distance dissimilarity index and network community structure we address the question of finding the community structure of a complex network in an earlier effort h zhou phys rev e 67 041908 2003 the concept of network random walking is introduced and a distance measure defined here we calculate based on this distance measure the dissimilarity index between nearest neighboring vertices of a network and design an algorithm to partition these vertices into communities that are hierarchically organized each community is characterized by an upper and a lower dissimilarity threshold the algorithm is applied to several artificial and real world networks and excellent results are obtained in the case of artificially generated random modular networks this method outperforms the algorithm based on the concept of edge betweenness centrality for yeast s protein protein interaction network we are able to identify many clusters that have well defined biological functions

interpolativity of at least and at most models of monotone fuzzy rule bases with multiple antecedent variables of the many desirable properties of fuzzy inference systems not all are known to co exist for instance a fuzzy inference system should be interpolative i e if a fuzzy set equivalent to one of the antecedent fuzzy sets appears on the input of such a system the inferred output should be equivalent to the respective consequent fuzzy set similarly the defuzzified output obtained from a system based on a monotone fuzzy rule base should be monotone i e if x x are crisp inputs to the system that are ordered x x then the corresponding defuzzified outputs from the system y y should also be ordered accordingly i e y y however the particular setting that ensures monotonicity need not simultaneously ensure interpolativity recently st pnicka and de baets have investigated and demonstrated the co existence of the above two properties in the case of fuzzy relational inference systems and single input single output siso rule bases an extension of these results to the multiple input single output miso case is not straightforward due to the lack of a natural ordering in higher dimensions in this work we study the miso case and show that similar results can be obtained when the monotone rule base is modeled based on at most and at least modifiers

on approximate reasoning with graded rules this contribution presents a comprehensive view on problems of approximate reasoning with imprecise knowledge in the form of a collection of fuzzy if then rules formalized by approximating formulas of a special type two alternatives that follow from the dual character of approximating formulas are developed in parallel the link to the theory of fuzzy control systems is also explained

new exact solutions of the broer kaup equations in 2 1 dimensional spaces abstract with the aid of maple several new kinds of exact solutions for the broer kaup equations in 2 1 dimensional spaces are obtained by using a new ansatz this approach can also be applied to other nonlinear evolution equations

generalized multiple riccati equations rational expansion method with symbolic computation to construct exact complexiton solutions of nonlinear partial differential equations in this paper based on symbolic computation and the idea of rational expansion method a generalized multiple riccati equations rational expansion method gmrere is proposed to uniformly construct a series of exact complexiton solutions for nonlinear partial differential equations compared with most existing tanh function methods and rational expansion methods the proposed method not only recovers some known solutions but also finds some new and general complexiton solutions the efficiency of the method can be demonstrated on 2 1 dimensional burgers equation

network landscape from a brownian particle s perspective given a complex biological or social network how many clusters should it be decomposed into we define the distance d i j from node i to node j as the average number of steps a brownian particle takes to reach j from i node j is a global attractor of i if d i j l d i k for any k of the graph it is a local attractor of i if j ensuremath in e i the set of nearest neighbors of i and d i j l d i l for any l ensuremath in e i based on the intuition that each node should have a high probability to be in the same community as its global local attractor on the global local scale we present a simple method to uncover a network s community structure this method is applied to several real networks and some discussion on its possible extensions is made

special solutions from the variable separation approach the davey stewartson equation a variable separation procedure for the davey stewartson ds equation is proposed by using a prior ansatz to its bilinear form the reduced equations for two variable separated fields have the same trilinear form although they possess different independent variables the trilinear equation can be changed to a spacetime symmetric form and can be solved by means of a boussinesq type equation system whenever a pair of solutions of the reduced fields are obtained a corresponding solution of the ds equation can be obtained algebraically the single dromion solution and some kinds of positon solutions are obtained explicitly

necessary and sufficient conditions for generalized uniform fuzzy partitions abstract the fundamental concept in the theory of fuzzy transform f transform is the fuzzy partition which is a generalization of the classical concept of partition the original definition assumes that every two normal fuzzy subsets in a partition overlap in such a way that the sum of the membership degrees at each point is equal to 1 this condition can be generalized by relaxing the assumption of normality for fuzzy sets the result is a denser fuzzy partition that may improve the approximation properties and the smoothness of the inverse f transform a fuzzy partition with this property will be referred to as general the problem is how a general fuzzy partition can be effectively constructed if we use a generating function with special properties then it is not immediately clear whether it defines a general fuzzy partition in this paper we find a necessary and sufficient condition that will enable the optimal generalized fuzzy partition to be designed more easily which is important in various practical applications of the f transform for example image processing time series analysis and solving differential equations with boundary conditions

the analysis and dissimilarity comparison of community structure abstract based on a database of collaboration recording in econophysics scientists and other networks hierarchical clustering method and the algorithm of girvan and newman are applied to detect their community structure the interesting results for community structure of econophysicists collaboration network are shown a dissimilarity function d is proposed to quantitatively measure the difference between community structures obtained by different methods using this measurement the differences between the process and community results obtained by aforementioned algorithms are given the effectiveness of hierarchical clustering method and gn algorithm for detecting community structure in various networks is discussed

stochastic exact solutions of the wick type stochastic nls equation based upon the hermite transformation and the extended sub equation expansion method soliton like solutions of the stochastic schrodinger equation in the white noise environment are obtained via maple

statistical mechanics of community detection starting from a general ansatz we show how community detection can be interpreted as finding the ground state of an infinite range spin glass our approach applies to weighted and directed networks alike it contains the ad hoc introduced quality function from j reichardt and s bornholdt phys rev lett 93 218701 2004 and the modularity q as defined by newman and girvan phys rev e 69 026113 2004 as special cases the community structure of the network is interpreted as the spin configuration that minimizes the energy of the spin glass with the spin states being the community indices we elucidate the properties of the ground state configuration to give a concise definition of communities as cohesive subgroups in networks that is adaptive to the specific class of network under study further we show how hierarchies and overlap in the community structure can be detected computationally efficient local update rules for optimization procedures to find the ground state are given we show how the ansatz may be used to discover the community around a given node without detecting all communities in the full network and we give benchmarks for the performance of this extension finally we give expectation values for the modularity of random graphs which can be used in the assessment of statistical significance of community structure

community detection by signaling on complex networks based on a signaling process of complex networks a method for identification of community structure is proposed for a network with n nodes every node is assumed to be a system which can send receive and record signals each node is taken as the initial signal source to excite the whole network one time then the source node is associated with an n dimensional vector which records the effects of the signaling process by this process the topological relationship of nodes on the network could be transferred into a geometrical structure of vectors in n dimensional euclidean space then the best partition of groups is determined by f statistics and the final community structure is given by the k means clustering method this method can detect community structure both in unweighted and weighted networks it has been applied to ad hoc networks and some real networks such as the zachary karate club network and football team network the results indicate that the algorithm based on the signaling process works well

generalized method and new exact wave solutions for 2 1 dimensional broer kaup kupershmidt system in this paper a new algebra method i e generalized elliptic equation rational expansion method is devised to uniformly construct a series of exact solutions for nonlinear partial differential equations compared with most existing tanh methods the proposed method not only recover some known solutions but also find some new and general solutions the efficiency of the method can be demonstrated on the 2 1 dimensional broer kaup kupershmidt system as a result we obtain many new types of solutions include rational formal solitary wave solutions rational formal triangular periodic wave solutions rational formal jacobi and weierstrass double period solutions and rational wave solutions

application of rational expansion method for stochastic differential equations abstract by means of the hermite transformation a new general ansatz and the symbolic computation system maple we apply the riccati equation rational expansion method 24 to uniformly construct a series of stochastic non traveling wave solutions for stochastic differential equations to illustrate the effectiveness of our method we take the stochastic mkdv equation as an example and successfully construct some new and more general solutions the method can also be applied to solve other nonlinear stochastic differential equation or equations

continuity issues of the implicational interpretation of fuzzy rules the implicational interpretation of fuzzy rules has received little attention in real world applications so far this is largely due to the fact that ensuring continuity of the resulting function is not a straightforward task this paper targets this subject departing from consistent linguistic descriptions rule bases we introduce sufficient conditions for the continuity of the implicational interpretation with mean of maximum defuzzification we demonstrate that continuity can be achieved under practically feasible conditions regardless of the dimensionality of the input

link between solitary waves and projective riccati equations many solitary wave solutions of nonlinear partial differential equations can be written as a polynomial in two elementary functions which satisfy a projective hence linearizable riccati system from that property the authors deduce a method for building these solutions by determining only a finite number of coefficients this method is much shorter and obtains more solutions than the one which consists of summing a perturbation series built from exponential solutions of the linearized equation they handle several examples for the henon heiles hamiltonian system they obtain several exact solutions one of them defines a new solitary wave solution for a coupled system of boussinesq and nonlinear schrodinger equations for a third order dispersive equation with two monomial nonlinearities they isolate all cases where the general solution is single valued

checking the coherence and redundancy of fuzzy knowledge bases checking the coherence of a set of rules is an important step in knowledge base validation coherence is also needed in the field of fuzzy systems indeed rules are often used regardless of their semantics and it sometimes leads to sets of rules that make no sense avoiding redundancy is also of interest in real time systems for which the inference engine is time consuming a knowledge base is potentially inconsistent or incoherent if there exists a piece of input data that respects integrity constraints and that leads to logical inconsistency when added to the knowledge base we more particularly consider knowledge bases composed of parallel fuzzy rules then coherence means that the projection on the input variables of the conjunctive combination of the possibility distributions representing the fuzzy rules leaves these variables completely unrestricted i e any value for these variables is possible or at least not more restrictive than integrity constraints fuzzy rule representations can be implication based or conjunction based we show that only implication based models may lead to coherence problems however unlike conjunction based models they allow to design coherence checking processes some conditions that a set of parallel rules has to satisfy in order to avoid inconsistency problems are given for certainty or gradual rules the problem of redundancy which is also of interest for fuzzy knowledge bases validation is addressed for these two kinds of rules

solving fuzzy relational equations via semitensor product the problem of solving max min fuzzy relational equations is investigated first we show that if there is a solution then there is a corresponding solution within the set of parameters briefly the parameter set solution pss then the semitensor product of matrices is used to convert the logical equations into algebraic equations via the vector expression of logical variables under this form every pss can be obtained it is proved that all the solutions can be revealed from their corresponding pss some examples are presented to demonstrate the algorithm to solve fuzzy relational equations

new similarity reductions of the boussinesq equation some new similarity reductions of the boussinesq equation which arises in several physical applications including shallow water waves and also is of considerable mathematical interest because it is a soliton equation solvable by inverse scattering are presented these new similarity reductions including some new reductions to the first second and fourth painleve equations cannot be obtained using the standard lie group method for finding group invariant solutions of partial differential equations they are determined using a new and direct method that involves no group theoretical techniques

a new coupled sub equations expansion method and novel complexiton solutions of 2 1 dimensional burgers equation in this paper based on symbolic computation and the idea of rational expansion method a new coupled sub equations method is devised to uniformly construct a series of exact complexiton solutions for nonlinear evolution equations compared with most existing tanh function methods and other sophisticated methods the proposed method not only recover some known solutions but also find some new and general solutions which include many new types of complexiton solutions the efficiency of the method can be demonstrated on 2 1 dimensional burgers equation

logical structure of fuzzy if then rules abstract this paper provides a logical basis for manipulation with fuzzy if then rules our theory is wide enough and it encompasses not only finding a conclusion by means of the compositional rule of inference due to lotfi a zadeh but also other kinds of approximate reasoning methods e g perception based deduction provided that there exists a possibility to characterize them within a formal logical system in contrast with other approaches employing variants of multiple valued first order logic the approach presented here employs fuzzy type theory of v novak which has sufficient expressive power to present the essential concepts and results in a compact elegant and justifiable form within the effectively formalized representation developed here based on a complete logical system it is possible to reconstruct numerous well known properties of cri related fuzzy inference methods albeit not from the analytic point of view as usually presented but as formal derivations of the logical system employed the authors are confident that eventually all relevant knowledge about fuzzy inference methods based on fuzzy if then rule bases will be represented formalized and backed up by proof within the well founded logical representation presented here an immediate positive consequence of this approach is that suddenly all elements of a fuzzy inference method based on fuzzy if then rules are first class citizens of the representation there are clear logically founded definitions for fuzzy if then rule bases to be consistent complete or independent

a new korteweg de vries equation based sub equation method and its application to the 2 1 dimensional korteweg de vries equation with the help of the symbolic computation system maple we present korteweg de vries equation based sub equation method being concise and straightforward it is applied to the 2 1 dimensional korteweg de vries equation it is shown that n soliton solution of the 2 1 dimensional korteweg de vries equation can be found by this new method the method can be applied to other nonlinear partial differential equations in mathematical physics

2 1 dimensional compacton solutions with and without completely elastic interaction properties taking the 2 1 dimensional broer kaup kupershmidt system as a simple example some special types of 2 1 dimensional compacton solutions are constructed it is shown that there is quite rich interaction behaviour between two travelling compactons for some types of compactons the interactions among them may not be completely elastic for some others the interactions are completely elastic there is no phase shift for the interactions of the 2 1 dimensional compactons discussed in this paper

finitary solvability conditions for systems of fuzzy relation equations in this paper we consider the problem of solving systems of fuzzy relation equations two types of these systems with different compositions are considered and processed simultaneously a new sufficient condition and new solvability criteria are proposed for systems of both types all these conditions are finitary and thus can be easily verified the sufficient condition and criteria of solvability characterize a relationship between a skeleton nxn matrix n is a number of equations and a vector of the right hand side

formal variable separation approach for nonintegrable models using a formal variable separation approach a nonlinear partial differential equation can be solved by solving ordinary different equations or even algebraic equations taking the kdv burgers and modified kdv burgers equations with background interaction as simple examples some explicit solitary wave solutions which are induced by background source and nonlinearity or dispersion are obtained

detecting community structure from coherent oscillation of excitable systems abstract many networks are proved to have community structures on the basis of the fact that the dynamics on networks are intensively affected by the related topology in this paper the dynamics of excitable systems on networks and a corresponding approach for detecting communities are discussed dynamical networks are formed by interacting neurons each neuron is described using the fhn model for noisy disturbance and appropriate coupling strength neurons may oscillate coherently and their behavior is tightly related to the community structure synchronization between nodes is measured in terms of a correlation coefficient based on long time series the correlation coefficient matrix can be used to project network topology onto a vector space then by the k means cluster method the communities can be detected experiments demonstrate that our algorithm is effective at discovering community structure in artificial networks and real networks especially for directed networks the results also provide us with a deep understanding of the relationship of function and structure for dynamical networks

generalized riccati equation rational expansion method and its application by directly extending the riccati equation rational expansion method a new method is developed for constructing a series of exact analytical solutions of an averaged dispersion managed fiber system equation adme including some new rational formal soliton like solutions triangle like solutions and rational solutions

infinite dimensional symmetry algebras and an infinite number of conserved quantities of the 2 1 dimensional davey stewartson equation an infinite dimensional symmetry algebra of the davey stewartson equation is explicitly presented it is shown that this algebra is a gauge generalization of the symmetry transformation for the schrodinger equation and that the virasoro algebra appears as the subalgebra an infinite number of conserved quantities associated with the transformations are also obtained

similarity reductions of the kp equation by a direct method basing on a direct method developed by clarkson and kruskal 1989 the kadomtsev petviashvili kp equation has been reduced to three types of 1 1 dimensional partial differential equations which are equivalent to the three types of the similarity reduction equations obtained by the classical lie approach but with different independent variables more arbitrary functions which have been missed by the classical lie approach have been included in the solutions of the kp equation for instance the third type of reduction obtained by the direct method can be divided into three subcases and the third type of solution of the kp equation obtained by the classical lie approach is only a special case of one subcase of the authors results

fuzzy inference systems preserving moser navara axioms abstract satisfiability of three naturally proposed axioms which are desirable for fuzzy inference system was discussed by moser and navara in 36 the fuzzy rule base models considered in this study were mainly the mamdani assilian ones and partly also logically motivated implicative fuzzy systems the investigation leads to the fact that often none of these fuzzy systems do satisfy the given axioms simultaneously therefore moser and navara proposed so called conditionally firing rules and proved that the simultaneous satisfaction of the three axioms is feasible under very mild and practically non restrictive conditions note that the inference mechanism tailored to the fuzzy rules in the investigation was the compositional rule of inference abb cri and similarly the concept of conditionally firing rules were stemming from the cri and the mamdani assilian model of a fuzzy rule base for the implicative interpretation of fuzzy rules the original axioms proposed by moser and navara were later on re defined by st pnicka and mandal with the aim to express the meaning of the original axioms initially proposed for the mamdani assilian rules furthermore conditionally firing implicative rules were proposed based on the so called bandler kohout subproduct abb bks inference mechanism and a study similar to the one by moser and navara was undertaken for them the study encompasses the satisfaction of the modified axioms for the use of implicative rules and the bks furthermore some additional results confirming the applicability of the conditionally firing rules satisfying the moser navara axioms are also provided including the universal approximation ability however the solvability criterions for fuzzy relational equations give a strong preference to the usage of the other combinations namely to the combination of cri with the implicative interpretation of fuzzy rules and to the combination of bks with the mamdani assilian interpretation of fuzzy rules therefore also these combinations of fuzzy inference mechanisms and interpretations of fuzzy rules should be investigated with respect to the satisfaction of moser navara axioms the main purpose of this article which extends the short conference contribution 47 by st pnicka is to provide such an investigation jointly with the review on conditionally firing rules and supplementary results

interpolativity of at least and at most models of monotone single input single output fuzzy rule bases interpolativity is one of the most important properties of a fuzzy inference system it is well known that normal antecedent fuzzy sets forming a ruspini partition constitute a practical setting ensuring interpolativity in case of a fuzzy rule base expressing a monotone relationship another desirable property is the monotonicity of the resulting function after defuzzification unfortunately this goal may often only be reached through the application of the at least and or at most modifiers to the antecedent and consequent fuzzy sets however this approach does not seem compatible with the practical setting of a ruspini partition this paper shows that the situation is less conflicting than it seems and that interpolativity can still be guaranteed in the same practical setting and interestingly from two different modeling points of view this paper addresses the case of single input single output fuzzy rules

on the infinite dimensional symmetry group of the davey stewartson equations the lie algebra of the group of point transformations leaving the davey stewartson equations dse s invariant is obtained the general element of this algebra depends on four arbitrary functions of time the algebra is shown to have a loop structure a property shared by the symmetry algebras of all known 2 1 dimensional integrable nonlinear equations subalgebras of the symmetry algebra are classified and used to reduce the dse s to various equations involving only two independent variables

fuzzy relational compositions abstract this paper investigates the fuzzy relational compositions defined by bandler and kohout it is indicated that these compositions have to be modified in order to capture the desired interpretation several alternative definitions are suggested and discussed the paper concludes with an overview of the properties of these improved fuzzy relational compositions

what are fuzzy rules and how to use them abstract fuzzy rules have been advocated as a key tool for expressing pieces of knowledge in fuzzy logic however there does not exist a unique kind of fuzzy rules nor is there only one type of fuzzy logic this diversity has caused many a misunderstanding in the literature of fuzzy control the paper is a survey of different possible semantics for a fuzzy rule and shows how they can be captured in the framework of fuzzy set and possibility theory it is pointed out that the interpretation of fuzzy rules dictates the way the fuzzy rules should be combined the various kinds of fuzzy rules considered in the paper gradual rules certainty rules possibility rules and others have different inference behaviors and correspond to various intended uses and applications the representation of fuzzy unless rules is briefly investigated on the basis of their intended meaning the problem of defining and checking the coherence of a block of parallel fuzzy rules is also briefly addressed this issue has been neglected in the fuzzy control literature although it looks important for validation purposes

implication based models of monotone fuzzy rule bases abstract in many modelling problems there is some inherent monotone relationship between one or more of the input variables and the output variable we consider the prototypical case of an increasing relationship between each of the input variables and the output variable when using fuzzy rule based models this desired monotonicity is reflected in the rule base given an appropriate ordering on the fuzzy sets involved in the respective input and output domains more specifically the larger the antecedent fuzzy sets the larger the consequent fuzzy set however fuzzy rule based modelling involves a final defuzzification step possibly resulting in a function that is no longer monotone in the context of mamdani assilian conjunctive fuzzy models ample attention has been paid to this problem both for the centre of gravity defuzzification and mean of maxima defuzzification methods in this paper we show that for implicative fuzzy models the non monotonicity problem can be circumvented by making explicit the semantics of the fuzzy rules by subjecting the antecedent and consequent fuzzy sets to the at least and or at most modifiers

symmetries and exact solutions of the sharma tass olver equation abstract the simple symmetry reduction procedure is repeatedly used to obtain infinitely many symmetries as well as exact solutions of the sharma tass olver sto equation some sets of exact solutions such as singular rational complexitons and both analytical and singular rational negaton positons with new soliton fission and fusion phenomena are obtained

infinitely many symmetries of the davey stewartson equation using a formal series symmetry method for the davey stewartson equation dse we find that there exist two sets of infinitely many formal series symmetries of the dse however different from the kadomtsev petviashvili equation kpe we failed to get infinitely many truncated symmetries only six truncated symmetries can be obtained simply from the formal series symmetries

a new variable coefficient korteweg de vries equation based sub equation method and its application to the 3 1 dimensional potential ytsf equation with the aid of maple we present variable coefficient korteweg de vries equation based sub equation method the key idea of our method is to take advantage of the variable coefficient korteweg de vries equation and its various solutions to generate various solutions of nonlinear evolution equations the efficiency of the method can be demonstrated on the 3 1 dimensional potential ytsf equation and we construct successfully its new styles of solutions

on the suitability of the bandler kohout subproduct as an inference mechanism fuzzy relational inference fri systems form an important part of approximate reasoning schemes using fuzzy sets the compositional rule of inference cri which was introduced by zadeh has attracted the most attention so far in this paper we show that the fri scheme that is based on the bandler kohout bk subproduct along with a suitable realization of the fuzzy rules possesses all the important properties that are cited in favor of using cri viz equivalent and reasonable conditions for their solvability their interpolative properties and the preservation of the indistinguishability that may be inherent in the input fuzzy sets moreover we show that under certain conditions the equivalence of first infer then aggregate fita and first aggregate then infer fati inference strategies can be shown for the bk subproduct much like in the case of cri finally by addressing the computational complexity that may exist in the bk subproduct we suggest a hierarchical inferencing scheme thus this paper shows that the bk subproduct based fri is as effective and efficient as the cri itself

localized excitations in 2 1 dimensional systems by means of a special variable separation approach a common formula with some arbitrary functions has been obtained for some suitable physical quantities of various 2 1 dimensional models such as the davey stewartson ds model the nizhnik novikov veselov nnv system asymmetric nnv equation asymmetric ds equation dispersive long wave equation broer kaup kupershmidt system long wave short wave interaction model maccari system and a general n m component ablowitz kaup newell segur akns system selecting the arbitrary functions appropriately one may obtain abundant stable localized interesting excitations such as the multidromions lumps ring soliton solutions breathers instantons etc it is shown that some types of lower dimensional chaotic patterns such as the chaotic chaotic patterns periodic chaotic patterns chaotic line soliton patterns chaotic dromion patterns fractal lump patterns and fractal dromion patterns may be found in higher dimensional soliton systems the interactions between the traveling ring type soliton solutions are completely elastic the traveling ring solitons pass through each other and preserve their shapes velocities and phases some types of localized weak solutions peakons are also discussed especially the interactions between two peakons are not completely elastic after the interactions the traveling peakons also pass through each other and preserve their velocities and phases however they completely exchange their shapes

measures of specificity of fuzzy sets under t indistinguishabilities the concept of measure of specificity of fuzzy sets is extended in this paper to measure of specificity under the knowledge of t indistinguishabilities four axioms of measure of specificity under t indistinguishabilities are given an algorithm to compute the inference independent set tfr from a fuzzy set and a t indistinguishability is used to measure the specificity of fuzzy sets under t indistinguishabilities satisfying the axioms

monotonicity of siso fuzzy relational inference with an implicative rule base a fuzzy relational inference fri mechanism is appraised based on the different desirable properties it possesses among these properties monotonicity of an fri has not received much attention in this work we investigate the monotonicity of a single input single output fri with an implicative form of the rule base in all the previous works that deal with monotonicity of an fri with the implicative form of rule base the employed fuzzy implications come from a residuated lattice it can be noticed that this rich underlying structure plays a major role in proving the results further we also modify the given monotone rule base this work differs from the previous works in that 1 the fuzzy implications employed in it do not come from any known residuated structure on text 0 1 and 2 the original rule base is employed without any alteration we determine conditions under which monotonicity of an fri where the rule base is modeled by a strict fuzzy implication can be ensured without transforming the original rule base thus the results in this work further augment the case for considering fuzzy implications other than those from the residuated setting to be used in applications

extensions of fuzzy relational compositions based on generalized quantifiers abstract the aim of this paper is to extend the fuzzy relational compositions motivated by their applications to medical diagnosis problem by bandler and kohout these compositions employ two quantifiers the universal quantifier and the existential quantifier as there exists a big gap between these two quantifiers that may be appropriately filled in by intermediate generalized quantifiers we take this as a motivation for our study in particular we introduce the concept of fuzzy relational compositions based on generalized quantifiers furthermore we show that the properties that are typically valid for standard fuzzy relational compositions are also valid for the compositions based on generalized quantifiers yet sometimes in a weaken form apart from fuzzy relational compositions the use of generalized quantifiers is also applied to images and preimages of fuzzy sets under fuzzy relations

application of the extended homotopy perturbation method to a kind of nonlinear evolution equations based on the homotopy perturbation method we propose a new extended homotopy perturbation method we apply the method to solve a kind of nonlinear evolution equations with the help of the symbolic computation system maple the success of the paper lies on the fact that we do not conform to the traditional homotopy mode but construct a new homotopy of the given equations the results reveal that we can obtain the approximation solution of a kind of nonlinear evolution equations

dynamical survey of a generalized zakharov equation and its exact travelling wave solutions we investigate the dynamical behavior of a generalized zakharov equation for the complex envelope of the high frequency wave and the real low frequency field by analyzing its phase portraits following a dynamical system approach in different parameter regions we depict phase portraits of a travelling wave system through discussing the bifurcation of phase portraits we unwrap explicit miscellaneous travelling waves including localized and periodic ones

new exact travelling wave solutions for the shallow long wave approximate equations based upon a generally projective riccati equation method which is a direct and unified algebraic method for constructing more general form travelling wave solutions of nonlinear partial differential equations and implemented in a computer algebraic system we consider the shallow long wave approximate equations new and more general form solutions are obtained including kink shaped solitons bell shaped solitons singular solitons and periodic solutions the properties of the new formal solitary wave solutions are shown by some figures

numerical solutions of coupled burgers equations with time and space fractional derivatives in this paper by introducing the fractional derivative in the sense of caputo the adomian decomposition method is directly extended to study the coupled burgers equations with time and space fractional derivatives as a result the realistic numerical solutions are obtained in a form of rapidly convergent series with easily computable components the figures show the effectiveness and good accuracy of the proposed method

exact solitary waves in a convecting fluid the perturbed korteweg de vries equation ut lambda 1uux lambda 2uxxx lambda 3uxxxx lambda 4 uux x lambda 5uxx 0 which describes the evolution of long shallow waves in a convecting fluid when the critical rayleigh number slightly exceeds its critical value admits two types of exact solitary wave solution

fuzzy transform as an additive normal form in this paper we recall a class of approximating formulas since they arose as a generalization of classical normal forms we denote them by the same term moreover we will show that the fuzzy transform f transform introduced in perfilieva i fuzzy approach to solution of differential equations with imprecise data application to reef growth problem in r v demicco g j klir eds fuzzy logic in geology academic press amsterdam 2003 pp 275 300 chapter 9 perfilieva i fuzzy transforms in j f peters a skowron eds transactions on rough sets ii rough sets and fuzzy sets lecture notes in computer science vol 3135 2004 pp 63 81 as an approximation method for continuous functions can be viewed as a particular case of normal form therefore the results valid for normal forms may be applied to f transforms as well

fuzzy transforms theory and applications the technique of direct and inverse fuzzy f transforms of three different types is introduced and approximating properties of the inverse f transforms are described all three types of the direct f transform are transformations from a function space to a finite dimensional vector space the first ordinary f transform is constructed on the basis of the ordinary algebra of reals while the other two types of the f transform are constructed on the basis of residuated lattice the core idea of the technique of f transforms is a fuzzy partition of a universe into fuzzy subsets factors clusters granules etc we claim that for a sufficient representation of a function defined on this universe we may consider its average values over fuzzy subsets from the partition thus a function can be associated with a mapping from a set of fuzzy subsets to the set of its thus obtained average values a number of theorems establishing best approximation properties of the inverse f transforms are proved in fact three types of the inverse f transform are the best approximations in average from below and from above respectively as one of many possible applications we present a method of image compression and reconstruction on the basis of the f transform

structural and functional clusters of complex brain networks recent research using the complex network approach has revealed a rich and complicated network topology in the cortical connectivity of mammalian brains it is of importance to understand the implications of such complex network structures in the functional organization of the brain activities here we study this problem from the viewpoint of dynamical complex networks we investigate synchronization dynamics on the corticocortical network of the cat by modeling each node cortical area of the network with a sub network of interacting excitable neurons we find that the network displays clustered synchronization behavior and the dynamical clusters coincide with the topological community structures observed in the anatomical network our results provide insights into the relationship between the global organization and the functional specialization of the brain cortex

on two approaches of finding exact solutions to nonlinear evolution equations in this work we give some discussions on the sec q tanh q method of finding exact solutions to the nonlinear evolution equations presented by liu and jiang we conclude that the method is just one special case of the generalized projective riccati equation method therefore these deformed hyperbolic function solutions do not pertain to a new class then based on the generalized projective riccati equation method more exact solutions of the hirota satsuma coupled kdv systems are obtained

arithmetic fuzzy models it is well known that a fuzzy rule base can be interpreted in different ways from a logical point of view the conjunctive interpretation is preferred while from a practical point of view the disjunctive interpretation has been dominantly present each of these interpretations results in a specific fuzzy relation that models the fuzzy rule base basic interpolation requirements naturally suggest a corresponding inference mechanism the direct image for the conjunctive interpretation and the subdirect image for the disjunctive interpretation interpolation then corresponds to solvability of some system of fuzzy relational equations in this paper we show that other types of fuzzy relations which are closely related to takagi sugeno t s models are of major interest as well these fuzzy relations are based on addition and multiplication only from which we get the name arithmetic fuzzy models under some mild requirements these fuzzy relations turn out to be solutions of the same systems of fuzzy relational equations the impact of these results is both theoretical and practical there exist simple solutions to systems of fuzzy relational equations other than the extremal solutions that have received all the attention so far which are moreover easy to implement

the relation between inference and interpolation in the framework of fuzzy systems abstract this papers aims at clarifying the meaning of different interpretations of the max min or more generally the max t norm rule in fuzzy systems it turns out that basically two distinct approaches play an important role in fuzzy logic and its applications fuzzy interpolation on the basis of an imprecisely known function and logical inference in the presence of fuzzy information

adaptive fuzzy logic control of dynamic balance and motion for wheeled inverted pendulums in this paper adaptive fuzzy logic control of dynamic balance and motion is investigated for wheeled inverted pendulums with parametric and functional uncertainties the proposed adaptive fuzzy logic control based on physical properties of wheeled inverted pendulums makes use of a fuzzy logic engine and a systematic online adaptation mechanism to approximate the unknown dynamics based on lyapunov synthesis the fuzzy control ensures that the system outputs track the given bounded reference signals to within a small neighborhood of zero and guarantees semi global uniform boundedness of all closed loop signals the effectiveness of the proposed control is verified through extensive simulations

detecting complex network modularity by dynamical clustering based on cluster desynchronization properties of phase oscillators we introduce an efficient method for the detection and identification of modules in complex networks the performance of the algorithm is tested on computer generated and real world networks whose modular structure is already known or has been studied by means of other methods the algorithm attains a high level of precision especially when the modular units are very mixed and hardly detectable by the other methods with a computational effort o kn on a generic graph with n nodes and k links

a backlund transformation and nonlinear superposition formula of a modified korteweg de vries type bilinear equation a modified korteweg de vries mkdv type bilinear equation that has been shown to pass the three soliton solution and the painleve tests see j math phys 2094 28 1987 2572 31 1990 is considered herein in this article a backlund transformation and a nonlinear superposition formula are proven rigorously as an application of the obtained results n soliton solutions are obtained therefore the integrability of this mkdv type bilinear equation is confirmed