Simulated size of the SRS, Runs and BDS statistics.
\r\n\tOne basic topic is that of expression manipulation: combining, expanding etc, and the applications of this scholar topic needs focusing on.
\r\n\r\n\tThe general topic of "polynomials" is very large, and here the focus is both on scholar/student basics of it, and on applications of some special polynomials in science and research.
\r\n\r\n\tAn important topic of the book is "algebraic curve". Here the approaches are multiple: basic/scholar on one hand, and applications on the other hand. It must be noticed the use of algebraic curves properties in the field of differential equations, for example for finding the singularities.
\r\n\r\n\tGrobner basis is a very modern and applied topic of algebra. Here we must outline the great importance of Grobner basis and polynomial ideals manipulation, in the differential equations field, an example being in fast finding normal forms of differential systems.
\r\n\r\n\tRelated to this last topic of the book, but applying to all specified topics, it must be noticed the importance of numeric algorithms. The importance of software algorithms in all fields of science is continuously increasing. Therefore, computational approach of the specified algebraic topics is very useful, with applications in other mathematical and scientific fields.
",isbn:"978-1-83968-393-0",printIsbn:"978-1-83968-392-3",pdfIsbn:"978-1-83968-394-7",doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!0,hash:"2a81efb05ce334905cc672188033b15d",bookSignature:"Dr. Adela Ionescu",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/9907.jpg",keywords:"expand, factoring, combining, simplifying, random polynomials, special polynomials, orthogonal polynomials, polynomial factorization, two variables polynomials, homogenization, parameterization, singularity, monomial order, polynomial ideal, leading monomial, normal form",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:null,numberOfDimensionsCitations:null,numberOfTotalCitations:null,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"November 26th 2019",dateEndSecondStepPublish:"December 17th 2019",dateEndThirdStepPublish:"February 15th 2020",dateEndFourthStepPublish:"May 5th 2020",dateEndFifthStepPublish:"July 4th 2020",remainingDaysToSecondStep:"10 days",secondStepPassed:!1,currentStepOfPublishingProcess:2,editedByType:null,kuFlag:!1,editors:[{id:"146822",title:"Dr.",name:"Adela",middleName:null,surname:"Ionescu",slug:"adela-ionescu",fullName:"Adela Ionescu",profilePictureURL:"https://mts.intechopen.com/storage/users/146822/images/system/146822.jpg",biography:"Dr. Adela Ionescu is a lecturer at the University of Craiova, Romania. She received her PhD degree from the Polytechnic University of Bucharest, Romania. Her research focuses on development and implementation of new methods in the qualitative and computational analysis of differential equations and their applications. This includes constructing adequate models for approaching the study of different industrial phenomena from a dynamical system standpoint and also from a computational fluid dynamics standpoint. By its optimizing techniques, the aim of the modeling is to facilitate the high understanding of the experimental phenomena and to implement new methods, techniques, and processes. Currently, Dr. Ionescu is working in developing new analytical techniques for linearizing nonlinear dynamical systems, with subsequent applications in experimental cases. The bifurcation theory and its applications in related fields is also a domain of interest for her. She has published six monographs and few scientific papers in high-impact journals. 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From chapter submission and review, to approval and revision, copyediting and design, until final publication, I work closely with authors and editors to ensure a simple and easy publishing process. I maintain constant and effective communication with authors, editors and reviewers, which allows for a level of personal support that enables contributors to fully commit and concentrate on the chapters they are writing, editing, or reviewing. I assist authors in the preparation of their full chapter submissions and track important deadlines and ensure they are met. I help to coordinate internal processes such as linguistic review, and monitor the technical aspects of the process. As an ASM I am also involved in the acquisition of editors. 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Chan and Manoj Kumar Tiwari",coverURL:"https://cdn.intechopen.com/books/images_new/3794.jpg",editedByType:"Edited by",editors:[{id:"252210",title:"Dr.",name:"Felix",surname:"Chan",slug:"felix-chan",fullName:"Felix Chan"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3621",title:"Silver Nanoparticles",subtitle:null,isOpenForSubmission:!1,hash:null,slug:"silver-nanoparticles",bookSignature:"David Pozo Perez",coverURL:"https://cdn.intechopen.com/books/images_new/3621.jpg",editedByType:"Edited by",editors:[{id:"6667",title:"Dr.",name:"David",surname:"Pozo",slug:"david-pozo",fullName:"David Pozo"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},chapter:{item:{type:"chapter",id:"57016",title:"Symbolic Time Series Analysis and Its Application in Social Sciences",doi:"10.5772/intechopen.70826",slug:"symbolic-time-series-analysis-and-its-application-in-social-sciences",body:'\nTime series has a long history in social sciences, especially in economics and finance. As it is well known, much of economics and finances are concerned with modeling dynamics, and systematization of data over time was a subject that appeared early. In particular, two empirical topics become important when working with time series in social sciences: inferences and forecasting. The cumulated historical data permitted to applied statistical methods in order to find evidence of causation between social variables, finding some support to social theories. Considering the nonexperimental nature of the social sciences, this also encourages the development of statistical techniques. In fact, while in physics, it is relatively easy to get hundreds of thousands of data for a given time series, in economics there are often only 50 or 100 data for a time series, and maybe we can obtain thousands of data in financial series. For this reason, much of the statistical effort, in particular econometric effort was focused on developing powerful statistical tests, considering the availability of small samples. This is an important different approach between econometrics and for example, statistical mechanics in theoretical physics.
\nWe can identify two main groups in time series econometrics: univariate time series analysis concerning with techniques for the analysis of dependence in adjacent observations. It has increased importance since 1970 based on the main ideas underlying in [1]; multivariate time series analysis based on the vector autoregressive (VAR) models, made popular by [2]. In the first group, we find all the autoregressive integrated moving average (ARIMA) models and the related generalized autoregressive conditional heteroscedasticity (GARCH) models developed by [3]. The second group is a generalization of the AR models and we can find two important developments based on this: cointegration proposed by [4] focusing on finding a statistical relationship between variables; and noncausality test developed by [5], which takes the concept of predetermination try to test if a variable causes another. Much of the development in time series econometrics is found in books such as [6–18].
\nIn summary, dependence and causation are two important topics in time series econometrics and time series analysis. These topics are related with the importance of inference and forecasting in social sciences. Econometrics has been focused in developing powerful test considering the available small samples. Most of these developments are based on linear models even if there are some developments considering nonlinearities; see for instance [19, 20].
\nTime series analysis in econometrics is mostly based on observations belonging to the set of the real numbers. Some variables can be categorical such as dummy variables. However, in this chapter, we will talk about a different approach that is known as symbolic time series analysis (STSA). It has been originally applied to physics and engineering as a statistical methodology to detect the very dynamic of highly noise time series. The application to social sciences such as economics or finance is very recent and there are some novel developments.
\nAs mentioned before, the application of STSA in social sciences requires a different approach due to data limitation. In this sense, the design of powerful test considering the availability of data is crucial. As abovementioned, dependence and causation are two important topics. In this sense, we review an independence test and a first approach on testing noncausality, both based on STSA. The information theory was adopted as an approach to analyze the symbolic time series and the approximation of Shannon Entropy as an important measure, applied to test design.
\nThe chapter is organized as follows. Section 2 presents the symbolic time series approach and its relation with the symbolic dynamics. In Section 3, we review some of the literature of STSA applied to the sciences. In Section 4, the information theory approach and Shannon Entropy measure is explained. Section 5 presents a review of the independence symbolic test. Section 6 focuses on causality test based on STSA. Section 7 discusses the difference between the proposed symbolic noncausality test and the traditional and well-known Granger noncausality test. Finally, in Section 8, we draw some conclusions and present some future lines of research.
\nThe concept of symbolization has its roots in dynamical systems theory, particularly in the study of nonlinear systems, which can exhibit bifurcation and chaos. In [21], it is asserted that symbolic dynamics is a method for studying nonlinear discrete-time systems by taking a previously codified trajectory using strings of symbols from a finite set, also called an alphabet. According to [22], symbolic dynamics and symbolic analysis are connected but are different concepts. In fact, the former is the practice of modeling a dynamical system by a discrete space. However, the latter is an empirical approach to characterize highly noisy data by considering a partition, discretizing the data, and obtaining a string representing the very dynamic of the process.
\nAs asserted by [23], symbolization involves transformation of raw time series measurements into a series of discretized symbols that are processed to extract information about the generating process. In this way, we can search for nonrandom patterns and dependence by transforming a given time series {x1, x2,…, xT} into a symbolic string {s1, s2, …, sT}.
\nThe STSA approach is easy to apply but the definition of the right partition is the most difficult thing to do. Generally, it applied an equiprobable partition implying to take the empirical distribution of a given time series {x1, x2,…, xT} and establishing two or more equally probable regions. For instance, for a Gaussian time series, we can define two equally probable regions considering as partition the mean equal to zero. After that, we can assign the symbol si = 0 for negative values and si = 1 for positive ones. In this way, we transform a continuously random series into a discrete string similar to the outcomes from flipping a coin.
\nIn [23], the applications of STSA techniques to the different fields of science are reviewed. According to the authors, the different applications suggest that symbolization can increase the efficiency of finding and quantifying information from the systems. Mechanical systems were one of the first applications where symbolic analysis was successfully used to characterize complex dynamics. In [24–26], symbolic methods to the analysis of experimental combustion data from internal combustion engines are applied. Their objective was to study the onset of combustion instabilities as the fueling mixture was leaned. STSA has also been applied in Astrophysics and Geophysics. For instance, [27] analyzes weak-reflected radar signals from the planet Venus to measure the rotational period. In [28], a binary symbolization to analyze solar flare events is utilized. Biology and Medicine is another field where STSA has been applied. There have been many recent applications of symbolic analysis for biological systems, most notably for laboratory measurements of neural systems and clinical diagnosis of neural pathologies. STSA has been applied in neurosciences. In [29, 30], symbolization data is applied to equal-sized interval to partition EEG signals to identify seizure precursors in electroencephalograms. [31] proposed a new damage localization method based on STSA to detect and localize a gradually evolving deterioration in the system. They assert that this method could be demanded for implementation in real-time observation application such as structural health monitoring. In [32], the STSA is used in human gait dynamics. The results of this study can have implication modeling physiological control mechanism and for quantifying human gait dynamics in physiological and stressed conditions. In [33], the heart-rate dynamics is studied by using partitions aligned on the data mean and ±1 and ±2 sample standard deviations, for a symbol-set size of 6. In [34], the prevalence of irreversibility in human heartbeat is analyzed applying STSA.
\nApplication of symbolization to fluid flow measurements has spanned a wide range of data types from global measurements of flow and pressure drop, to formation and coalescence of bubbles and drops, to spatiotemporal measurements of turbulence. In [35], an approach for transforming images of complex flow fields (as well as other textured fields) into a symbolic representation is developed. In [36], STSA is applied to the networks of genes, which is important underlying the normal development and function of organisms. Information about the structure of the genome of humans and other organisms is increasing exponentially. In [37], equiprobable symbols are used for analyzing measurements from free liquid jets in order to readily discriminate between random and nonrandom behavior. In [38], STSA is applied to the detection of incipient fault in commercial aircraft gas turbine engines. In [39], combustion instability in a swirl-stabilized combustor is investigated using STSA. Chemistry-related applications of symbolic techniques have been developed for chemical systems involving spontaneous oscillations or propagating reaction fronts. In [40], a type of symbolization for improving the performance of Fourier-transform ion-cyclotron mass spectrometry is applied. Artificial Intelligence, Control, and Communication are fields where symbolization has been incorporated. In [41], a phase-space partitioning to model communication is used. An example application of symbolization to communication is found in [42], utilizing small perturbations to encode messages in oscillations of the Belousov-Zhabotinsky (BZ) reaction. In robotics, a symbolic time series–based statistical learning method to construct the generative models of the gaits (i.e., the modes of walking) for a robot, see [43], has been developed. Efficacy of the proposed algorithm is demonstrated by laboratory experimentation to model and then infer the hidden dynamics of different gaits for the T-hex walking robot. In [44], an algorithm to intuitively cluster groups of agent trails from networks based on STSA is proposed. The authors assert that temporal trails generated by agents traveling to various locations at different time epochs are becoming more prevalent in large social networks. The algorithm was applied to real world network trails obtained from merchant marine ships GPS locations. It is able to intuitively detect and extract the underlying patterns in the trails and form clusters of similar trails.
\nThe methods of data symbolization have also been applied for data mining, classification, and rule discovery. In [45], rule discovery techniques to real-valued time series via a process of symbolization are applied. Finally, we find some applications of STSA in Social Science. In [46–48], STSA and minimal spanning tree (MST) are applied to construct cluster of financial asset with application to portfolio theory. Utilizing a similar methodology, in [49], the dynamics of exchange market is studied, and in [50], the international hotel industry in Spain is analyzed. In [51, 52], STSA and entropy are applied to measure informational efficiency in financial markets.
\nThe term entropy was first used by Rudolf Clausius in [53] related to the second law of thermodynamics. Subsequently, the communication theory [54] used the Shannon entropy as a measure of uncertainty where the maximum entropy corresponds to the maximum degree of uncertainty. In this sense, a random process will take the maximum entropy value. In fact, English language is not a random process; some patterns such as “THE” are more probable than sequences such as “DXC”. Note, that in a random process, the two sequences should have the same probability. This principle is very relevant because if a symbolic string is random, the entropy should be the maximum.
\nThe entropy measure (H) must meet the following conditions:
H(P) should be a function of the probability distribution of the n events expressed as the vector P = (p1, p2, …, pn).
(Continuity), H(P) should be a continuous function of vector P.
(Symmetry), the measure should be unchanged if the outcomes pi are re-ordered.
(Expansible), Event of probability zero should not contribute to the entropy, H(p1, p2, …, pn, 0) = H(p1, p2, …, pn).
(Minimum), the measure should take value 0 when there is not uncertainty.
(Maximum), the measure should be maximal if all the outcomes are equally likely. It means p1 = p2 = … = pn = 1/n.
For equiprobable events, the entropy increases with the number of outcomes. H(p1 = 1/(n + 1), …,pn + 1 = 1/(n + 1)) > H(p1 = 1/n,…,pn = 1/n).
In [54], the Shannon entropy function is proposed:
\nThe entropy is frequently measured in bits by using log base 2 satisfying all the properties already mentioned. Note that the maximum property is confirmed solving the following Lagrangian expression (2).
\nThe Shannon entropy is concaved with a global maximum when all the probabilities are equal. In addition, when pi = 0, the convention that 0.log0 = 0 is used. Thus, adding zero, probability terms do not change the entropy value.
\nIn order to clarify the concept of Shannon, consider two possible events and their respective probabilities p and q = 1−p. The Shannon entropy will be defined by Eq. (3).
\nFigure 1 shows graphically the function shape, note that the maximum is obtained when the probability is 0.5 for each event. This case corresponds to a random event; on the other hand, note that a certain event (when probability of one event is 1) will produce entropy equal to 0.
\nShape of the Shannon entropy function. Note that maximum happens when the process is random (p = 0.5).
In general, [55] showed that any measure satisfying all the properties must take the following form:
\nIn order to normalize the Shannon entropy, c usually takes the value 1/log2(n) allowing to compare events of different sizes.
\nSTSA seems to present a good performance when detecting independence in time series. A variety of dynamical processes are present in economics. Linearity, nonlinearity, deterministic chaos, and stochastic models have been applied when modeling a complex reality. In [56], a runs test is designed, asserting that the problem of testing randomness arises frequently in quality control of manufactured products. It is remarked that detecting dependence in time series is an essential task for econometricians and applied economist. In [57], the well-known BDS test is introduced, considered as a powerful test to detect nonlinearity. In [58], a simple and powerful test based on STSA is proposed and the results are compared with the BDS and runs test. On one hand, it is found that BDS is not able to detect processes such as the chaotic Anosov and the stochastic processes nonlinear sign model (NLSIGN), nonlinear autoregressive model (NLAR), and nonlinear moving average model (NLMA). On the other hand, runs test cannot detect the chaotic Anosov, the logistic process, the bilinear, the NLAR, and the NLMA stochastic processes. The experiments show that the test based on STSA has no problem detecting all these dynamics. It is concluded that proposed test is simple, easy to compute, and is powerful with respect to the other two tests. In particular, for small samples, it is the only one able to detect models such as chaotic Anosov and nonlinear moving average (NLMA). Besides, the test is applied to financial time series to detect nonlinearity on the residuals after applying a GARCH model. In this case, the BDS rejected the independence few times whereas the SRS test still detects nonlinearity in the residuals. It seems that BDS considers that the GARCH(1,1) model is a good model most of the time. However, the symbolic test suggests that GARCH(1,1) would not be a good model considering all the nonlinear components.
\nHere, we review briefly the test and repeat some experiments comparing the results with the well-known BDS and runs tests. At first, let us consider a finite time series generated by an independent or random process-sized T* {xt}t = 1,2,…,T*. Define a partition in the series in “a” equiprobable regions obtaining the symbolized time series {st}t = 1,2,…,T*, where each symbol st takes a symbolic value from the alphabet A = {A1,A2,…,Aa}. Since, we want to derive a general statistic for different alphabet sizes a and different subsequences lengths w, we have to make two considerations: (1) from now, we will call n to the quantity of possible events. That is n = aw, where for the simplest case (w = 1) implies n = a, then the quantity of events is equal to the symbol-set size; (2) in practice, we have a finite sample size T*, there is no problem for w = 1, but when we compute subsequences or time-windows w of consecutive symbols we loss observations. For example, when we compute the frequency for two consecutive symbols, we have a total sample size T*−1. In general, we can define the sample size T = T* + w−1, again for the trivial case w = 1, T* = T
\nNote that defining Si for i = 1,2,…,n as the sum of the total i events in the time series, we can derive the multidimensional variable S = {Si/T} being distributed as a multinomial with E(Si/T) = (1/n), Var(Si/T) = (1/n)(n-1)/nT and Cov(Si/T,Sj/T) = −(1/n)(1/nT) ∀i ≠ j. As we will see, frequencies of the events should be important in the statistic and the vector of the n frequencies Si/T could be approximated by a multivariate normal distribution N(1/n,σ2Σ) where σ2 is (1/nT) and Σ is a idempotent matrix as in (5)
\nFor convenience, we can define the normalized vector variable {εi} = {(Si/T)-(1/n)}i = 1,2,…,n having a multivariate normal distribution N(ø,σ2Σ), being ø, the null vector. Then, the statistic can be defined as a quadratic form in random normal variables (6).
\nIn [58] is applied the distribution of quadratic forms in normal variables presented in [59]. X = (ε1/σ,ε2/σ,…,εn/σ) is distributed multivariate normal N(ø,Σ). The theorem indicates that tr(ΑΣ) = n−1, and thus X’ΑX distributes Chi-square with (n−1) degrees of freedom. In this case, Α is the identity matrix I, and Σ is symmetric, singular, and idempotent. Remembering that σ2 = (1/nT), then we obtain that the distribution of the symbolic randomness statistic (SRS) as in (7).
\nNote that in practice computing the statistic is very simple. We just have to consider the symbols (a) and subsequences or length (w) and compute the frequencies for each event (n = aw) in the time series.
\nThe algorithm to compute the test is as follows:
\nStep 1: Considering time series {xt}t = 1,2,…,T*, compute the empirical distribution, and define equiprobable regions according to the quantity of symbols or the alphabet size.
\nStep 2: According to the partition, translate {xt}t = 1,2,…,T* into {st}t = 1,2,…,T*, the symbolic time series when w = 1.
\nStep 3: Compute different symbolic time series for different lengths w, remember that the obtained series in step 2 corresponds to w = 1.
\nStep 4: For each w, compute the frequency of the n different events Si/T for i = 1,2,…,n.
\nStep 5: For each w, compute the SRS(a,w) = Tn{Σ(Si/T - 1/n)2} as shown in Eq. (7).
\nStep 6: Compare the SRS(a,w) with the Chi-2 with n-1 degree of freedom at 0.05 of significance, under the independence null hypothesis. When SRS(a,w) is larger than the critical value we reject the null hypothesis.
\nIn [58], it is found that the statistic introduced in (7) is related to the Shannon entropy (H). We can derive the approximation expressed in Eq. (8).
\nNote the generalization implied in STSA permits to study different dynamical process. For instance, consider a string of the first 3000 letters from the book “A Christmas Carol”, s1 = {marleywasdeadtobeginwith…scroogecar} and a random string of 3000 letters from an alphabet of 26, s2 = {iskynbmhjp…vbbihjfkk}. Imagine testing this kind of process with BDS or runs test. However, note that would be easy to test this dynamics with the symbolic test. In this case, we can define an alphabet of 26 letters and the string. On the one hand, applying the SRS(26,1) and SRS(26,2) for the s1, we obtain the following values 2102.40 and 12331.26, respectively. On the other hand, SRS(26,1) and SRS(26,2) for the string s2 are 25.79 and 690.26, respectively. Considering that a Chi-2 with 25 degree of freedom at 95% is 37.65 and a Chi-2 with 675 degree of freedom (262–1) at 95% is 736.55. Since, the statistics for s1 are large than the critical value, we can conclude that the process is not random. However, since the statistics for s2 are less than critical values, we cannot reject the hypothesis of independence.
\nIn [58] is shown that the test is conservative, rejecting the null hypothesis less time than expected. However, it is powerful in detecting nonrandom and nonlinear processes. Considering the four sample sizes, selecting two symbols and length 4 presents decent results in most of the cases. Selecting three symbols seems to be a relative good option for size of 200 or larger and three symbols for a sample size of 500 or larger. The best result is given for a sample of 2000 applying three symbols and length 4. Table 1 presents the experiments using 1000 Monte Carlo simulations on Normal, Logistic, NLMA, Anosov, and NLSIGN processes reproducing the experiments in [58].
\nSample size | \nTest | \nNormal (%) | \nLogistic (%) | \nNLMA (%) | \nAnosov (%) | \nNLSIGN (%) | \n
---|---|---|---|---|---|---|
T = 50 | \nSRS(2,3) | \n1.20 | \n41.00 | \n1.30 | \n2.90 | \n0.20 | \n
SRS(3,2) | \n0.70 | \n100.00 | \n0.40 | \n0.80 | \n0.50 | \n|
BDS | \n9.70 | \n68.10 | \n7.60 | \n18.10 | \n12.00 | \n|
RUN test | \n2.90 | \n23.90 | \n1.30 | \n3.90 | \n2.20 | \n|
T = 500 | \nSRS(2,3) | \n2.10 | \n19.30 | \n13.50 | \n2.30 | \n9.90 | \n
SRS(3,2) | \n0.40 | \n100.00 | \n1.70 | \n0.80 | \n1.10 | \n|
SRS(4,3) | \n3.20 | \n100.00 | \n97.50 | \n93.80 | \n17.40 | \n|
BDS | \n3.60 | \n66.40 | \n7.20 | \n5.30 | \n4.40 | \n|
RUN test | \n3.80 | \n14.70 | \n16.30 | \n5.50 | \n24.10 | \n|
T = 2000 | \nSRS(2,3) | \n1.90 | \n14.40 | \n62.90 | \n2.50 | \n64.80 | \n
SRS(3,2) | \n0.30 | \n100.00 | \n25.30 | \n1.00 | \n3.80 | \n|
SRS(4,3) | \n2.50 | \n100.00 | \n100.00 | \n100.00 | \n92.30 | \n|
SRS(5,3) | \n1.70 | \n100.00 | \n100.00 | \n100.00 | \n92.20 | \n|
BDS | \n2.80 | \n80.40 | \n14.60 | \n3.60 | \n4.00 | \n|
RUN test | \n4.40 | \n12.20 | \n50.00 | \n5.70 | \n84.30 | \n
Simulated size of the SRS, Runs and BDS statistics.
Note that the symbolic test is more conservative than BDS and Runs test when rejecting independence in a normal random process. However, the symbolic test is powerful in detecting nonlinearities in the studied processes. For a sample of 50, Logistic model is detected 100% by the symbolic test, but BDS detects 68%, and Runs test rejects independence 23.90% of the time. Logistic model is still hard to be detected by the run test when sample increases to 2000. Note that NLMA model is detected by the symbolic test when sample is 500 or larger, but it is not detected by BDS and Runs test. It is interesting to note that the chaotic process of Anosov is detected by the symbolic test for a sample larger than 500 but both BDS and Runs tests reject independence less than 6% of the cases. NLSIGN is hard to be detected, for a sample of 2000 the symbolic test detects more than 90% of the cases and Runs test detects 84% of the cases. However, BDS cannot detect the NLSIGN process. In [58] similar results are obtained, the proposed SRS is the only one that is able to detect chaotic Anosov and nonlinear process NLMA when T = 2000.
\nThe present section reviews the symbolic noncausality test (SNC) and discusses the differences with the classical Granger noncausality test. As in the case of independence test, the main idea here is to derive the asymptotic distribution for the statistic when there is no causality between the series. A full explanation of the test is shown in [60].
\nLet us consider that X and Y are two independent random time series sized T + 1 and the symbolized time series can be expressed as Sx = {sx1,sx2,..,sxT + 1} and Sy = {sy1,sy2,…,syT + 1}. To test causality, we have to define two new series, grouping Sx and Sy in the following way:
\n(1) Sxy = {(sx1, sy2), (sx2, sy3),…,(sxt−1,syt),…,(sxT,sxT + 1)}
\n(2) Syx = {(sx1, sy2), (sx2, sy3),…,(sxt−1,syt),…,(sxT,sxT + 1)}
\nIf the alphabet is composed by three symbols, the combination (sxt−1, syt) takes a value from the set of nine possible events {(1,1), (1,2), (1,3), (2,1), (2,2),(2,3),(3,1),(3,2),(3,3)}. Note that each event should be independent with probability 1/9 (Sx and Sy are random). Only if at least one event were deviated from 1/9, would there be evidence of noncausality.
\nAn alphabet of a = 3 symbols determines n = 32 = 9 possible events in the set of pairs {(xt-1,yt)} or {(yt−1, xt)}. Considering “a” symbols and the events n = a2, the vector of the n frequencies Exyi/T and Eyxi/T could be approximated by a multivariate normal distribution N(1/n,σ2Ω) where σ2 is (1/nT) and Ω is a idempotent matrix as in (9).
\nFollowing a similar approach as in Section 5, the statistics for the both hypothesis can be defined as in (10) and (11).
\nThe term in brackets in (10), (11) are quadratic forms in random normal variables. Applying the theorem presented in [59], in the present case where vector X = (ε1/σ,ε2/σ,…,εn/σ) is distributed multivariate normal N(ø,Ω). As mentioned in Section 5, tr(ΑΩ) = n-1, thus X’ΑX distributes Chi-square with (n−1) degrees of freedom. In this case, Α is the identity matrix I and Ω is symmetric, singular, and idempotent.
\nNote that we derive the test assuming that X and Y are random processes. However, we can apply the test for stationary time series and optionally apply an autoregressive process if we want to remove linear dependence and testing the noncausality between the residuals of the two series.
\nFinally, the statistics of noncausality SNC(X → Y) and SNC(Y → X) are defined as in (14) and (15).
\nNote that in practice, computing the statistic is very simple. In summary, the test works as follows:
\nStep 1: Consider time series {xt}t = 1,2,…,T + 2 and {yt}t = 1,2,…,T + 2 we can optionally apply an AR(1) to both series as in (12) and (13) in order to eliminate autocorrelation and define the new residuals time series {uxt}t = 1,2,…,T + 1 and {uyt}t = 1,2,…,T + 1. Note that 1 observation is lost after applying AR(1).
\nStep 2: In {uxt}t = 1,2,…,T + 1 and {uyt}t = 1,2,…,T + 1 apply a partition in “a” equiprobable regions and translate the series into {sxt}t = 1,2,…,T + 1 and {syt}t = 1,2,…,T + 1.
\nStep 3: According to the two hypothesis, X → Y and Y → X define the two sets Sxy = {(sx1, sy2), (sx2,sy3),…,(sxt-1,syt),…,(sxT,sxT + 1)} and Syx = {(sx1,sy2), (sx2,sy3),…,(sxt-1,syt),…,(sxT, sxT + 1)}.
\nStep 4: For Sxy and Syx, compute the frequency of the n = a2 different events Exyi/T and Eyxi/T considering i = 1,2,…, a2.
\nStep 5: Taking into account Eqs. (14) and (15) compute the SNC(X → Y) = nT{Σ[(Exyi/T)–(1/n)]2} and SNC(Y → X) = nT{Σ[(Eyxi/T) − (1/n)]2}.
\nStep 6: Finally, two null hypotheses must be contrasted: X does not cause Y, and Y does not cause X. In the first case SNC(X → Y) should be compared with a Chi-2 with n-1 degree of freedom at 0.05 of significance, if SNC(X → Y) is larger than the critical value the null hypothesis is rejected. The same should be done with SNC(Y → X).
\nThe concept of causality into the experimental practice is due to Clive Granger. The classical approach of Granger causality is based on temporal properties. Although the principle was formulated for wide classes of systems, the autoregressive modeling framework proposed by Granger was basically a linear model, and as mentioned in [61] the choice was made due to practical reasons. Granger noncausality test is among the most applied tool testing causality. Three limitations should be noted: (1) the classical test has a good performance when the process is linear. This is because it is based on the vector autoregressive model (VAR); (2) there are extension of the classical test to consider nonlinear causality but they are related with a particular nonlinear model; (3) some authors assert that empirical time series are generally contaminated with noise producing what is known as spurious causality or not allowing to detect the causality.
\nSCN test presented in [60] is a nonparametric noncausality test based on the symbolic time series analysis. The idea is to develop a complementary test to the Granger noncausality, showing strengths in the points where the Granger test is weak. In this sense, the proposed SNC test performs well detecting nonlinear processes, in particular the chaotic processes. In addition, the mentioned problem related with spurious causality should be alleviated. In fact, according to some experiments nonlinear models such as NLAR model, Lorenz map, and models with exponential terms are not detected by Granger test but the SNC identifies these processes. The test is based on information theory considering an approximation of the entropy as the measure of uncertainty of a random variable. Information theory is considered to be a subset of communication theory. However, in [62] is consider that it is much more. It has fundamental contributions to make in statistical physics, computer science, and statistical inference, and in probability and statistics. It is important to highlight and is an important idea relating symbolic analysis, information theory, and the concept of noise. Information theory considers that communication between A and B is a physical process in an imperfect ambient contaminated by noise. Another important concept is the discrete channel, defined as a system consisting of an input alphabet X and output alphabet Y and a probability transition matrix p(y|x) that expresses the probability of observing the output symbol y given that we send the symbol x.
\nTo compare the performance between the classical Granger noncausality and the proposed SNC test, the following stochastic and deterministic models were simulated:
AR(1). We consider two independent series generated by autoregressive (AR) processes: Xt = 0.2 + 0.45Xt−1 + ε1t and Yt = 0.8 + 0.5Yt-1 + ε2t. Where ε1t and ε2t are i.i.d. and normally distributed (0,1).
Nonlinear with exponential component. Xt = 1.4–0.5Xt−1eYt−1 + ε1t and Yt = 0.4 + 0.23Yt−1 + ε2t; where ε1t and ε2t are i.i.d. normal(0,1).
NLAR (Autoregressive Nonlinear). Xt = 0.2│Xt-1│/(2 + │Xt-1│) + ε1t and Yt = 0.7│Yt-1│/(1 + │Xt-1│) + ε2t; where ε1t and ε2t are i.i.d. normal(0,1).
Lorenz: Xt = 1.96Xt−1−0.8Xt−1Yt−1; Yt = 0.2Yt−1 + 0.8X2t−1; with initial conditions X1, Y1 generated randomly. This is a discrete version of the Lorenz process as in [63].
Table 2 shows the results of the power experiments applying the SNC and the Granger noncausality test to 10,000 Monte Carlo simulations for the four models and for different sample sizes (T = 50, 100, 500, 1000, and 5000).
\nSample size | \nModel | \nSymbolic noncausality | \nGranger noncausality | \n||
---|---|---|---|---|---|
X → Y | \nY → X | \nX → Y | \nY → X | \n||
T = 50 | \nAR(1) (None) | \n0.40 | \n0.45 | \n5.66 | \n5.25 | \n
T = 100 | \n0.42 | \n0.37 | \n5.28 | \n5.09 | \n|
T = 500 | \n0.41 | \n0.27 | \n5.47 | \n5.14 | \n|
T = 1000 | \n0.39 | \n0.42 | \n5.18 | \n5.14 | \n|
T = 5000 | \n0.34 | \n0.46 | \n5.30 | \n5.09 | \n|
T = 50 | \nNLAR (X → Y) | \n0.01 | \n0.01 | \n0.05 | \n0.05 | \n
T = 100 | \n0.73 | \n0.34 | \n4.82 | \n4.74 | \n|
T = 500 | \n5.96 | \n0.31 | \n4.94 | \n5.16 | \n|
T = 1000 | \n17.87 | \n0.29 | \n5.01 | \n5.05 | \n|
T = 5000 | \n98.02 | \n0.39 | \n6.51 | \n5.00 | \n|
T = 50 | \nNonlinear exponential (Y → X) | \n0.51 | \n3.76 | \n2.89 | \n16.89 | \n
T = 100 | \n0.28 | \n11.85 | \n2.78 | \n13.36 | \n|
T = 500 | \n0.43 | \n89.50 | \n2.53 | \n11.48 | \n|
T = 1000 | \n0.40 | \n99.22 | \n2.73 | \n11.29 | \n|
T = 5000 | \n1.42 | \n100.00 | \n2.67 | \n11.19 | \n|
T = 50 | \nLorenz (X → Y, Y → X) | \n96.61 | \n31.90 | \n30.77 | \n13.86 | \n
T = 100 | \n99.99 | \n90.49 | \n28.52 | \n12.64 | \n|
T = 500 | \n100.00 | \n100.00 | \n23.60 | \n11.74 | \n|
T = 1000 | \n100.00 | \n100.00 | \n24.42 | \n11.69 | \n|
T = 5000 | \n100.00 | \n100.00 | \n23.87 | \n11.52 | \n
Simulated power of the SNC and the Granger non causality statistic.
Following [60], a 60% acceptance or rejection of the null hypothesis is considered as a threshold. SNC and Granger noncausality correctly identifies noncausality in AR(1) process. Table 2 suggests that SNC is more conservative in the rejection of causality with percentages less than 5%. The nonlinear model with an exponential component implies causality from Y to X. Note that SNC detects the causality when the sample size is 500 or larger. However, Granger test does not detect causality in any case. As asserted by [58] the NLAR process is very difficult to detect. Note that SCN is the only one detecting the causality when T = 5000. The Lorenz discrete map is also chaotic, and it is detected by SNC starting from T = 100. However, note that Granger test never detects the causality. In particular, is highlighted that Granger test is not able to detect the model with an exponential component, the NLAR model and the chaotic Lorenz map.
\nFinally, we compare both tests with real data from US. In particular, we consider two well-known relationships in economics: the Phillips curve [64] about the relation between unemployment and inflation rates, the Okun’s law [65] establishing a relation between unemployment and economic rate. We take annual data for the US unemployment rate, inflation rate, and economic growth for the period 1948–2016 representing a total of 69 observations. Table 3 shows the results of the Granger noncausality test and the symbolic test considering a partition of two symbols.
\nNull hypothesis | \nGranger | \nSNC(2 symbols) | \n
---|---|---|
Phillips curve | \n||
Unemployment does not cause inflation | \n0.04 | \n1.53 | \n
Inflation does not cause unemployment | \n16.90* | \n9.41* | \n
Okun’s law | \n||
Unemployment does not cause economic growth | \n3.37 | \n2.94 | \n
Economic growth does not cause unemployment | \n61.01* | \n9.65* | \n
SNC and the Granger non causality for the Phillips Curve and Okun’s Law in US.
Indicates rejection of the null hypothesis at the 5% level significance.
The results are similar for both tests. On one hand, Granger and symbolic tests detect causality from inflation to unemployment in the Phillips curve. On the other hand, the two tests detect causality running from economic growth to unemployment in the Okun’s law. The economic theory suggests that inflation increases unemployment while economic growth reduces it. Note that STSA allows thinking about causality in a more general way, whereas Granger noncausality needs to think of continuous measured variables, this should not be a problem for STSA. Let us consider the following example; we now can test the hypothesis of causality from economic growth (G) and inflation (P) to unemployment (U). The main problem is that we have to test causality from a two-dimensional variable to a one dimensional. Symbolization permits to transform the two-dimensional problem in one dimensional and then to apply the symbolic test as explained. We can follow a similar approach as in [66] where STSA is applied to dynamic regimes. Figure 2 shows the transformation of the variable (G, P) in a symbolic variable with an alphabet of four symbols (I: low economic growth and low inflation, II: low economic growth and high inflation, III: high economic growth and high inflation, IV: high economic growth and low inflation) considering as partition the mean of each variable. Note that now the application of symbolic causality is easy, the hypothesis that the economic regime (G, P) does not cause unemployment is rejected since the SNC is 31.76 and Chi-2 with 15 degree of freedom (42–1) at 95% is 25.00. The opposite hypothesis is not rejected because the SNC is 24.71. It is not possible to test this type of causality with the traditional Granger noncausality test.
\nTwo-dimensional variable (economic growth and inflation) is transformed into a four symbol variable.
STSA is a powerful tool being applied to many scientific fields. There are recent applications in robotic, biology, medicine, communication, and engineering. However, applications in social sciences are very recent. The main difficult is the few historical data produced by the social processes. Social sciences are used to applied statistical tests for proving their hypothesis. However, there is much work to do in developing statistical tests based on STSA to be applied in social sciences. There are some very recent efforts applied to economics and finance using STSA. In particular, we present a symbolic independence test, which seems to be powerful in detecting nonlinearities compared with well-known BDS and runs test. The symbolic test is better detecting models such as the chaotic Anosov and Logistic or some stochastic models such as NLMA or NLSIGN. A second symbolic test about causality detects complex processes such as NLAR, nonlinear exponential, or the Lorenz chaotic process when the traditional Granger noncausality cannot. The symbolic causality also enables causality to be tested in a more general perspective. The application of test from a two-dimensional economic variable to a one-dimensional economic variable is a clear example of the potential of STSA in economics and social sciences in general.
\nOne future research line could be to develop a powerful nonlinear test for multidimensional variables. As it was explained, STSA permits to transform a multidimensional time series in a one-dimensional time series simplifying the analysis. This could have important applications in relationships involving vector functions. A more general line of research is to find methodologies to define the optimal partition. As mentioned before, equiprobable partition is generally applied but to find the right partition is still a theoretical and practical weakness in STSA.
\nOver the last decade the emergence of high-throughput screening platforms and the increase in availability of large-scale-omics data, as well as clinical data from electronic health records comprising phenotypic, therapeutic and environmental factors information opened the possibility to mechanistically understand diseases and diseases stages at the molecular level. Thereby, a great number of wealth data in many kidney and cardiovascular conditions was generated, however these findings were neither translated nor reached the clinical setting and are still enclosed in peer-reviewed literature and across general scope expression profiling databases. Simultaneously it has become apparent that the existing systems to integrate and correlate this data are either inadequate or non-existent. Due to the multi-factorial molecular phenotype of disease, it is evident that development of novel therapeutic and disease detection approaches should be based upon the study of the entire “System” simultaneously. Figure 1 gives a general overview in the fundamental difference between conventional and systems approaches, whereby in the context of conventional approaches a hypothesis is put forward that is assumed to be of importance in the disease or biological condition. This hypothesis is then tested and either validated or refuted based on the outcome of this hypothesis-driven methodology. Yet, it is obvious that it is easy to investigate any hypothesis and then choose the one that appears most correct, in the real world constraints such as time and financial resources do not allow for such an approach, and hypotheses are usually generated on a best-guess basis which can lead to a substantial amount of bias, resulting in skewed or partial insights and can often be misleading. In order to avoid such scenarios, research driven by the data itself rather than a hypothesis has been proposed a long time ago, but could not be properly implemented due to the lack of unbiased large-scale data or the ability to integrate disparate data in the first place. Additionally, a successful systems approach requires underlying prior knowledge, such as physicochemical parameters in how molecules interact with each other, what reactions they are involved in and other unconnected information. This knowledge has only slowly been accumulated through conventional research and has only over the last 10–15 years been available to such an extent where a systems approach became feasible. Data-driven systems biology-based diagnostic and prognostic models consisting of relevant panels of molecules—key branches of the cellular network, appear to more accurately reflect pathophysiology than traditional hypothesis-driven approaches, consequently, may have a much higher chance of success and implementation in the clinical setting. Of the most pronounced effects is the crossing between research borders and the urge for multidisciplinary integration of biology, chemistry, computing sciences, mathematics, and medicine to tackle the complexity of such system. To get a holistic view of a system’s biology, multiple and different types of observations must be combined, such as clinical which includes pathological, demographical, epidemiological, and as well as molecular, which includes large-scale genotyping, gene expression, proteomics, metabolomics, and lipidomics data. The downside of such an approach in disease analytics or data integration is the rise in complexity both in output as well as in methods needed to generate those, and the skills required to interpret and contextualise outcome parameters. However, biological and disease models generated this way allow for a higher confidence in generating testable hypotheses, disease classifications on a molecular level and identification of overlapping and divergent pathways of malignant conditions. Ultimately, the removal of bias and integration of all available data, both clinical and biological, leads to a far better understanding of disease and enables the identification of intervention points with higher confidence and accuracy.
Overview of general differences between conventional and Systems Biology approaches in biological and disease analysis research. Red arrows show the path of the conventional hypothesis-driven methodology including testing of a hypothesis, usually employing lab-based investigations, and re-adjusting the hypothesis dependent on outcomes. Blue arrows denote a systems approach, where data are integrated and analysed, producing a model system and a hypothesis that can be verified using conventional methods. Outputs of such an approach are usually fed back into the model or the data analysis stream to refine models, adjust hypothesis or confirm the established model.
The standard resource for disease taxonomy relies primarily on the International Classification of Diseases (ICD) which displays information on diseases and health conditions, and a continuous monitoring of the associated epidemiological statistical trends World Health Organisation [1]. The foundations of the ICD disease classification relies mainly in a type of evidence-based medicine with distinction of clinical features, including patient symptoms, histological assessment, and evaluation of risk factors [2]. While widely used in the clinical setting, in the era of “big-data” and precision medicine, its rigid hierarchical structure lacks the flexibility needed to accommodate the fast and expanding molecular-insights of disease-phenotypes captured across many -omics platforms [3]. Moreover, to support this notion of undefined disease boundaries across current disease classification, we can observe the existence of co-occurring conditions that if seen as a unified biological network, could provide information about common multi-functional genes, cellular pathways, as well the impact of lifestyle [4]. Additionally, analysis of disease progression with the presence of overlapping conditions through evaluation of temporal correlation and disease progression patterns condensed from a population can become useful in the prediction and prevention at the patient’s individual level in future disease-associate events [5].
Further disease taxonomy refinement can be achieved by applying network analysis [3] of combined disease phenotypes sourced from ICD-9 with protein-protein interactions (PPI’s) data from STRING [6] and additional curation efforts of gene-disease associations (GDA) from several data sources. The network analysis allowed for reclassified of pancreatic cancer into 11 subclasses, which is consistent with the number of molecular subtypes observed in the Bailey et al. [7] study. They also proposed the use of such approach in drug repurposing, for instance therapy with metformin, a well-known agent used to treat type 2 diabetes mellitus (T2DM), that could regulate the imbalanced status of the microbiota community in the gut mucosae, a known cause of pathological chronic bowel inflammation as occurs in Crohn’s disease and ulcerative colitis [8], and also act as preventable agent to reduce the risk of colorectal cancer. Moreover, molecular profiling associated with histologic assessment seems to yield enhanced probabilistic scores in graft survival predictions. For instance, joint integration of multi-center histology features in renal biopsies and gene-array data yielded a new molecular score system able to predict renal graft survival [9] and improving the diagnosis of antibody-mediated rejection of transplanted in hearts [10]. Such approaches can also be implemented to assess disease trajectory, treatment selection and monitoring in many neoplasms, and could be specially tailored for cases where the tumour primary site is of unknown origin [11].
Over the last 15 years, the rise of systems biology as a research field has changed how we look at human normal physiological function and has helped to uncover disease complexity. Now scientists use systems biology approaches to understand the big picture of how all the pieces interact in an organism. The inference of genotype-phenotype relationships boosted by the assembly of a high-quality human genome opened the avenue for the development of reference maps of interactome networks, [12] consisting of binary association pairs, for instance PPI’s, protein-DNA/RNA, or protein-metabolite interactions. Figure 2 shows the essential biological molecular interactions governing cell behaviour in an over-simplified biological system. A curated compilation of high-quality sources of binary interactions is considered a prime resource in the Systems Biology field and thereby enabling a deeper understanding of the larger picture—be it at the level of the organism, organ, tissue, or cell—by putting its components together. It’s in stark contrast to decades of reductionist biology, which merely focuses on the properties of its individual components [13]. Most disease conditions exhibit expression of complex disease phenotypes [13], such as obesity, metabolic syndrome, autoimmune diseases and renal diseases.
Description of the essential known relationships/interactions in an over-simplified biological system. Transcription factor (TF), microRNA (miRNA), post-translational modifications (PTMs). The illustration does not account for epigenetic modifications, for instance DNA methylation and histone modifications known to occur and regulate gene expression. Dark coloured arrows denote entity associations, while self-circular arrows describe self-pair interactions or modifications.
Using the words of Ronald Germain to provide a definition of Systems Biology, he advocates that: “There are an endless number of definitions, it’s even worse than the elephant,” that infamous elephant that stymies the attempts of blind men to describe it because each feels just one part, “Some people think of it as bioinformatics, taking an enormous amount of information and processing it.” “The other school of thought thinks of it as computational biology, computing on how the systems work. You need both parts.” Ironically, to best understand this novel approach, we should take a reductionist approach to defining its parts. The system, it seems, is more than the sum of its parts [14]. Systems Biology requires comprehensive data at all molecular levels, a profound understanding of biological systems, data-criteria based assessment and in-deep understanding of the limitations of the techniques used in the experimental setup. Moreover, systems biology requires prior knowledge either published or sourced from biological databases and newly predicted and frequent molecular events requires further in vivo/vitro validation [15]. Systems Biology is cross-disciplinary: “[…] a scientific approach that combines the principles of engineering, mathematics, physics, and computer science with extensive experimental data to develop a quantitative as well as a deep conceptual understanding of biological phenomena, permitting prediction and accurate simulation of complex (emergent) biological behaviours” (Ronald Germain in [14]). Furthermore, systems biology promotes understanding of the functional roles and interplays of all molecules in cells in health and disease. Also provides a framework for large-scale data-driven analysis and predictions based on prior knowledge of experimentally identified interactions and pathways [16]. Thus, more relevant that the underlying high-throughput screening methods, including genomics, proteomics, metabolomics, and also bioinformatics approaches is the use of such methods in a integrative manner to holistically understand how nonlinear processes and their outcomes are regulated in a biological system [17].
Over the last 10 years, major efforts to reclassify diseases based on molecular insights from advances in molecular biology, bioinformatics and high-throughput screening yielded novel disease subtypes among many disease conditions. The use of multiple data types, including clinical endpoints—omics and ontology-based data have been used to reconstitute disease phenotypes, classify and to refine disease-relationships [18]. Nevertheless, the development of a molecular-based disease taxonomy that links global molecular networks with pathological phenotype landscapes remains elusive. Systems medicine can be perceived as a multi-disciplinary collaborative effort driven by the application of systems biology approaches, which includes methodological workflows from high-throughput-omics technologies to generate data, warehousing management systems for data flow and handling and methods for data analytics and interpretation in the context of biomedical research [19]. Ultimately, with further adoption of a systems-based approach patients will benefit of a measurable improvement of their health status since processes of disease onset and progression will be mechanistically identified, leading to new insights regarding disease-disease boundaries, and disease subtyping which facilitates ideal pharmacological interventions as drug repurposing [20]. For instance, the identification of digoxin, a drug used as therapy for atrial fibrillation and congestive heart failure [21] as potential drug candidate for pharmacological intervention in medulloblastoma subtypes 3 and 4 [22]. The authors of the study implemented an integrative systems biology approach using genomic data and collating existing drug-drug, drug-targets interactions information into a tridimensional functional-drug network. This approach involved handling omic data sets such as DNA-seq—mutated genes, copy-number variation (CNV)—repeated sections of the genome, RNA-seq and methylation profiles, combined with clinical measurements of patient outcomes (survival data) and fused using network-based and probabilistic methods that yielded a network composite with disrupted driver signalling networks and potential drug candidates [22].
The advent of new high-throughput technologies (sequencing, array-based and mass spectrometry) led to an explosion of available data, not only by the number of experiments performed, but also by the data density obtained per experiment. Here, we will provide description of detection platforms handling molecular datasets; for medical imaging data types and analysis strategies please see the following review [23].
Microarray technologies have been widely used in research for primary screening, including gene expression profiling and providing genotype-phenotype relationship. Moreover, if properly designed, microarrays will not only provide information on gene expression and expressed single nucleotide polymorphisms (SNPs), but also detect exon junctions and fusion genes [24]. However, identical to PCR-based techniques, the design of probes requires prior knowledge. Therefore, microarrays are mostly applied in the quantification of known sequences and not for the discovery of new variants, transcripts or other unknown features [25]. Microarrays have numerous limitations. For instance, they render an indirect measurement of the relative concentration of a particular nucleic acid sequence [26]. Another limitation is based that a DNA-array can only detect sequences that the array was designed for. In addition, non-coding RNA’s that are not yet recognised as expressed are typically not represented on an array [26]. Microarrays are still considered a reliable technique for routine and/or initial screening that allows multiplex quantitation of microRNAs and gene probes expression in a fast, simple and affordable way. Nevertheless, the continuous drop in the cost of NGS at a level that virtually matches the cost of DNA microarray-based platforms, thus is foreseen that DNA-arrays will be fully replaced by sequencing methods within the next decade [26].
The use of omics technologies, including quantitative proteomics methods aims to identify and quantify the dynamics of protein abundance, in order to gain a deeper understanding of the associated biological functions. Thereby, the quantification of the expression level and state of all proteins at a given time can characterise physiological-states at the cellular-level [27]. Mass spectrometry (MS) technology, particularly tandem mass spectrometry (MS/MS), has been utilised as a discovery engine in proteomics [28]. This technology allows for identification and simultaneously quantification of hundreds or even thousands of proteins in an experimental setup, which enables real-time comparisons for instance between two or more physiological states [29]. Furthermore, peptide sequence composition will directly impact on ionisation efficiency, and their intensities observed in a spectrum often do not reflect their abundances, [30] thereby many label-free or label-based quantitation methods have arisen to allow comparative proteomic analysis. For instance, label-free proteomic approaches such as ion intensity, spectral counting have a simplified workflow when compared to labelling techniques; have no theoretical limit concerning multiplexing capability providing an improved proteome coverage, but lower quantification accuracy when compared with labelling methods (e.g. iTRAQ: isobaric tags for relative and absolute quantitation, SILAC: stable isotope labelling by/with amino acids in cell culture) [30]. In proteomics, several algorithms have been developed to query and cross compare MS data. The most popular used to identify proteins from raw MS data are for instance, MASCOT, SeQuest, OMSSA, X!Tandem [31], Andromeda [32], MS-GF [33], Paragon [34] and more recently, Morpheus [35] and an improved SEQUEST-like algorithm—ProLuCID [36]. The rise in the number of algorithms and specialised computational tools for analysis of MS-based proteomics data sets led to the development of workflows/pipelines such as PEAKS [37], MaxQuant [38], OpenMS Proteomics Pipeline (TOPP) [39], Trans-Proteomic Pipeline (TPP) [40] and others for further downstream data analysis—Perseus [41].
In many metabolomics studies the identification and quantification of metabolites mainly rely on the application of analytical methods based on mass spectrometry (MS) (either coupled with a liquid or gas-chromatograph) and nuclear magnetic resonance (NMR) spectroscopy [42]. Metabolites are defined as small molecules, usually less than 1000 Da, which suffer several changes during cellular metabolism [43]. The selection of a particular platform depends upon the aims of the experimental study and is typically driven by establishing a compromise among sensitivity, specificity, and scanning speed [44]. Metabolomics approaches can be globally split either by the full range measurement/analysis of all compounds in a given sample—untargeted metabolomics, or targeted metabolomics, in which a set of predefined and biochemically well-characterised compounds are measured in a sample [44]. MS has become an essential method for non-targeted profiling of metabolites in complex bio-samples, particularly low-abundance metabolites, due to its high sensitivity and selectivity capabilities when using liquid chromatography (LC) coupled to tandem MS/MS [45]. Metabolomics data from NMR and MS platforms are complex because they usually contain thousands distinct peaks therefore, multivariate statistical analysis plays an important role in metabolomics for reducing data dimensions, differentiating similar spectra, and in the development of predictive models [46]. Metabolomics is used as a screening tool in current healthcare settings, and could be greatly utilised to monitor therapy efficacy, and assess potential drug side-effects [47].
In the field of biomedical research adopting an unbiased approach or “hypothesis-free” (depending of the author and field of study, also defined as hypothesis-generating approach, data-driven research, or discovery research) to research can bring several benefits when compared with the widely used scientific approach—hypothesis-driven research (traditional approach). In which, the latter, in some cases encourages poor scientific practices by forcing/imposing qualitative and weak hypotheses that Are not prepared for strong statistical inference or quantitative analysis (QA) modelling, thereby in such cases an explicitly exploratory approach should be set as default [48]. In order to overcome this problem, large-scale approaches such as expression profiling started to become very popular in the mid ‘90s, and beginning of 2000, with the advent, rapid development and availability of high-throughput mass spectrometry, other methods followed [49]. Computational methods to analyse this flood of data were developed accordingly, however the majority only focused on one specific technology or experimental setup and up to this day are very often not interchangeable in other technological platforms. Large-scale approaches employed in omics research need a different analysis methodology, which is especially true if integrative analysis techniques are employed. True integrative (as opposed to integrating linear relationship data such as gene-protein data) approaches go beyond simple data fusion and gave rise to the field of Systems Biology. On the other hand, hypothesis-generating research (systems biology-derived hypotheses) and hypothesis-driven research are complementary, thus combining both approaches will certainly sustain more chances of a complete understanding of complex biological systems, than either approach on its own [48]. With the advent of high-throughput technologies their application in the biomedical field was a foreseen logical step. However, until recently integration of multi-omic data was not a common approach in former analysis workflows. The literature and publicly available databases are awash with data, yet the main approach of integrating all this information in a disease-specific context is traditionally based on meta-analysis at best or cannot be accomplished using standard computational methods. This molecular information can then be integrated in a further stage by means of meta-analysis or by cross-normalisation of data from different acquisition platforms [50]. A combinatorial stepwise data integration (Figure 3) approach can be used in order to incorporate data from different biological layers of information to predict phenotypic outcomes [51]. On the other side, by recreating the cell environment and dynamics by describing their interactions on a qualitative and quantitative manner and relying on underlying data (prior biological knowledge) for connectivity, e.g. PPI’s, molecular co-occurrence, ontologies and enzymatic reactions [52]. Large-scale data sets for instance derived from multi-omics platforms may also be used to infer novel relationships by network learning approaches using Bayesian inference models [51] and extracting molecular information from multi-layered networks. This approach (as in many others) is challenging since it requires enough statistical power, higher number of samples to deduce all the possible interactions. Another challenge is due to the lack of uniformisation regarding the ‘gold ‘standards (criterions for evaluation) for accepting or rejecting relationships of the inferred model; however the ability to recreate a well-accepted interaction can at least be used for benchmarking methods in biological systems [53].
Purposed workflow for a data-driven approach. Data generation from omics platforms plus existing biological information (a), development of a multi-omics database (b), selection of suitable modelling methods (c), model validation and use for hypothesis-generating research (d), lead optimization and candidate selection (e).
Databases form the basis for most applications in bioinformatics. The number of biological databases available now is enormous, the journal of Nucleic Acids Research (NAR) catalogues a total of 1737 molecular biology databases (2018 edition) [54]. The 2018 edition contains an enormous set of 181 papers that describe the adding of 82 new biological databases, 84 updates and as well 15 databases published elsewhere. However, a prominent issue concerns that many databases are not maintained over time and abandoned, yet they persist in database listings. There are many different types of databases, ranging from primary databases containing sequence data such as nucleic acid or protein; secondary databases or also known as pattern databases hosts, that results from the analysis of the sequences held in primary databases.
The Gene Expression Omnibus (GEO) [55] is a public repository that functions as both warehouse of raw microarray and other gene-based high-throughput data, and additionally serves as a platform for gene differential expression (DE) analysis using the GEO2R tool across a multitude of experimental conditions of user-submitted pre-processed data sets. In the same way, the European counterpart for storing of high-throughput genomics exists such as the European Bioinformatics Institute (EMBL-EBI) throughout the ArrayExpress database [56]. These data resources are both in compliance with community guidelines for description of an experimental setup for microarray and high-throughput NGS experiment. Comparatively, there is currently much less support for sharing of proteomics and metabolomics data sets despite the increasing demand. Public efforts for proteomic data sharing yielded the Proteomics Identification Database (PRIDE) that contains over 10,100 user-submitted MS-based raw proteomic data sets (September 2018) [57]. PeptideAtlas [58] handles re-analysed data sets via the TPP pipeline to provide end-users a consistently view over their data. MetaboLights [59] hosts user-submitted metabolomics experiments, which currently houses 439 experiments (November 2018). The standards for reporting proteomics and metabolomics experiments are coordinated by the Human Proteome Organisation’s Proteomics Standards Initiative (HUPO-PSI), and Metabolomics Standards Initiative (MSI) respectively.
Our group developed more specialised databases resources in several disease conditions handling pre-selected data sets containing DE molecules. In nephrology, we developed the Chronic Kidney Disease database (CKDdb) [60] storing microRNA, genomics, peptidomics, proteomics and metabolomics information relevant to CKD, collected from over 300 studies in the literature and integrated into the Pan-omics Analysis DataBase (PADB). The PADB framework (
Many modern high-throughput technologies lead to the generation of exceptionally large-scale and complex datasets, which includes PPI’s, protein-DNA interactions, kinase-substrate interactions, qualitative and quantitative genetic-interactions gene co-expression [64]. The “Big Data” challenge can be fulfilled by the development of Bioinformatics tools to handle these large-datasets to reduce their complexity to a level that enables rationale interpretation and in this way is more likely to provide new biological insights to the Life Sciences. The compilation (not an exhaustive list) of many web-based, standalone tools and R-based packages are described in Table 1. They allow the accomplishment of different-omics tasks such as feature selection, sample classification, multivariate methods. Cytoscape [65] is a tool primarily designed for network visualisation and analysis and has useful plugins available through the hosting website. Cytoscape makes use of a wide wealth variety of plugins to extend its functionality which are designed by the scientific community. The platform counts with several freely available apps/plugins (over 300 apps available on November 2018) for a diverse array of uses and analysis types.
Name | Description | Webpage | Ref. |
---|---|---|---|
iClusterPlus | Integrative clustering | [84] | |
mixomics | Data integration (CCA,PLS,PCA) | [85] | |
omicade4 | MCIA and CIA | [86] | |
pwOmics | Pathway-based integration of omics | [87] | |
PRESTO | Dimensionality reduction of multivariate data | [88] | |
caret | Classification and regression training | cran.r-project.org/web/packages/caret | — |
GEO2R | Identify DE genes using GEOquery & limma R packages | [55] | |
Metabo Analyst | Metabolomics analysis | metaboanalyst.ca | [89] |
Networkanalyst/INMEX | Integration of gene DE via network approaches | networkanalyst.ca | [90] |
ExAtlas | Meta-analysis & visualisation of gene DE | [91] | |
Elastic net | Gene DE with fitted GLM | [92] | |
ATHENA | Integration of genomics with clinical data | [93] | |
Network propagation | Gene DE, mutations, PPI’s | [94] |
Web-based, standalone tools and R packages dedicated to different-omics tasks such as feature selection, sample classification, multivariate approaches in data integration and meta-analysis.
PMA, Penalised Multivariate Analysis; RGCCA, Regularised and Sparse Generalised Canonical Correlation Analysis for Multiblock Data; caret, Classification and REgression Training; ATHENA, Analysis Tool for Heritable and Environmental Network Associations; CCA, Canonical-Correlation Analysis; PLS, Partial Least Squares; PCA, Principal Component Analysis; CIA, Co-Inertia Analysis; MCIA, Multiple Co-Inertia Analysis; GO, gene ontology; DE, differential expression; GLM, generalised linear models.
The Gene Ontology (GO) consortium [66] aims to capture the increasing knowledge on gene function in a controlled vocabulary applicable to a wide range of organisms. GO represents genes and gene products attributes on matters of their associated biological processes (BP), cellular components (CC) and molecular functions (MF). GO is considered roughly hierarchical, with ‘child’ elements (terms) being more specific than their ‘parent’ elements (terms), nevertheless, a ‘child’ element (term) might have more than one parent element. The ClueGO app [67] is used for the integration and visualisation of GO and pathway terms sourced from KEGG [68], WikiPathways [69] and Reactome [70]. The resultant ClueGO network is established based in kappa statistics which shows the agreement on how any given gene and/or gene products pairs share similar terms. The ClueGO analysis output is conditioned by thresholding of the kappa coefficient, in which a higher coefficient conducts only to the visualisation of close-related terms with very identical gene products. While, lower kappa coefficients will let visualisation of less associated terms.
The conclusion of the Human Genome Project led to the massification of research related with uncovering genotype—disease phenotype associations [71]. This event translated in a disparate growth in the number of publications and on the other side a limited and slow paced biocuration of these newly discovered evidences. Currently, DisGeNET [72] unifies biomedical literature evidence based on GDA collated from a multitude of databases. This database makes use of the Medical Subjects Headings (MeSH) tree structure for disease classification by a Unified Medical Language System. The potential of the database is extended by disgenet2r package and optional programmatic access.
STRING database [6] collates molecular information to cover both known and predicted PPI’s. All molecular interaction data is originally from primary interaction databases such as IntAct [73], BioGRID [74] and additional text-mining, coexpression and high-throughput experiments and computationally predicted PPIs. The up-to-date database version 10.5 comprises nearly 26 million PPI with a confidence score greater than 0.9 of more than 9 million proteins across 2031 organisms. GeneMANIA is another source for PPIs analysis and is accessible via web interface [75], and also as a Cytoscape app that can be used to detect related genes of a input query by means of a “guilt-by-association” strategy, which explores the realisation that a protein function can be obtained from another by seeing whether it interacts with another of known function. The app uses a large database of functional interaction networks, indexing 2152 association networks containing more than 500 million interactions mapped to 166,084 genes from nine organisms.
Multi-omics datasets might not only contain protein and gene data, but also expression profiles of chemical compounds. While it is easy and straightforward to combine protein/DNA/RNA expression data using common identifiers, this is not the case for metabolism end-products—metabolites. This requires a guilt-by-association, which explores the rationale that metabolites are frequently produced by enzymes and a shift in metabolite expression can reflect an up-stream shift in protein or gene expression. This involves semantic searches in enzyme repositories—BRENDA to identify potential proteins and has some inherent pitfalls such as uncertainty which enzyme/isoform is responsible for the metabolic change. Additionally, the same compound could also be generated by several proteins, which adds to the uncertainty. Therefore, metabolic datasets are often treated as separate entities in multi-omics studies and analysed independently and then converged only at the level of final outcomes [76]. The MetScape 3 app [77] for the Cytoscape can perform joint analysis of both metabolomic and gene expression data and allows visualisation of the entire fused network, or by selecting custom views based on metabolic pathways When dealing with large-scale datasets, there is the option to use a concept file based on pre-computed gene set enrichment analysis (GSEA), along with statistical and fold-change thresholds.
Transcription factors (TF) are critical for the regulation of gene expression since they control if gene’s DNA is transcribed into RNA [78]. A compendium on non-redundant TF and TF binding sites can be found at JASPAR [79]. The number of human TF ranges from 1500 to 2600, depending on source and stringency [78]. Direct analysis of modulated events due to TFs is not only valuable but might shed light on hidden elements that conventional pathway analysis cannot reveal. However, many TF binding sites and modulated genes are very hypothetical and often a random guess. Therefore, network-based analysis and interpretation involving TF elements should be taken with caution. CyTargetLinker [80] for extends existing biological networks by adding interactions associated with regulatory elements such as TF-target, miRNA-target or drug-targets. The application requires a loaded network with network attributes preferentially mapped to Ensembl, NCBI gene, UniProt, miRBase or DrugBank. Similarly, in CluePedia [81] users can perform miRNA analysis, by matching it to target-genes via selection of different database resources custom versions. Users can upload a list of genes and query the app to perform gene/miRNA enrichments. Then it will generate a miRNA-target interaction network that can be reused for inline integration with GO and pathway term clustering [81] within ClueGO.
PathVisio [82] allows drawing, edition, and visualisation of pathways handling gene, protein and metabolite data that can be further cross-mapped via the BridgeDb [83]. Inference of relevant pathways is based on an archive of pre-existent pathway maps from WikiPathways [69] and Reactome [70], establishing pathway over-representation based on a Z-score statistical procedure under the hypergeometric distribution and a P-value ranking based on a permutation procedure (randomisation test) that compares actual and permuted Z-scores. Pathways with a permuted P < 0.05 are considered significant by default.
KEGG is an integrated database resource of biological systems integrating genomic, compound and functional information. KEGG allows analysis of datasets from high-throughput omics technologies by uploading a list of genes/proteins or metabolites along with optional statistical scores and fold-change values. After converting to KEGG internal identifiers, the molecular data is matched (KEGG mapper) into a collection of curated pathways, covering metabolism, signalling transduction pathways, specific pathways for several disease conditions and drug development.
The availability of large-scale multi-omics data has opened the avenue to gain an unrivalled insight in disease-associated molecular pathophysiological changes. Simultaneously it has become apparent that systems to integrate and correlate this data are either inadequate or non-existent. The literature and publicly available databases are awash with data, yet the main approach of integrating all this information in a disease-specific context is traditionally based on meta-analysis at best or cannot be accomplished using standard computational methods. In order to better model complex organisms, samples from multiple tissues of the same individuals should be studied simultaneously using omics data, which will require the development of novel analysis methods. Acquiring the relevant tissues and/or body fluid sources from Human study cohorts can of course be difficult, thereby comparative systems biology may help identify which organisms may be similar enough in each aspect to be used as models. It is sometimes suggested that omics technologies and systems biology have failed to deliver many breakthrough enhancements to the treatment of complex diseases. In some cases, it may be that in fact such diseases are not truly one disease from a system or reductionist point-of-view, but several with the same or similar phenotypic end-points—i.e., with the current terminology they are unknown subtypes of disease. If this is the case, then the overlap between the systems is poor and statistical methods which the approach relies on require very large cohorts for identification of these subtypes and subsequent description of each system. Other possibilities are that longitudinal data or samples from different tissues are required. Other relevant concerns arise from biomarker validation studies, such as correlated observations (i.e. multiple observations per patient), multiplicity (testing multiple biomarkers or endpoints), multiple clinical endpoints (interest in more than one relevant endpoint) and selection bias (from retrospective data or observational study). Data-driven investigations using systems biology approaches, although offer complete views over the function of biological systems in health and disease its limited by the state of completeness of prior biological information.
The research leading to these results has received funding from the European Union’s Seventh Framework Programme FP7/2007–2013 under grant agreement FP7-PEOPLE-2013-ITN-608332. The funder had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
The authors declare that there is no conflict of interest regarding the publication of this manuscript.
IntechOpen celebrates Open Access academic research of women scientists: Call Opens on February 11, 2018 and closes on March 8th, 2018.
",metaTitle:'Call for Applications: "IntechOpen Women in Science 2018" Book Collection',metaDescription:"IntechOpen celebrates Open Access academic research of women scientists: Call Opens on February 11, 2018 and closes on March 8th, 2018.",metaKeywords:null,canonicalURL:"/page/women-in-science-book-collection-2018/",contentRaw:'[{"type":"htmlEditorComponent","content":"On February 9th, 2018, which marks the official celebration of UNESCO’s International Day of Women and Girls in Science, we have announced we are seeking contributors for the upcoming “IntechOpen Women in Science 2018” Book Collection. The program aims to support women scientists worldwide whose academic needs include quality assurance, peer-review, fast publishing, collaboration among complementary authors, immediate exposure, and post-publishing citations reporting.
\\n\\nAPPLYING FOR THE “INTECHOPEN WOMEN IN SCIENCE 2018” OPEN ACCESS BOOK COLLECTION
\\n\\nWomen scientists can apply for one book topic, either as an editor or with co-editors, for a publication of an OA book in any of the scientific categories that will be evaluated by The Women in Science Book Collection Committee, led by IntechOpen’s Editorial Board. Submitted proposals will be sent to designated members of the IntechOpen Editorial Advisory Board who will evaluate proposals based on the following parameters: the proposal’s originality, the topic’s relation to recent trends in the corresponding scientific field, and significance to the scientific community.
\\n\\nThe submissions are now closed. All applicants will be notified on the results in due time. Thank you for participating!
\\n"}]'},components:[{type:"htmlEditorComponent",content:"On February 9th, 2018, which marks the official celebration of UNESCO’s International Day of Women and Girls in Science, we have announced we are seeking contributors for the upcoming “IntechOpen Women in Science 2018” Book Collection. The program aims to support women scientists worldwide whose academic needs include quality assurance, peer-review, fast publishing, collaboration among complementary authors, immediate exposure, and post-publishing citations reporting.
\n\nAPPLYING FOR THE “INTECHOPEN WOMEN IN SCIENCE 2018” OPEN ACCESS BOOK COLLECTION
\n\nWomen scientists can apply for one book topic, either as an editor or with co-editors, for a publication of an OA book in any of the scientific categories that will be evaluated by The Women in Science Book Collection Committee, led by IntechOpen’s Editorial Board. Submitted proposals will be sent to designated members of the IntechOpen Editorial Advisory Board who will evaluate proposals based on the following parameters: the proposal’s originality, the topic’s relation to recent trends in the corresponding scientific field, and significance to the scientific community.
\n\nThe submissions are now closed. All applicants will be notified on the results in due time. Thank you for participating!
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