adaptive fuzzy rule based classification systems this paper proposes an adaptive method to construct a fuzzy rule based classification system with high performance for pattern classification problems the proposed method consists of two procedures an error correction based learning procedure and an additional learning procedure the error correction based learning procedure adjusts the grade of certainty of each fuzzy rule by its classification performance that is when a pattern is misclassified by a particular fuzzy rule the grade of certainty of that rule is decreased on the contrary when a pattern is correctly classified the grade of certainty is increased because the error correction based learning procedure is not meaningful after all the given patterns are correctly classified we cannot adjust a classification boundary in such a case to acquire a more intuitively acceptable boundary we propose an additional learning procedure we also propose a method for selecting significant fuzzy rules by pruning unnecessary fuzzy rules which consists of the error correction based learning procedure and the concept of forgetting we can construct a compact fuzzy rule based classification system with high performance

a new gradient descent approach for local learning of fuzzy neural models the majority of reported learning methods for takagi sugeno kang tsk fuzzy neural models to date mainly focus on improvement of their accuracy however one of the key design requirements in building an interpretable fuzzy model is that each obtained rule consequent must match well with the system local behavior when all the rules are aggregated to produce the overall system output this is one of the distinctive characteristics from black box models such as neural networks therefore how to find a desirable set of fuzzy partitions and hence identify the corresponding consequent models which can be directly explained in terms of system behavior presents a critical step in fuzzy neural modeling in this paper a new learning approach considering both nonlinear parameters in the rule premises and linear parameters in the rule consequents is proposed unlike the conventional two stage optimization procedure widely practiced in the field where the two sets of parameters are optimized separately the consequent parameters are transformed into a dependent set on the premise parameters thereby enabling the introduction of a new integrated gradient descent learning approach thus a new jacobian matrix is proposed and efficiently computed to achieve a more accurate approximation of the cost function by using the second order levenberg marquardt optimization method several other interpretability issues regarding the fuzzy neural model are also discussed and integrated into this new learning approach numerical examples are presented to illustrate the resultant structure of the fuzzy neural models and the effectiveness of the proposed new algorithm and compared with the results from some well known methods

a vectorization optimization method based type 2 fuzzy neural network for noisy data classification this paper proposes a vectorization optimization method vom based type 2 fuzzy neural network vom2fnn for noisy data classification in handling problems with uncertainties such as noisy data type 2 fuzzy systems usually outperform their type 1 counterparts hence type 2 fuzzy sets are adopted in the antecedent parts to model the uncertainty to consider the classification problems the discriminative capability is crucial to determine the performance therefore a vom is proposed in the consequent parts to increase the discriminability and reduce the parameters compared with other existing fuzzy neural networks the novelty of the proposed vom2fnn is its consideration of both uncertainty and discriminability the effectiveness of the proposed vom2fnn is demonstrated by three classification problems experimental results and theoretical analysis indicate that the proposed vom2fnn performs better than the other fuzzy neural networks

two level linear programming decentralized planning has long been recognized as an important decision making problem many approaches based on the concepts of large scale system decomposition have generally lacked the ability to model the type of truly independent subsystems which often exist in practice multilevel programming models partition control over decision variables among ordered levels within a hierarchical planning structure a planner at one level of the hierarchy may have his objective function and set of feasible decisions determined in part by other levels however his control instruments may allow him to influence the policies at other levels and thereby improve his own objective function this paper examines the special case of the two level linear programming problem geometric characterizations and algorithms are presented with some examples the goal is to demonstrate the tractability of such problems and motivate a wider interest in their study

a fuzzy model with online incremental svm and margin selective gradient descent learning for classification problems this paper proposes a new incremental learning approach to endow a takagi sugeno type fuzzy classification model with high generalization ability the proposed fuzzy model is learned through incremental support vector machine svm and margin selected gradient descent learning and is called fm3 in this learning approach training samples are fed incrementally one by one instead of all in one batch the fm3 evolves from an empty rule set a one pass clustering algorithm is used to determine the number of rules and initial fuzzy sets in the rule antecedent part an online incremental linear svm is proposed to tune the rule consequent parameters to endow the fm3 with high generalization ability the use of incremental instead of batch svm enables the fm3 to handle online training problems with only one new sample available at a time for antecedent parameter learning a margin selected gradient descent algorithm is proposed to prevent overtraining simulation results and comparisons with svms and fuzzy classifiers with different learning algorithms demonstrate the advantage of the fm3

existence and derivation of optimal affine incentive schemes for stackelberg games with partial information a geometric approach through a geometric approach it is shown that a sufficiently large class of incentive stackelberg problems with perfect or partial dynamic information admits optimal incentive schemes that are affine in the available information as a byproduct of the analysis explicit expressions for these affine incentive schemes are obtained and the general results are applied to two different classes of stackelberg game problems with partial dynamic information

fast rate of formation of dead core for the heat equation with strong absorption and applications to fast blow up we consider the dead core problem for the semilinear heat equation with strong absorption ut uxx up with 0 p 1 and positive boundary values we investigate the dead core rate i e the rate at which the solution reaches its first zero surprisingly we find that the dead core rate is faster than the one given by the corresponding ode this stands in sharp contrast with known results for the related extinction quenching and blow up problems moreover we find that the dead core rate is actually quite unstable the ode rate can be recovered if the absorption term is replaced by a t x up for a suitable bounded uniformly positive function a t x

a self organizing ts type fuzzy network with support vector learning and its application to classification problems a self organizing takagi sugeno ts type fuzzy network with support vector learning sotfn sv is proposed in this paper the proposed sotfn sv is inspired by analysis of ts type fuzzy systems and composite kernel support vector machine svm sotfn sv is a fuzzy system constructed by the hybridization of fuzzy clustering and svm the antecedent part of sotfn sv is generated via fuzzy clustering of the input data and then svm is used to tune the consequent part parameters to give the network better generalization performance for demonstration sotfn sv is applied to several classification problems especially the skin color classification problem in the skin color classification application each color pixel is represented by hue and saturation hs color space to represent color information by histogram as accurately as possible a nonuniform partition of hs space is proposed for comparison svms and other fuzzy systems trained by svm or neural networks are applied to the same classification problems the advantages of sotfn sv are verified by comparisons with the results of these methods

pattern formation in a simple chemical system with general orders of autocatalysis and decay i stability analysis in this preliminary paper we introduce a mathematical model based on an autocatalytic reaction scheme with termination and general reaction orders rigorous stability analysis and numerical solutions are presented which illustrate that the problem can for certain parameter values admit a stable stationary pattern in the concentration of the autocatalyst and reactant this pattern forms at the rear of a permanent form travelling wave or pulse solution

a simple model for sustained oscillations in isothermal branched chain or autocatalytic reactions in a well stirred open system i stationary states and local stabilities the behaviour of a simple autocatalytic or branched chain reaction a b rightarrow 2b text rate k 1 ab coupled with a surface controlled decay of the catalyst b rightarrow c text rate k 2 b 1 rb is considered under isothermal well stirred open conditions the c s t r this system has a unique physically acceptable stationary state at any given residence time if the saturation term r is zero this solution is always stable although it may exhibit damped oscillatory responses characteristic of a stable focus small non zero values of r do not introduce qualitative changes however for sufficiently large surface effects such that r k 1 k 2 the stable focus may become unstable at a point of hopf bifurcation this leads to the appearance of sustained oscillations in the concentrations a and b for relatively stable catalysts such that k 2 is non zero but very small compared with k 1 a 0 where a 0 is the concentration of reactant a in the feed to the reactor the governing kinetic equations can be reduced to especially simple asymptotic forms these in turn allow the analytical determination of the point of hopf bifurcation in terms of the residence time t res at which the change in stability occurs numerical solution of the full equations reveals that the asymptotic expressions provide a very good prediction for the dependence of t res on k 1 a 0 k 2 and r even when k 2 approx k 1 a 0 systems which have some autocatalyst b in the feed show an important qualitative change at long residence times there is a second point of hopf bifurcation at which the focal stationary state becomes stable again oscillations die out at this point and in the limit of infinitely long residence times the behaviour approaches that of the corresponding closed system

optimal incentive strategy for leader follower games an optimal incentive strategy by which the leader suffers the least losses in punishing the follower s deviation from the decision desired by the leader is defined sufficient conditions for the existence of optimal incentive strategy are given static and dynamic leader follower games with quadratic cost functionals are investigated it is shown that leader follower games with quadratic cost functionals admit optimal incentive strategies under the follower s decision variable being scalar there exists a unique linear optimal incentive strategy such an incentive strategy can be explicitly determined

self adaptive neuro fuzzy inference systems for classification applications this paper presents a self adaptive neuro fuzzy inference system sanfis that is capable of self adapting and self organizing its internal structure to acquire a parsimonious rule base for interpreting the embedded knowledge of a system from the given training data set a connectionist topology of fuzzy basis functions with their universal approximation capability is served as a fundamental sanfis architecture that provides an elasticity to be extended to all existing fuzzy models whose consequent could be fuzzy term sets fuzzy singletons or functions of linear combination of input variables without a priori knowledge of the distribution of the training data set a novel mapping constrained agglomerative clustering algorithm is devised to reveal the true cluster configuration in a single pass for an initial sanfis construction estimating the location and variance of each cluster subsequently a fast recursive linear nonlinear least squares algorithm is performed to further accelerate the learning convergence and improve the system performance good generalization capability fast learning convergence and compact comprehensible knowledge representation summarize the strength of sanfis computer simulations for the iris wisconsin breast cancer and wine classifications show that sanfis achieves significant improvements in terms of learning convergence higher accuracy in recognition and a parsimonious architecture

the development of travelling waves in a simple isothermal chemical system iii cubic and mixed autocatalysis autocatalytic chemical reactions can support isothermal travelling waves of constant speed and form this paper extends previous studies to cubic autocatalysis and to mixed systems where quadratic and cubic autocatalyses occur concurrently aligned text a text b rightarrow 2 text b quad text rate k text q ab quad quad 1 text a 2 text b rightarrow 3 text b quad text rate k text c ab 2 quad quad 2 endaligned for pure cubic autocatalysis the wave has at large times a constant asymptotic speed v 0 where v 0 frac 1 sqrt 2 in the appropriate dimensionless units this result is confirmed by numerical investigation of the initial value problem perturbations to this stable wave speed decay at long times as t frac 3 2 e frac 1 8 t the mixed system is governed by a non dimensional parameter mu k text q k text c a 0 which measures the relative rates of transformation by quadratic and cubic modes in the mixed case mu neq 0 the reaction diffusion wave has a form appropriate to a purely cubic autocatalysis so long as mu lies between textstyle frac 1 2 and 0 when mu exceeds textstyle frac 1 2 the reaction wave loses its symmetrical form and all its properties steadily approach those of quadratic autocatalysis the value mu textstyle frac 1 2 is the value at which rates of conversion by the two paths are equal

the evolution of reaction diffusion waves in a class of scalar reaction diffusion equations algebraic decay rates in this paper we consider an initial boundary value problem for the generalized fisher kolmogorov petrovskii piscounov fkpp equation of order m 1 with the non negative initial data being of o x at large x dimensionless distance where 1 m 1 the corresponding problem when 1 m 1 having been considered in detail by needham and barnes nonlinearity 12 1999 41 58 using matched asymptotic expansions we are able to obtain the complete structure of the solution to the initial boundary value problem for large t time which exhibits the formation of a permanent form reaction diffusion travelling wave structure this being in contrast to the case when 1 m 1 where the large t time structure exhibits the formation of an accelerating phase wave

a study on reduced support vector machines recently the reduced support vector machine rsvm was proposed as an alternate of the standard svm motivated by resolving the difficulty on handling large data sets using svm with nonlinear kernels it preselects a subset of data as support vectors and solves a smaller optimization problem however several issues of its practical use have not been fully discussed yet for example we do not know if it possesses comparable generalization ability as the standard svm in addition we would like to see for how large problems rsvm outperforms svm on training time in this paper we show that the rsvm formulation is already in a form of linear svm and discuss four rsvm implementations experiments indicate that in general the test accuracy of rsvm are a little lower than that of the standard svm in addition for problems with up to tens of thousands of data if the percentage of support vectors is not high existing implementations for svm is quite competitive on the training time thus from this empirical study rsvm will be mainly useful for either larger problems or those with many support vectors experiments in this paper also serve as comparisons of 1 different implementations for linear svm and 2 standard svm using linear and quadratic cost functions

effect of rule weights in fuzzy rule based classification systems this paper examines the effect of rule weights in fuzzy rule based classification systems each fuzzy if then rule in our classification system has antecedent linguistic values and a single consequent class we use a fuzzy reasoning method based on a single winner rule in the classification phase the winner rule for a new pattern is the fuzzy if then rule that has the maximum compatibility grade with the new pattern when we use fuzzy if then rules with certainty grades the winner is determined as the rule with the maximum product of the compatibility grade and the certainty grade in this paper the effect of rule weights is illustrated by drawing classification boundaries using fuzzy if then rules with without certainty grades it is also shown that certainty grades play an important role when a fuzzy rule based classification system is a mixture of general rules and specific rules through computer simulations we show that comprehensible fuzzy rule based systems with high classification performance can be designed without modifying the membership functions of antecedent linguistic values when we use fuzzy if then rules with certainty grades

a maximizing discriminability based self organizing fuzzy network for classification problems a maximizing discriminability based self organizing fuzzy network mdsofn that can classify highly confusable patterns is proposed in this paper the underlying notion of the proposed mdsofn is to split the generation of fuzzy rules into linear discriminant analysis lda and gaussian mixture model gmm in lda the weights are updated by seeking directions that are efficient for discrimination in gmm parameter learning adopts the gradient descent method to reduce the cost function since lda derived fuzzy rules increase the discriminative capability among different classes the proposed mdsofn can classify highly confusable patterns the effectiveness of the proposed mdsofn is demonstrated by two classification problems a detailed comparative performance analysis for the fuzzy networks using lda principal component analysis pca and the support vector machine svm with various noise types is presented experimental results and theoretical analysis indicate that the lda derived fuzzy network performs better than the pca based fuzzy network and the svm based fuzzy network

quenching phenomena in strongly degenerate diffusion equations with strong absorption abstract we examine the degenerate parabolic equation u t u p u xx u q u 0 with boundary value u 1 in a bounded real interval where p 1 and q 1 p 1 when investigating the evolution of the dead core set u t 0 we find that the two regimes q p and q 1 p show completely different behavior finally we rule out the possibility of quenching in infinite time under certain assumptions on p q and the size of

on a singular initial boundary value problem for a reaction diffusion equation arising from a simple model of isothermal chemical autocatalysis in this paper we examine the evolution that occurs when a localized input of an autocatalyst b is introduced into an expanse of a reactant a the reaction is autocatalytic of order p so a rightarrow b at rate k a b p with rate constant k we examine the case when 0 p 1 with p geq 1 having been examined by needham merkin phil trans r soc lond a 337 261 274 1991 in particular we show that the fully reacted state is not achieved as t rightarrow infty via the propagation of a travelling wavefront as for p geq 1 but is approached uniformly in space as t rightarrow infty

uncorrelated fuzzy neighborhood preserving analysis based feature projection for driver drowsiness recognition driver drowsiness is reported as one of the main causal factors in many traffic accidents as it progressively impairs the driver s awareness about external events drowsiness detection can be approached through monitoring physiological signals while driving to correlate drowsiness with the change in the corresponding patterns of the electroencephalogram eeg electrooculogram eog and electrocardiogram ecg signals the main challenge in such an approach is to extract a set of features that can highly discriminate between the different drowsiness levels this paper proposes a new fuzzy neighborhood preserving analysis fnpa feature projection method that is used to extract the discriminant information relevant to the loss of attention caused by drowsiness unlike existing methods fnpa considers the fuzzy memberships of the input measurements into the different classes while constructing the graph laplacian thus it is able to identify both the discriminant and the geometrical structure of the input data while accounting for the overlapping nature of the drowsiness patterns furthermore in order to address the singularity problem that occurs in many real world problems the singular value decomposition svd and later the qr decomposition are utilized to extract a set of statistically uncorrelated features presenting the uncorrelated fnpa ufnpa in the current preliminary study with datasets collected from 31 subjects only while performing a driving simulation task the proposed method is capable of accurately classifying the drowsiness levels using a small number of features with an average accuracy of 93 on the other hand the possibility of developing a subject independent drowsiness recognition system is also investigated when the problem is converted into a binary classification task as imposed by the number of drowsiness levels exhibited by the drivers with accuracies ranging from 82 to 84

designing and learning of adjustable quasi triangular norms with applications to neuro fuzzy systems we introduce a new class of operators called quasi triangular norms they are denoted by h and parameterized by a parameter spl nu h a sub 1 a sub 2 a sub n spl nu from the construction of function h it follows that it becomes a t norm for spl nu 0 and a dual t conorm for spl nu 1 for spl nu close to 0 function h resembles a t norm and for spl nu close to 1 it resembles a t conorm in the paper we also propose adjustable quasi implications and a new class of neuro fuzzy systems most neuro fuzzy systems proposed in the past decade employ engineering implications defined by a t norm as the minimum or product in our proposition a quasi implication i a b spl nu varies from an engineering implication t a b to corresponding s implication as spl nu goes from 0 to 1 consequently the structure of neuro fuzzy systems presented in this work is determined in the process of learning learning procedures are derived and simulation examples are presented

support vector learning for fuzzy rule based classification systems to design a fuzzy rule based classification system fuzzy classifier with good generalization ability in a high dimensional feature space has been an active research topic for a long time as a powerful machine learning approach for pattern recognition problems the support vector machine svm is known to have good generalization ability more importantly an svm can work very well on a high or even infinite dimensional feature space this paper investigates the connection between fuzzy classifiers and kernel machines establishes a link between fuzzy rules and kernels and proposes a learning algorithm for fuzzy classifiers we first show that a fuzzy classifier implicitly defines a translation invariant kernel under the assumption that all membership functions associated with the same input variable are generated from location transformation of a reference function fuzzy inference on the if part of a fuzzy rule can be viewed as evaluating the kernel function the kernel function is then proven to be a mercer kernel if the reference functions meet a certain spectral requirement the corresponding fuzzy classifier is named positive definite fuzzy classifier pdfc a pdfc can be built from the given training samples based on a support vector learning approach with the if part fuzzy rules given by the support vectors since the learning process minimizes an upper bound on the expected risk expected prediction error instead of the empirical risk training error the resulting pdfc usually has good generalization moreover because of the sparsity properties of the svms the number of fuzzy rules is irrelevant to the dimension of input space in this sense we avoid the curse of dimensionality finally pdfcs with different reference functions are constructed using the support vector learning approach the performance of the pdfcs is illustrated by extensive experimental results comparisons with other methods are also provided

branches of positive and free boundary solutions for some singular quasilinear elliptic problems we study the existence and multiplicity of solutions strictly positive or nonnegative having a free boundary the boundary of the set where the solution vanishes of some one dimensional quasilinear problems of eigenvalue type with possibly singular nonlinear terms

an interval type 2 neural fuzzy classifier learned through soft margin minimization and its human posture classification application this paper proposes an interval type 2 neural fuzzy classifier learned through soft margin minimization it2nfc smm and applies it to human body posture classification the it2nfc smm consists of interval type 2 zero order takagi sugeno t s fuzzy rules established through online structure learning the antecedent part of the it2nfc smm uses interval type 2 fuzzy sets to decrease the number of rules and manage noisy data for parameter learning the consequent parameters are learned through a linear support vector machine svm for soft margin minimization to improve the generalization ability the proposed svm based learning addresses the problem that the orders of the fuzzy rules in computing the outputs of an interval type 2 fuzzy system depend on the consequent values that are unknown in advance to address this problem the it2nfc smm uses weighted bound set boundaries to simplify the type reduction operation and a novel crisp to interval linear svm learning algorithm based on the soft margin minimization the antecedent parameters are tuned using the gradient descent algorithm the it2nfc smm is applied to a vision based human body posture classification system the system uses two cameras and novel classification features extracted from a silhouette of the human body to classify the four postures of standing bending sitting and lying the classification performance of the it2nfc smm is verified through results in clean and noisy classification examples and through the posture classification problem as well as through comparisons with various type 1 and type 2 fuzzy classifiers the overall result shows that the it2nfc smm achieves higher classification rates with a smaller or similar model size than the classifiers used for comparison especially for noisy classification problems

existence and multiplicity results for a class of semilinear elliptic equations abstract we study the existence and multiplicity of nonnegative solutions as well as the behavior of corresponding parameter dependent branches to the equation u 1 u u m u n in a bounded domain r n endowed with the zero dirichlet boundary data where 0 m 1 and n 0 when 0 the obtained solutions can be seen as steady states of the corresponding reaction diffusion equation describing a model of isothermal autocatalytic chemical reaction with termination in addition to the main new results we formulate a few relevant conjectures

an interval type 2 neural fuzzy system for online system identification and feature elimination we propose an integrated mechanism for discarding derogatory features and extraction of fuzzy rules based on an interval type 2 neural fuzzy system nfs in fact it is a more general scheme that can discard bad features irrelevant antecedent clauses and even irrelevant rules high dimensional input variable and a large number of rules not only enhance the computational complexity of nfss but also reduce their interpretability therefore a mechanism for simultaneous extraction of fuzzy rules and reducing the impact of or eliminating the inferior features is necessary the proposed approach namely an interval type 2 neural fuzzy system for online system identification and feature elimination it2nfs sife uses type 2 fuzzy sets to model uncertainties associated with information and data in designing the knowledge base the consequent part of the it2nfs sife is of takagi sugeno kang type with interval weights the it2nfs sife possesses a self evolving property that can automatically generate fuzzy rules the poor features can be discarded through the concept of a membership modulator the antecedent and modulator weights are learned using a gradient descent algorithm the consequent part weights are tuned via the rule ordered kalman filter algorithm to enhance learning effectiveness simulation results show that it2nfs sife not only simplifies the system architecture by eliminating derogatory irrelevant antecedent clauses rules and features but also maintains excellent performance

design of natural classification kernels using prior knowledge a new class of kernels has been designed to enhance the usability of prior knowledge prior knowledge is shown to improve the generalization ability of kernel algorithms for binary classification problems the prior knowledge is expressed in natural language via fuzzy rules first the concepts of a fuzzy rule base and prior confidence region are proposed to formulate the prior knowledge then the new kernels which are referred to as natural classification kernels ncks are represented by fuzzy equivalence relations based on the formulation of prior knowledge an nck is interpreted as a measure of similarities between samples it is proven that ncks have two desired properties 1 transitivity with respect to the triangular norms and 2 the ability to provide higher similarities to spatially closer samples from the same class using transitivity a large number of ncks may be directly obtained by means of triangular norms additionally the theoretical results show that the second property makes it possible for the support vector machine svm and convex hull separation algorithm to generalize from training samples to test samples in the prior confidence region finally some synthetic datasets and a benchmark dataset are employed to validate the proposed approach

the formation of the dead core in parabolic reaction diffusion problems on donne des conditions pour l existence d une region a concentration de reactant nulle pour des problemes paraboliques non lineaires de reaction diffusion

a control theoretic view on incentives the idea of declaring a reward punishment for a decision maker according to his particular choice of action in order to induce certain desired behavior on the part of the decision maker is known as incentive threat this practice is age old however only in recent years have the notions been formalized in the development of a control theoretic view on incentives we first investigate the deterministic version of the incentive problem this reveals the basic simple idea behind the problem it also illustrates the different possibilities introduced by the presence of dynamics and multi follower nature of the problem this is followed by two variants of the stochastic version of the problem where we concentrate on the role of uncertainties relationship to economic literature is also discussed

three level incentive schemes using follower s strategies in differential games we deal with three level incentive differential games in which first and second leaders have access not only to slate information but also to information on follower s strategies we derive sufficient conditions for three level incentive schemes using information on follower s strategies in both linear and non linear differential games and show that three level incentive schemes using information on follower s strategies depend on an initial state value

asymptotic behavior of the solutions of the dead core problem u u pup 0 1 1 this equation originates from the study of a class of models for the reaction diffusion processes of a gas inside a chemical reactor 2 81 from the mathematical point of view the major interest of equation 1 1 lies in the competition of the linear diffusion and the nonlinear fast p 0 t 0 with initial and boundary conditions

the evolution of travelling waves in fractional order autocatalysis with decay ii the initial boundary value problem in this paper we examine an initial boundary value problem for a singular reaction diffusion equation arising from a model of isothermal chemical autocatalysis with termination we consider the case where the reaction and termination orders m and n respectively are fractional that is 0 0 k being a parameter which measures the relative strength of the termination step to that of the autocatalysis we show that solutions approach the equilibrium state 1 k for k 1 we demonstrate that the problem exhibits solutions which decay to zero with contracting support in finite t finally for m n we show that traveling waves with semi infinite support occ

support vector machines for histogram based image classification traditional classification approaches generalize poorly on image classification tasks because of the high dimensionality of the feature space this paper shows that support vector machines svm can generalize well on difficult image classification problems where the only features are high dimensional histograms heavy tailed rbf kernels of the form k x y e sup spl rho spl sigma sub i sup xia yia b with a spl les 1 and b spl les 2 are evaluated on the classification of images extracted from the corel stock photo collection and shown to far outperform traditional polynomial or gaussian radial basis function rbf kernels moreover we observed that a simple remapping of the input x sub i spl rarr x sub i sup a improves the performance of linear svm to such an extend that it makes them for this problem a valid alternative to rbf kernels

the evolution of travelling waves in fractional order autocatalysis with decay i permanent form travelling waves this paper considers a model isothermal autocatalytic reaction scheme with termination when the reaction orders m n are fractional i e 0 n and k in 0 k c where kc depends upon m and n it is further established that these wavefronts are of excitable rather than fisher kolmogorov type and have only semi infinite support that is the reaction is totally dormant ahead of the wavefront these features are in contrast to the case when m n geq 1 as studied by merkin needham and scott proc roy soc london ser a 424 1989 pp 187 209 merkin and needham j engrg math 23 1989 pp 343 356 and needham and merkin phil trans roy soc london ser a 337 1991 pp 261 274 it should be noted that the corresponding reaction diffusion equations are singular in the sense that the reaction and decay terms are not lipsch

an online self constructing neural fuzzy inference network and its applications a self constructing neural fuzzy inference network sonfin with online learning ability is proposed in this paper the sonfin is inherently a modified takagi sugeno kang tsk type fuzzy rule based model possessing neural network learning ability there are no rules initially in the sonfin they are created and adapted as online learning proceeds via simultaneous structure and parameter identification in the structure identification of the precondition part the input space is partitioned in a flexible way according to an aligned clustering based algorithm as to the structure identification of the consequent part only a singleton value selected by a clustering method is assigned to each rule initially afterwards some additional significant terms selected via a projection based correlation measure for each rule will be added to the consequent part incrementally as learning proceeds the combined precondition and consequent structure identification scheme can set up an economic and dynamically growing network a main feature of the sonfin in the parameter identification the consequent parameters are tuned optimally by either least mean squares or recursive least squares algorithms and the precondition parameters are tuned by a backpropagation algorithm to enhance the knowledge representation ability of the sonfin a linear transformation for each input variable can be incorporated into the network so that much fewer rules are needed or higher accuracy can be achieved

the evolution of traveling waves in a simple isothermal chemical system modeling quadratic autocatalysis with strong decay abstract in this paper we study a reaction diffusion system for an isothermal chemical reaction scheme governed by a quadratic autocatalytic step a b 2 b and a decay step b c where a b and c are the reactant the autocatalyst and the inner product respectively previous numerical studies and experimental evidences demonstrate that if the autocatalyst is introduced locally into this autocatalytic reaction system where the reactant a initially distributes uniformly in the whole space then a pair of waves will be generated and will propagate outwards from the initial reaction zone one crucial feature of this phenomenon is that for the strong decay case the formation of waves is independent of the amount of the autocatalyst b introduced into the system it is this phenomenon of kpp type which we would like to address in this paper to study the propagation of reactant and autocatalyst analytically we first use the tail behavior of waves to construct a pair of generalized super sub solutions for the approximate system of the autocatalytic reaction system note that the autocatalytic reaction system does not enjoy comparison principle together with a family of truncated problems we can establish the existence of a family of traveling waves with the minimal speed second we use this pair of generalized super sub solutions to show that the propagation of waves is fully determined by the rate of decay of the initial data at infinity in the sense of aronson weinberger formulation which in turn confirms the aforementioned numerical and experimental results

regularity for degenerate evolution equations with strong absorption abstract in this manuscript we study geometric regularity estimates for degenerate parabolic equations of p laplacian type 2 p under a strong absorption condition p u u t 0 u q in t 0 t where 0 q 1 this model is interesting because it yields the formation of dead core sets i e regions where non negative solutions vanish identically we shall prove sharp and improved parabolic c regularity estimates along the set f 0 u t u 0 t the free boundary where p p 1 q 1 1 p 1 some weak geometric and measure theoretical properties as non degeneracy positive density porosity and finite speed of propagation are proved as an application we prove a liouville type result for entire solutions a specific analysis for blow up type solutions will be done as well the results are new even for dead core problems driven by the heat operator

support vector learning mechanism for fuzzy rule based modeling a new approach this paper describes a fuzzy modeling framework based on support vector machine a rule based framework that explicitly characterizes the representation in fuzzy inference procedure the support vector learning mechanism provides an architecture to extract support vectors for generating fuzzy if then rules from the training data set and a method to describe the fuzzy system in terms of kernel functions thus it has the inherent advantage that the model does not have to determine the number of rules in advance and the overall fuzzy inference system can be represented as series expansion of fuzzy basis functions the performance of the proposed approach is compared to other fuzzy rule based modeling methods using four data sets

rule base self generation and simplification for data driven fuzzy models data driven fuzzy modeling has been used in a wide variety of applications however in fuzzy rule based models acquired from numerical data redundancy often exists in the form of redundant rules or similar fuzzy sets this results in unnecessary structural complexity and decreases the interpretability of the system in this paper a rule base self extraction and simplification method is proposed to establish interpretable fuzzy models from numerical data a fuzzy clustering technique associated with the proposed fuzzy partition validity index is used to extract the initial fuzzy rule base and find out the optimal number of fuzzy rules to reduce the complexity of fuzzy models while keeping good model accuracy some approximate similarity measures are presented and a parameter fine tuning mechanism is introduced to improve the accuracy of the simplified model using the proposed similarity measures the redundant fuzzy rules are removed and similar fuzzy sets are merged to create a common fuzzy set in the rule base the simplified rule base is computationally efficient and linguistically interpretable the approach has been successfully applied to fuzzy models of non linear function approximation dynamical system modeling and mechanical property prediction for hot rolled steels

support vector based fuzzy neural network for pattern classification fuzzy neural networks fnns for pattern classification usually use the backpropagation or c cluster type learning algorithms to learn the parameters of the fuzzy rules and membership functions from the training data however such kinds of learning algorithms usually cannot minimize the empirical risk training error and expected risk testing error simultaneously and thus cannot reach a good classification performance in the testing phase to tackle this drawback a support vector based fuzzy neural network svfnn is proposed for pattern classification in this paper the svfnn combines the superior classification power of support vector machine svm in high dimensional data spaces and the efficient human like reasoning of fnn in handling uncertainty information a learning algorithm consisting of three learning phases is developed to construct the svfnn and train its parameters in the first phase the fuzzy rules and membership functions are automatically determined by the clustering principle in the second phase the parameters of fnn are calculated by the svm with the proposed adaptive fuzzy kernel function in the third phase the relevant fuzzy rules are selected by the proposed reducing fuzzy rule method to investigate the effectiveness of the proposed svfnn classification it is applied to the iris vehicle dna satimage ijcnn1 datasets from the uci repository statlog collection and ijcnn challenge 2001 respectively experimental results show that the proposed svfnn for pattern classification can achieve good classification performance with drastically reduced number of fuzzy kernel functions

a ts type maximizing discriminability based recurrent fuzzy network for classification problems this work proposes a takagi sugeno ts type maximizing discriminability based recurrent fuzzy network mdrfn that can classify highly confusable patterns the discriminative capability plays a significant role in determining classification performance to increase the discriminative capability the proposed mdrfn considers minimum classification error mce and minimum training error mte in mce the weights are updated by maximizing the discrimination among different classes in mte the parameter learning adopts the gradient descent method to reduce the cost function therefore the novelty of mdrfn is that it not only minimizes the cost function but maximizes the discriminative capability as well the effectiveness of the proposed mdrfn is demonstrated by three temporal classification problems in the experiments other rfns including the singleton type recurrent neural fuzzy network srnfn ts type rfn trfn and simple rfn srfn are compared analysis results indicate that the proposed mdrfn exhibits excellent classification performance

three level stackelberg decision problems three level stackelberg decision problems are studied by using the inducible region concept through a systematic derivation it is identified that the leader s control has dual purposes which in general are not separable a special class of problems is then considered where explicit results are obtained

review lecture instabilities and oscillations in chemical reactions in closed and open systems this lecture is chiefly concerned with isothermal oscillations in homogeneous systems and with finding and validating self consistent models emphasis is laid on satisfying basic physical principles and on preserving chemical reasonableness in as simple a manner as possible the goal is to devise a scheme that can be applied to a wide variety of circumstances to predict new behaviour as well as to interpret what is known and to form a foundation for later developments and elaborations this core of the scheme called the autocatalator combines an autocatalytic step a 2b rightarrow 3b rate k 1 ab 2 with catalyst decay b rightarrow c rate k 2 b these core reactions may display reversibility and they may be accompanied by uncatalysed conversion a rightarrow b text rate k u a particular stress is given to the problem of closed systems in closed systems oscillations cannot be indefinitely sustained in former days it was customary to ignore this inconvenience and to repeal the law of conservation of matter today a less unsatisfactory account is possible

well posedness and qualitative behaviour of a semi linear parabolic cauchy problem arising from a generic model for fractional order autocatalysis in this paper we examine a semi linear parabolic cauchy problem with non lipschitz nonlinearity which arises as a generic form in a significant number of applications specifically we obtain a well posedness result and examine the qualitative structure of the solution in detail the standard classical approach to establishing well posedness is precluded owing to the lack of lipschitz continuity for the nonlinearity here existence and uniqueness of solutions is established via the recently developed generic approach to this class of problem meyer needham 2015 the cauchy problem for non lipschitz semi linear parabolic partial differential equations london mathematical society lecture note series vol 419 which examines the difference of the maximal and minimal solutions to the problem from this uniqueness result the approach of meyer needham allows for development of a comparison result which is then used to exhibit global continuous dependence of solutions to the problem on a suitable initial dataset the comparison and continuous dependence results obtained here are novel to this class of problem this class of problem arises specifically in the study of a one step autocatalytic reaction which is schematically given by a b at rate apbq where a and b are the concentrations of a and b respectively with 0 p q 1 and well posedness for this problem has been lacking up to the present

bifurcation diagrams of a p laplacian dirichlet problem with allee effect and an application to a diffusive logistic equation with predation abstract we study bifurcation diagrams of positive solutions for the p laplacian dirichlet problem p u x f u 0 1 x 1 u 1 u 1 0 f u u p 1 g u where p 1 p y y p 2 y p u is the one dimensional p laplacian 0 is a bifurcation parameter and g is of allee effect type assuming one suitable condition on g we prove that on the u plane the bifurcation diagram consists of exactly one continuous curve with exactly one turning point where the curve turns to the right hence the problem has at most two positive solutions for each 0 more precisely we are able to prove the exact multiplicity of positive solutions we give an application to a p laplacian diffusive logistic equation with predation of holling type ii functional response to this logistic equation with multiparameters more precisely we give a complete description of the structure of the bifurcation diagrams

general fuzzy min max neural network for clustering and classification this paper describes a general fuzzy min max gfmm neural network which is a generalization and extension of the fuzzy min max clustering and classification algorithms of simpson 1992 1993 the gfmm method combines supervised and unsupervised learning in a single training algorithm the fusion of clustering and classification resulted in an algorithm that can be used as pure clustering pure classification or hybrid clustering classification it exhibits a property of finding decision boundaries between classes while clustering patterns that cannot be said to belong to any of existing classes similarly to the original algorithms the hyperbox fuzzy sets are used as a representation of clusters and classes learning is usually completed in a few passes and consists of placing and adjusting the hyperboxes in the pattern space this is an expansion contraction process the classification results can be crisp or fuzzy new data can be included without the need for retraining while retaining all the interesting features of the original algorithms a number of modifications to their definition have been made in order to accommodate fuzzy input patterns in the form of lower and upper bounds combine the supervised and unsupervised learning and improve the effectiveness of operations a detailed account of the gfmm neural network its comparison with the simpson s fuzzy min max neural networks a set of examples and an application to the leakage detection and identification in water distribution systems are given

derivation of necessary and sufficient conditions for single stage stackelberg games via the inducible region concept the inducible region is defined as the collection of all the possible outcomes it is typically a subset of the entire decision space the best the leader can obtain is then the optimal outcome in this inducible region necessary and sufficient conditions are derived by first delineating the inducible region and then obtaining a leader s optimal strategy if it exists if not an e strategy always exists provided that the leader s stackelberg cost is bounded

short time behaviour of a singular solution to the heat equation with absorption on considere l evolution aux temps petits de l interface qui apparait dans le probleme aux limites u t u xx u p u o t 1 t 0 u x o 0 x 0 pour p 1 on construit une solution interieure d ordre zero consistante avec une interface mobile ou u est zero

regularity for the fully nonlinear dead core problem we establish new geometric regularity estimates for reaction diffusion equations with strong absorption terms the model is given by a fully nonlinear elliptic equation with measurable coefficients and a mu holder continuous convection term f x d 2u f u the lack of lipschitz regularity of the map u mapsto f u allows the existence of plateaus i e nonnegative solutions may vanish identically within an a priori unknown region the dead core of the solution we prove that at any touching ground point z in partial u 0 solutions are varkappa mu differentiable for a sharp value varkappa mu ge 2 and in fact varkappa 1 infty the proof is based on a new flatness improvement method we apply this new regularity estimate to establish a liouville type theorem for entire solutions to dead core problems and also to obtain measure estimates on the touching ground boundary the results obtained in this article are new even for dead core problems ruled by linear equations