Factors that affect virus survival and efficacy of antiviral coatings [2, 14].
\r\n\tHydrogen gas is the key energy source for hydrogen-based society. Ozone dissolved water is expected as the sterilization and cleaning agent that can comply with the new law enacted by the US Food and Drug Administration (FDA). The law “FDA Food Safety Modernization Act” requires sterilization and washing of foods to prevent food poisoning and has a strict provision that vegetables, meat, and fish must be washed with non-chlorine cleaning agents to make E. coli adhering to food down to “zero”. If ozone dissolved water could be successively applied in this field, electrochemistry would make a significant contribution to society.
\r\n\r\n\t
\r\n\tOxygen-enriched water is said to promote the growth of farmed fish. Hydrogen dissolved water is said to be able to efficiently remove minute dust on the silicon wafer when used in combination with ultrasonic irradiation.
\r\n\tAt present researches on direct water electrolysis have shown significant progress. For example, boron-doped diamonds and complex metal oxides are widely used as an electrode, and the interposing polymer electrolyte membrane (PEM) between electrodes has become one of the major processes of water electrolysis.
\r\n\t
\r\n\tThe purpose of this book is to show the latest water electrolysis technology and the future of society applying it.
The choice of initial attributes for description of an object in an artificial intelligence (AI) problem is the first stage of any simulation of an informational process (representation of information for its further use).
\nAt the 60–70th of the twentieth century, many authors (see, for example, [1]) offered to use predicate calculus for AI problem solving. The resolution method seemed to be a very easy and clear tool to solve problems dealing with compound objects, which can be described by properties of its elements and relations between these elements.
\nUntil the notion of NP-complete problem (in particular, described in [2, 3]) was not widely adopted, such an approach seemed to be very convenient, but many such-a-way formalized problems occurred to be NP-complete or even algorithmic unsolvable.
\nWhile developing the effective algorithms deciding discrete problems, determination of estimations for number of steps of their run becomes one of the important problems. The absence of the proved estimations for number of an algorithm run steps is considered as an insufficient research of this algorithm. It is especially relevant for problems with big input. It concerns, in particular, to the algorithms deciding various AI problems. At practical use of an algorithm, it is important that it has polynomial upper bound of number of its run steps. The NP-completeness or NP-hardness of a problem means now that the polynomial algorithm of its decision is not known.
\nIn 2007, the author proved NP-completeness of a series of AI problems formalized with the help of predicate calculus formulas [4], proved upper bounds for number of steps of algorithms solving these problems [5], and offered a level description of goal formulas for decreasing the number of proof steps [6]. Such a level description is based on the extraction of a common up to the names of its arguments sub-formula of the set of elementary conjunctions of atomic predicate formulas. These sub-formulas define generalized characteristics of an object.
\nExtraction of such sub-formulas allows to construct logic-predicate networks [7], which may change its configuration (the number of layers and the number of cells in the layer) during the process of training.
\nExtraction of these sub-formulas may serve as an instrument for constructing a multi-agent description of an object, when every agent can describe only a part of the object (these parts are intersected), but every agent gives its own names to the elements of the whole object [8].
\nHere, some AI problems formalized in such a way are under consideration. For these problems, the solving algorithms and upper bounds of their run are obtained. These upper bounds permit to point out the parameters of the problem, which mostly influence on the complexity of the algorithm, and to offer approaches permitting to decrease the complexity.
\nA model example illustrating the described approach and algorithms is given.
\nLet an investigated object be presented as a set of its elements
Let the set
Here and below, the notation \n
The introduced descriptions allow to solve many artificial intelligence problems [9]. Main of these problems may be formulated as follows.
\nThe solution of these problems may be reduced to the proof of logic sequents
\nrespectively, and determination of the values for \n
Note that the proof of any of the sequent (1), (2), or (3) answers only the question “whether it is true?” Strictly speaking, in the sequents (1)–(3), instead of the symbols \n
If one uses an exhaustive or a logical algorithm (derivation in a sequent calculus or proof by resolution method), the algorithm gives the values for \n
The proof of sequents (1) and (3) is based on the proof of the sequent
\nwhere \n
An
or, more roughly,
\nWhile using a
The number of steps (i.e., the number of comparisons) required for the solution of the system and, hence, for the logical algorithm solving (4) is
\nwhere
The above-received estimations are exponential over the length of \n
The received estimations cannot be essentially decreased up to polynomial ones if
Problem (2) is strictly connected with the so-called “open” problem ISOMORPHISM OF GRAPHS [3], for which it is not proved neither its polynomiality nor its NP-completeness.
\nThese standard images allow to form a description (up to mirror image) of almost all boxes. Such a description is a disjunction of four elementary conjunctions containing, respectively, 10, 8, 10, 8 variables and 30 + 2, 23 + 1, 28 + 4, 33 + 4 atomic formulas with predicates
Given a “box” inside a complex contour image containing
Can seem that many atomic formulas such as
Below, the designation \n
The notion of level description of classes was introduced in [6]. Such a description essentially allows to decrease the number of steps for an algorithm solving every of the above-formulated problems. This notion is based on the extraction of “frequently” appeared “sub-formulas” \n
Repeat the above-described procedure with all formulas \n
The solution of the problem of the form (4) with the use of the level description of classes is decomposed on the sequential (
For every
Introduce new
Substitute \n
Add all constant atomic
At last check
The decreasing of the number of steps for an algorithm solving every of the above formulated problems (1)–(3) with the use of a level description follows from the fact that in items 1, 2, and 5, we solve the same problem as it was formulated in Section 1 and has the number (4). The estimations of number of steps exponentially depend on the parameters of the formula, i.e., on the right part of implication. That is why the term “small complexity” for \n
Why did we use quotation marks for the term “sub-formulas?” Such formulas (elementary conjunctions) \n
The substitutions λR,P and λR,Q are called unifiers of R with P and Q, respectively.
\nFor example, let A(x,y,z) = p1(x) & p1(y) & p1(z) & p2(x, y) & p3(x, z), B(x,y,z) = p1(x) & p1(y) & p1(z) & p2(x, z) & p3(x, z)
\nIs the formula
The formula
An algorithm of extraction of a maximal (having a maximal number of literals) common up to the names of arguments sub-formula
This algorithm allows to construct a level description for a set of goal elementary conjunctions. Essential difference between maximal common up to the names of arguments sub-formulas and sub-formulas in the level description consists in the fact that in the level description it is needed to extract sub-formulas with “small complexity” but not a maximal one. An algorithm of level description construction is in [6]. It consists in sequential pairwise extraction of common up to the names of variables sub-formulas of \n
Let
Return to the example in the previous section. There, we have seen a description of a class of “boxes” represented in Figure 1. According to these descriptions, we have received that given a “box” inside a complex contour image containing
Standard different contour images of a “box”.
Pairwise extraction of common up to the names of variables of elementary conjunctions, corresponding to these images, allows to extract common up to the names of variables sub-formulas corresponding to the images represented in Figure 2
\nImages corresponding to extraction of common sub-formulas.
These sub-formulas contain, respectively, 8, 8, 7, 7, 7, 8 variables and 18, 15, 11, 11, 15, 16 atomic formulas.
\nThe following extraction by means of pairwise partial deduction between common sub-formulas corresponding to images
Image corresponding to the second extraction of common sub-formulas.
Elementary conjunction P
Elementary conjunctions
For example, a sub-formula corresponding to the image ab is P12(x1,x1,x2,x3,x4,x5,x8,x9,x10) = p1(x1) & V(x2,x5,x8) & V(x2,x1,x8) & V(x5,x4,x10) & V(x5,x3,x10) & V(x8,x2,x10) & V(x10,x8,x5) & V(x10,x5,x9) & V(x10,x8,x9). The unifier of P12(x1,x1,x2,x3,x4,x5,x8,x9,x10) with the description of a is an identical substitution, and with the description of b, it is a substitution of x4,x5,x6,x7,x8 instead of x2,x4,x5,x9,x10. Descriptions of images c and d are not unified with it.
\nThe three-level description of the image b takes the form Ab2(x12,x4,x5,x6,x7) = p12(x12) & V(x5,x4,x7) & V(x5,x7,x6) or Ab2(x32,x4,x5,x6,x7) = p32(x32) & V(x3,x2,x8) & V(x5,x4,x7) & V(x5,x7,x6).
\nGiven a “box” inside a complex contour image containing
Elementary conjunctions
Elementary conjunctions obtained from the class description by means of second-level predicates instead of the corresponding sub-formulas contain respectively 2, 0, 2, 2 “new” variables and 7, 4, 11, 16 “new” atomic formulas. The proof of the sequence from S
As O(
Traditional neuron network deals with binary or many-valued characteristics of an object and is an adder of weighted inputs followed by a function mapping the result into the segment [0, 1]. The neuron network configuration is fixed and only the weights may be changed.
\nA logic-predicate network is described later. The inputs for this network are atomic formulas setting properties of the elements composing an investigated object and relations between them [7]. The proposed model of logic-predicate network has two blocks: a training block and a recognition block. The input of every block is an elementary conjunction of atomic predicate formulas or their negations. Configuration of the recognition block is formed after an implementation of the training block and may be changed with its help.
\nThe training block is a “slowly running” block. At the same time, the recognition block is a “quickly running” one. The base of the proposed predicate network is a logic-objective approach to AI problems and level description of classes.
\nThe scheme of the logic-predicate network is presented in Figure 4
\nScheme of the logic-predicate network.
At a training stage of logic-predicate network construction, we have a training set of objects. Let a training set of objects ω1,…, ωK be given to form an initial variant of the network training block. Replace every constant \n
Construct a level description for these goal formulas with the use of algorithm of level description. The first approximation to the recognition block is formed. Formulas \n
The recognition block tries to identify a new object according to the level description of classes, obtained in the training block.
\nIf after the “recognition block” run an object is not recognized or has wrong classification, then it is possible to train anew the network. The description of the “wrong” object must be added to the input set of the training block. The training block extracts common sub-formulas of this description and previously received formulas forming the recognition block. Some sub-formulas in the level description would be changed. Then, the recognition block is reconstructed.
\nGiven a training set for the class of contour images of “boxes” presented in Figure 1 (Section 2). Pairwise extraction of common up to the names of variables of elementary conjunctions, corresponding to these images, allows to extract common sub-formulas corresponding to the images presented in Figures 2 and 3 (Section 3). Fragments of the images corresponding to a three-level network are presented in Figure 5.
\nFragments of the images corresponding to a three-level network.
Given, a new image represented in Figure 6 for recognition, the network would not recognize it because the first-level predicate is not valid.
\nControl image.
Add the description of this control image to the input data of the training block. The extraction of common sub-formulas for this description and the formula defining the first-level predicate gives a formula corresponding to the image represented in Figure 7.
\nImage corresponding to the new first-level predicate.
New second-level predicates correspond to three images represented in Figure 8.
\nImages corresponding to three new second-level predicates.
The set of the third-level predicates coincides with the set of previous second-level predicates. So, the recognition block is constructed anew and represents four-level description of the class. Fragments of the images corresponding to a four-level network are presented in Figure 9.
\nFragments of the images corresponding to a four-level network.
A problem of multi-agent description of a complex object is under consideration in this section. It is supposed that every agent knows only a part of an investigated object description. Moreover, she does not know the true names of elements and gives them names arbitrary. It is similar to the parable about tree blind men who feel an elephant. To overcome such a paradox, it is supposed that every two agents have information concerning some common part of an object. The main difficulty in this problem is to find and identify these parts [8].
\nLet an investigated object is represented as a set of its elements \n
Information (description) of an object is an elementary conjunction of atomic formulas with predicates
There are
As every agent uses her own notifications for the names of the object elements, it is needed to find all common up to the names of arguments sub-formulas
Below, the arguments of information will be omitted. Let every agent
Change all constants in
For every pair of elementary conjunctions
For every pair
For every
With the use of the unifiers obtained in items 2–4 change the names of variables in
Write down the conjunction
To estimate the number of the algorithm run steps, we estimate every item of the algorithm.
Item 1 requires not more than \n
Item 2 requires \n
“steps” for an algorithm based on the derivation in the predicate calculus.
It is needed to summarize the above estimates for
Consistency checking of the formulas
For every
The number of “steps” required for the changing of the names of variables in
The number of “steps” required for the deleting of the repeated conjunctive terms is not more than \n
The whole number of the algorithm run steps is O(
The analysis of the received estimation shows that the main contribution is made by the summarized number of partial deduction checking (item 2).
\nLet the initial predicates be
Fragments of the image received by three agents.
According to the item 1 of the algorithm, all constants in the fragment descriptions are replaced by variables in such a way that different constants are changed by different variables and the names of variables in
I′1(x1,…,x6) = V(x1,x2,x4) & V(x1,x5,x4) & V(x1,x3,x2) & V(x1,x3,x5) & V(x1,x3,x4) & V(x2,x1,x3) & V(x2,x3,x5) & V(x3,x2,x1) &V(x3,x6,x2) & V(x3,x6,x1) & L(x2,x1,x5),
\nI′2(y1,…,y6) = V(y3,y1,y4) & V(y1,y2,y3) & V(y1,y5,y3) & V(y1,y6,y2) & V(y1,y6,y5) & V(y1,y6,y3) & L(y2,y1,y5),
\nI′3(z1,…,z8) = V(z1,z5,z3) & V(z1,z3,z2) & V(z1,z5,z2) & V(z3,z1,z7) & V(z3,z1,z6) & V(z3,z7,z4) & V(z3,z6,z4) & V(z3,z4,z1) & V(z4,z2,z3) & V(z4,z3,z8) & V(z4,z2,z8) & L(z7,z6,z3).
\nAccording to the item 2 of the algorithm, find maximal common up to the names of arguments sub-formula of formulas I′1(x1,…,x6) and I′2(y1,…,y6). It is C12(u0,…,u4) of the form C12(u0,…,u4) = V(u0,u1,u2) & V(u0,u3,u2) & V(u0,u4,u1) & V(u0,u4,u3) & V(u0,u4,u2) & L(u1,u0,u3).
\nIt has unifiers
I′1(u0,u1,u2,u3,u4,x6) = V(u1,u0,u4) & V(u1,u4,u3) & V(u4,u1,u0) & V(u4,x6,u1) & V(u4,x6,u0) & C12(u0, …, u4),
\nI′2(u0,u1,u2,y4,u3,u4) = V(u2,u0,y4) & C12(u0,…,u4).
\nMaximal common up to the names of arguments sub-formula of I′2(y1,…,y6) and I′3(z1,…,z8) is C23(v0,v2,v4,v5,v6,v7) of the form
\nC23(v0,v2,v4,v5,v6,v7) = V(v6,v2,v7) & V(v2,v4,v6) & V(v2,v5,v6) &V(v2,v0,v4) & V(v2,v0,v5).
\nIt has unifiers
I′2(v2,v4,v6,v7,v5,v0) = V(v2,v0,v6) & L(v4,v2,v5) & C23(v0,v2,v4,v5,v6,v7),
\nI′3(v0,z2,v2,v6,z5,v5,v4,v7) = V(v2,v6,v0) & V(v0,z5,v2) & V(v0,v2,z2) & V(v0,v5,z2) & V(v6,z2,v2) & V(v6,v2,v7) & L(v4,v5,v2) & C23(v0,v2,v4,v5,v6,v7).
\nAs I′2(v2,v4,v6,v7,v5,v0) contains V(v2,v0,v6) and I′3(v0,z2,v2,v6,z5,v5,v4,v7) contains V(v2,v6,v0) and according to the definition of the predicate V, the formula V(x,y,z) & V(x,z,y) is a contradiction, so substitutions with this unifiers cannot give a consistent description of the object. After deleting from I′2(y1,…,y6) and I′3(z1,…,z8), the variables y1 and z3, respectively, a new maximal common up to the names of arguments their sub-formula C’23(v0,v2,v4,v5,v6,v7) of the form C’23(v0,v1,v2) = L(v1,v0,v2) will be received with the unifiers
I′2(v0,v1,v2,y4,y5,y6) = V(v2,v0,y4) & V(v0,v1,v2) & V(v0,y5,v2) & V(v0,y6,v1) &V(v0,y6,y5) & V(v0,y6,v2) & C’23(v0,v1,v2),
\nI′3(z1,z2,v2,z4,z5,v0,v1,z8) = V(z1,z5,v2) & V(z1,v2,z2) & V(z1,z5,z2) & V(v2,z1,v1) & V (v2,z1,v0) & V(v2,v1,z4) & V(v2,v0,z4) & V(v2,z4,z1) & V(z4,z2,v2) & V(z4,v2,z8) & V(z4,z2,z8) & C’23(v0,v1,v2).
\nMaximal common up to the names of arguments sub-formula of I1(x1,…,x6) and I3(z1,…,z8) is C13(w0, …,w6) in the form
\nC13(w0, …,w6) = V(w2,w4,w6) & V(w2,w5,w6) & V(w2,w0,w4) & V(w2,w0,w5) & V(w0,w1,w2).
\nIt has unifiers
I′1(w2,w4,w0,w6,w5,w1) = V(w2,w0,w6) & V(w0,w1,w4) & V(w0,w4,w2) & L(w2,w4,w5) & C13(w0,…,w6),
\nI′3(w0,z2,w2,w6,w1,w5,w4,z8) = V(w0,w2,w3) & V(w0,w1,w3) & V(w2,w6,w0) & V(w6,w3,w2) & V(w6,w2,w7) & V(w6,w3,w7) & C13(w0,…,w6).
\nAs I′1(w2,w4,w0,w6,w5,w1) contains V(w2,w0,w6), I3(w0,z2,w2,w6,w1,w5,w4,z8) contains V(w2,w6,w0) and according to the definition of the predicate V, the formula V(x,y,z) & V(x,z,y) is a contradiction, so substitutions with this unifiers cannot give a consistent description of the object.
\nAfter deleting from I′1(x1,…,x6) and I′3(z1,…,z8) literals with the variables x1 and z3, respectively, a new maximal common up to the names of arguments their sub-formula
\nC′13(w0,w1,w2) of the form C’13(w0,w1,w2) = L(w1,w0,w2)
\nwill be received with the unifiers
I′1(w0,w1,x3,x4,w2,x6) = V(w0,w1,x4) & V(w0,w2,x4) & V(w0,x3,w1) & V(w0,x3,w2) & V(w0,x3,x4) & V(w1,w0,x3) & V(w1,x3,w2) & V(x3,w1,w0) & V(x3,x6,w1) & V(x3,x6,w0) & C’13(w0,w1,w2),
\nI′3(z1,z1,w2,w1,w0,z6,z7,z8) = V(z1,w0,w2) & V(z1,w2,z2) & V(z1,w0,z2) & V(w2,z1,z7) & V(w2,z1,z6) & V(w2,z7,w1) & V(w2,z6,w1) & V(w2,w1,z1) & V(w1,z2,w2) & V(w1,w2,z8) & V(w1,z2,z8) & C′13(w0,w1,w2).
\nAccording to the item 4 of the algorithm, we identify new variables substituted instead of the same initial variable. That is we identify the following variables:
\nu0 and w0 (are substituted instead of the variable x1),
u1 and w1 (are substituted instead of the variable x2),
u2 and w2 (are substituted instead of the variable x4),
u0 and v0 (are substituted instead of the variable y1),
u1 and v1 (are substituted instead of the variable y2),
u2 and v2 (are substituted instead of the variable y3),
v0 and w0 (are substituted instead of the variable z6),
v1 and w1 (are substituted instead of the variable z3),
v2 and w2 (are substituted instead of the variable z7).
The identified variables denote as α 0, α 1, and α 2. So, we have the equalities u0 = v0 = w0 = α 0, u1 = v1 = w1 = α 1, u2 = v2 = w2 = α 2.
\nAs a result, we have the following descriptions of the fragments:
\nI″1(α 0, α 1,u4,u2, α 2,x6) = V(α 0, α 1,u2) & V(α 0, α 2,u2) & V(α 0,u4, α 1) & V(α 0,u4, α 2) & V(α 0,u4,u2) & V(α 1, α 0,u4) & V(α 1,u4, α 2) & V(x3, α 1, α 0) & V(u4,x6, α 1) & V(u4,x6, α 0) & L(α 1, α 0, α 2),
\nI″2(α0, α 1,u2,y4, α 2,u4) = V(u2, α 0,y4) & V(α 0, α 1,u2) & V(α 0, α 2,u2) & V(α 0,u4, α 1) & V(α 0,u4, α 2) & V(α 0,u4,u2) & L(α 1, α 0, α 2),
\nI″3(z1,z2, α 2,z4,z5, α 0, α 1,z8) = V(z1,z5, α 2) & V(z1, α 2,z2) & V(z1,z5,z2) & V(α 2,z1, α 1) & V(α 2,z1, α 0) & V(α 2, α 1,z4) & V(α 2, α 0,z4) & V(α 2,z4,z1) & V(z4,z2, α 2) & V(z4, α 2,z8) & V(z4,z2,z8) & L(α 1, α 0, α 2).
\nTheir conjunction
\nV(α0, α 1,u2) & V(α 0, α 2,u2) & V(α 0,u4, α 1) & V(α 0,u4, α 2) & V(α 0,u4,u2) &
\nV(α 1, α 0,u4) & V(α 1,u4, α 2) & V(x3, α 1, α 0) & V(u4,x6, α 1) & V(u4,x6, α 0) &
\nV(u2, α 0,y4) & V(z1,z5, α 2) & V(z1, α 2,z2) & V(z1,z5,z2) & V(α 2,z1, α 1) &
\nV(α 2,z1, α 0) & V(α 2, α 1,z4) & V(α 2, α 0,z4) &V(α 2,z4,z1) & V(z4,z2, α 2) &
\nV(z4, α 2,z8) & V(z4,z2,z8) & L(α 1, α 0, α 2)
\nallows to “stick together” the images of fragments according to the same variable. The image corresponding to the result of “sticking” is presented in Figure 11.
\nImage corresponding to the result of “sticking”.
If a description of the investigated object is presented in the database, it may be found according the principle “the nearest neighbor” with the use of metric for predicate formulas presented in [13].
\nLogic-predicate approach to an AI problem has a rather powerful capability, essentially when an investigated object is a compound one and is characterized by properties of its elements and relations between them.
\nSetting of pattern recognition problems considered in Section 2 (except the problem (2)) differs from the classical one. The setting of the problems (1) and (3), in which it is needed to find parts of an investigated object, turns out to be a rather difficult one in the frameworks of a standard approach in the frameworks of which an object is regarded as a whole indivisible one.
\nIn particular, an exponential estimation for number of propositional variables in a formula simulating a predicate formula in a finite domain for planning problems
The problem (2) is polynomial equivalent to an “open” problem ISOMORPHISM OF GRAPHS [3] and the problems (1) and (3) are NP-complete.
\nA notion of level description of classes has been introduced in Section 3 in order to decrease the number of steps of algorithms solving these problems. Such a description reduces the solution of the main problem to a series of solutions of the same form problems with the inputs with the essentially less notation lengths. At the same time, the constructing of a level description still deals with big input data. So, a problem with big input data is solving only once, and then the problem with the essentially less input data is solving repeatedly.
\nThe idea of decomposition of a problem to a series of the “less dimension” problems is not a new one and is frequently used. The difficulty consists in a precise definition of the term “common sub-formula of small complexity.”
\nThe development of a precise definition and of an algorithm for the extraction of a common up to the names of arguments sub-formula of two elementary conjunctions (and their unifiers) allows not only to work out an algorithm of level description construction but also to find an approach to the solution of some else AI problems.
\nNote that the extracted sub-formulas define generalized characteristics of an object. This has an analogy in medical diagnostics: initial characteristics are symptoms and the generalized ones are syndromes.
\nLevel description of classes allowed to introduce the notion of logic-predicate network described in Section 4. Such a network may be regarded as a self-training network which changes its configuration after an additional training. It corresponds to the fact that in the process of a man training, new notions and relations between them are formed in a human brain.
\nThe presence of an algorithm for the extraction of a common up to the names of arguments sub-formula of two elementary conjunctions (and their unifiers) allows to find an approach to a problem of multi-agent description of an object described in Section 5. Just an extraction of such sub-formulas and determining of their unifiers with the input formulas makes possible to “stick together” such parts of descriptions in which different agents gives different names to one element of the whole object.
\nNote that the formulation of the problem (1) from Section 2 coincides with the one for a well-known problem CONJUNCTIVE BOOLEAN QUERY from [3]. The difference is in the implementation of these problems. While repeated implementation of the problem (1) the premise S(ω) of the sequent \n
While repeated implementation of the problem CONJUNCTIVE BOOLEAN QUERY, the premise S(ω) of the sequent \n
The possibility of reduction of an object description length by means of adding a formula setting some properties of initial predicates to the premise of a sequent was mentioned in the model example in Section 2. Properties of initial predicates also were used in the item 3 of the algorithm of multi-agent description. In fact, in the both cases instead the sequent of the form (4) \n
To solve the problem (2) and to extract a maximal common up to the names of arguments sub-formula of two elementary conjunctions it is needed to check whether two elementary conjunctions are isomorphic. A polynomial in time rough algorithm for such a checking was offered in [12] by Petrov. Numerical experiments with this algorithm give over 99.95% of valid results.
\nEnteric and respiratory viruses can potentially be transmitted via contaminated environmental surfaces [1, 2]. Infectious viruses present on fomites may be transferred to the fingers and/or hands when touching various surface types under a broad spectrum of environmental conditions [3]. Transfer efficiency is affected by factors including virus species, inoculum size, and skin condition [4]. Subsequent contact with the eyes, nose, or mouth with contaminated fingers and hands may then provide access to susceptible human hosts [5]. Disinfection of environmental surfaces lowers the numbers of infectious microorganisms, thereby reducing the risk for transmission [6, 7]. However, such surfaces are subjected to continuous recontamination events, particularly in high-traffic areas and facilities including hospitals, daycare centers, schools and office buildings where fomites are more likely to serve as reservoirs of pathogens [8, 9, 10].
There are hundreds of liquid-based formulations that are registered as disinfectants with governmental regulatory agencies around the world, and a subset of those also carry label kill claims against non-enveloped and enveloped viruses. The efficacy testing that is required for the issuance of product label claims is performed using internationally-recognized standard test methods such as those produced by the American Standard for Test Materials (ASTM) and the European Standard (EN), among others. Liquid disinfectants can be applied to hard, non-porous surfaces using spray devices, towelettes (wipes), or as bulk liquid volumes to address large, soiled areas. To achieve the antiviral inactivation claims specified on product labels, disinfectants must be used according to the manufacturer’s instructions which may require maintaining a completely wetted surface for up to 10 minutes. However, the habits and practices of product users are contrary to the directions specified on the label. A recent survey of American adults conducted on behalf of the American Cleaning Institute in 2020 revealed that 26% of respondents adhere to label directions during household disinfection routines; however, an equal percentage of those surveyed did profess to wiping surfaces until dry immediately after spraying with no adherence to contact time instructions [11]. An additional 16% of respondents claimed to use a single-pass method for disinfectant wipes rather than the multiple passes that are generally required to maintain surface wetness for several minutes.
The importance of correct disinfection usage has been of increased concern during the COVID-19 pandemic. Alternative disinfecting surface treatments that are capable of inactivating infectious agents, in particular viruses, are under research and development [12, 13]. A number of new and diverse antiviral coatings and films have been synthesized, and fixed or immobilized applications including solids (e.g., antimicrobial plastics), paints, and metals are increasingly of interest for their antiviral capabilities. The factors affecting virus survival and the efficacy of antiviral coatings have been reviewed [2, 14] and include virus structure (i.e. enveloped, non-enveloped), the presence of organic soil (dirt), temperature, relative humidity, coating composition, and contact time (Table 1). The ability of treated surfaces to remain continuously active after repeated cleanings and use of liquid disinfectants is also critical (Figure 1). Unfortunately, there are no generally accepted methods for evaluating anti-viral surface coatings, making it difficult to compare the efficacy of different materials and studies. More research is warranted to better understand breadth of antiviral efficacy of these novel disinfecting technologies, and whether they can exact measurable and meaningful impacts on public health.
Factor | Impact |
---|---|
Type of virus | Non-enveloped viruses are generally more resistant than enveloped viruses |
Relative humidity | Drying rates of deposited viruses are affected, impacting viability |
Temperature | Protein denaturation results in loss of structural integrity of virus |
Soil (dirt) load | Increased demand on antiviral actives, decreasing availability for virus inactivation |
Coating composition | Mechanisms of antiviral action differ among viruses and vary according to formulation |
Contact Time | Time required for at least a 99.9% (3 log10) reduction in titer may range from minutes to hours |
Continuously active antiviral surface coatings: a) coating applied to hard, nonporous surface demonstrates antiviral activity following virus deposition; b) coated surfaces are cleaned/disinfected with wiping action with passage of time, c) residual coating demonstrates continuous antiviral efficacy following surface cleaning events (
A number of formulations have been developed and assessed over the past two decades that are capable of antiviral inactivation for extended periods of time following surface application (Table 2) [12, 13, 14, 15, 16]. Such applications have been considered as continuously active disinfectants and impart self-disinfecting properties to treated surfaces. There are many industry-based and third-party contract laboratory studies that have evaluated the antiviral properties of these surface treatments. However, few have been published to-date in peer-reviewed scientific journals [17], with an even smaller subgroup assessing efficacy against infectious viral agents. Continuously active disinfectants are generally evaluated for residual inactivation efficacy using a controlled, standardized wear and abrasion procedure such as that described in United States EPA Protocol #01-1A [18]. Briefly, a product applied to a hard non-porous surface is subjected to alternating dry and moistened wiping procedures over a specified time period (≥ 24 hours) with intermittent reinoculations of the test organism. A minimum of 12 wear cycles is required, and the remaining film of test product is challenged by a final dose of the target organism (≥ 4.8 log10) for up to 5 minutes of contact time. Residual efficacy depends in part on the amount of disinfectant remaining on the surface after the wear and abrasion testing which indicates its durability. Products that are readily removed from surfaces during repeated wet and dry wiping events could require regular reapplication to ensure proper performance against target microbes. As with standard disinfection, residual effectiveness generally follows the hierarchy of susceptibility of viruses to disinfectants, where enveloped viruses are more susceptible to inactivation than non-enveloped viruses [19].
Coating* | Type of viruses tested against†,‡ | Mechanism of inactivation |
---|---|---|
Silane polymer QAC | Influenza, HCoV-229E, SARS-CoV-2, feline calicivirus | Behaves as a surfactant; disrupts lipid and protein structure |
Copper | Influenza A, hepatitis A, feline calicivirus, adenovirus, HCoV- 229E, SARS-CoV2 | Reactive oxygen species; protein and nucleic acid denaturization |
Silver | Influenza, SARS-CoV2, HCoV-229E, murine norovirus | Reaction with sulfhydryl groups in proteins; prevention of viral attachment to host cells |
Zinc | Murine norovirus, SARS-CoV-2, influenza | Inhibiting proteolytic cleavage, preventing synthesis of viral polypeptides |
Titanium dioxide | Influenza, adenovirus; SARS-Co-2 | Generation of reactive hydroxyl radicals |
Quaternary ammonium compounds (QAC) have been in general use by industry and consumers for almost 70 years, mostly as rapid-action (≤ 10 minutes contact time) spray disinfectants for contaminated surfaces. They are considered as cationic surfactants or detergents, and are highly effective at disrupting the inner membranes of bacteria and lipid bilayers of enveloped viruses. QAC have undergone formulation changes to enhance effectiveness against non-enveloped viruses [20]. When combined with silane and polymers, they can be applied as a surface coating with antimicrobial properties [21]. Silane-QAC are long-chain molecules comprised of three principal components: 1) a silane base for covalent bonding to surfaces; 2) a centrally-located positively-charged nitrogen component, and 3) a long chain ‘spear’ consisting of a methyl hydrocarbon group. They can be applied to hard surfaces and to fabrics, and their virucidal efficacies may persist from 24 hours to weeks on treated surfaces.
Peer-reviewed studies evaluating the effectiveness of QAC-based surface coating treatments against viruses are currently limited. A quaternary ammonium polymer coating applied to stainless steel coupons demonstrated greater than 99.9% (>3 log10) reduction during 2 hours of contact against SARS-CoV-2 and human coronavirus 229E in the presence of 5% organic soil, although wear testing was not performed to assess residual antiviral activity [22]. Another study evaluating a QAC applied onto acrylic surfaces against subsequent SARS-CoV-2 and human coronavirus 229E contamination events demonstrated rapid inactivation upon contact (>90% [>1 log10] reduction); however, just one cleaning event of the coating using a water-based detergent and microfiber cloth substantially reduced product efficacy [23]. More peer-reviewed research is needed to better understand the breadth of QAC coating efficacy against the spectrum of non-enveloped and enveloped viruses, and under varying soil load and environmental conditions. Additional studies are also warranted to assess the durability of these coatings following simulated touches and cleaning events, and the resulting impacts on antiviral effectiveness.
Titanium dioxide (TiO2) is a photocatalytic inorganic chemistry that can be applied to a wide variety of surface types to provide antiviral protection. It does not inactivate viruses directly, but acts as a catalyst in the presence of UVA light (wavelength 315 to 400 nm) to generate reactive oxygen species that cause structural damage to viruses. The presence of moisture (in the air or on the surface) and oxygen are necessary for TiO2 to be an effective antiviral agent. Light intensity is also key in driving the photocatalytic reaction. Residual photocatalytic activity may also occur in the dark after exposure to UV light, but is dependent on the prior exposure intensity.
Most of the studies evaluating the antimicrobial effectiveness of TiO2 have focused on bacteria, and data on viruses remains scant in the literature [16]. TiO2 has demonstrated >3 log10 reduction against influenza A within 4 hours, and > 1 log10 inactivation of feline calicivirus within 8 hours [24]. TiO2 coatings have also been modified with fluorine to increase the production of reactive oxygen species under the low UVA-intensity fluorescent lighting that is typically found within indoor settings. Bacteriophage MS2, feline calicivirus, and murine norovirus infectivity levels were reduced by 2.6, 2.0, and 2.6 log10, respectively, on fluorinated TiO2surfaces [25]. The antiviral action of TiO2 can be further enhanced within indoor environments by the addition of metals [26, 27]. A 1% silver-amended TiO2 formulation yielded >4.00 log10 reduction of influenza A and enterovirus following a 20-minute exposure in the presence of a low intensity (15 W) UVA lamp [28]. More recently, infectious SARS-CoV-2 was reduced to levels below detection on TiO2 and TiO2-Silver (Ag) ceramic-coated tiles within 5 hours of exposure [15].
Metals such as copper, silver, and gold have been recognized since ancient times as having some health benefits, and the antibacterial properties of metals have since been well-studied [29]. In contrast, the mechanisms of metal inactivation of specific viruses remain unclear, although a number have been proposed and evaluated. Certain metals in trace amounts are critical to the function of viral proteins and genetic processes; however, levels in excess cause structural damage and affect viability [14]. The presence of these metals stimulates the generation of reactive oxygen species and damages viral envelopes as well as nucleocapsid proteins [30]. Metals can be incorporated into plastics and fabrics, used as actives in coating formulations, and fashioned directly into surfaces for direct use (e.g., copper sheets for incorporation into high-touch surfaces).
The antimicrobial properties of copper have been extensively studied, with efficacy demonstrated over a broad range of temperature and humidity values [1]. The proposed antiviral mechanisms of solid-state copper, copper oxides, and copper alloys against enveloped and non-enveloped viruses have been thoroughly reviewed [31]. Copper (I), (II), (III) ions act directly by denaturing viral surface proteins, and indirectly by the formation of reactive oxygen species that damage viral RNA and DNA. Copper surfaces inactivated infectious influenza A (H1N1) within 6 hours by 3 to 4 log10, relative to virus levels remaining on stainless steel coupons [32]. Although copper has demonstrated broad-spectrum antimicrobial activity, it may be impractical to replace bulk materials within high-traffic areas (e.g., clinical settings) with copper products or components. The recent development of cold- and thermally-applied copper sprays, as well as fixed copper nanoparticle coatings and paints, enables continuously active disinfection measures against a spectrum of viruses [16]. Copper nanoparticles in the oxide form have shown promise against herpes simplex virus, human norovirus, and influenza A (H1N1) [31]. When applied using the cold spray technique, copper nanoparticles reduced infectious influenza A virus particles to levels below detection within 10 minutes [33].
The antimicrobial properties of silver have been known for more than a century. Much of the research investigating the antimicrobial properties of silver has examined inactivation in suspension, where lower doses are required to achieve inactivation effects relative to other metals [34]. Silver binds with disulfide (S-S) and sulfhydryl (-SH) groups in proteins, facilitates the production of reactive oxygen species (e.g., free radicals), and is believed to inhibit entry of HIV-1 into CD4+ host cells [35]. Unlike copper, the efficacy of silver decreases markedly at relative humidity levels <20% [1], and solid-state silver appears to be much less effective against bacteriophage Qβ and influenza A than solid-state copper [36]. For surface applications, silver nanoparticles have been extensively researched. Silver nitrate and silver nanoparticles in surface coatings reduced recoverable levels of feline calicivirus and murine norovirus for up to 150 days [37]. Silver has also been incorporated into fabrics (hospital gowns, pillowcases, cotton sheets), textiles, and membranes, demonstrating antiviral properties against feline calicivirus and murine norovirus, as well as enveloped viruses [16, 38].
The antiviral properties of zinc have been researched for the past several decades. Zinc inhibits proteolytic cleavage and the synthesis of viral polypeptides by human rhinovirus [39], and interferes with polymerase function and protein production by herpes simplex virus 1 [16]. For surface applications, pure zinc, itself, does not exhibit high levels of antiviral activity. A 1 log10 reduction of murine norovirus on pure zinc was measured within 2 hours, relative to complete inactivation of the test virus via synergism when exposed to a copper-silver-zinc alloy [40]. On plastic coupons with incorporated silver/copper-zeolites, >1.7 log10 and > 3.8 log10 reductions were achieved for human coronavirus 229E and feline calicivirus, respectively, within 24 hours [41]. More recently, zinc ion-embedded polyamide fibers were found to reduce levels of infectious influenza A and SARS-CoV-2 by approximately 2 log10 within 30 minutes [42].
Research efforts are ongoing for the development of novel and continuously active coatings that are capable of maintaining low levels of bioburden while inactivating pathogenic microorganisms. A thorough review has been published of these coatings and their proposed mechanisms of action [14, 43]. The antiviral actives include biopolymers (e.g., antimicrobial peptides), synthetic polymers (e.g., polyethyleneimines, and graphene [14, 44, 45]. Natural product-based surface coatings and super-hydrophobic surfaces are also under development [46, 47]. Although many of these innovative technologies demonstrate promising antiviral effectiveness, further assessments of efficacy against additional types of viruses under various conditions are required. Reproducibility data generated among different lab groups would also be ideal to ensure product efficacy and reliability. Further, scaling up from the lab bench to assess these technologies under real-world conditions (i.e. placement into high-traffic, high-touch areas) will provide insight as to the consistency of their efficacy.
From this review, it is clear that promising antiviral continuously active disinfectants are a reality. However, many obstacles exist before their widespread implementation. These include:
Development and validation of standard methods for testing the efficacy of antiviral continuously active disinfectants. Ideally, these methods would indicate appropriate experimental conditions including relative humidity and temperature, organic soil load matrices, and evaluation of virucidal efficacy against enveloped and non-enveloped viruses.
Establishing an acceptable contact time for a 3 log10 (99.9%) decrease in infectious virus. Some continuously active disinfectants can achieve this goal within a few minutes, and others may require 1 to 2 hours.
Demonstration of the reduction in illnesses within facilities in which continuously active disinfectants are used. This is an ideal requirement, but difficult to achieve because of the high cost and multiple routes by which enteric and respiratory viruses can be transmitted. Reductions in hospital-acquired infections have been demonstrated with the use of copper [48, 49] and silane QAC [50] disinfectants, but such studies are not always ideal because of limitations inherent in epidemiological studies, and extracting precision is usually lacking. Further, more information is needed as to the potential human health and environmental impacts of silane QAC usage in these settings.
Application of quantitative microbial risk assessment (QMRA) to quantify the cost/benefits of continuously active disinfectants. QMRA is a lower-cost approach to documenting the probability of disease reduction that can be achieved. It can be used to estimate the difference in benefits from a continuously active disinfectant that inactivates 99.9% of the virus within 1 minute vs. one that achieves this within 2 hours.
Education of regulators, public health officials, and the general public is necessary to ultimately achieve the benefits of continuously active disinfectants. There is concern that their use may provide a false sense of security, causing consumers to clean and disinfect less frequently. Continuously active disinfectants should be looked upon as an additional barrier, and not as a replacement for routine cleaning and disinfection.
The authors have no conflict of interest to declare.
IntechOpen’s Academic Editors and Authors have received funding for their work through many well-known funders, including: the European Commission, Bill and Melinda Gates Foundation, Wellcome Trust, Chinese Academy of Sciences, Natural Science Foundation of China (NSFC), CGIAR Consortium of International Agricultural Research Centers, National Institute of Health (NIH), National Science Foundation (NSF), National Aeronautics and Space Administration (NASA), National Institute of Standards and Technology (NIST), German Research Foundation (DFG), Research Councils United Kingdom (RCUK), Oswaldo Cruz Foundation, Austrian Science Fund (FWF), Foundation for Science and Technology (FCT), Australian Research Council (ARC).
",metaTitle:"Open Access Funding",metaDescription:"Open Access Funding",metaKeywords:null,canonicalURL:"/page/open-access-funding",contentRaw:'[{"type":"htmlEditorComponent","content":"Open Access publication costs can often be designated directly in the grants or in specific budgets allocated for that purpose. Many of the most important funding organisations encourage, and even request, that the projects they fund are made available at no cost to the wider public. IntechOpen strives to maintain excellent relationships with these funders and ensures compliance with mandates.
\\n\\nIn order to help Authors identify appropriate funding agencies and institutions, we have created a list, based on extensive research on various OA resources (including ROARMAP and SHERPA/JULIET) of organizations that have funds available. Before consulting our list we encourage you to petition your own institution or organization for Open Access funds or check the specifications of your grant with your funder to ascertain if publication costs are included. Where you are in receipt of a grant you should clarify:
\\n\\nIf you are associated with any of the institutions in our list below, you can apply to receive OA publication funds by following the instructions provided in the links. Please consult the Open Access policies or grant Terms and Conditions of any institution with which you are linked to explore ways to cover your publication costs (also accessible by clicking on the link in their title).
\\n\\nPlease note that this list is not a definitive one and is updated regularly. To suggest possible modifications or the inclusion of your institution/funder, please contact us at funders@intechopen.com
\\n\\nPlease be aware that you must be a member, or grantee, of the institutions/funders listed in order to apply for their Open Access publication funds.
\\n\\nOpen Access publication costs can often be designated directly in the grants or in specific budgets allocated for that purpose. Many of the most important funding organisations encourage, and even request, that the projects they fund are made available at no cost to the wider public. IntechOpen strives to maintain excellent relationships with these funders and ensures compliance with mandates.
\n\nIn order to help Authors identify appropriate funding agencies and institutions, we have created a list, based on extensive research on various OA resources (including ROARMAP and SHERPA/JULIET) of organizations that have funds available. Before consulting our list we encourage you to petition your own institution or organization for Open Access funds or check the specifications of your grant with your funder to ascertain if publication costs are included. Where you are in receipt of a grant you should clarify:
\n\nIf you are associated with any of the institutions in our list below, you can apply to receive OA publication funds by following the instructions provided in the links. Please consult the Open Access policies or grant Terms and Conditions of any institution with which you are linked to explore ways to cover your publication costs (also accessible by clicking on the link in their title).
\n\nPlease note that this list is not a definitive one and is updated regularly. To suggest possible modifications or the inclusion of your institution/funder, please contact us at funders@intechopen.com
\n\nPlease be aware that you must be a member, or grantee, of the institutions/funders listed in order to apply for their Open Access publication funds.
\n\n