witten s lectures on crumpling abstract crumpling is a distortion brought about by a strong compression of a surface in which energy condenses in extremely small regions rather than being stored uniformly scaling laws describe how much energy goes into how little space as crumpling of a sheet proceeds a network of ridges and vertices develops the precise nature of these geometrical singularities depends on the stretching and bending characteristics it is shown that for two dimensional surfaces in three dimensional space energy mainly condenses in stretching ridges the scaling arguments are put on a firm basis by using the mathematical description of an elastic membrane through the von karman equations and the universal properties of ridges are discussed from this theory one can understand that crumpling confers strength finally it is sketched how energy condensation and its scaling laws depend on the dimensions of the confined sheet and embedding space

initial value problems for the second order mixed monotone type of impulsive differential equations in banach spaces in this paper we use the coupled fixed point theorem for mixed monotone condensing operators to obtain an existence and uniqueness theorem of solutions of initial value problems for the second order mixed monotone type of impulsive differential equations and its application

the method of mixed monotony and first order differential systems on considere des problemes aux valeurs initiales et aux valeurs limites periodiques pour des equations differentielles d ordre 1 on developpe la methode de monotonie mixte pour etudier la construction de suites monotones qui converge vers la solution unique

existence and uniqueness of fixed points for some mixed monotone operators abstract in this paper we introduce the e concave convex operator without any compact or continuous assumptions we prove the existence and uniqueness of fixed points giving monotone iterative sequences for the unique fixed point for the operator finally we apply the results to an integral equation of polynomial type which possesses items of measurable functions

quasi solutions vector lyapunov functions and monotone method the notion of quasi solution which was introduced earlier has been developed in this paper further the notion of coupled quasi solutions and coupled maximal and minimal solutions has been introduced it is shown that the idea of quasi solutions leads to isolated subsystems and has obtained error estimates between solutions and quasi solutions also monotone iterative techniques have been developed to obtain coupled maximal and minimal quasi solutions

monotone method for equations describing transport phenomena in a banach space in this paper monotone methods have been developed for equations arising in transport processes in a banach space this method proves the existence of extremal solutions for such equations the advantage of the method for such type of equations is that the successive iterates are solutions of the corresponding initial value problems

existence and uniqueness of fixed points for mixed monotone operators with applications in this paper we study the uniqueness and existence of fixed points of mixed monotone operators in the partially ordered banach space our conclusions essentially improve the relevant results obtained by liang and others moreover as an application of our results we prove the existence and uniqueness of a positive solution for a class of integral equations which cannot be solved by using previously available methods

bayesian measures of model complexity and fit summary we consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined using an information theoretic argument we derive a measure pd for the effective number of parameters in a model as the difference between the posterior mean of the deviance and the deviance at the posterior means of the parameters of interest in general pd approximately corresponds to the trace of the product of fisher s information and the posterior covariance which in normal models is the trace of the hat matrix projecting observations onto fitted values its properties in exponential families are explored the posterior mean deviance is suggested as a bayesian measure of fit or adequacy and the contributions of individual observations to the fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages adding pd to the posterior mean deviance gives a deviance information criterion for comparing models which is related to other information criteria and has an approximate decision theoretic justification the procedure is illustrated in some examples and comparisons are drawn with alternative bayesian and classical proposals throughout it is emphasized that the quantities required are trivial to compute in a markov chain monte carlo analysis

on solvability of functional equations and system of functional equations arising in dynamic programming the purpose of this paper is to study solvability of two classes of functional equations and a class of system of functional equations arising in dynamic programming of multistage decision processes by using fixed point theorems a few existence and uniqueness theorems of solutions and iterative approximation for solving these classes of functional equations are established under certain conditions some existence theorems of coincidence solutions for the class of system of functional equations are shown some examples are given to demonstrate the advantage of our results than existing ones in the literature

coupled fixed points for mixed monotone condensing operators and an existence theorem of the solutions for a class of functional equations arising in dynamic programming abstract in this paper the existence and iterative approximation of coupled fixed points for mixed monotone condensing set valued operators are discussed the results presented here extend and improve the corresponding results of d guo and v lakshmikantham coupled fixed points of nonlinear operators 1 2 as an application we utilize the results obtained in section 2 to study the existence problem of solutions for a class of functional equations arising in dynamic programming

fixed points of discontinuous multivalued increasing operators in banach spaces with applications by using relatively weakly compactness conditions we obtain existence theorems of fixed points for discontinuous multivalued increasing operators in banach spaces as an application we utilize the results obtained in section 2 to lead to the existence principles for integral inclusions of hammerstein type multivalued maps

the principle and models of dynamic programming v in this article we introduce two new concepts namely dynamic geometry and dynamic pattern the former can be further developed in conjunction with computer graphics while the latter can be further developed in conjunction with the concept of dp in the sense of zelkowitz et al

on fixed point theorems of mixed monotone operators and applications abstract in this paper we obtain some new existence and uniqueness theorems of positive fixed point of mixed monotone operators in banach spaces partially ordered by a cone finally we apply the main theorem to a nonlinear parabolic partial differential equation some results are new even for increasing or decreasing operators

compensation of gaussian curvature in developable cones is local we use the angular deficit scheme v borrelli f cazals and j m morvan comput aided geom des 20 319 2003 to determine the distribution of gaussian curvature in developable cones d cones e cerda s chaieb f melo and l mahadevan nature london 401 46 1999 numerically these d cones are formed by pushing a thin elastic sheet into a circular container negative gaussian curvatures are identified at the rim where the sheet touches the container around the rim there are two narrow bands with positive gaussian curvatures the integral of the negative gaussian curvature near the rim is almost completely compensated by that of the two adjacent bands this suggests that the gauss bonnet theorem which constrains the integral of gaussian curvature globally does not explain the spontaneous curvature cancellation phenomenon t liang and t a witten phys rev e 73 046604 2006 the locality of the compensation seems to increase for decreasing d cone thickness the angular deficit scheme also provides a way to confirm the curvature cancellation phenomenon

asymptotic equivalence of bayes cross validation and widely applicable information criterion in singular learning theory in regular statistical models the leave one out cross validation is asymptotically equivalent to the akaike information criterion however since many learning machines are singular statistical models the asymptotic behavior of the cross validation remains unknown in previous studies we established the singular learning theory and proposed a widely applicable information criterion the expectation value of which is asymptotically equal to the average bayes generalization loss in the present paper we theoretically compare the bayes cross validation loss and the widely applicable information criterion and prove two theorems first the bayes cross validation loss is asymptotically equivalent to the widely applicable information criterion as a random variable therefore model selection and hyperparameter optimization using these two values are asymptotically equivalent second the sum of the bayes generalization error and the bayes cross validation error is asymptotically equal to 2 n where is the real log canonical threshold and n is the number of training samples therefore the relation between the cross validation error and the generalization error is determined by the algebraic geometrical structure of a learning machine we also clarify that the deviance information criteria are different from the bayes cross validation and the widely applicable information criterion

a monotone iterative scheme for nonlinear reaction diffusion systems having nonmonotone reaction terms abstract a monotone scheme is proposed for the solution of weakly coupled systems of reaction diffusion equations without any monotonicity property of the nonlinear reaction terms the considerations are taken within the framework of weak solutions

viscosity solutions of fully nonlinear parabolic systems abstract in this paper we discuss the viscosity solutions of the weakly coupled systems of fully nonlinear second order degenerate parabolic equations and their cauchy dirichlet problem we prove the existence uniqueness and continuity of viscosity solution by combining perron s method with the technique of coupled solutions the results here generalize those in proc london math soc 63 1991 212 240 and comm partial differential equations 16 1991 1095 1128

semiparametric regression of multidimensional genetic pathway data least squares kernel machines and linear mixed models we consider a semiparametric regression model that relates a normal outcome to covariates and a genetic pathway where the covariate effects are modeled parametrically and the pathway effect of multiple gene expressions is modeled parametrically or nonparametrically using least squares kernel machines lskms this unified framework allows a flexible function for the joint effect of multiple genes within a pathway by specifying a kernel function and allows for the possibility that each gene expression effect might be nonlinear and the genes within the same pathway are likely to interact with each other in a complicated way this semiparametric model also makes it possible to test for the overall genetic pathway effect we show that the lskm semiparametric regression can be formulated using a linear mixed model estimation and inference hence can proceed within the linear mixed model framework using standard mixed model software both the regression coefficients of the covariate effects and the lskm estimator of the genetic pathway effect can be obtained using the best linear unbiased predictor in the corresponding linear mixed model formulation the smoothing parameter and the kernel parameter can be estimated as variance components using restricted maximum likelihood a score test is developed to test for the genetic pathway effect model variable selection within the lskm framework is discussed the methods are illustrated using a prostate cancer data set and evaluated using simulations

fixed points for mixed monotone multivalued operators in banach spaces with applications abstract in this paper the existence and iterative approximation of fixed points for a class of systems of mixed monotone multivalued operator are discussed we present some new fixed point theorems of mixed monotone operators and increasing operators which need not be continuous or satisfy a compactness condition we also give some applications to differential inclusions with discontinuous right hand side in banach spaces and to hammerstein integral inclusions on r n

fixed point theorems for mixed monotone operators and applications to integral equations abstract the purpose of this paper is to present some coupled fixed point theorems for a mixed monotone operator in a complete metric space endowed with a partial order by using altering distance functions we also present an application to integral equations

multidimensional fixed point theorems under ψ φ contractive conditions in partially ordered complete metric spaces in this paper we study the existence and uniqueness of coincidence points for nonlinear mappings of any number of arguments under a weak contractive condition our results generalize extend and unify several classical and very recent related results in the literature see aydi et al 2011 berinde 2010 gnana bhaskar and lakshmikantham 2006 berzig and samet 2012 borcut and berinde 2012 choudhury et al 2011 karapinar and luong 2012 lakshmikantham and iric 2009 luong and thuan 2011 roldan 2012

multidimensional coincidence point results for compatible mappings in partially ordered fuzzy metric spaces in recent times coupled tripled and quadruple fixed point theorems have been intensively studied by many authors in the context of partially ordered complete metric spaces using different contractivity conditions roldan et al showed a unified version of these results for nonlinear mappings in any number of variables which were not necessarily permuted or ordered introducing the notion of multidimensional coincidence point very recently choudhury et al proved coupled coincidence point results in the context of fuzzy metric spaces in the sense of george and veeramani in this paper using the idea of coincidence point for nonlinear mappings in any number of variables we study a fuzzy contractivity condition to ensure the existence of coincidence points in the framework of fuzzy metric spaces provided with hadzic type t norms then we present an illustrative example in which our methodology leads to the existence of coincidence points but previous theorems cannot be applied

existence theorems of solutions for certain classes of functional equations arising in dynamic programming in this paper we study the existence uniqueness and iterative approximation of solutions for certain classes of functional equations arising in dynamic programming of multistage decision processes the results presented here generalize improve and unify the corresponding results of other authors

fixed point theorems of φ concave ψ convex mixed monotone operators and applications abstract in this paper concave convex operators are introduced and some new existence and uniqueness theorems of fixed points of mixed monotone operators with such concavity and convexity are obtained moreover some applications to nonlinear integral equations on bounded or unbounded regions are given

fixed point theorems for generalized contractions in partially ordered metric spaces with semi monotone metric abstract in this paper we study the existence and uniqueness of coupled fixed points for mixed monotone mappings in partially ordered metric spaces with semi monotone metric as an application we prove the existence and uniqueness of the solution for a first order differential equation with periodic boundary conditions

coupled fixed points of nonlinear operators with applications a partir de quasi solutions couplees des problemes aux valeurs initiales pour des equations differentielles ordinaires on introuit le concept de points fixes couples abstraits pour certains operateurs on donne des theoremes d existence

fixed points of generalized e concave generalized e convex operators and their applications in this paper we present the definitions of generalized e concave operators and generalized e convex operators which are the generalizations of e concave operators and e convex operators respectively without compactness or continuity assumption of generalized e concave operators and generalized e convex operators we have proved the existence uniqueness and monotone iterative techniques of their fixed points our results are even new to e concave operators and e convex operators finally we apply the results to the singular boundary value problems for second order differential equations

new fixed point theorems for mixed monotone operators and local existence uniqueness of positive solutions for nonlinear boundary value problems abstract in this article we present a new fixed point theorem for a class of general mixed monotone operators which extends the existing corresponding results moreover we establish some pleasant properties of nonlinear eigenvalue problems for mixed monotone operators based on them the local existence uniqueness of positive solutions for nonlinear boundary value problems which include neumann boundary value problems three point boundary value problems and elliptic boundary value problems for lane emden fowler equations is proved the theorems for nonlinear boundary value problems obtained here are very general

monotone iterative techniques of v lakshmikantham for a boundary value problem for systems of impulsive differential difference equations by means of the monotone iterative techniques of v lakshmikantham a couple of minimal and maximal quasisolutions of a two point boundary value problem for a system of impulsive differential difference equations are constructed

iterative method for coupled quasi solutions of mixed monotone operator equations in this paper we obtain some new existence theorems of the coupled quasi fixed points for mixed monotone operators under more general conditions our results improve and extend many well known results finally we apply our results to hammerstein integral equations

scaling properties of randomly folded plastic sheets we study the scaling properties of randomly folded aluminum sheets of different thicknesses h and widths l we found that the fractal dimension d 2 30 0 01 and the force scaling exponent delta 0 21 0 02 are independent of the sheet thickness and close to those obtained in numerical simulations with a coarse grained model of triangulated self avoiding surfaces with bending and stretching rigidity so our findings suggest that finite bending rigidity and self avoidance play the predominant roles in the scaling behavior of randomly folded plastic sheets

iterative method for solutions and coupled quasi solutions of nonlinear integro differential equations of mixed type in banach spaces we consider in this paper the existence of solutions coupled minimal and maximal quasi solutions and iterative approximation of the unique solution for the following initial value problems ivp of the nonlinear integro di erential equations of mixed type in ordered banach spaces e u f t u u tu su t i u t0 x0 1 where i t0 t0 a a 0 x0 e f c i e e e e e and

bhaskar guo lakshmikantam ciric type results via new functions with applications to integral equations abstract in this paper by using the c class functions we present some coupled coincidence point results for a pair of mappings satisfying generalized weakly contractive condition in the context of ordered b metric spaces also an application to study the existence of solutions for the nonlinear integral equations and example are given to support our theoretical results

a note on the theorem of lakshmikantham and leela we study the initial value problem u f t u u 0 u 0 in a real banach space using the fixed point principle of daher and the theorem of monch and von harten we obtain a theorem which is an extension of that established by lakshmikantham and leela in 1

existence theorems of coupled fixed points abstract by associating with a mixed monotone operator a monotone operator on product space several existence theorems of coupled fixed points are proved

monotone iterative technique for differential equations in a banach space iffis continuous steps i and iii are standard and straightforward it is step ii that deserves attention this in turn leads to three possibilities namely to show that the sequence of approximate solutions is a a cauchy sequence b relatively compact so that one can appeal to ascoli s theorem and c a monotone sequence in a cone the first two possibilities are well known and are discussed in 2 31 this paper is devoted to the investigation of c which leads to the development of a monotone iterative technique in an arbitrary cone

bayesian varying coefficient kernel machine regression to assess neurodevelopmental trajectories associated with exposure to complex mixtures exposure to environmental mixtures can exert wide ranging effects on child neurodevelopment however there is a lack of statistical methods that can accommodate the complex exposure response relationship between mixtures and neurodevelopment while simultaneously estimating neurodevelopmental trajectories we introduce bayesian varying coefficient kernel machine regression bvckmr a hierarchical model that estimates how mixture exposures at a given time point are associated with health outcome trajectories the bvckmr flexibly captures the exposure response relationship incorporates prior knowledge and accounts for potentially nonlinear and nonadditive effects of individual exposures this model assesses the directionality and relative importance of a mixture component on health outcome trajectories and predicts health effects for unobserved exposure profiles using contour plots and cross sectional plots bvckmr also provides information about interactions between complex mixture components the bvckmr is applied to a subset of data from progress a prospective birth cohort study in mexico city on exposure to metal mixtures and temporal changes in neurodevelopment the mixture include metals such as manganese arsenic cobalt chromium cesium copper lead cadmium and antimony results from a subset of programming research in obesity growth environment and social stressors data provide evidence of significant positive associations between second trimester exposure to copper and bayley scales of infant and toddler development cognition score at 24 months and cognitive trajectories across 6 24 months we also detect an interaction effect between second trimester copper and lead exposures for cognition at 24 months in summary bvckmr provides a framework for estimating neurodevelopmental trajectories associated with exposure to complex mixtures

fixed point theorems for a class of mixed monotone operators with applications abstract in this paper we provide several unique existence theorems for fixed points for mixed monotone operators without continuity and compactness and apply them to study a class of integral equations

mixed monotone iterative technique for a class of semilinear impulsive evolution equations in banach spaces abstract this paper deals with the existence of mild l quasi solutions to the initial value problem for a class of semilinear impulsive evolution equations in an ordered banach space e under a new concept of upper and lower solutions a new monotone iterative technique on the initial value problem of impulsive evolution equations has been established the results improve and extend some relevant results in ordinary differential equations and partial differential equations an example is also given

effect of ridge ridge interactions in crumpled thin sheets we study whether and how the energy scaling based on the single ridge approximation is revised in an actual crumpled sheet namely in the presence of ridge ridge interactions molecular dynamics simulation is employed for this purpose in order to improve the data quality modifications are introduced to the common protocol as crumpling proceeds we find that the average storing energy changes from being proportional to one third of the ridge length to a linear relation while the ratio of bending and stretching energies decreases from 5 to 2 the discrepancy between previous simulations and experiments on the material dependence for the power law exponent is resolved we further determine the average ridge length to scale as 1 d 1 3 the ridge number as d 2 3 and the average storing energy per unit ridge length as d 0 881 where d denotes the volume density of the crumpled ball these results are accompanied by experimental proofs and are consistent with mean field predictions finally we extend the existent simulations to the high pressure region and verify the existence of a scaling relation that is more general than the familiar power law at covering the whole density range