stimulated facilitated diffusion when a substrate is transported through a membrane by means of diffusion and at the same time by means of a molecular carrier which itself is transported through the membrane by diffusion we speak of facilitated diffusion this is a well known transport mechanism which has been extensively studied 2 6 7 9 11 12 151 a classic example of facilitated diffusion is the transport of oxygen 0 through membranes filled with hemoglobin hb or myoglobin mb 7 h ere the presence of a carrier hb or mb may increase the flow of oxygen through the membrane considerably 7 hence the flux through the membrane may be quite sensitive to the concentration of carriers and to substances which affect this concentration thus it was observed that the presence of carbon dioxide co may affect the flux of o2 through a membrane containing hb carriers 8 however somewhat surprisingly it was observed that an appropriate concentration gradient of the co could actually enhance the flow of o2 through the membrane to the point of pushing the o2 through the membrane against an adverse pressure gradient in this paper we shall derive a few basic properties of the facilitated diffusion mechanism on the basis of the classical model for this mechanism 6 and we shall extend this model to incorporate the effect of coz and explain the anomaly described above in addition we shall derive the general shape of the concentration profiles for 02 hb and hboz the carrier oxygen complex inside the membrane both when co2 is absent and when it is present typical curves are given in fig 1 in our model the effect of the co is to cause an inhomogeneity inside the membrane which in turn leads to the possibility of the membrane acting as an oxygen pump formally the model resembles that used by thomas et al 5 111 to describe a membrane in which glucose can be transported against a concentration gradient

regularized kernel discriminant analysis with a robust kernel for face recognition and verification we propose a robust approach to discriminant kernel based feature extraction for face recognition and verification we show for the first time how to perform the eigen analysis of the within class scatter matrix directly in the feature space this eigen analysis provides the eigenspectrum of its range space and the corresponding eigenvectors as well as the eigenvectors spanning its null space based on our analysis we propose a kernel discriminant analysis kda which combines eigenspectrum regularization with a feature level scheme er kda finally we combine the proposed er kda with a nonlinear robust kernel particularly suitable for face recognition verification applications which require robustness against outliers caused by occlusions and illumination changes we applied the proposed framework to several popular databases yale ar xm2vts and achieved state of the art performance for most of our experiments

a hybrid iterative scheme for mixed equilibrium problems and fixed point problems the purpose of this paper is to investigate the problem of finding a common element of the set of solutions of a mixed equilibrium problem mep and the set of common fixed points of finitely many nonexpansive mappings in a real hilbert space first by using the well known kkm technique we derive the existence and uniqueness of solutions of the auxiliary problems for the mep second by virtue of this result we introduce a hybrid iterative scheme for finding a common element of the set of solutions of mep and the set of common fixed points of finitely many nonexpansive mappings furthermore we prove that the sequences generated by the hybrid iterative scheme converge strongly to a common element of the set of solutions of mep and the set of common fixed points of finitely many nonexpansive mappings

on a class of nonconvex equilibrium problems in this paper we introduce a new class of equilibrium problems known as nonconvex equilibrium problems we suggest some algorithms for solving nonconvex equilibrium problems by using the auxiliary principle technique the convergence of the proposed methods either requires partially relaxed strongly monotonicity or pseudomononicity we also introduce the concept of well posedness for the nonconvex equilibrium problems as special cases we obtain a number of known and new results for solving various classes of equilibrium and variational inequality problems our results can be considered a significant improvement of the previously known results

invex equilibrium problems in this paper we introduce a new class of equilibrium problems known as invex equilibrium problems in the setting of invexity this class of equilibrium problems includes equilibrium problems variational inequalities and variational like inequalities as special cases we use the auxiliary principle technique to suggest and analyze some iterative schemes for solving invex equilibrium problems and study the convergence criteria of these methods under some mild conditions we also consider the concept of well posedness for invex equilibrium problems our results represent significant and important refinements of the previously known results

on a predictor corrector method for solving invex equilibrium problems abstract in this paper we use the auxiliary principle technique in conjunction with the bregman function to suggest and analyze a predictor corrector method for solving invex equilibrium problems we also study the convergence criteria of this new method under some mild conditions we obtain as special cases new and known methods for solving variational like inequalities and equilibrium problems

mixed quasi variational inequalities in this paper we use the resolvent operator and auxiliary principle techniques to suggest and analyze several iterative algorithms for solving mixed quasi variational inequalities and related problems we study the convergence criteria of these algorithms under mild conditions we also study the global stability and existence of a unique solution of these quasi variational inequalities by using the dynamical systems approach our results represent refinement and improvement of the previously known results for variational inequalities

three step iterative algorithm for a system of set valued variational inclusions with h η monotone operators abstract in this paper we introduce and study a new system of set valued variational inclusions with h monotone operators we prove the convergence of a new three step iterative algorithm for this system of set valued variational inclusions the results in this paper extend and improve some known results from the literature

new approximation schemes for general variational inequalities in this paper we suggest and consider a class of new three step approximation schemes for general variational inequalities our results include ishikawa and mann iterations as special cases we also study the convergence criteria of these schemes

salient feature and reliable classifier selection for facial expression classification a novel facial expression classification fec method is presented and evaluated the classification process is decomposed into multiple two class classification problems a choice that is analytically justified and unique sets of features are extracted for each classification problem specifically for each two class problem an iterative feature selection process that utilizes a class separability measure is employed to create salient feature vectors sfvs where each sfv is composed of a selected feature subset subsequently two class discriminant analysis is applied on the sfvs to produce salient discriminant hyper planes sdhs which are used to train the corresponding two class classifiers to properly integrate the two class classification results and produce the fec decision a computationally efficient and fast classification scheme is developed during each step of this scheme the most reliable classifier is identified and utilized thus a more accurate final classification decision is produced the jaffe and the mmi databases are used to evaluate the performance of the proposed salient feature and reliable classifier selection sfrcs methodology classification rates of 96 71 and 93 61 are achieved under the leave one sample out evaluation strategy and 85 92 under the leave one subject out evaluation strategy

semi supervised dimension reduction using trace ratio criterion in this brief we address the trace ratio tr problem for semi supervised dimension reduction we first reformulate the objective function of the recent work semi supervised discriminant analysis sda in a tr form we also observe that in sda the low dimensional data representation f is constrained to be in the linear subspace spanned by the training data matrix x i e f xt w in order to relax this hard constraint we introduce a flexible regularizer f xt w 2 which models the regression residual into the reformulated objective function with such relaxation our method referred to as tr based flexible sda tr fsda can better cope with data sampled from a certain type of nonlinear manifold that is somewhat close to a linear subspace in order to address the non trivial optimization problem in tr fsda we further develop an iterative algorithm to simultaneously solve for the low dimensional data representation f and the projection matrix w moreover we theoretically prove that our iterative algorithm converges to the optimum based on the newton raphson method the experiments on two face databases one shape image database and one webpage database demonstrate that tr fsda outperforms the existing semi supervised dimension reduction methods

on iterative methods for equilibrium problems abstract in this paper we introduce a hybrid iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of finitely many nonexpansive mappings we prove that the approximate solution converges strongly to a solution of a class of variational inequalities under some mild conditions which is the optimality condition for some minimization problem we also give some comments on the results of plubtieng and punpaeng s plubtieng r punpaeng a general iterative method for equilibrium problems and fixed point problems in hilbert spaces j math anal appl 336 2007 455 469 results obtained in this paper may be viewed as an improvement and refinement of the previously known results in this area

approximation solvability of a class of nonlinear set valued variational inclusions involving a η monotone mappings abstract a new class of nonlinear set valued variational inclusions involving a monotone mappings in a hilbert space setting is introduced and then based on the generalized resolvent operator technique associated with a monotonicity the existence and approximation solvability of solutions using an iterative algorithm is investigated

co coercivity and its role in the convergence of iterative schemes for solving variational inequalities this paper stresses the role of co coercivity and related notions in the convergence of iterative schemes for solving monotone but not necessarily strongly or even strictly monotone variational inequalities the analysis will be conducted within the conceptual framework of the auxiliary problem principle

hemiequilibrium like problems abstract in this paper we introduce and consider a new class of equilibrium problems known as hemiequilibrium like problems this new class includes hemiequilibrium equilibrium like problems and several classes of variational inequalities as special cases a number of iterative methods for solving hemiequilibrium like problems are suggested and analyzed by using the auxiliary principle technique we also study the convergence analysis of these iterative methods under some mild conditions the results obtained in this paper can be considered as a novel application of the auxiliary principle technique

some characterizations of strongly preinvex functions in this paper a new class of generalized convex function is introduced which is called the strongly preinvex function we study some properties of strongly preinvex function in particular we establish the equivalence among the strongly preinvex functions strongly invex functions and strongly monotonicity under some suitable conditions as special cases one can obtain several new and previously known results for preinvex invex functions

a general framework for dimensionality reducing data visualization mapping in recent years a wealth of dimension reduction techniques for data visualization and preprocessing has been established nonparametric methods require additional effort for out of sample extensions because they provide only a mapping of a given finite set of points in this letter we propose a general view on nonparametric dimension reduction based on the concept of cost functions and properties of the data based on this general principle we transfer nonparametric dimension reduction to explicit mappings of the data manifold such that direct out of sample extensions become possible furthermore this concept offers the possibility of investigating the generalization ability of data visualization to new data points we demonstrate the approach based on a simple global linear mapping as well as prototype based local linear mappings in addition we can bias the functional form according to given auxiliary information this leads to explicit supervised visualization mappings with discriminative properties comparable to state of the art approaches

graph embedding and extensions a general framework for dimensionality reduction a large family of algorithms supervised or unsupervised stemming from statistics or geometry theory has been designed to provide different solutions to the problem of dimensionality reduction despite the different motivations of these algorithms we present in this paper a general formulation known as graph embedding to unify them within a common framework in graph embedding each algorithm can be considered as the direct graph embedding or its linear kernel tensor extension of a specific intrinsic graph that describes certain desired statistical or geometric properties of a data set with constraints from scale normalization or a penalty graph that characterizes a statistical or geometric property that should be avoided furthermore the graph embedding framework can be used as a general platform for developing new dimensionality reduction algorithms by utilizing this framework as a tool we propose a new supervised dimensionality reduction algorithm called marginal fisher analysis in which the intrinsic graph characterizes the intraclass compactness and connects each data point with its neighboring points of the same class while the penalty graph connects the marginal points and characterizes the interclass separability we show that mfa effectively overcomes the limitations of the traditional linear discriminant analysis algorithm due to data distribution assumptions and available projection directions real face recognition experiments show the superiority of our proposed mfa in comparison to lda also for corresponding kernel and tensor extensions

sensitivity analysis for parametric generalized implicit quasi variational like inclusions involving p η accretive mappings abstract in this paper using proximal point mapping technique of p accretive mapping and the property of the fixed point set of set valued contractive mappings we study the behavior and sensitivity analysis of the solution set of a parametric generalized implicit quasi variational like inclusion involving p accretive mapping in real uniformly smooth banach space further under suitable conditions we discuss the lipschitz continuity of the solution set with respect to the parameter the technique and results presented in this paper can be viewed as extension of the techniques and corresponding results given in r p agarwal y j cho n j huang sensitivity analysis for strongly nonlinear quasi variational inclusions appl math lett 13 2002 19 24 s dafermos sensitivity analysis in variational inequalities math oper res 13 1988 421 434 x p ding sensitivity analysis for generalized nonlinear implicit quasi variational inclusions appl math lett 17 2 2004 225 235 x p ding parametric completely generalized mixed implicit quasi variational inclusions involving h maximal monotone mappings j comput appl math 182 2 2005 252 269 x p ding c l luo on parametric generalized quasi variational inequalities j optim theory appl 100 1999 195 205 z liu l debnath s m kang j s ume sensitivity analysis for parametric completely generalized nonlinear implicit quasi variational inclusions j math anal appl 277 1 2003 142 154 r n mukherjee h l verma sensitivity analysis of generalized variational inequalities j math anal appl 167 1992 299 304 m a noor sensitivity analysis framework for general quasi variational inclusions comput math appl 44 2002 1175 1181 m a noor sensitivity analysis for quasivariational inclusions j math anal appl 236 1999 290 299 j y park j u jeong parametric generalized mixed variational inequalities appl math lett 17 2004 43 48

dimensionality reduction using similarity induced embeddings the vast majority of dimensionality reduction dr techniques rely on the second order statistics to define their optimization objective even though this provides adequate results in most cases it comes with several shortcomings the methods require carefully designed regularizers and they are usually prone to outliers in this paper a new dr framework that can directly model the target distribution using the notion of similarity instead of distance is introduced the proposed framework called similarity embedding framework sef can overcome the aforementioned limitations and provides a conceptually simpler way to express optimization targets similar to existing dr techniques deriving a new dr technique using the sef becomes simply a matter of choosing an appropriate target similarity matrix a variety of classical tasks such as performing supervised dr and providing out of sample extensions as well as new novel techniques such as providing fast linear embeddings for complex techniques are demonstrated in this paper using the proposed framework six data sets from a diverse range of domains are used to evaluate the proposed method and it is demonstrated that it can outperform many existing dr techniques

on the algorithmic implementation of multiclass kernel based vector machines in this paper we describe the algorithmic implementation of multiclass kernel based vector machines our starting point is a generalized notion of the margin to multiclass problems using this notion we cast multiclass categorization problems as a constrained optimization problem with a quadratic objective function unlike most of previous approaches which typically decompose a multiclass problem into multiple independent binary classification tasks our notion of margin yields a direct method for training multiclass predictors by using the dual of the optimization problem we are able to incorporate kernels with a compact set of constraints and decompose the dual problem into multiple optimization problems of reduced size we describe an efficient fixed point algorithm for solving the reduced optimization problems and prove its convergence we then discuss technical details that yield significant running time improvements for large datasets finally we describe various experiments with our approach comparing it to previously studied kernel based methods our experiments indicate that for multiclass problems we attain state of the art accuracy

incremental nonlinear dimensionality reduction by manifold learning understanding the structure of multidimensional patterns especially in unsupervised cases is of fundamental importance in data mining pattern recognition and machine learning several algorithms have been proposed to analyze the structure of high dimensional data based on the notion of manifold learning these algorithms have been used to extract the intrinsic characteristics of different types of high dimensional data by performing nonlinear dimensionality reduction most of these algorithms operate in a batch mode and cannot be efficiently applied when data are collected sequentially in this paper we describe an incremental version of isomap one of the key manifold learning algorithms our experiments on synthetic data as well as real world images demonstrate that our modified algorithm can maintain an accurate low dimensional representation of the data in an efficient manner

mixed equilibrium problems and optimization problems in this paper we introduce and analyze a new hybrid iterative algorithm for finding a common element of the set of solutions of mixed equilibrium problems and the set of fixed points of an infinite family of nonexpansive mappings furthermore we prove some strong convergence theorems for the hybrid iterative algorithm under some mild conditions we also discuss some special cases results obtained in this paper improve the previously known results in this area

on sufficiency of the kuhn tucker conditions if all the functions fo x f x f x are convex on c then these conditions are also sufficient various classes of functions have been defined for the purpose of weakening this limitation of convexity in mathematical programming mangasarian 11 has speculated that pseudo convexity of x and quasiconvexity off x are the weakest conditions that can be imposed so that the above conditions are sufficient for optimality it will be shown that there are other wide classes of functions for which the conditions are sufficient 545

iterative approximation of a solution of multi valued variational like inclusion in banach spaces a p η proximal point mapping approach in this paper we introduce a class of p accretive mappings an extension of m accretive mappings c e chidume k r kazmi h zegeye iterative approximation of a solution of a general variational like inclusion in banach spaces int j math math sci 22 2004 1159 1168 and p accretive mappings y p fang n j huang h accretive operators and resolvent operator technique for solving variational inclusions in banach spaces appl math lett 17 2004 647 653 in real banach spaces we prove some properties of p accretive mappings and give the notion of proximal point mapping termed as p proximal point mapping associated with p accretive mapping further using p proximal point mapping technique we prove the existence of solution and discuss the convergence analysis of iterative algorithm for multi valued variational like inclusions in real banach space the theorems presented in this paper extend and improve many known results in the literature

stacked denoising autoencoders learning useful representations in a deep network with a local denoising criterion we explore an original strategy for building deep networks based on stacking layers of denoising autoencoders which are trained locally to denoise corrupted versions of their inputs the resulting algorithm is a straightforward variation on the stacking of ordinary autoencoders it is however shown on a benchmark of classification problems to yield significantly lower classification error thus bridging the performance gap with deep belief networks dbn and in several cases surpassing it higher level representations learnt in this purely unsupervised fashion also help boost the performance of subsequent svm classifiers qualitative experiments show that contrary to ordinary autoencoders denoising autoencoders are able to learn gabor like edge detectors from natural image patches and larger stroke detectors from digit images this work clearly establishes the value of using a denoising criterion as a tractable unsupervised objective to guide the learning of useful higher level representations

a class of nonconvex functions and pre variational inequalities abstract a class of nonconvex functions is introduced called semi preinvex function which includes the classes of preinvex functions and arc connected convex functions the fritz john conditions of the mathematical programming problem are derived for these kinds of functions the pre variational inequality is given as a necessary condition and also a sufficient condition for a mathematical programming for invex functions the type i function related to unconstrained problems is given as an equivalent form of the pre variational inequality existence theorems for the solution of the pre variational inequality are also proved

on general hemiequilibrium problems in this paper we introduce and analyze a new class of equilibrium problems known as general hemiequilibrium problems it is shown that this class includes hemiequilibrium problems hemivariational inequalities and complementarity problems as special cases we use the auxiliary principle techniques to suggest some iterative type methods for solving multivalued hemiequilibrium problems we also analyze the convergence analysis of these new iterative methods under some mild conditions as special cases we obtain several new and known methods for solving variational inequalities and equilibrium problems

differentiable non convex functions and general variational inequalities abstract in this paper we introduce a new class of non convex functions which is called the g convex functions we prove that the minimum of the differentiable non convex functions on the non convex sets can be characterized by a class of variational inequalities which is called the general variational inequality essentially using the projection technique we establish the equivalence between the general variational inequalities and the fixed point problems as well as with the wiener hopf equations this equivalent formulation is used to suggest and analyze some iterative algorithms for solving the general variational inequalities we also discuss the convergence analysis of these iterative methods several special cases are also discussed

some aspects of variational inequalities abstract in this paper we provide an account of some of the fundamental aspects of variational inequalities with major emphasis on the theory of existence uniqueness computational properties various generalizations sensitivity analysis and their applications we also propose some open problems with sufficient information and references so that someone may attempt solution s in his her area of special interest we also include some new results which we have recently obtained

on invex sets and preinvex functions abstract in this paper we consider the class of the invex function introduced by hanson we show that under certain condition an invex function defined on an invex set a is preinvex on a similarly a quasiinvex function defined on an invex set a is pre quasiinvex

acquiring linear subspaces for face recognition under variable lighting previous work has demonstrated that the image variation of many objects human faces in particular under variable lighting can be effectively modeled by low dimensional linear spaces even when there are multiple light sources and shadowing basis images spanning this space are usually obtained in one of three ways a large set of images of the object under different lighting conditions is acquired and principal component analysis pca is used to estimate a subspace alternatively synthetic images are rendered from a 3d model perhaps reconstructed from images under point sources and again pca is used to estimate a subspace finally images rendered from a 3d model under diffuse lighting based on spherical harmonics are directly used as basis images in this paper we show how to arrange physical lighting so that the acquired images of each object can be directly used as the basis vectors of a low dimensional linear space and that this subspace is close to those acquired by the other methods more specifically there exist configurations of k point light source directions with k typically ranging from 5 to 9 such that by taking k images of an object under these single sources the resulting subspace is an effective representation for recognition under a wide range of lighting conditions since the subspace is generated directly from real images potentially complex and or brittle intermediate steps such as 3d reconstruction can be completely avoided nor is it necessary to acquire large numbers of training images or to physically construct complex diffuse harmonic light fields we validate the use of subspaces constructed in this fashion within the context of face recognition

pre invex functions in multiple objective optimization and called such functions convexlike if s is a convex set and if f is a convex function then clearly f is convexlike elster and nehse obtained a saddlepoint optimality condition for convexlike mathematical programs hayashi and komiya 9 also considered convexlike functions and developed a gordan type theorem of the alternative involving convexlike functions and in addition considered lagrangian duality for convexlike programs hanson 7 considered differentiable functions f s r for which there exists an n dimensional vector function q q u such that for all x u e s