, Reasonably Near, Far, Never | \n\t\t
Expected Output Variables
However, from these outputs the probability of receiving over time t can also be derived, according to the equation.
where
PP(t) is the probability of payment over time t
PDR is the probability distribution function
EDR is the expected Date of Receipt
E is the remaining part of the probability distribution function PDR, independent of EDR
Thus, we can state the variables PPW and PPM with parameter values for t of 7 and 30, respectively. The probabilities can also be defined in fuzzy sets.
\n\t\t\t\tOutput Variables\n\t\t\t | \n\t\t\t\n\t\t\t\tLinguistic terms\n\t\t\t | \n\t\t|
PPW | \n\t\t\tProbability of Payment in a Week | \n\t\t\tNull, Very Low, Low, Medium, High, Very High | \n\t\t
PPM | \n\t\t\tProbability of Payment in a Month | \n\t\t\tNull, Very Low, Low, Medium, High, Very High | \n\t\t
Probability Output Variables
Likewise, the expected date of payment can be derived from the quantile equation, which is the inverted probability density function.
where ER is the Expected date of payment resulted from the probability distribution PP(t).
We defined the fuzzy set limits upon querying against a huge database containing over 5 years of financial records, in such way that each set should have the same number of clients belonging to it. To that end, we had to rearrange the database to group the results per client.
\n\t\t\t\tClient\n\t\t\t | \n\t\t\t\n\t\t\t\tAverage Delay\n\t\t\t | \n\t\t\t\n\t\t\t\tMaximum Delay\n\t\t\t | \n\t\t\t\n\t\t\t\tAmount Owed\n\t\t\t | \n\t\t\t\n\t\t\t\tMaximum Owed\n\t\t\t | \n\t\t\t\n\t\t\t\tNumber of Cases\n\t\t\t | \n\t\t\t\n\t\t\t\tTime as Client\n\t\t\t | \n\t\t
Incs. Co. | \n\t\t\t5.666 | \n\t\t\t18 | \n\t\t\t0.00 | \n\t\t\t150.00 | \n\t\t\t24 | \n\t\t\t235 | \n\t\t
Sol. Llc. | \n\t\t\t0.2222 | \n\t\t\t12 | \n\t\t\t230.00 | \n\t\t\t15500.00 | \n\t\t\t4 | \n\t\t\t346 | \n\t\t
White Ss. | \n\t\t\t18.5426 | \n\t\t\t128 | \n\t\t\t57.50 | \n\t\t\t6500.50 | \n\t\t\t16 | \n\t\t\t1448 | \n\t\t
... | \n\t\t\t... | \n\t\t\t... | \n\t\t\t... | \n\t\t\t... | \n\t\t\t... | \n\t\t\t... | \n\t\t
Accounting Database records grouped by each client
We defined the Gaussian function as a membership function for each set, on input and output. After querying the dataset, we defined the sets’ limits as can be show in the table and figures.
where c is the center of the function, and σ is the variance. Then, we defined as the set’s limits c±σ.
\n\t\t\t\tVariable\n\t\t\t | \n\t\t\t\n\t\t\t\tLow/Short/New\n\t\t\t | \n\t\t\t\n\t\t\t\tMiddle/Known\n\t\t\t | \n\t\t\t\n\t\t\t\tHigh/Long/Old Known\n\t\t\t | \n\t\t|||
\n\t\t\t\tInf.Lim.\n\t\t\t | \n\t\t\t\n\t\t\t\tSup.Lim.\n\t\t\t | \n\t\t\t\n\t\t\t\tInf.Lim.\n\t\t\t | \n\t\t\t\n\t\t\t\tSup.Lim.\n\t\t\t | \n\t\t\t\n\t\t\t\tInf.Lim.\n\t\t\t | \n\t\t\t\n\t\t\t\tSup.Lim.\n\t\t\t | \n\t\t|
\n\t\t\t\tAPD\n\t\t\t | \n\t\t\t0 | \n\t\t\t13.91 | \n\t\t\t13.91 | \n\t\t\t34.91 | \n\t\t\t34.91 | \n\t\t\t222 | \n\t\t
\n\t\t\t\tAO\n\t\t\t | \n\t\t\t0 | \n\t\t\t272.66 | \n\t\t\t272.66 | \n\t\t\t3723.53 | \n\t\t\t3723.53 | \n\t\t\t50084 | \n\t\t
\n\t\t\t\tMPD\n\t\t\t | \n\t\t\t0 | \n\t\t\t100.45 | \n\t\t\t100.45 | \n\t\t\t200.45 | \n\t\t\t200.45 | \n\t\t\t1009 | \n\t\t
\n\t\t\t\tMAO\n\t\t\t | \n\t\t\t0 | \n\t\t\t845.00 | \n\t\t\t845.00 | \n\t\t\t5593.75 | \n\t\t\t5593.75 | \n\t\t\t50084 | \n\t\t
\n\t\t\t\tTC\n\t\t\t | \n\t\t\t0 | \n\t\t\t234 | \n\t\t\t234 | \n\t\t\t1304 | \n\t\t\t1304 | \n\t\t\t2233 | \n\t\t
\n\t\t\t\tNDC\n\t\t\t | \n\t\t\t1 | \n\t\t\t3 | \n\t\t\t3 | \n\t\t\t10 | \n\t\t\t10 | \n\t\t\t38 | \n\t\t
Sets’ limits defined upon database querying
Fuzzy Sets’ Plots of Variable Average Payment Date
As performed in the work of [27], we have built the fuzzy rules upon querying the database shown in table 6 for each combination of the input sets. That would give 729 rules. But before querying a database, we cut some combinations that would never happen in practice or could be intuitively disposed. Some examples are the following rules:
If APD is long and MPD is short and...
If AO is high and MAO is short and...
If TC is new and NDC is high and...
By cutting infeasible rules, the rules database has been reduced to 288 rules. The outputs for each rule, both for expected date and amount of receipt, have been determined upon querying the history database. Nevertheless, some situations never happened, so we had to decide the output for these rules by asking the experts. That procedure trimmed down the rule database to only 53 rules
For a given rule, we found an average difference between the due date and the payment date.
where
APDi is the average payment date for the client i;
STDi is the standard deviation for the difference between due dates and payment dates of the client i.
After querying the database for any given rule, we built out a histogram of each fuzzy output variable corresponding to that rule. Table 8 shows a histogram found for the following rule:
“if APD is Middle and AO is Low and MPD is Long and MAO is Low and TC is Old Known and NDC is Low”
\n\t\t\t | \n\t\t\t\tNone/Near\n\t\t\t | \n\t\t\t\n\t\t\t\tLittle/Reasonably Near\n\t\t\t | \n\t\t\t\n\t\t\t\tEnough/Far\n\t\t\t | \n\t\t\t\n\t\t\t\tIntegral/Never\n\t\t\t | \n\t\t
\n\t\t\t\tExpected Date of Receipt\n\t\t\t | \n\t\t\t3 | \n\t\t\t2 | \n\t\t\t1 | \n\t\t\t0 | \n\t\t
\n\t\t\t\tExpected Amount of Receipt\n\t\t\t | \n\t\t\t0 | \n\t\t\t0 | \n\t\t\t1 | \n\t\t\t5 | \n\t\t
Histogram for a given rule
The output set was chosen as the one that the rule result better fits into, which is Near for Expected Date of Receipt and Integral for Expected Amount of Receipt.
In order to have a separation between the rules database development and the validation, we defined distinct periods for querying and for validation. The database in the form shown in table 6 has been cut into these two periods, 2 years and a half each, forming a new database grouped by period. This database is shown in table 9.
\n\t\t\t\tClient\n\t\t\t | \n\t\t\t\n\t\t\t\tPeriod\n\t\t\t | \n\t\t\t\n\t\t\t\tAverage Delay\n\t\t\t | \n\t\t\t\n\t\t\t\tMaximum Delay\n\t\t\t | \n\t\t\t\n\t\t\t\tAmount Owed\n\t\t\t | \n\t\t\t\n\t\t\t\tMaximum Owed\n\t\t\t | \n\t\t\t\n\t\t\t\tNumber of Cases\n\t\t\t | \n\t\t\t\n\t\t\t\tTime as Client\n\t\t\t | \n\t\t
Incs. Co. | \n\t\t\t1 | \n\t\t\t5.666 | \n\t\t\t18 | \n\t\t\t0.00 | \n\t\t\t150.00 | \n\t\t\t24 | \n\t\t\t235 | \n\t\t
Incs. Co. | \n\t\t\t2 | \n\t\t\t7.183 | \n\t\t\t18 | \n\t\t\t120.00 | \n\t\t\t250.00 | \n\t\t\t33 | \n\t\t\t622 | \n\t\t
Sol. Llc. | \n\t\t\t1 | \n\t\t\t0.2222 | \n\t\t\t12 | \n\t\t\t230.00 | \n\t\t\t15500.00 | \n\t\t\t4 | \n\t\t\t346 | \n\t\t
Sol. Llc. | \n\t\t\t2 | \n\t\t\t0.3333 | \n\t\t\t12 | \n\t\t\t230.00 | \n\t\t\t15500.50 | \n\t\t\t4 | \n\t\t\t733 | \n\t\t
... | \n\t\t\t\n\t\t\t | ... | \n\t\t\t... | \n\t\t\t... | \n\t\t\t... | \n\t\t\t... | \n\t\t\t... | \n\t\t
Database split into 2 periods
The validation period was replicated multiple times in order to perform a continuous validation from first until the last date of the period. For each date, a snapshot of the database of table 6 was taken in order to simulate the Fuzzy Prediction.
Schema of database snapshots taken for every date in the periods for simulation
\n\t\t\t\tCurrent Date\n\t\t\t | \n\t\t\t\n\t\t\t\tId\n\t\t\t | \n\t\t\t\n\t\t\t\tClient\n\t\t\t | \n\t\t\t\n\t\t\t\tDescription\n\t\t\t | \n\t\t\t\n\t\t\t\tValue\n\t\t\t | \n\t\t\t\n\t\t\t\tDue Date\n\t\t\t | \n\t\t\t\n\t\t\t\tPayment\n\t\t\t | \n\t\t
... | \n\t\t\t... | \n\t\t\t... | \n\t\t\t... | \n\t\t\t... | \n\t\t\t... | \n\t\t\t... | \n\t\t
23/04/12 | \n\t\t\t23129 | \n\t\t\tIncs. Co. | \n\t\t\tMaintenance apr/12 | \n\t\t\t99.00 | \n\t\t\t20/04/12 | \n\t\t\t\n\t\t |
23/04/12 | \n\t\t\t23137 | \n\t\t\tSol. Llc. | \n\t\t\tDevelopment apr/12 | \n\t\t\t1342.00 | \n\t\t\t25/04/12 | \n\t\t\t23/04/12 | \n\t\t
23/04/12 | \n\t\t\t23144 | \n\t\t\tWhite Ss. | \n\t\t\tFin. SSAS fee apr/12 | \n\t\t\t49.90 | \n\t\t\t11/04/12 | \n\t\t\t\n\t\t |
... | \n\t\t\t... | \n\t\t\t... | \n\t\t\t... | \n\t\t\t... | \n\t\t\t... | \n\t\t\t... | \n\t\t
24/04/12 | \n\t\t\t23129 | \n\t\t\tIncs. Co. | \n\t\t\tMaintenance apr/12 | \n\t\t\t99.00 | \n\t\t\t20/04/12 | \n\t\t\t24/04/12 | \n\t\t
24/04/12 | \n\t\t\t23137 | \n\t\t\tSol. Llc. | \n\t\t\tDevelopment apr/12 | \n\t\t\t1342.00 | \n\t\t\t25/04/12 | \n\t\t\t23/04/12 | \n\t\t
24/04/12 | \n\t\t\t23144 | \n\t\t\tWhite Ss. | \n\t\t\tFin. SSAS fee apr/12 | \n\t\t\t49.90 | \n\t\t\t11/04/12 | \n\t\t\t\n\t\t |
... | \n\t\t\t... | \n\t\t\t... | \n\t\t\t... | \n\t\t\t... | \n\t\t\t... | \n\t\t\t... | \n\t\t
Database with time dimension
The fuzzy system was implemented using Mamdani [26] as the inference machine, because of its simplicity in processing the rules and values and ease to be implemented in this case. Then it was deployed on an important Brazilian Financial Accounting System whose aim was to infer how much of the accounts receivable could be received within a week or a month, and what would be the default rate. The fuzzy system was set up as follows.
\n\t\t\t\tInput Fuzzy Sets\n\t\t\t | \n\t\t\t\n\t\t\t\tGaussian\n\t\t\t | \n\t\t
\n\t\t\t\tOutput Fuzzy Sets\n\t\t\t | \n\t\t\t\n\t\t\t\tTriangle\n\t\t\t | \n\t\t
\n\t\t\t\tImplication Method\n\t\t\t | \n\t\t\t\n\t\t\t\tAND/OR\n\t\t\t | \n\t\t
\n\t\t\t\tAggregation Method\n\t\t\t | \n\t\t\t\n\t\t\t\tProduct\n\t\t\t | \n\t\t
\n\t\t\t\tDefuzzification Method\n\t\t\t | \n\t\t\t\n\t\t\t\tCentre of gravity\n\t\t\t | \n\t\t
Fuzzy Settings
After defining and validating the rules database, we performed a simulation of prediction the default rate in a period of 2 years and a half. Since we have a probability as an output, we had to apply the Monte Carlo method to generate random numbers and get real results from the simulations and confront them against the real values [30].
We used the database shown in table 10 to perform simulations on any record for every invoice which was supposed to be paid. The fuzzy system would give an expected date and amount to be received. So we applied for a given record some calculations using equations 19, 21 and 22 to get probabilities of payment within a day, a week and a month. With the Monte Carlo method, we have gotten a number of random values to be applied in the probability distribution as shown in the equations 21 and 22. If that random number would be greater less than the corresponding probability value, calculated in the equations 21 and 22, it means the debt has been paid.
The algorithm for the simulation was defined as follows.
Flowchart of the simulation
Then, we performed simulations to predict:
the default rate of customers
the future revenue within a short period (a month)
the revenue within a long term (a year)
The default rate is assumed to be the percentage of invoices that are delayed or paid after the due date:
where DR(t) is the default rate at the date t.
Then we applied the Fuzzy system to give an expected percentage of invoices that were about to be paid after due date, and compared to what happened in fact. We repeated the experiments 100 times, in order to have more accurate values. The results are outlined in table 12.
\n\t\t\t\tId\n\t\t\t | \n\t\t\t\n\t\t\t\tClient\n\t\t\t | \n\t\t\t\n\t\t\t\tAmount Received\n\t\t\t | \n\t\t\t\n\t\t\t\tDue Date\n\t\t\t | \n\t\t\t\n\t\t\t\tPayment Date\n\t\t\t | \n\t\t\t\n\t\t\t\tAmount Estimated\n\t\t\t | \n\t\t\t\n\t\t\t\tEstimated Payment Date\n\t\t\t | \n\t\t
\n\t\t\t\t...\n\t\t\t | \n\t\t\t\n\t\t\t\t...\n\t\t\t | \n\t\t\t\n\t\t\t\t...\n\t\t\t | \n\t\t\t\n\t\t\t\t...\n\t\t\t | \n\t\t\t\n\t\t\t\t...\n\t\t\t | \n\t\t\t\n\t\t\t\t...\n\t\t\t | \n\t\t\t\n\t\t\t\t...\n\t\t\t | \n\t\t
19027 | \n\t\t\tYork S. | \n\t\t\t195.85 | \n\t\t\t03/12/12 | \n\t\t\t03/12/12 | \n\t\t\t\n\t\t\t\t190.0±15.0\n\t\t\t | \n\t\t\t46±40 days after | \n\t\t
19028 | \n\t\t\tBennetts | \n\t\t\t314.25 | \n\t\t\t20/12/12 | \n\t\t\t01/02/13 | \n\t\t\t\n\t\t\t\t330.0±20.0\n\t\t\t | \n\t\t\t12±4 days after | \n\t\t
19033 | \n\t\t\tHouth | \n\t\t\t160.00 | \n\t\t\t11/10/12 | \n\t\t\t10/10/12 | \n\t\t\t\n\t\t\t\t150.0±10.0\n\t\t\t | \n\t\t\t2±1 days after | \n\t\t
19041 | \n\t\t\tYork S. | \n\t\t\t195.00 | \n\t\t\t19/09/12 | \n\t\t\t03/12/12 | \n\t\t\t\n\t\t\t\t190.0±15.0\n\t\t\t | \n\t\t\t\n\t\t\t\t46±40 days after\n\t\t\t | \n\t\t
19045 | \n\t\t\tN. Shots | \n\t\t\t149.00 | \n\t\t\t06/09/12 | \n\t\t\t13/09/12 | \n\t\t\t180.0±20.0 | \n\t\t\t\n\t\t\t\t7±5 days after\n\t\t\t | \n\t\t
19048 | \n\t\t\tNet Sol. | \n\t\t\t1081.22 | \n\t\t\t11/11/12 | \n\t\t\t12/11/12 | \n\t\t\t\n\t\t\t\t1050.0±100\n\t\t\t | \n\t\t\t6±1 days after | \n\t\t
19062 | \n\t\t\tYamada | \n\t\t\t225.00 | \n\t\t\t09/12/12 | \n\t\t\t05/04/13 | \n\t\t\t200.0±20.0 | \n\t\t\t68±43 days after | \n\t\t
... | \n\t\t\t... | \n\t\t\t... | \n\t\t\t... | \n\t\t\t... | \n\t\t\t... | \n\t\t\t... | \n\t\t
Some results from predictions. Correct estimations are bolded.
The following plots show how the default rate is predicted from the Fuzzy system over time. One data series is the actual default rate per month, and the other is the average prediction after simulating a 100 times.
Prediction of the Default Rate
By applying this procedure, one can infer the revenue over a period, using the expected amount to be paid as the output value in addition to the expected date of payment. The expected revenue is then set to be:
where
PERi is the Predicted revenue for the period i
PEPRi is the Predicted revenue from past periods of period i
DRi is the default rate for period i
ERi is the original expected revenue for period i
We processed the results from the default rate prediction and built several snapshots out of the simulations to forecast the revenue over each period by taking into account recent real records up to the current period.
The results are outlined in the plots shown in figure 12.
To calculate how much the enterprise expects to receive in the long term, we performed random simulations on the probabilities given by the fuzzy system for the whole period. By checking the history for each client until the present moment in the simulation, and an estimative of when this client will pay is obtained. For validation we compared the predicted default rate against the real default rate that happened in the period. The system was validated with a 12 month period simulation using past values for 100 times. This strategy was able to give a prediction of the default rate with an 80% accuracy.
Bar charts comparing the expected, real and predicted revenue for one year
As can be seen, the fuzzy system has learned the expert’s knowledge, therefore acting as a process expert and releasing them from the task of analysing, judging, and change the chosen values, then becoming able to do other activities.
The results produced by this initiative show how the default issue can be addressed by the use of Fuzzy Systems. The default in the economy is a serious problem, and although this problem cannot be solved easily, the facility to predict it can prevent bad clients to buy services for which it is not able to pay. Moreover, the Fuzzy System can be used to infer and forecast a more accurate cash flow, instead of traditional approaches.
One important advantage of this fuzzy system to forecast defaults is that it needed just a little piece of information to predict when a given customer would default a payment and under which probability. The simulation using quantitative techniques such as Monte Carlo method turned out a good estimation because of the stochastic nature of this process. Many models of the probability of default rely on statistical methods to infer the probabilities. This is an interesting option when there is little data available on the customers to forecast default or bankruptcy by taking into account TTC probabilities.
The system has been applied in an Accounting System having aided financial analysts with predictions on cash flow and liquidity. One drawback of this system though is the lack of good predictions on new clients’ transactions, but even in these cases the predictions are within the margin established by the fuzzy sets. However these results can be improved by performing risk and credit analysis or taking into account more information from the clients in the fuzzy system.
Artificial neural networks (ANN), which are mathematical models for function approximation, classification, pattern recognition, nonlinear control, etc., have been successfully applied in the field of time series analysis and forecasting instead of linear models such as 1970s ARIMA [1] since 1980s [2, 3, 4, 5, 6, 7]. In [2], Casdagli used a radial basis function network (RBFN) which is a kind of feed-forward neural network with Gaussian hidden units to predict chaotic time series data, such as the Mackey-Glass, the Ikeda map, and the Lorenz chaos in 1989. In [3, 4], Lendasse et al. organized a time series forecasting competition for neural network prediction methods with a five-block artificial time series data named CATS since 2004. The goal of CATS competition was to predict 100 missing values of the time series data in five sets which included 980 known values and 20 successive unknown values in each set (details are in Section 3.1). There were 24 submissions to the competition, and five kinds of methods were selected by the IJCNN2004: filtering techniques including Bayesian methods, Kalman filters, and so on; recurrent neural networks (RNNs); vector quantization; fuzzy logic; and ensemble methods. As the comment of the organizers, the different prediction precisions were reported though the similar prediction methods were used for the know-how and experience of the authors. So the development of time series forecasting by ANN is still on the way.
\nAs a kind of classifiers or a kind of function approximators, the advances of the ANN are bought out by the nonlinear transforms to the input space. In fact, units (or neurons) with nonlinear firing functions connected to each other usually produce higher dimensional output space and various feature spaces in the networks. Additionally, as a connective system, it is not necessary to design fixed mathematical models for different nonlinear phenomena, but adjusting the weights of connections between units. So according to the report of NN3—Artificial Neural Networks and Computational Intelligence Forecasting Competition [5], there have been more than 5000 publications of time series forecasting using ANN till 2007.
\nTo find the suitable parameters of ANN, such as weights of connections between neurons, error back-propagation (BP) algorithm [6] is generally utilized in the training process of ANN. However, due to every sample data (a pair of the input data and the output data) is used in the BP method, noise data influences the optimization of the model, and robustness of the model becomes weak for unknown input. Another problem of ANN models is how to determine the structure of the network, i.e., the number of layers and the number of neurons in each layer. To overcome these problems of BP, Kuremoto et al. [7] adopted a reinforcement learning (RL) method “stochastic gradient ascent (SGA)” [8] to adjust the connection weights of units and the particle swarm optimization (PSO) to find the optimal structure of ANN. SGA, which is proposed by Kimura and Kobayshi, improved Williams’ REINFORCE [9], which uses rewards to modify the stochastic policies (likelihood). In SGA learning algorithm, the accumulated modification of policies named “eligibility trace” is used to adjust the parameters of model (see Section 2). In the case of time series forecasting, the reward of RL system can be defined as a suitable error zone to instead of the distance (error) between the output of the model and the teach data which is used in BP learning algorithm. So the sensitivity to noise data is possible to be reduced, and the robustness to the unknown data may be raised. As a deep learning method for time series forecasting, Kuremoto et al. [10] firstly applied Hinton and Salakhutdinov’s deep belief net (DBN) which is a kind of stacked auto-encoder (SAE) composed by multiple restricted Boltzmann machines (RBMs) [11]. An improved DBN for time series forecasting is proposed in [12], which DBN is composed by multiple RBMs and a multilayer perceptron (MLP) [6]. The improved DBN with RBMs and MLP [6] gives its priority to the conventional DBN [5] for time series forecasting due to the continuous output unit is used; meanwhile the conventional one had a binary value unit in the output layer.
\nAs same as the RL method, SGA adopted to MLP, RBFN, and self-organized fuzzy neural network (SOFNN) [7]; the prediction precision of DBN utilized SGA may also be raised comparing to the BP learning algorithm. Furthermore, it is available to raise the prediction precision by a hybrid model which forecasts the future data by the linear model ARIMA at first and modifying the forecasting by the predicted error given by an ANN which is trained by error time series [13, 14].
\nIn this chapter, we concentrate to introduce the DBN which is composed by multiple RBMs and MLP and show the higher efficiency of the RL learning method SGA for the DBN [15, 16] comparing to the conventional learning method BP using the results of time series forecasting experiments. Kinds of benchmark data including artificial time series data CATS [3], natural phenomenon time series data provided by Aalto University [18], and TSDL [18] were used in the experiments.
\nThe model of time series forecasting is given as the following:
\nDenote t = 1, 2, 3, …, where T is the time, n is the dimensionality of the input of function f(x), \n
A deep belief net (DBN) composed by restricted Boltzmann machines (RBMs) and multilayer perceptron (MLP) is shown in Figure 1.
\nThe structure of DBN for time series forecasting.
Restricted Boltzmann machine (RBM) is a kind of probabilistic generative neural network which composed by two layers of units: visible layer and hidden layer (see Figure 2).
\nThe structure of RBM.
Units of different layers connect to each other with weights \n
Here \n
where \n
Multilayer perceptron (MLP) is the most popular neural network which is generally composed by three layers of units: input layer, hidden layer, and output layer (see Figure 3).
\nThe structure of MLP.
The output of the unit \n
Here n is the dimensionality of the input, K is the number of hidden units, and \n
The learning rules of MLP using error back-propagation (BP) method [5] are given as follows:
\nwhere \n
The learning algorithm of MLP using BP is as follows:
\nStep 1. Observe an input \n
Step 2. Predict a future data \n
Step 3. Calculate the modification of connection weights, \n
Step 4. Modify the connections,
\nStep 5. For the next time step \n
As same as the training process proposed in [10], the training process of DBN is performed by two steps. The first one, pretraining, utilizes the learning rules of RBM, i.e., Eqs. (4–6), for each RBM independently. The second step is a fine-tuning process using the pretrained parameters of RBMs and BP algorithm. These processes are shown in Figure 4 and Eqs. (11)–(13).
\nThe training of DBN by BP method.
In the case of reinforcement learning (RL), the output is decided by a probability distribution, e.g., the Gaussian distribution \n
The learning algorithm of stochastic gradient ascent (SGA) [7] is as follows.
\nStep 1. Observe an input \n
Step 2. Predict a future data \n
Step 3. Receive a scalar reward/punishment \n
where \n
Step 4. Calculate characteristic eligibility \n
where \n
Step 5. Calculate the modification \n
where \n
Step 6. Improve the policy Eq. (16) by renewing its internal variable \n
where \n
Step 7. For the next time step \n
Characteristic eligibility \n
The calculation of \n
The \n
The learning rate \n
where is \n
The learning errors given by different learning rates.
The number of RBM that constitute the DBN and the number of neurons of each layer affects prediction performance seriously. In [9], particle swarm optimization (PSO) method is used to decide the structure of DBN, and in [13] it is suggested that random search method [16] is more efficient. In the experiment of time series forecasting by DBN and SGA shown in this chapter, these meta-parameters were decided by the random search, and the exploration limits are shown as the following.
The number of RBMs: [0–3]
The number of units in each layer of DBN: [2–20]
Fixed learning rate of SGA in Eq. (21): [10−5–10−1]
Discount factor in Eq. (19): [10−5–10−1]
Coefficient in Eq. (27) [0.5–2.0]
The optimization algorithm of these meta-parameters by the random search method is as follows:
\nStep 1. Set random values of meta-parameters beyond the exploration limitations.
\nStep 2. Predict a future data \n
Step 3. If the error between \n
or else if the error is not changed,
\nstop the exploration,
\nelse return to step 1.
\nCATS time series data is the artificial benchmark data for forecasting competition with ANN methods [3, 4].This artificial time series is given with 5000 data, among which 100 are missed (hidden by competition the organizers). The missed data exist in five blocks:
Elements 981 to 1000
Elements 1981 to 2000
Elements 2981 to 3000
Elements 3981 to 4000
Elements 4981 to 5000
The mean square error \n
where \n
CATS benchmark data.
The prediction results of different blocks of CATS data are shown in Figure 7. Comparing to the conventional learning method of DBN, i.e., using Hinton’s RBM unsupervised learning method [6, 8] and back-propagation (BP), the proposed method which used the reinforcement learning method SGA instead of BP showed its superiority in the sense of the average prediction precision E1 (see Figure 7f). In addition, the proposed method, DBN with SGA, yielded the highest prediction (E1 measurement) comparing to all previous studies such as MLP with BP, the best prediction of CATS competition IJCNN’04 [4], the conventional DBNs with BP [9, 11], and hybrid models [13]. The details are shown in Table 1.
\nThe prediction results of different methods for CATS data: (a) block 1; (b) block 2; (c) block 3; (d) block 4; (e) block 5; and (f) results of the long-term forecasting.
Method | \nE1 | \n
---|---|
DBN(SGA) [18] | \n170 | \n
DBN(BP) + ARIMA [14] | \n244 | \n
DBN [11] (BP) | \n257 | \n
Kalman Smoother (the best of IJCNN ‘04) [4] | \n408 | \n
DBN [9] (2 RBMs) | \n1215 | \n
MLP [9] | \n1245 | \n
A hierarchical Bayesian learning (the worst of IJCNN ‘04) [4] | \n1247 | \n
ARIMA [1] | \n1715 | \n
ARIMA+MLP(BP) [12] | \n2153 | \n
ARIMA+DBN(BP) [14] | \n2266 | \n
The long-term forecasting error comparison of different methods using CATS data.
The meta-parameters obtained by random search method are shown in Table 2. And we found that the MSE of learning, i.e., given by one-ahead prediction results, showed that the proposed method has worse convergence compared to the conventional BP training. In Figure 8, the case of the first block learning MSE of two methods is shown. The convergence of MSE given by BP converged in a long training process and SGA gave unstable MSE of prediction. However, as the basic consideration of a sparse model, the better results of long-term prediction of the proposed method may successfully avoid the over-fitting problem which is caused by the model that is built too strictly by the training sample and loses its robustness for unknown data.
\n\n | DBN with SGA | \nDBN with BP | \n
---|---|---|
The number of RBMs | \n3 | \n1 | \n
Learning rate of RBM | \n0.048-0.055-0.026 | \n0.042 | \n
Structure of DBN (the number of units and layers) | \n14-14-18-19-18-2 | \n5-11-2-1 | \n
Learning rate of SGA or BP | \n0.090 | \n0.090 | \n
Discount factor \n | \n0.082 | \n— | \n
Coefficient \n | \n1.320 | \n— | \n
Meta-parameters of DBN used for the CATS data (block 1).
Change of the learning error during fine-tuning (CATS data [1–980]).
Three types of natural phenomenon time series data provided by Aalto University [17] were used in the one-ahead forecasting experiments of real time series data.
CO2: Atmospheric CO2 from continuous air samples weekly averages atmospheric CO2 concentration derived from continuous air samples, Hawaii, 2225 data
Sea level pressures: Monthly values of the Darwin sea level pressure series, A.D. 1882–1998, 1300 data
Sunspot number: Monthly averages of sunspot numbers from A.D. 1749 to the present 3078 values
The prediction results of these three datasets are shown in Figure 9. Short-term prediction error is shown in Table 3. DBN with the SGA learning method showed its priority in all cases.
\nPrediction results by DBN with BP and SGA. (a) Prediction result of CO2 data. (b) Prediction result of Sea level pressure data. (c) Prediction result of Sun spot number data.
Data | \nDBN with BP | \nDBN with SGA | \n
---|---|---|
CO2 | \n0.2671 | \n0.2047 | \n
Sea level pressure | \n0.9902 | \n0.9003 | \n
Sun spot number | \n733.51 | \n364.05 | \n
Prediction MSE of real time series data [17].
The efficiency of random search to find the optimal meta-parameters, i.e., the structure of RBM and MLP, learning rates, discount factor, etc. which are explained in Section 2.5 is shown in Figure 10 in the case of DBN with SGA learning algorithm. The random search results are shown in Table 4.
\nChanges of learning error by random search for DBN with SGA.
Data series | \nTotal data | \nTesting data | \nDBN with BP (the number of units) | \nDBN with SGA (the number of units) | \n
---|---|---|---|---|
CO2 | \n2225 | \n225 | \n15-17-17-1 | \n20-18-7-2 | \n
Sea level pressure | \n1400 | \n400 | \n16-18-18-1 | \n16-20-8-7-2 | \n
Sun spot number | \n3078 | \n578 | \n20-20-17-18-1 | \n19-19-20-10-2 | \n
Meta-parameters of DBN used for real time series forecasting.
We also used seven types of natural phenomenon time series data of TSDL [18]. The data to be predicted was chosen based on [19] which are named as Lynx, Sunspots, River flow, Vehicles, RGNP, Wine, and Airline. The short-term (one-ahead) prediction results are shown in Figure 11 and Table 5.
\nPrediction results of natural phenomenon time series data of TSDL. (a) Prediction result of Lynx; (b) prediction result of sunspots; (c) prediction result of river flow; (d) prediction result of vehicles; (e) prediction result of RGNP; (f) prediction result of wine; and (g) prediction result of airline.
Data | \nDBN with BP | \nDBN with SGA | \n
---|---|---|
Lynx | \n0.6547 | \n0.3593 | \n
Sunspots | \n999.54 | \n904.35 | \n
River flow | \n24262.24 | \n16980.46 | \n
Vehicles | \n6.0670 | \n6.1919 | \n
RGNP | \n771.79 | \n469.72 | \n
Wine | \n138743.80 | \n224432.02 | \n
Airline | \n380.60 | \n375.25 | \n
Prediction MSE of time series data of TSDL.
From Table 5, it can be confirmed that SGA showed its priority to BP except the cases of Vehicles and Wine. From Table 6, an interesting result of random search for meta-parameter showed that the structures of DBN for different datasets were different, not only the number of units on each layer but also the number of RBMs. In the case of SGA learning method, the number of layer for Sunspots, River flow, and Wine were more than DBN using BP learning.
\nSeries | \nTotal data | \nTesting data | \nDBN with BP | \nDBN with SGA | \n
---|---|---|---|---|
Lynx | \n114 | \n14 | \n19-16-1 | \n7-14-2 | \n
Sunspots | \n288 | \n35 | \n20-18-11-1 | \n10-12-12-17-2 | \n
River flow | \n600 | \n100 | \n20-17-18-1 | \n19-20-5-18-5-2 | \n
Vehicles | \n252 | \n52 | \n20-13-20-1 | \n20-11-5-2 | \n
RGNP | \n85 | \n15 | \n18-20-1 | \n19-15-2 | \n
Wine | \n187 | \n55 | \n16-15-12-1 | \n18-12-13-11-2 | \n
Airline | \n144 | \n12 | \n15-4-1 | \n13-7-2 | \n
Size of time series data and structure of prediction network.
The experiment results showed the DBN composed by multiple RBMs and MLP is the state-of-the-art predictor comparing to all conventional methods in the case of CATS data. Furthermore, the training method for DBN may be more efficient by the RL method SGA for real time series data than using the conventional BP algorithm. Here let us glance back at the development of this useful deep learning method.
Why the DBN composed by multiple RBMs and MLP [11, 13] is better than the DBN with multiple RBMs only [9]?
The output of the last RBM of DBN, a hidden unit of the last RBM in DBN, has a binary value during pretraining process. So the weights of connections between the unit and units of the visible layer of the last RBM are affected and with lower complexity than using multiple units with continuous values, i.e., MLP, or so-called full connections in deep learning architecture.
How are RL methods active at ANN training?
In 1992, Williams proposed to adopt a RL method named REINFORCE to modify artificial neural networks [8]. In 2008, Kuremoto et al. showed the RL method SGA is more efficient than the conventional BP method in the case of time series forecasting [6]. Recently, researchers in DeepMind Ltd. adopted RL into deep neural networks and resulted a famous game software AlphaGo [20, 21, 22, 23].
Why SGA is more efficient than BP?
Generally, the training process for ANN by BP uses mean square error as loss function. So every sample data affects the learning process and results including noise data. Meanwhile, SGA uses reward which may be an error zone to modify the parameters of model. So it has higher robustness for the noisy data and unknown data for real problems.
\nA deep belief net (DBN) composed by multiple restricted Boltzmann machines (RBMs) and multilayer perceptron (MLP) for time series forecasting were introduced in this chapter. The training method of DBN is also discussed as well as a reinforcement learning (RL) method; stochastic gradient ascent (SGA) showed its priority to the conventional error back-propagation (BP) learning method. The robustness of SGA comes from the utilization of relaxed prediction error during the learning process, i.e., different from the BP method which adopts all errors of every sample to modify the model. Additionally, the optimization of the structure of DBN was realized by random search method. Time series forecasting experiments used benchmark CATS data, and real time series datasets showed the effectiveness of the DBN. As for the future work, there are still some problems that need to be solved such as how to design the variable learning rate and reward which influence the learning performance strongly and how to prevent the explosion of characteristic eligibility trace in SGA.
\nOve Odredbe i uvjeti ističu pravila i regulacije u svezi korištenja IntechOpenove stranice www.intechopen.com i svih poddomena u vlasništvu IntechOpena, tvrtke sa sjedištem u 5 Princes Gate Court, London, SW7 2QJ, Ujedinjeno Kraljevstvo.
',metaTitle:"Odredbe i uvjeti",metaDescription:"Ove Odredbe i uvjeti ističu pravila i regulacije u svezi korištenja IntechOpenove stranice www.intechopen.com i svih poddomena u vlasništvu IntechOpena, tvrtke sa sjedištem u 5 Princes Gate Court, London, SW7 2QJ, Ujedinjeno Kraljevstvo.",metaKeywords:null,canonicalURL:"/page/cro-terms-and-conditions",contentRaw:'[{"type":"htmlEditorComponent","content":"Pristupom na stranicu www.intechopen.com slažete se s ovim odredbama, sa svim primjenjivim zakonskim odredbama, te se slažete s poštovanjem svih lokalnih zakona. Korištenje i/ili pristup ovoj stranici temelji se na potpunom prihvaćanju ovih odredbi. Svi materijali na ovoj stranici zaštićeni su primjenjivim zakonima o autorskim pravima i žigu.
\\n\\nSljedeća terminologija odnosi se na Odredbe i uvjete, te na sve naše ugovore:
\\n\\nKlijent, stranka, vi, vaš odnosi se na vas, osobu koja pristupa ovoj stranici i prihvaća IntechOpenove Odredbe i uvjete;
\\n\\nKompanija, tvrtka, mi, naše odnosi se na tvrtku IntechOpen;
\\n\\nStranke, strane odnosi se na klijenta i na nas, ili samo na klijenta ili nas.
\\n\\nSve odredbe koje se odnose na ponudu, prihvat ili razmatranje plaćanja, a za koja mi pružamo asistenciju klijentu, bilo na ugovoreni ili fiksni način, a s ciljem da se ostvare potrebe i želje klijenta u svezi s našim uslugama, su podložne zakonskim odredbama Ujedinjenog Kraljevstva.
\\n\\nOsim ako nije suprotno navedeno, IntechOpen i/ili svi davatelji licence vlasnici su intelektualnog vlasništva nad svim materijalima na www.intechopen.com. Sva prava intelektualnog vlasništva su pridržana. Stranice sa www.intechopen.com možete gledati, preuzimati, dijeliti, dijeliti poveznice i printati za osobnu uporabu, a temeljem pravila sadržanih u ovim Odredbama i uvjetima.
\\n\\nMi koristimo kolačiće. Korištenjem IntechOpenove stranice slažete se s korištenjem kolačića u skladu s IntechOpenovom Politikom privatnosti. Većina modernih, interaktivnih stranica koristi kolačiće kako bi omogućila ponovno pronalaženje korisničkih detalja kod svakog posjeta. Na našoj stranici kolačići se uglavnom koriste kako bi omogućili funkcionalnost i olakšali posjetiteljima korištenje stranice.
\\n\\nIntechOpen ili njegovi suradnici niti u jednom slučaju neće biti odgovorni za štete (štete uključuju gubitak podataka ili profita, druge poslovne prekide, te sve ostale štete) koje nastanu zbog korištenja materijala na IntechOpenovoj stranici ili nemogućnosti da se iste koriste, čak i ako je IntechOpen ili njegov predstavnik o takvoj šteti obaviješten pismenim ili usmenim putem. Neke jurisdikcije ne dozvoljavaju ograničenja garancija ili ograničenja obveza za posljedične ili slučajne štete pa se u tom slučaju ova ograničenja možda ne odnose na vas.
\\n\\nMaterijali koji se pojavljuju na IntechOpenovoj stranici mogu sadržavati manje greške, tipfelere ili fotografske greške. IntechOpen može napraviti promjene na bilo kojem materijalu koji se nalazi na stranici u bilo koje vrijeme.
\\n\\nIntechOpen nije formalno povezan niti s jednom vanjskom stranicom čije poveznice vode na www.intechopen.com, osim ako to nije izravno navedeno. Iz tog razloga IntechOpen nije odgovoran za sadržaj koji se pojavljuje na takvim stranicama. Poveznica na IntechOpenovu stranicu ne implicira povezanost sa IntechOpenom. Korištenje takvih poveznica isključiva je odgovornost korisnika.
\\n\\nZadržavamo pravo vlasništva nad cjelokupnom stranicom www.intechopen.com i nad svim materijalom na toj stranici. Koristeći se našim uslugama, slažete se da maknete sve poveznice na našu stranicu odmah nakon što to od vas zatražimo. Također, zadržavamo pravo da ove Odredbe i uvjete, i politiku o poveznicama izmjenimo u bilo koje vrijeme. Koristeći se poveznicama na naše stranice slažete se s ovim Odredbama i uvjetima.
\\n\\nAko smatrate da je bilo koja poveznica na našoj stranici sumnjiva iz bilo kojeg razloga, molimo vas da nas kontaktirate. U tom slučaju razmotrit ćemo micanje poveznice s naše stranice, iako nismo obvezni to napraviti.
\\n\\nBez prethodne privole i izričite pisane dozvole, ne možete stvarati okvire oko naših stranica ili koristiti druge tehnike koje na bilo koji način mogu promijeniti prezentaciju ili izgled naše stranice.
\\n\\nIntechOpen može ove Odredbe izmijeniti u bilo koje vrijeme i bez prethodne obavijesti. Koristeći ovu stranicu vi se slažete s trenutnim Odredbama i uvjetima koje su na snazi.
\\n\\nOve Odredbe i uvjeti su sastavljeni u skladu s odredbama prava Ujedinjenog Kraljevstva, a za sve sporove nadležan je sud u Londonu, Ujedinjeno Kraljevstvo.
\\n"}]'},components:[{type:"htmlEditorComponent",content:"Pristupom na stranicu www.intechopen.com slažete se s ovim odredbama, sa svim primjenjivim zakonskim odredbama, te se slažete s poštovanjem svih lokalnih zakona. Korištenje i/ili pristup ovoj stranici temelji se na potpunom prihvaćanju ovih odredbi. Svi materijali na ovoj stranici zaštićeni su primjenjivim zakonima o autorskim pravima i žigu.
\n\nSljedeća terminologija odnosi se na Odredbe i uvjete, te na sve naše ugovore:
\n\nKlijent, stranka, vi, vaš odnosi se na vas, osobu koja pristupa ovoj stranici i prihvaća IntechOpenove Odredbe i uvjete;
\n\nKompanija, tvrtka, mi, naše odnosi se na tvrtku IntechOpen;
\n\nStranke, strane odnosi se na klijenta i na nas, ili samo na klijenta ili nas.
\n\nSve odredbe koje se odnose na ponudu, prihvat ili razmatranje plaćanja, a za koja mi pružamo asistenciju klijentu, bilo na ugovoreni ili fiksni način, a s ciljem da se ostvare potrebe i želje klijenta u svezi s našim uslugama, su podložne zakonskim odredbama Ujedinjenog Kraljevstva.
\n\nOsim ako nije suprotno navedeno, IntechOpen i/ili svi davatelji licence vlasnici su intelektualnog vlasništva nad svim materijalima na www.intechopen.com. Sva prava intelektualnog vlasništva su pridržana. Stranice sa www.intechopen.com možete gledati, preuzimati, dijeliti, dijeliti poveznice i printati za osobnu uporabu, a temeljem pravila sadržanih u ovim Odredbama i uvjetima.
\n\nMi koristimo kolačiće. Korištenjem IntechOpenove stranice slažete se s korištenjem kolačića u skladu s IntechOpenovom Politikom privatnosti. Većina modernih, interaktivnih stranica koristi kolačiće kako bi omogućila ponovno pronalaženje korisničkih detalja kod svakog posjeta. Na našoj stranici kolačići se uglavnom koriste kako bi omogućili funkcionalnost i olakšali posjetiteljima korištenje stranice.
\n\nIntechOpen ili njegovi suradnici niti u jednom slučaju neće biti odgovorni za štete (štete uključuju gubitak podataka ili profita, druge poslovne prekide, te sve ostale štete) koje nastanu zbog korištenja materijala na IntechOpenovoj stranici ili nemogućnosti da se iste koriste, čak i ako je IntechOpen ili njegov predstavnik o takvoj šteti obaviješten pismenim ili usmenim putem. Neke jurisdikcije ne dozvoljavaju ograničenja garancija ili ograničenja obveza za posljedične ili slučajne štete pa se u tom slučaju ova ograničenja možda ne odnose na vas.
\n\nMaterijali koji se pojavljuju na IntechOpenovoj stranici mogu sadržavati manje greške, tipfelere ili fotografske greške. IntechOpen može napraviti promjene na bilo kojem materijalu koji se nalazi na stranici u bilo koje vrijeme.
\n\nIntechOpen nije formalno povezan niti s jednom vanjskom stranicom čije poveznice vode na www.intechopen.com, osim ako to nije izravno navedeno. Iz tog razloga IntechOpen nije odgovoran za sadržaj koji se pojavljuje na takvim stranicama. Poveznica na IntechOpenovu stranicu ne implicira povezanost sa IntechOpenom. Korištenje takvih poveznica isključiva je odgovornost korisnika.
\n\nZadržavamo pravo vlasništva nad cjelokupnom stranicom www.intechopen.com i nad svim materijalom na toj stranici. Koristeći se našim uslugama, slažete se da maknete sve poveznice na našu stranicu odmah nakon što to od vas zatražimo. Također, zadržavamo pravo da ove Odredbe i uvjete, i politiku o poveznicama izmjenimo u bilo koje vrijeme. Koristeći se poveznicama na naše stranice slažete se s ovim Odredbama i uvjetima.
\n\nAko smatrate da je bilo koja poveznica na našoj stranici sumnjiva iz bilo kojeg razloga, molimo vas da nas kontaktirate. U tom slučaju razmotrit ćemo micanje poveznice s naše stranice, iako nismo obvezni to napraviti.
\n\nBez prethodne privole i izričite pisane dozvole, ne možete stvarati okvire oko naših stranica ili koristiti druge tehnike koje na bilo koji način mogu promijeniti prezentaciju ili izgled naše stranice.
\n\nIntechOpen može ove Odredbe izmijeniti u bilo koje vrijeme i bez prethodne obavijesti. Koristeći ovu stranicu vi se slažete s trenutnim Odredbama i uvjetima koje su na snazi.
\n\nOve Odredbe i uvjeti su sastavljeni u skladu s odredbama prava Ujedinjenog Kraljevstva, a za sve sporove nadležan je sud u Londonu, Ujedinjeno Kraljevstvo.
\n"}]},successStories:{items:[]},authorsAndEditors:{filterParams:{sort:"featured,name"},profiles:[{id:"6700",title:"Dr.",name:"Abbass A.",middleName:null,surname:"Hashim",slug:"abbass-a.-hashim",fullName:"Abbass A. Hashim",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/6700/images/1864_n.jpg",biography:"Currently I am carrying out research in several areas of interest, mainly covering work on chemical and bio-sensors, semiconductor thin film device fabrication and characterisation.\nAt the moment I have very strong interest in radiation environmental pollution and bacteriology treatment. The teams of researchers are working very hard to bring novel results in this field. I am also a member of the team in charge for the supervision of Ph.D. students in the fields of development of silicon based planar waveguide sensor devices, study of inelastic electron tunnelling in planar tunnelling nanostructures for sensing applications and development of organotellurium(IV) compounds for semiconductor applications. I am a specialist in data analysis techniques and nanosurface structure. I have served as the editor for many books, been a member of the editorial board in science journals, have published many papers and hold many patents.",institutionString:null,institution:{name:"Sheffield Hallam University",country:{name:"United Kingdom"}}},{id:"54525",title:"Prof.",name:"Abdul Latif",middleName:null,surname:"Ahmad",slug:"abdul-latif-ahmad",fullName:"Abdul Latif Ahmad",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"20567",title:"Prof.",name:"Ado",middleName:null,surname:"Jorio",slug:"ado-jorio",fullName:"Ado Jorio",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"Universidade Federal de Minas Gerais",country:{name:"Brazil"}}},{id:"47940",title:"Dr.",name:"Alberto",middleName:null,surname:"Mantovani",slug:"alberto-mantovani",fullName:"Alberto Mantovani",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"12392",title:"Mr.",name:"Alex",middleName:null,surname:"Lazinica",slug:"alex-lazinica",fullName:"Alex Lazinica",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/12392/images/7282_n.png",biography:"Alex Lazinica is the founder and CEO of IntechOpen. After obtaining a Master's degree in Mechanical Engineering, he continued his PhD studies in Robotics at the Vienna University of Technology. Here he worked as a robotic researcher with the university's Intelligent Manufacturing Systems Group as well as a guest researcher at various European universities, including the Swiss Federal Institute of Technology Lausanne (EPFL). During this time he published more than 20 scientific papers, gave presentations, served as a reviewer for major robotic journals and conferences and most importantly he co-founded and built the International Journal of Advanced Robotic Systems- world's first Open Access journal in the field of robotics. Starting this journal was a pivotal point in his career, since it was a pathway to founding IntechOpen - Open Access publisher focused on addressing academic researchers needs. Alex is a personification of IntechOpen key values being trusted, open and entrepreneurial. Today his focus is on defining the growth and development strategy for the company.",institutionString:null,institution:{name:"TU Wien",country:{name:"Austria"}}},{id:"19816",title:"Prof.",name:"Alexander",middleName:null,surname:"Kokorin",slug:"alexander-kokorin",fullName:"Alexander Kokorin",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/19816/images/1607_n.jpg",biography:"Alexander I. Kokorin: born: 1947, Moscow; DSc., PhD; Principal Research Fellow (Research Professor) of Department of Kinetics and Catalysis, N. Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow.\r\nArea of research interests: physical chemistry of complex-organized molecular and nanosized systems, including polymer-metal complexes; the surface of doped oxide semiconductors. He is an expert in structural, absorptive, catalytic and photocatalytic properties, in structural organization and dynamic features of ionic liquids, in magnetic interactions between paramagnetic centers. The author or co-author of 3 books, over 200 articles and reviews in scientific journals and books. He is an actual member of the International EPR/ESR Society, European Society on Quantum Solar Energy Conversion, Moscow House of Scientists, of the Board of Moscow Physical Society.",institutionString:null,institution:{name:"Semenov Institute of Chemical Physics",country:{name:"Russia"}}},{id:"62389",title:"PhD.",name:"Ali Demir",middleName:null,surname:"Sezer",slug:"ali-demir-sezer",fullName:"Ali Demir Sezer",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/62389/images/3413_n.jpg",biography:"Dr. Ali Demir Sezer has a Ph.D. from Pharmaceutical Biotechnology at the Faculty of Pharmacy, University of Marmara (Turkey). He is the member of many Pharmaceutical Associations and acts as a reviewer of scientific journals and European projects under different research areas such as: drug delivery systems, nanotechnology and pharmaceutical biotechnology. Dr. Sezer is the author of many scientific publications in peer-reviewed journals and poster communications. Focus of his research activity is drug delivery, physico-chemical characterization and biological evaluation of biopolymers micro and nanoparticles as modified drug delivery system, and colloidal drug carriers (liposomes, nanoparticles etc.).",institutionString:null,institution:{name:"Marmara University",country:{name:"Turkey"}}},{id:"61051",title:"Prof.",name:"Andrea",middleName:null,surname:"Natale",slug:"andrea-natale",fullName:"Andrea Natale",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"100762",title:"Prof.",name:"Andrea",middleName:null,surname:"Natale",slug:"andrea-natale",fullName:"Andrea Natale",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"St David's Medical Center",country:{name:"United States of America"}}},{id:"107416",title:"Dr.",name:"Andrea",middleName:null,surname:"Natale",slug:"andrea-natale",fullName:"Andrea Natale",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"Texas Cardiac Arrhythmia",country:{name:"United States of America"}}},{id:"64434",title:"Dr.",name:"Angkoon",middleName:null,surname:"Phinyomark",slug:"angkoon-phinyomark",fullName:"Angkoon Phinyomark",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/64434/images/2619_n.jpg",biography:"My name is Angkoon Phinyomark. I received a B.Eng. degree in Computer Engineering with First Class Honors in 2008 from Prince of Songkla University, Songkhla, Thailand, where I received a Ph.D. degree in Electrical Engineering. My research interests are primarily in the area of biomedical signal processing and classification notably EMG (electromyography signal), EOG (electrooculography signal), and EEG (electroencephalography signal), image analysis notably breast cancer analysis and optical coherence tomography, and rehabilitation engineering. I became a student member of IEEE in 2008. During October 2011-March 2012, I had worked at School of Computer Science and Electronic Engineering, University of Essex, Colchester, Essex, United Kingdom. In addition, during a B.Eng. I had been a visiting research student at Faculty of Computer Science, University of Murcia, Murcia, Spain for three months.\n\nI have published over 40 papers during 5 years in refereed journals, books, and conference proceedings in the areas of electro-physiological signals processing and classification, notably EMG and EOG signals, fractal analysis, wavelet analysis, texture analysis, feature extraction and machine learning algorithms, and assistive and rehabilitative devices. I have several computer programming language certificates, i.e. Sun Certified Programmer for the Java 2 Platform 1.4 (SCJP), Microsoft Certified Professional Developer, Web Developer (MCPD), Microsoft Certified Technology Specialist, .NET Framework 2.0 Web (MCTS). I am a Reviewer for several refereed journals and international conferences, such as IEEE Transactions on Biomedical Engineering, IEEE Transactions on Industrial Electronics, Optic Letters, Measurement Science Review, and also a member of the International Advisory Committee for 2012 IEEE Business Engineering and Industrial Applications and 2012 IEEE Symposium on Business, Engineering and Industrial Applications.",institutionString:null,institution:{name:"Joseph Fourier University",country:{name:"France"}}},{id:"55578",title:"Dr.",name:"Antonio",middleName:null,surname:"Jurado-Navas",slug:"antonio-jurado-navas",fullName:"Antonio Jurado-Navas",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/55578/images/4574_n.png",biography:"Antonio Jurado-Navas received the M.S. degree (2002) and the Ph.D. degree (2009) in Telecommunication Engineering, both from the University of Málaga (Spain). He first worked as a consultant at Vodafone-Spain. From 2004 to 2011, he was a Research Assistant with the Communications Engineering Department at the University of Málaga. In 2011, he became an Assistant Professor in the same department. From 2012 to 2015, he was with Ericsson Spain, where he was working on geo-location\ntools for third generation mobile networks. Since 2015, he is a Marie-Curie fellow at the Denmark Technical University. His current research interests include the areas of mobile communication systems and channel modeling in addition to atmospheric optical communications, adaptive optics and statistics",institutionString:null,institution:{name:"University of Malaga",country:{name:"Spain"}}}],filtersByRegion:[{group:"region",caption:"North America",value:1,count:5766},{group:"region",caption:"Middle and South America",value:2,count:5227},{group:"region",caption:"Africa",value:3,count:1717},{group:"region",caption:"Asia",value:4,count:10366},{group:"region",caption:"Australia and Oceania",value:5,count:897},{group:"region",caption:"Europe",value:6,count:15789}],offset:12,limit:12,total:118187},chapterEmbeded:{data:{}},editorApplication:{success:null,errors:{}},ofsBooks:{filterParams:{topicId:"23"},books:[{type:"book",id:"10656",title:"Intellectual Property",subtitle:null,isOpenForSubmission:!0,hash:"135df9b403b125a6458eba971faab3f6",slug:null,bookSignature:"Dr. Sakthivel Lakshmana Prabu and Dr. Suriyaprakash TNK",coverURL:"https://cdn.intechopen.com/books/images_new/10656.jpg",editedByType:null,editors:[{id:"91590",title:"Dr.",name:"Sakthivel",surname:"Lakshmana Prabu",slug:"sakthivel-lakshmana-prabu",fullName:"Sakthivel Lakshmana Prabu"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"10658",title:"Multilingualism",subtitle:null,isOpenForSubmission:!0,hash:"a6bf171e05831c00f8687891ab1b10b5",slug:null,bookSignature:"Prof. Xiaoming Jiang",coverURL:"https://cdn.intechopen.com/books/images_new/10658.jpg",editedByType:null,editors:[{id:"189844",title:"Prof.",name:"Xiaoming",surname:"Jiang",slug:"xiaoming-jiang",fullName:"Xiaoming Jiang"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"10662",title:"Pedagogy",subtitle:null,isOpenForSubmission:!0,hash:"c858e1c6fb878d3b895acbacec624576",slug:null,bookSignature:"",coverURL:"https://cdn.intechopen.com/books/images_new/10662.jpg",editedByType:null,editors:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"10913",title:"Indigenous Populations",subtitle:null,isOpenForSubmission:!0,hash:"c5e8cd4e3ec004d0479494ca190db4cb",slug:null,bookSignature:"",coverURL:"https://cdn.intechopen.com/books/images_new/10913.jpg",editedByType:null,editors:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"10914",title:"Racism",subtitle:null,isOpenForSubmission:!0,hash:"0737383fcc202641f59e4a5df02eb509",slug:null,bookSignature:"",coverURL:"https://cdn.intechopen.com/books/images_new/10914.jpg",editedByType:null,editors:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}],filtersByTopic:[{group:"topic",caption:"Agricultural and Biological Sciences",value:5,count:14},{group:"topic",caption:"Biochemistry, Genetics and Molecular Biology",value:6,count:3},{group:"topic",caption:"Business, Management and Economics",value:7,count:1},{group:"topic",caption:"Chemistry",value:8,count:6},{group:"topic",caption:"Computer and Information Science",value:9,count:6},{group:"topic",caption:"Earth and Planetary Sciences",value:10,count:7},{group:"topic",caption:"Engineering",value:11,count:15},{group:"topic",caption:"Environmental Sciences",value:12,count:2},{group:"topic",caption:"Immunology and Microbiology",value:13,count:3},{group:"topic",caption:"Materials Science",value:14,count:5},{group:"topic",caption:"Mathematics",value:15,count:1},{group:"topic",caption:"Medicine",value:16,count:24},{group:"topic",caption:"Neuroscience",value:18,count:1},{group:"topic",caption:"Pharmacology, Toxicology and Pharmaceutical Science",value:19,count:2},{group:"topic",caption:"Physics",value:20,count:2},{group:"topic",caption:"Psychology",value:21,count:4},{group:"topic",caption:"Social Sciences",value:23,count:2},{group:"topic",caption:"Technology",value:24,count:1},{group:"topic",caption:"Veterinary Medicine and Science",value:25,count:1}],offset:12,limit:12,total:5},popularBooks:{featuredBooks:[{type:"book",id:"9385",title:"Renewable Energy",subtitle:"Technologies and Applications",isOpenForSubmission:!1,hash:"a6b446d19166f17f313008e6c056f3d8",slug:"renewable-energy-technologies-and-applications",bookSignature:"Tolga Taner, Archana Tiwari and Taha Selim Ustun",coverURL:"https://cdn.intechopen.com/books/images_new/9385.jpg",editors:[{id:"197240",title:"Associate Prof.",name:"Tolga",middleName:null,surname:"Taner",slug:"tolga-taner",fullName:"Tolga Taner"}],equalEditorOne:{id:"186791",title:"Dr.",name:"Archana",middleName:null,surname:"Tiwari",slug:"archana-tiwari",fullName:"Archana Tiwari",profilePictureURL:"https://mts.intechopen.com/storage/users/186791/images/system/186791.jpg",biography:"Dr. Archana Tiwari is Associate Professor at Amity University, India. Her research interests include renewable sources of energy from microalgae and further utilizing the residual biomass for the generation of value-added products, bioremediation through microalgae and microbial consortium, antioxidative enzymes and stress, and nutraceuticals from microalgae. She has been working on algal biotechnology for the last two decades. She has published her research in many international journals and has authored many books and chapters with renowned publishing houses. She has also delivered talks as an invited speaker at many national and international conferences. Dr. Tiwari is the recipient of several awards including Researcher of the Year and Distinguished Scientist.",institutionString:"Amity University",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"3",totalChapterViews:"0",totalEditedBooks:"1",institution:{name:"Amity University",institutionURL:null,country:{name:"India"}}},equalEditorTwo:{id:"197609",title:"Prof.",name:"Taha Selim",middleName:null,surname:"Ustun",slug:"taha-selim-ustun",fullName:"Taha Selim Ustun",profilePictureURL:"https://mts.intechopen.com/storage/users/197609/images/system/197609.jpeg",biography:"Dr. Taha Selim Ustun received a Ph.D. in Electrical Engineering from Victoria University, Melbourne, Australia. He is a researcher with the Fukushima Renewable Energy Institute, AIST (FREA), where he leads the Smart Grid Cybersecurity Laboratory. Prior to that, he was a faculty member with the School of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, USA. His current research interests include power systems protection, communication in power networks, distributed generation, microgrids, electric vehicle integration, and cybersecurity in smart grids. He serves on the editorial boards of IEEE Access, IEEE Transactions on Industrial Informatics, Energies, Electronics, Electricity, World Electric Vehicle and Information journals. Dr. Ustun is a member of the IEEE 2004 and 2800, IEC Renewable Energy Management WG 8, and IEC TC 57 WG17. He has been invited to run specialist courses in Africa, India, and China. He has delivered talks for the Qatar Foundation, the World Energy Council, the Waterloo Global Science Initiative, and the European Union Energy Initiative (EUEI). His research has attracted funding from prestigious programs in Japan, Australia, the European Union, and North America.",institutionString:"Fukushima Renewable Energy Institute, AIST (FREA)",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"1",totalChapterViews:"0",totalEditedBooks:"0",institution:{name:"National Institute of Advanced Industrial Science and Technology",institutionURL:null,country:{name:"Japan"}}},equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"8985",title:"Natural Resources Management and Biological Sciences",subtitle:null,isOpenForSubmission:!1,hash:"5c2e219a6c021a40b5a20c041dea88c4",slug:"natural-resources-management-and-biological-sciences",bookSignature:"Edward R. Rhodes and Humood Naser",coverURL:"https://cdn.intechopen.com/books/images_new/8985.jpg",editors:[{id:"280886",title:"Prof.",name:"Edward R",middleName:null,surname:"Rhodes",slug:"edward-r-rhodes",fullName:"Edward R Rhodes"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"9027",title:"Human Blood Group Systems and Haemoglobinopathies",subtitle:null,isOpenForSubmission:!1,hash:"d00d8e40b11cfb2547d1122866531c7e",slug:"human-blood-group-systems-and-haemoglobinopathies",bookSignature:"Osaro Erhabor and Anjana Munshi",coverURL:"https://cdn.intechopen.com/books/images_new/9027.jpg",editors:[{id:"35140",title:null,name:"Osaro",middleName:null,surname:"Erhabor",slug:"osaro-erhabor",fullName:"Osaro Erhabor"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"7841",title:"New Insights Into Metabolic Syndrome",subtitle:null,isOpenForSubmission:!1,hash:"ef5accfac9772b9e2c9eff884f085510",slug:"new-insights-into-metabolic-syndrome",bookSignature:"Akikazu Takada",coverURL:"https://cdn.intechopen.com/books/images_new/7841.jpg",editors:[{id:"248459",title:"Dr.",name:"Akikazu",middleName:null,surname:"Takada",slug:"akikazu-takada",fullName:"Akikazu Takada"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"8558",title:"Aerodynamics",subtitle:null,isOpenForSubmission:!1,hash:"db7263fc198dfb539073ba0260a7f1aa",slug:"aerodynamics",bookSignature:"Mofid Gorji-Bandpy and Aly-Mousaad Aly",coverURL:"https://cdn.intechopen.com/books/images_new/8558.jpg",editors:[{id:"35542",title:"Prof.",name:"Mofid",middleName:null,surname:"Gorji-Bandpy",slug:"mofid-gorji-bandpy",fullName:"Mofid Gorji-Bandpy"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"9668",title:"Chemistry and Biochemistry of Winemaking, Wine Stabilization and Aging",subtitle:null,isOpenForSubmission:!1,hash:"c5484276a314628acf21ec1bdc3a86b9",slug:"chemistry-and-biochemistry-of-winemaking-wine-stabilization-and-aging",bookSignature:"Fernanda Cosme, Fernando M. Nunes and Luís Filipe-Ribeiro",coverURL:"https://cdn.intechopen.com/books/images_new/9668.jpg",editors:[{id:"186819",title:"Prof.",name:"Fernanda",middleName:null,surname:"Cosme",slug:"fernanda-cosme",fullName:"Fernanda Cosme"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"7847",title:"Medical Toxicology",subtitle:null,isOpenForSubmission:!1,hash:"db9b65bea093de17a0855a1b27046247",slug:"medical-toxicology",bookSignature:"Pınar Erkekoglu and Tomohisa Ogawa",coverURL:"https://cdn.intechopen.com/books/images_new/7847.jpg",editors:[{id:"109978",title:"Prof.",name:"Pınar",middleName:null,surname:"Erkekoglu",slug:"pinar-erkekoglu",fullName:"Pınar Erkekoglu"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"8620",title:"Mining Techniques",subtitle:"Past, Present and Future",isOpenForSubmission:!1,hash:"b65658f81d14e9e57e49377869d3a575",slug:"mining-techniques-past-present-and-future",bookSignature:"Abhay Soni",coverURL:"https://cdn.intechopen.com/books/images_new/8620.jpg",editors:[{id:"271093",title:"Dr.",name:"Abhay",middleName:null,surname:"Soni",slug:"abhay-soni",fullName:"Abhay Soni"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"9660",title:"Inland Waters",subtitle:"Dynamics and Ecology",isOpenForSubmission:!1,hash:"975c26819ceb11a926793bc2adc62bd6",slug:"inland-waters-dynamics-and-ecology",bookSignature:"Adam Devlin, Jiayi Pan and Mohammad Manjur Shah",coverURL:"https://cdn.intechopen.com/books/images_new/9660.jpg",editors:[{id:"280757",title:"Dr.",name:"Adam",middleName:"Thomas",surname:"Devlin",slug:"adam-devlin",fullName:"Adam Devlin"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"9122",title:"Cosmetic Surgery",subtitle:null,isOpenForSubmission:!1,hash:"207026ca4a4125e17038e770d00ee152",slug:"cosmetic-surgery",bookSignature:"Yueh-Bih Tang",coverURL:"https://cdn.intechopen.com/books/images_new/9122.jpg",editors:[{id:"202122",title:"Prof.",name:"Yueh-Bih",middleName:null,surname:"Tang",slug:"yueh-bih-tang",fullName:"Yueh-Bih Tang"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"9043",title:"Parenting",subtitle:"Studies by an Ecocultural and Transactional Perspective",isOpenForSubmission:!1,hash:"6d21066c7438e459e4c6fb13217a5c8c",slug:"parenting-studies-by-an-ecocultural-and-transactional-perspective",bookSignature:"Loredana Benedetto and Massimo Ingrassia",coverURL:"https://cdn.intechopen.com/books/images_new/9043.jpg",editors:[{id:"193200",title:"Prof.",name:"Loredana",middleName:null,surname:"Benedetto",slug:"loredana-benedetto",fullName:"Loredana Benedetto"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"9731",title:"Oxidoreductase",subtitle:null,isOpenForSubmission:!1,hash:"852e6f862c85fc3adecdbaf822e64e6e",slug:"oxidoreductase",bookSignature:"Mahmoud Ahmed Mansour",coverURL:"https://cdn.intechopen.com/books/images_new/9731.jpg",editors:[{id:"224662",title:"Prof.",name:"Mahmoud Ahmed",middleName:null,surname:"Mansour",slug:"mahmoud-ahmed-mansour",fullName:"Mahmoud Ahmed Mansour"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}}],offset:12,limit:12,total:5227},hotBookTopics:{hotBooks:[],offset:0,limit:12,total:null},publish:{},publishingProposal:{success:null,errors:{}},books:{featuredBooks:[{type:"book",id:"9385",title:"Renewable Energy",subtitle:"Technologies and Applications",isOpenForSubmission:!1,hash:"a6b446d19166f17f313008e6c056f3d8",slug:"renewable-energy-technologies-and-applications",bookSignature:"Tolga Taner, Archana Tiwari and Taha Selim Ustun",coverURL:"https://cdn.intechopen.com/books/images_new/9385.jpg",editors:[{id:"197240",title:"Associate Prof.",name:"Tolga",middleName:null,surname:"Taner",slug:"tolga-taner",fullName:"Tolga Taner"}],equalEditorOne:{id:"186791",title:"Dr.",name:"Archana",middleName:null,surname:"Tiwari",slug:"archana-tiwari",fullName:"Archana Tiwari",profilePictureURL:"https://mts.intechopen.com/storage/users/186791/images/system/186791.jpg",biography:"Dr. Archana Tiwari is Associate Professor at Amity University, India. Her research interests include renewable sources of energy from microalgae and further utilizing the residual biomass for the generation of value-added products, bioremediation through microalgae and microbial consortium, antioxidative enzymes and stress, and nutraceuticals from microalgae. She has been working on algal biotechnology for the last two decades. She has published her research in many international journals and has authored many books and chapters with renowned publishing houses. She has also delivered talks as an invited speaker at many national and international conferences. Dr. Tiwari is the recipient of several awards including Researcher of the Year and Distinguished Scientist.",institutionString:"Amity University",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"3",totalChapterViews:"0",totalEditedBooks:"1",institution:{name:"Amity University",institutionURL:null,country:{name:"India"}}},equalEditorTwo:{id:"197609",title:"Prof.",name:"Taha Selim",middleName:null,surname:"Ustun",slug:"taha-selim-ustun",fullName:"Taha Selim Ustun",profilePictureURL:"https://mts.intechopen.com/storage/users/197609/images/system/197609.jpeg",biography:"Dr. Taha Selim Ustun received a Ph.D. in Electrical Engineering from Victoria University, Melbourne, Australia. He is a researcher with the Fukushima Renewable Energy Institute, AIST (FREA), where he leads the Smart Grid Cybersecurity Laboratory. Prior to that, he was a faculty member with the School of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, USA. His current research interests include power systems protection, communication in power networks, distributed generation, microgrids, electric vehicle integration, and cybersecurity in smart grids. He serves on the editorial boards of IEEE Access, IEEE Transactions on Industrial Informatics, Energies, Electronics, Electricity, World Electric Vehicle and Information journals. Dr. Ustun is a member of the IEEE 2004 and 2800, IEC Renewable Energy Management WG 8, and IEC TC 57 WG17. He has been invited to run specialist courses in Africa, India, and China. He has delivered talks for the Qatar Foundation, the World Energy Council, the Waterloo Global Science Initiative, and the European Union Energy Initiative (EUEI). His research has attracted funding from prestigious programs in Japan, Australia, the European Union, and North America.",institutionString:"Fukushima Renewable Energy Institute, AIST (FREA)",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"1",totalChapterViews:"0",totalEditedBooks:"0",institution:{name:"National Institute of Advanced Industrial Science and Technology",institutionURL:null,country:{name:"Japan"}}},equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"8985",title:"Natural Resources Management and Biological Sciences",subtitle:null,isOpenForSubmission:!1,hash:"5c2e219a6c021a40b5a20c041dea88c4",slug:"natural-resources-management-and-biological-sciences",bookSignature:"Edward R. Rhodes and Humood Naser",coverURL:"https://cdn.intechopen.com/books/images_new/8985.jpg",editors:[{id:"280886",title:"Prof.",name:"Edward R",middleName:null,surname:"Rhodes",slug:"edward-r-rhodes",fullName:"Edward R Rhodes"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"9027",title:"Human Blood Group Systems and Haemoglobinopathies",subtitle:null,isOpenForSubmission:!1,hash:"d00d8e40b11cfb2547d1122866531c7e",slug:"human-blood-group-systems-and-haemoglobinopathies",bookSignature:"Osaro Erhabor and Anjana Munshi",coverURL:"https://cdn.intechopen.com/books/images_new/9027.jpg",editors:[{id:"35140",title:null,name:"Osaro",middleName:null,surname:"Erhabor",slug:"osaro-erhabor",fullName:"Osaro Erhabor"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"7841",title:"New Insights Into Metabolic Syndrome",subtitle:null,isOpenForSubmission:!1,hash:"ef5accfac9772b9e2c9eff884f085510",slug:"new-insights-into-metabolic-syndrome",bookSignature:"Akikazu Takada",coverURL:"https://cdn.intechopen.com/books/images_new/7841.jpg",editors:[{id:"248459",title:"Dr.",name:"Akikazu",middleName:null,surname:"Takada",slug:"akikazu-takada",fullName:"Akikazu Takada"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"8558",title:"Aerodynamics",subtitle:null,isOpenForSubmission:!1,hash:"db7263fc198dfb539073ba0260a7f1aa",slug:"aerodynamics",bookSignature:"Mofid Gorji-Bandpy and Aly-Mousaad Aly",coverURL:"https://cdn.intechopen.com/books/images_new/8558.jpg",editors:[{id:"35542",title:"Prof.",name:"Mofid",middleName:null,surname:"Gorji-Bandpy",slug:"mofid-gorji-bandpy",fullName:"Mofid Gorji-Bandpy"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"9668",title:"Chemistry and Biochemistry of Winemaking, Wine Stabilization and Aging",subtitle:null,isOpenForSubmission:!1,hash:"c5484276a314628acf21ec1bdc3a86b9",slug:"chemistry-and-biochemistry-of-winemaking-wine-stabilization-and-aging",bookSignature:"Fernanda Cosme, Fernando M. Nunes and Luís Filipe-Ribeiro",coverURL:"https://cdn.intechopen.com/books/images_new/9668.jpg",editors:[{id:"186819",title:"Prof.",name:"Fernanda",middleName:null,surname:"Cosme",slug:"fernanda-cosme",fullName:"Fernanda Cosme"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"7847",title:"Medical Toxicology",subtitle:null,isOpenForSubmission:!1,hash:"db9b65bea093de17a0855a1b27046247",slug:"medical-toxicology",bookSignature:"Pınar Erkekoglu and Tomohisa Ogawa",coverURL:"https://cdn.intechopen.com/books/images_new/7847.jpg",editors:[{id:"109978",title:"Prof.",name:"Pınar",middleName:null,surname:"Erkekoglu",slug:"pinar-erkekoglu",fullName:"Pınar Erkekoglu"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"8620",title:"Mining Techniques",subtitle:"Past, Present and Future",isOpenForSubmission:!1,hash:"b65658f81d14e9e57e49377869d3a575",slug:"mining-techniques-past-present-and-future",bookSignature:"Abhay Soni",coverURL:"https://cdn.intechopen.com/books/images_new/8620.jpg",editors:[{id:"271093",title:"Dr.",name:"Abhay",middleName:null,surname:"Soni",slug:"abhay-soni",fullName:"Abhay Soni"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"9660",title:"Inland Waters",subtitle:"Dynamics and Ecology",isOpenForSubmission:!1,hash:"975c26819ceb11a926793bc2adc62bd6",slug:"inland-waters-dynamics-and-ecology",bookSignature:"Adam Devlin, Jiayi Pan and Mohammad Manjur Shah",coverURL:"https://cdn.intechopen.com/books/images_new/9660.jpg",editors:[{id:"280757",title:"Dr.",name:"Adam",middleName:"Thomas",surname:"Devlin",slug:"adam-devlin",fullName:"Adam Devlin"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"9122",title:"Cosmetic Surgery",subtitle:null,isOpenForSubmission:!1,hash:"207026ca4a4125e17038e770d00ee152",slug:"cosmetic-surgery",bookSignature:"Yueh-Bih Tang",coverURL:"https://cdn.intechopen.com/books/images_new/9122.jpg",editors:[{id:"202122",title:"Prof.",name:"Yueh-Bih",middleName:null,surname:"Tang",slug:"yueh-bih-tang",fullName:"Yueh-Bih Tang"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}}],latestBooks:[{type:"book",id:"9550",title:"Entrepreneurship",subtitle:"Contemporary Issues",isOpenForSubmission:!1,hash:"9b4ac1ee5b743abf6f88495452b1e5e7",slug:"entrepreneurship-contemporary-issues",bookSignature:"Mladen Turuk",coverURL:"https://cdn.intechopen.com/books/images_new/9550.jpg",editedByType:"Edited by",editors:[{id:"319755",title:"Prof.",name:"Mladen",middleName:null,surname:"Turuk",slug:"mladen-turuk",fullName:"Mladen Turuk"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"10065",title:"Wavelet Theory",subtitle:null,isOpenForSubmission:!1,hash:"d8868e332169597ba2182d9b004d60de",slug:"wavelet-theory",bookSignature:"Somayeh Mohammady",coverURL:"https://cdn.intechopen.com/books/images_new/10065.jpg",editedByType:"Edited by",editors:[{id:"109280",title:"Dr.",name:"Somayeh",middleName:null,surname:"Mohammady",slug:"somayeh-mohammady",fullName:"Somayeh Mohammady"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"9313",title:"Clay Science and Technology",subtitle:null,isOpenForSubmission:!1,hash:"6fa7e70396ff10620e032bb6cfa6fb72",slug:"clay-science-and-technology",bookSignature:"Gustavo Morari Do Nascimento",coverURL:"https://cdn.intechopen.com/books/images_new/9313.jpg",editedByType:"Edited by",editors:[{id:"7153",title:"Prof.",name:"Gustavo",middleName:null,surname:"Morari Do Nascimento",slug:"gustavo-morari-do-nascimento",fullName:"Gustavo Morari Do Nascimento"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"9888",title:"Nuclear Power Plants",subtitle:"The Processes from the Cradle to the Grave",isOpenForSubmission:!1,hash:"c2c8773e586f62155ab8221ebb72a849",slug:"nuclear-power-plants-the-processes-from-the-cradle-to-the-grave",bookSignature:"Nasser Awwad",coverURL:"https://cdn.intechopen.com/books/images_new/9888.jpg",editedByType:"Edited by",editors:[{id:"145209",title:"Prof.",name:"Nasser",middleName:"S",surname:"Awwad",slug:"nasser-awwad",fullName:"Nasser Awwad"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"8098",title:"Resources of Water",subtitle:null,isOpenForSubmission:!1,hash:"d251652996624d932ef7b8ed62cf7cfc",slug:"resources-of-water",bookSignature:"Prathna Thanjavur Chandrasekaran, Muhammad Salik Javaid, Aftab Sadiq",coverURL:"https://cdn.intechopen.com/books/images_new/8098.jpg",editedByType:"Edited by",editors:[{id:"167917",title:"Dr.",name:"Prathna",middleName:null,surname:"Thanjavur Chandrasekaran",slug:"prathna-thanjavur-chandrasekaran",fullName:"Prathna Thanjavur Chandrasekaran"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"9644",title:"Glaciers and the Polar Environment",subtitle:null,isOpenForSubmission:!1,hash:"e8cfdc161794e3753ced54e6ff30873b",slug:"glaciers-and-the-polar-environment",bookSignature:"Masaki Kanao, Danilo Godone and Niccolò Dematteis",coverURL:"https://cdn.intechopen.com/books/images_new/9644.jpg",editedByType:"Edited by",editors:[{id:"51959",title:"Dr.",name:"Masaki",middleName:null,surname:"Kanao",slug:"masaki-kanao",fullName:"Masaki Kanao"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"10432",title:"Casting Processes and Modelling of Metallic Materials",subtitle:null,isOpenForSubmission:!1,hash:"2c5c9df938666bf5d1797727db203a6d",slug:"casting-processes-and-modelling-of-metallic-materials",bookSignature:"Zakaria Abdallah and Nada Aldoumani",coverURL:"https://cdn.intechopen.com/books/images_new/10432.jpg",editedByType:"Edited by",editors:[{id:"201670",title:"Dr.",name:"Zak",middleName:null,surname:"Abdallah",slug:"zak-abdallah",fullName:"Zak Abdallah"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"9671",title:"Macrophages",subtitle:null,isOpenForSubmission:!1,hash:"03b00fdc5f24b71d1ecdfd75076bfde6",slug:"macrophages",bookSignature:"Hridayesh Prakash",coverURL:"https://cdn.intechopen.com/books/images_new/9671.jpg",editedByType:"Edited by",editors:[{id:"287184",title:"Dr.",name:"Hridayesh",middleName:null,surname:"Prakash",slug:"hridayesh-prakash",fullName:"Hridayesh Prakash"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"8415",title:"Extremophilic Microbes and Metabolites",subtitle:"Diversity, Bioprospecting and Biotechnological Applications",isOpenForSubmission:!1,hash:"93e0321bc93b89ff73730157738f8f97",slug:"extremophilic-microbes-and-metabolites-diversity-bioprospecting-and-biotechnological-applications",bookSignature:"Afef Najjari, Ameur Cherif, Haïtham Sghaier and Hadda Imene Ouzari",coverURL:"https://cdn.intechopen.com/books/images_new/8415.jpg",editedByType:"Edited by",editors:[{id:"196823",title:"Dr.",name:"Afef",middleName:null,surname:"Najjari",slug:"afef-najjari",fullName:"Afef Najjari"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"9731",title:"Oxidoreductase",subtitle:null,isOpenForSubmission:!1,hash:"852e6f862c85fc3adecdbaf822e64e6e",slug:"oxidoreductase",bookSignature:"Mahmoud Ahmed Mansour",coverURL:"https://cdn.intechopen.com/books/images_new/9731.jpg",editedByType:"Edited by",editors:[{id:"224662",title:"Prof.",name:"Mahmoud Ahmed",middleName:null,surname:"Mansour",slug:"mahmoud-ahmed-mansour",fullName:"Mahmoud Ahmed Mansour"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},subject:{topic:{id:"1028",title:"Hemodynamics",slug:"hemodynamics",parent:{title:"Hematology",slug:"hematology"},numberOfBooks:2,numberOfAuthorsAndEditors:16,numberOfWosCitations:10,numberOfCrossrefCitations:2,numberOfDimensionsCitations:7,videoUrl:null,fallbackUrl:null,description:null},booksByTopicFilter:{topicSlug:"hemodynamics",sort:"-publishedDate",limit:12,offset:0},booksByTopicCollection:[{type:"book",id:"7042",title:"Highlights on Hemodynamics",subtitle:null,isOpenForSubmission:!1,hash:"ab4cb86baa2cadb67630b31257cb04b2",slug:"highlights-on-hemodynamics",bookSignature:"Theodoros Aslanidis",coverURL:"https://cdn.intechopen.com/books/images_new/7042.jpg",editedByType:"Edited by",editors:[{id:"200252",title:"Dr.",name:"Theodoros",middleName:null,surname:"Aslanidis",slug:"theodoros-aslanidis",fullName:"Theodoros Aslanidis"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"1653",title:"Hemodynamics",subtitle:"New Diagnostic and Therapeutic Approaches",isOpenForSubmission:!1,hash:"2cf4b686414a77f0c867007f5062914f",slug:"hemodynamics-new-diagnostic-and-therapeutic-approaches",bookSignature:"A. Seda Artis",coverURL:"https://cdn.intechopen.com/books/images_new/1653.jpg",editedByType:"Edited by",editors:[{id:"99453",title:"Dr.",name:"Aise Seda",middleName:null,surname:"Artis",slug:"aise-seda-artis",fullName:"Aise Seda Artis"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}],booksByTopicTotal:2,mostCitedChapters:[{id:"36116",doi:"10.5772/36263",title:"The Evaluation of Renal Hemodynamics with Doppler Ultrasonography",slug:"the-evaluation-of-renal-hemodynamics-with-renal-doppler-ultrasonography",totalDownloads:10998,totalCrossrefCites:2,totalDimensionsCites:4,book:{slug:"hemodynamics-new-diagnostic-and-therapeutic-approaches",title:"Hemodynamics",fullTitle:"Hemodynamics - New Diagnostic and Therapeutic Approaches"},signatures:"Mahir Kaya",authors:[{id:"107675",title:"Dr.",name:"Mahir",middleName:null,surname:"Kaya",slug:"mahir-kaya",fullName:"Mahir Kaya"}]},{id:"36121",doi:"10.5772/34272",title:"Carnosine and Its Role on the Erythrocyte Rheology",slug:"carnosine-and-its-role-on-the-erythrocyte-rheology",totalDownloads:1870,totalCrossrefCites:0,totalDimensionsCites:2,book:{slug:"hemodynamics-new-diagnostic-and-therapeutic-approaches",title:"Hemodynamics",fullTitle:"Hemodynamics - New Diagnostic and Therapeutic Approaches"},signatures:"A. Seda Artis and Sami Aydogan",authors:[{id:"99453",title:"Dr.",name:"Aise Seda",middleName:null,surname:"Artis",slug:"aise-seda-artis",fullName:"Aise Seda Artis"},{id:"110016",title:"Prof.",name:"Sami",middleName:null,surname:"Aydogan",slug:"sami-aydogan",fullName:"Sami Aydogan"}]},{id:"36119",doi:"10.5772/36876",title:"How Ozone Treatment Affects Erythrocytes",slug:"how-ozone-treatment-affects-erythrocytes",totalDownloads:3898,totalCrossrefCites:0,totalDimensionsCites:1,book:{slug:"hemodynamics-new-diagnostic-and-therapeutic-approaches",title:"Hemodynamics",fullTitle:"Hemodynamics - New Diagnostic and Therapeutic Approaches"},signatures:"Sami Aydogan and A. Seda Artis",authors:[{id:"99453",title:"Dr.",name:"Aise Seda",middleName:null,surname:"Artis",slug:"aise-seda-artis",fullName:"Aise Seda Artis"},{id:"110016",title:"Prof.",name:"Sami",middleName:null,surname:"Aydogan",slug:"sami-aydogan",fullName:"Sami Aydogan"}]}],mostDownloadedChaptersLast30Days:[{id:"62838",title:"Introductory Chapter: Hemodynamic Management. The Problem of Monitoring Choice",slug:"introductory-chapter-hemodynamic-management-the-problem-of-monitoring-choice",totalDownloads:537,totalCrossrefCites:0,totalDimensionsCites:0,book:{slug:"highlights-on-hemodynamics",title:"Highlights on Hemodynamics",fullTitle:"Highlights on Hemodynamics"},signatures:"Theodoros Aslanidis",authors:[{id:"200252",title:"Dr.",name:"Theodoros",middleName:null,surname:"Aslanidis",slug:"theodoros-aslanidis",fullName:"Theodoros Aslanidis"}]},{id:"36119",title:"How Ozone Treatment Affects Erythrocytes",slug:"how-ozone-treatment-affects-erythrocytes",totalDownloads:3900,totalCrossrefCites:0,totalDimensionsCites:1,book:{slug:"hemodynamics-new-diagnostic-and-therapeutic-approaches",title:"Hemodynamics",fullTitle:"Hemodynamics - New Diagnostic and Therapeutic Approaches"},signatures:"Sami Aydogan and A. Seda Artis",authors:[{id:"99453",title:"Dr.",name:"Aise Seda",middleName:null,surname:"Artis",slug:"aise-seda-artis",fullName:"Aise Seda Artis"},{id:"110016",title:"Prof.",name:"Sami",middleName:null,surname:"Aydogan",slug:"sami-aydogan",fullName:"Sami Aydogan"}]},{id:"36116",title:"The Evaluation of Renal Hemodynamics with Doppler Ultrasonography",slug:"the-evaluation-of-renal-hemodynamics-with-renal-doppler-ultrasonography",totalDownloads:10998,totalCrossrefCites:2,totalDimensionsCites:4,book:{slug:"hemodynamics-new-diagnostic-and-therapeutic-approaches",title:"Hemodynamics",fullTitle:"Hemodynamics - New Diagnostic and Therapeutic Approaches"},signatures:"Mahir Kaya",authors:[{id:"107675",title:"Dr.",name:"Mahir",middleName:null,surname:"Kaya",slug:"mahir-kaya",fullName:"Mahir Kaya"}]},{id:"62847",title:"Cerebral Hemodynamics in Pediatric Hydrocephalus: Evaluation by Means of Transcranial Doppler Sonography",slug:"cerebral-hemodynamics-in-pediatric-hydrocephalus-evaluation-by-means-of-transcranial-doppler-sonogra",totalDownloads:455,totalCrossrefCites:0,totalDimensionsCites:0,book:{slug:"highlights-on-hemodynamics",title:"Highlights on Hemodynamics",fullTitle:"Highlights on Hemodynamics"},signatures:"Branislav Kolarovszki",authors:[{id:"92436",title:"Associate Prof.",name:"Branislav",middleName:null,surname:"Kolarovszki",slug:"branislav-kolarovszki",fullName:"Branislav Kolarovszki"}]},{id:"63370",title:"Functioning of the Cardiovascular System of Women in Different Phases of the Ovarian-Menstrual Cycle",slug:"functioning-of-the-cardiovascular-system-of-women-in-different-phases-of-the-ovarian-menstrual-cycle",totalDownloads:389,totalCrossrefCites:0,totalDimensionsCites:0,book:{slug:"highlights-on-hemodynamics",title:"Highlights on Hemodynamics",fullTitle:"Highlights on Hemodynamics"},signatures:"Olena Lutsenko",authors:[{id:"225667",title:"Mrs.",name:"Olena Ivanivna",middleName:null,surname:"Lutsenko",slug:"olena-ivanivna-lutsenko",fullName:"Olena Ivanivna Lutsenko"}]},{id:"62523",title:"Influence of Branching Patterns and Active Contractions of the Villous Tree on Fetal and Maternal Blood Circulations in the Human Placenta",slug:"influence-of-branching-patterns-and-active-contractions-of-the-villous-tree-on-fetal-and-maternal-bl",totalDownloads:339,totalCrossrefCites:0,totalDimensionsCites:0,book:{slug:"highlights-on-hemodynamics",title:"Highlights on Hemodynamics",fullTitle:"Highlights on Hemodynamics"},signatures:"Yoko Kato",authors:[{id:"249827",title:"Prof.",name:"Yoko",middleName:null,surname:"Kato",slug:"yoko-kato",fullName:"Yoko Kato"}]},{id:"36122",title:"Soluble Guanylate Cyclase Modulators in Heart Failure",slug:"soluble-guanylate-cyclase-modulators-in-heart-failure",totalDownloads:1598,totalCrossrefCites:0,totalDimensionsCites:0,book:{slug:"hemodynamics-new-diagnostic-and-therapeutic-approaches",title:"Hemodynamics",fullTitle:"Hemodynamics - New Diagnostic and Therapeutic Approaches"},signatures:"Veselin Mitrovic and Stefan Lehinant",authors:[{id:"111559",title:"Dr.",name:"Stefan",middleName:null,surname:"Lehinant",slug:"stefan-lehinant",fullName:"Stefan Lehinant"}]},{id:"62149",title:"3D Numerical Study of Metastatic Tumor Blood Perfusion and Interstitial Fluid Flow Based on Microvasculature Response to Inhibitory Effect of Angiostatin",slug:"3d-numerical-study-of-metastatic-tumor-blood-perfusion-and-interstitial-fluid-flow-based-on-microvas",totalDownloads:356,totalCrossrefCites:0,totalDimensionsCites:0,book:{slug:"highlights-on-hemodynamics",title:"Highlights on Hemodynamics",fullTitle:"Highlights on Hemodynamics"},signatures:"Gaiping Zhao",authors:[{id:"172001",title:"Ph.D.",name:"Gaiping",middleName:null,surname:"Zhao",slug:"gaiping-zhao",fullName:"Gaiping Zhao"}]},{id:"36118",title:"Hemodynamics Study Based on Near-Infrared Optical Assessment",slug:"hemodynamics-study-based-on-near-infrared-optical-assessment",totalDownloads:2352,totalCrossrefCites:0,totalDimensionsCites:0,book:{slug:"hemodynamics-new-diagnostic-and-therapeutic-approaches",title:"Hemodynamics",fullTitle:"Hemodynamics - New Diagnostic and Therapeutic Approaches"},signatures:"Chia-Wei Sun and Ching-Cheng Chuang",authors:[{id:"116138",title:"Dr",name:"Chia-Wei",middleName:null,surname:"Sun",slug:"chia-wei-sun",fullName:"Chia-Wei Sun"}]},{id:"36120",title:"Regulation of Renal Hemodyamics by Purinergic Receptors in Angiotensin II -Induced Hypertension",slug:"regulation-of-renal-hemodynamics-by-purinergic-receptors-in-angiotensin-ii-induced-hypertension",totalDownloads:1323,totalCrossrefCites:0,totalDimensionsCites:0,book:{slug:"hemodynamics-new-diagnostic-and-therapeutic-approaches",title:"Hemodynamics",fullTitle:"Hemodynamics - New Diagnostic and Therapeutic Approaches"},signatures:"Martha Franco, Rocío Bautista-Pérez and Oscar Pérez-Méndez",authors:[{id:"113134",title:"Dr.",name:"Martha",middleName:null,surname:"Franco",slug:"martha-franco",fullName:"Martha Franco"}]}],onlineFirstChaptersFilter:{topicSlug:"hemodynamics",limit:3,offset:0},onlineFirstChaptersCollection:[],onlineFirstChaptersTotal:0},preDownload:{success:null,errors:{}},aboutIntechopen:{},privacyPolicy:{},peerReviewing:{},howOpenAccessPublishingWithIntechopenWorks:{},sponsorshipBooks:{sponsorshipBooks:[{type:"book",id:"10176",title:"Microgrids and Local Energy Systems",subtitle:null,isOpenForSubmission:!0,hash:"c32b4a5351a88f263074b0d0ca813a9c",slug:null,bookSignature:"Prof. Nick Jenkins",coverURL:"https://cdn.intechopen.com/books/images_new/10176.jpg",editedByType:null,editors:[{id:"55219",title:"Prof.",name:"Nick",middleName:null,surname:"Jenkins",slug:"nick-jenkins",fullName:"Nick Jenkins"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}}],offset:8,limit:8,total:1},route:{name:"profile.detail",path:"/profiles/174732/pascale-besse",hash:"",query:{},params:{id:"174732",slug:"pascale-besse"},fullPath:"/profiles/174732/pascale-besse",meta:{},from:{name:null,path:"/",hash:"",query:{},params:{},fullPath:"/",meta:{}}}},function(){var e;(e=document.currentScript||document.scripts[document.scripts.length-1]).parentNode.removeChild(e)}()