single and multi peak solutions for a nonlinear maxwell schrodinger system with a general nonlinearity abstract for the following elliptic system in r 3 e 2 v v x v x v f v v 2 lim x x 0 we construct positive solutions u and which concentrate at several given isolated local minimum components of v as e 0 the potential v is a strictly positive continuous function and the nonlinearity f is subcritical near infinity and superlinear near zero and satisfies only the berestycki lions condition

design of decentralized critical observers for networks of finite state machines a formal method approach abstract motivated by safety critical applications in cyber physical systems in this paper we study the notion of critical observability and design of observers for networks of finite state machines fsms critical observability corresponds to the possibility of detecting if the current state of an fsm is in a given region of interest called set of critical states a critical observer detects on line the occurrence of critical states when a large scale network of fsms is considered the construction of such an observer is prohibitive because of the large computational effort needed we propose a decentralized architecture for critical observers of networks of fsms where on line detection of critical states is performed by local critical observers each associated with an fsm of the network which do not need to interact for the efficient design of decentralized critical observers we first extend on the fly algorithms traditionally used in the community of formal methods for the verification and control design of fsms we then extend to networks of fsms bisimulation theory traditionally given in the community of formal methods for single fsms the proposed techniques provide a remarkable computational complexity reduction as discussed throughout the paper and also demonstrated by means of illustrative examples

semiclassical solutions for choquard equations with berestycki lions type conditions abstract this paper is concerned with existence of multiple semiclassical states for a class of choquard equation under the classic berestycki lions type assumptions assumed on the nonlinearity we obtain multiplicity of semiclassical solutions for the equation by using a method of penalization argument we study further the concentration phenomena of such solutions and show that they converge to the least energy solutions of the associated limit problem as the parameter e goes to 0

multi peak solutions for nonlinear choquard equation in the plane in this paper we consider the nonlinear choquard equation in the plane with general nonlinearity satisfying berestycki lions condition by means of global penalization method we obtain the existence of multi peak solutions which concentrate near local minimal points of potential in this paper we consider the nonlinear choquard equation in the plane with general nonlinearity satisfying berestycki lions condition by means of global penalization method we obtain the existence of multi peak solutions which concentrate near local minimal points of potential

multiplicity results for some nonlinear schrodinger equations with potentials multiple semiclassical standing waves for a class of nonlinear schrodinger equations with potentials are found by means of a perturbative variational method

cross modal learning to rank via latent joint representation cross modal ranking is a research topic that is imperative to many applications involving multimodal data discovering a joint representation for multimodal data and learning a ranking function are essential in order to boost the cross media retrieval i e image query text or text query image in this paper we propose an approach to discover the latent joint representation of pairs of multimodal data e g pairs of an image query and a text document via a conditional random field and structural learning in a listwise ranking manner we call this approach cross modal learning to rank via latent joint representation cml 2 text r in cml 2 text r the correlations between multimodal data are captured in terms of their sharing hidden variables e g topics and a hidden topic driven discriminative ranking function is learned in a listwise ranking manner the experiments show that the proposed approach achieves a good performance in cross media retrieval and meanwhile has the capability to learn the discriminative representation of multimodal data

optimal sensor activation for diagnosing discrete event systems the problem of dynamic sensor activation for event diagnosis in partially observed discrete event systems is considered diagnostic agents are able to activate sensors dynamically during the evolution of the system sensor activation policies for diagnostic agents are functions that determine which sensors are to be activated after the occurrence of a trace of events the sensor activation policy must satisfy the property of diagnosability of centralized systems or codiagnosability of decentralized systems a policy is said to be minimal if there is no other policy with strictly less sensor activation that achieves diagnosability or codiagnosability to compute minimal policies we propose language partition methods that lead to efficient computational algorithms specifically we define window based language partitions for scalable algorithms to compute minimal policies by refining partitions one is able to refine the solution space over which minimal solutions are computed at the expense of more computation thus a compromise can be achieved between fineness of solution and complexity of computation

a survey on learning to hash nearest neighbor search is a problem of finding the data points from the database such that the distances from them to the query point are the smallest learning to hash is one of the major solutions to this problem and has been widely studied recently in this paper we present a comprehensive survey of the learning to hash algorithms categorize them according to the manners of preserving the similarities into pairwise similarity preserving multiwise similarity preserving implicit similarity preserving as well as quantization and discuss their relations we separate quantization from pairwise similarity preserving as the objective function is very different though quantization as we show can be derived from preserving the pairwise similarities in addition we present the evaluation protocols and the general performance analysis and point out that the quantization algorithms perform superiorly in terms of search accuracy search time cost and space cost finally we introduce a few emerging topics

semi classical ground states concentrating on the nonlinear potential for a dirac equation abstract we study the semi classical limit of the least energy solutions to the nonlinear dirac equation i e k 1 3 k k u a u p x u p 2 u for x r 3 since the dirac operator is unbounded from below and above the associate energy functional is strongly indefinite and since the problem is considered in the global space r 3 the palais smale condition is not satisfied new phenomena and mathematical interests arise in the use of the calculus of variations we prove that the equation has the least energy solutions for all e 0 small and additionally these solutions converge to the least energy solutions of the associate limit problem and concentrate to the maxima of the nonlinear potential p x in certain sense as e 0

singularly perturbed critical choquard equations abstract in this paper we study the semiclassical limit for the singularly perturbed choquard equation e 2 u v x u e 3 r 3 q y g u y x y d y q x g u in r 3 where 0 3 e is a positive parameter v q are two continuous real function on r 3 and g is the primitive of g which is of critical growth due to the hardy littlewood sobolev inequality under suitable assumptions on g we first establish the existence of ground states for the critical choquard equation with constant coefficients next we establish existence and multiplicity of semi classical solutions and characterize the concentration behavior by variational methods

concentrating standing waves for the gross pitaevskii equation in trapped dipolar quantum gases abstract we are concerned with the following singularly perturbed gross pitaevskii equation describing bose einstein condensation of trapped dipolar quantum gases e 2 u v x u 1 u 2 u 2 k u 2 u 0 in r 3 u 0 u h 1 r 3 where e is a small positive parameter 1 2 r denotes the convolution k x 1 3 cos 2 x 3 and x is the angle between the dipole axis determined by 0 0 1 and the vector x under certain assumptions on 1 2 r 2 we construct a family of positive solutions u e h 1 r 3 which concentrates around the local minima of v as e 0 our main results extend the results in j byeon and l jeanjean 2007 6 which dealt with singularly perturbed schrodinger equations with a local nonlinearity to the nonlocal gross pitaevskii type equation

a fast optimization method for general binary code learning hashing or binary code learning has been recognized to accomplish efficient near neighbor search and has thus attracted broad interests in recent retrieval vision and learning studies one main challenge of learning to hash arises from the involvement of discrete variables in binary code optimization while the widely used continuous relaxation may achieve high learning efficiency the pursued codes are typically less effective due to accumulated quantization error in this paper we propose a novel binary code optimization method dubbed discrete proximal linearized minimization dplm which directly handles the discrete constraints during the learning process specifically the discrete thus nonsmooth nonconvex problem is reformulated as minimizing the sum of a smooth loss term with a nonsmooth indicator function the obtained problem is then efficiently solved by an iterative procedure with each iteration admitting an analytical discrete solution which is thus shown to converge very fast in addition the proposed method supports a large family of empirical loss functions which is particularly instantiated in this paper by both a supervised and an unsupervised hashing losses together with the bits uncorrelation and balance constraints in particular the proposed dplm with a supervised ell 2 loss encodes the whole nus wide database into 64 b binary codes within 10 s on a standard desktop computer the proposed approach is extensively evaluated on several large scale data sets and the generated binary codes are shown to achieve very promising results on both retrieval and classification tasks

nonlinear scalar field equations with general nonlinearity abstract consider the nonlinear scalar field equation 0 1 u f u in r n u h 1 r n where n 3 and f satisfies the general berestycki lions conditions we are interested in the existence of positive ground states of nonradial solutions and in the multiplicity of radial and nonradial solutions very recently mederski 2017 made a major advance in that direction through the development in an abstract setting of a new critical point theory for constrained functionals in this paper we propose an alternative more elementary approach which permits to recover mederski s results on 0 1 the keys to our approach are an extension to the symmetric mountain pass setting of the monotonicity trick and a new decomposition result for bounded palais smale sequences

multi peak solution for nonlinear magnetic choquard type equation in this paper we study a class of nonlinear magnetic choquard type equation involving a magnetic potential and nonlocal nonlinearities by using the method of penalization argument we show that there exists a family of solutions having multiple concentration regions which are concentrate at the minimum points of potential v

existence and asymptotic behavior of vector solutions for coupled nonlinear kirchhoff type systems abstract this paper deals with the following linearly coupled nonlinear kirchhoff type system a 1 b 1 r 3 u 2 d x u 1 u f u v in r 3 a 2 b 2 r 3 v 2 d x v 2 v g v u in r 3 u v h 1 r 3 where a i 0 b i 0 i 0 are constants for i 1 2 0 is a parameter and f g c r r under the general berestycki lions type assumptions on f and g we establish the existence of positive vector solutions and positive vector ground state solutions respectively by using variational methods we also study the asymptotic behavior of these solutions as 0

minimization of communication of event occurrences in acyclic discrete event systems the problem of minimizing communication of event occurrences in systems modeled by finite state automata is considered there are n communicating agents observing the behavior of the system for purposes of control or diagnosis a set of communication policies for the agents is said to be minimal if communications of event occurrences cannot be removed without affecting the correctness of the solution under an assumption on the absence of cycles other than self loops in the system model an algorithm that computes a set of minimal communication policies in polynomial time in the number of states of the system is presented

existence and concentration of positive solutions for a quasilinear equation in rn abstract we study existence and concentration of positive solutions for quasilinear elliptic equations of the form e 2 u e 2 u 2 u v x u h u in r n n 3 as e 0 where the potential v r n r has a positive infimum and inf v inf v for some bounded domain in r n and h is a nonlinearity without some growth conditions such as ambrosetti rabinowitz

bilinear optimized product quantization for scalable visual content analysis product quantization pq has been recognized as a useful technique to encode visual feature vectors into compact codes to reduce both the storage and computation cost recent advances in retrieval and vision tasks indicate that high dimensional descriptors are critical to ensuring high accuracy on large scale data sets however optimizing pq codes with high dimensional data is extremely time consuming and memory consuming to solve this problem in this paper we present a novel pq method based on bilinear projection which can well exploit the natural data structure and reduce the computational complexity specifically we learn a global bilinear projection for pq where we provide both non parametric and parametric solutions the non parametric solution does not need any data distribution assumption the parametric solution can avoid the problem of local optima caused by random initialization and enjoys a theoretical error bound besides we further extend this approach by learning locally bilinear projections to fit underlying data distributions we show by extensive experiments that our proposed method dubbed bilinear optimization product quantization achieves competitive retrieval and classification accuracies while having significant lower time and space complexities

concentration phenomena for a class of fractional kirchhoff equations in rn with general nonlinearities abstract in this paper we study the following class of fractional kirchhoff problems e 2 s m e 2 s n u s 2 s u v x u f u in r n u h s r n u 0 in r n where e 0 is a small parameter s 0 1 n 2 s is the fractional laplacian v r n r is a positive continuous function m 0 r is a kirchhoff function satisfying suitable conditions and f r r fulfills berestycki lions type assumptions of subcritical or critical type using suitable variational arguments we prove the existence of a family of positive solutions u e which concentrates at a local minimum of v as e 0

on kirchhoff type equations with critical sobolev exponent abstract we study the following brezis nirenberg problem of kirchhoff type a b u 2 d x u u q 2 u u 2 u in u 0 on where r 4 is a bounded domain with the smooth boundary 2 q 4 and a b are positive parameters we obtain some new existence and nonexistence results depending on the values of the above parameters which improve some known results

hashing with angular reconstructive embeddings large scale search methods are increasingly critical for many content based visual analysis applications among which hashing based approximate nearest neighbor search techniques have attracted broad interests due to their high efficiency in storage and retrieval however existing hashing works are commonly designed for measuring data similarity by the euclidean distances in this paper we focus on the problem of learning compact binary codes using the cosine similarity specifically we proposed novel angular reconstructive embeddings are method which aims at learning binary codes by minimizing the reconstruction error between the cosine similarities computed by original features and the resulting binary embeddings furthermore we devise two efficient algorithms for optimizing our are in continuous and discrete manners respectively we extensively evaluate the proposed are on several large scale image benchmarks the results demonstrate that are outperforms several state of the art methods

multi peak solutions to kirchhoff equations in r3 with general nonlinearity abstract we are concerned with the existence of multi peak solutions to kirchhoff equation 0 1 2 a b r 3 u 2 d x u v x u f u x r 3 where 0 is a small parameter a b 0 are constants under general conditions of f we construct a family positive solutions u h 1 r 3 which concentrates around the isolated components of positive local minima of v as 0 our result generalize the previous results on single peak solutions to multi peak solutions

singularly perturbed elliptic problems with nonautonomous asymptotically linear nonlinearities abstract we consider a class of singularly perturbed elliptic problems with nonautonomous asymptotically linear nonlinearities the dependence on the spatial coordinates comes from the presence of a potential and of a function representing a saturation effect we investigate the existence of nontrivial nonnegative solutions concentrating around local minima of both the potential and of the saturation function necessary conditions to locate the possible concentration points are also given

concentration for a bi harmonic schrodinger equation with critical nonlinearity abstract this paper concerns the following fourth order problem 4 2 u v x u p x f u u 2 2 u x r n u x 0 as x where 2 2 n n 4 v and p are spatial distributions of external potentials by variational methods the concentration phenomena of the solutions as 0 is considered

a multi view embedding space for modeling internet images tags and their semantics this paper investigates the problem of modeling internet images and associated text or tags for tasks such as image to image search tag to image search and image to tag search image annotation we start with canonical correlation analysis cca a popular and successful approach for mapping visual and textual features to the same latent space and incorporate a third view capturing high level image semantics represented either by a single category or multiple non mutually exclusive concepts we present two ways to train the three view embedding supervised with the third view coming from ground truth labels or search keywords and unsupervised with semantic themes automatically obtained by clustering the tags to ensure high accuracy for retrieval tasks while keeping the learning process scalable we combine multiple strong visual features and use explicit nonlinear kernel mappings to efficiently approximate kernel cca to perform retrieval we use a specially designed similarity function in the embedded space which substantially outperforms the euclidean distance the resulting system produces compelling qualitative results and outperforms a number of two view baselines on retrieval tasks on three large scale internet image datasets

existence and symmetry of positive ground states for a doubly critical schrodinger system n n 2 and 1 1 satisfying 2 this problem is related to coupled nonlinear schrodinger equations with critical exponent for bose einstein condensate for different ranges of n and 0 we obtain positive ground state solutions via some quite different methods which are all radially symmetric it turns out that the least energy level depends heavily on the relations among and 2 besides for sufficiently small 0 positive solutions are also obtained via a variational perturbation approach note that the palais smale condition can not hold for any positive energy level which makes the study via variational methods rather complicated

bose fluids and positive solutions to weakly coupled systems with critical growth in dimension two abstract we prove using variational methods the existence in dimension two of positive vector ground states solutions for the bose einstein type systems u 1 u 1 u e u 2 1 v e u v 1 in v 2 v 2 v e v 2 1 u e u v 1 in u v h 0 1 where is a bounded smooth domain 1 2 1 the first eigenvalue of h 0 1 1 2 0 and is either positive small or large or negative small the nonlinear interaction between two bose fluids is assumed to be of critical exponential type in the sense of j moser for small solutions the system is asymptotically equivalent to the corresponding one in higher dimensions with power like nonlinearities

scalable similarity search with topology preserving hashing hashing based similarity search techniques is becoming increasingly popular in large data sets to capture meaningful neighbors the topology of a data set which represents the neighborhood relationships between its subregions and the relative proximities between the neighbors of each subregion e g the relative neighborhood ranking of each subregion should be exploited however most existing hashing methods are developed to preserve neighborhood relationships while ignoring the relative neighborhood proximities moreover most hashing methods lack in providing a good result ranking since there are often lots of results sharing the same hamming distance to a query in this paper we propose a novel hashing method to solve these two issues jointly the proposed method is referred to as topology preserving hashing tph tph is distinct from prior works by also preserving the neighborhood ranking based on this framework we present three different tph methods including linear unsupervised tph semisupervised tph and kernelized tph particularly our unsupervised tph is capable of mining semantic relationship between unlabeled data without supervised information extensive experiments on four large data sets demonstrate the superior performances of the proposed methods over several state of the art unsupervised and semisupervised hashing techniques

existence and concentration result for the kirchhoff type equations with general nonlinearities in this paper we study the existence and concentration behaviors of positive solutions to the kirchhoff type equations varepsilon 2 m left varepsilon 2 n int mathbf r n nabla u 2 mathrm d x right delta u v x u f u quad rm in mathbf r n quad u in h 1 mathbf r n n geqq 1 where m and v are continuous functions under suitable conditions on m and general conditions on f we construct a family of positive solutions u varepsilon varepsilon in 0 tilde varepsilon which concentrates at a local minimum of v after extracting a subsequence ek

the existence and concentration of positive solutions for a nonlinear schrodinger poisson system with critical growth we consider the schrodinger poisson system e2 u v x u x u f u u2 in r3 where the nonlinear term f is of critical growth in this paper we construct a solution u of the above elliptic system which concentrates at an isolated component of positive locally minimum points of v as 0 under certain conditions on f in particular the monotonicity of f s s3 and the so called ambrosetti rabinowitz condition are not required

learning discriminative binary codes for large scale cross modal retrieval hashing based methods have attracted considerable attention for efficient cross modal retrieval on large scale multimedia data the core problem of cross modal hashing is how to learn compact binary codes that construct the underlying correlations between heterogeneous features from different modalities a majority of recent approaches aim at learning hash functions to preserve the pairwise similarities defined by given class labels however these methods fail to explicitly explore the discriminative property of class labels during hash function learning in addition they usually discard the discrete constraints imposed on the to be learned binary codes and compromise to solve a relaxed problem with quantization to obtain the approximate binary solution therefore the binary codes generated by these methods are suboptimal and less discriminative to different classes to overcome these drawbacks we propose a novel cross modal hashing method termed discrete cross modal hashing dch which directly learns discriminative binary codes while retaining the discrete constraints specifically dch learns modality specific hash functions for generating unified binary codes and these binary codes are viewed as representative features for discriminative classification with class labels an effective discrete optimization algorithm is developed for dch to jointly learn the modality specific hash function and the unified binary codes extensive experiments on three benchmark data sets highlight the superiority of dch under various cross modal scenarios and show its state of the art performance

segregated and synchronized vector solutions to linearly coupled systems of schrodinger equations in this paper we study the following linearly coupled system e2 ui pi x ui ui3 j in ijuj ui h1 r3 i 1 n where e 0 is a small parameter pi x are positive potentials and ij ji 0 i j are coupling constants for i j 1 n we investigate the effect of potentials to the structure of the solutions more precisely we construct multi spikes solutions concentrating near the local maximum point x0i of pi x when x0i x0j pi x0i pj x0j a i j i j 1 n the components have spikes clustering at the same point as e 0 when x0i x0j i j the components have spikes clustering at the different points as e 0

optimal sensor selection for discrete event systems with partial observation for discrete event systems under partial observation we study the problem of selection of an optimal set of sensors that can provide sufficient yet minimal events observation information the sufficiency of the observed information is captured as the fulfillment of a desired formal property selection of sensors can be viewed as a selection of an observation mask and also of an equivalence class of events a sensor set is called optimal if any coarser selection of the corresponding equivalence class of events results in some significant loss of the events observation information we study an optimal selection of sensors over the set of general nonprojection observation masks we show that this problem is np hard in general for mask monotonic properties we present a top down and a bottom up algorithm each of polynomial complexity we show that observerness is not mask monotonic we show that the computational complexity can be further improved if the property is preserved under the projection via an intermediary observation mask that is an observer our results are obtained in a general setting so that they can be adapted for an optimal selection of sensors for a variety of applications

iterative quantization a procrustean approach to learning binary codes for large scale image retrieval this paper addresses the problem of learning similarity preserving binary codes for efficient similarity search in large scale image collections we formulate this problem in terms of finding a rotation of zero centered data so as to minimize the quantization error of mapping this data to the vertices of a zero centered binary hypercube and propose a simple and efficient alternating minimization algorithm to accomplish this task this algorithm dubbed iterative quantization itq has connections to multiclass spectral clustering and to the orthogonal procrustes problem and it can be used both with unsupervised data embeddings such as pca and supervised embeddings such as canonical correlation analysis cca the resulting binary codes significantly outperform several other state of the art methods we also show that further performance improvements can result from transforming the data with a nonlinear kernel mapping prior to pca or cca finally we demonstrate an application of itq to learning binary attributes or classemes on the imagenet data set

modeling the shape of the scene a holistic representation of the spatial envelope in this paper we propose a computational model of the recognition of real world scenes that bypasses the segmentation and the processing of individual objects or regions the procedure is based on a very low dimensional representation of the scene that we term the spatial envelope we propose a set of perceptual dimensions naturalness openness roughness expansion ruggedness that represent the dominant spatial structure of a scene then we show that these dimensions may be reliably estimated using spectral and coarsely localized information the model generates a multidimensional space in which scenes sharing membership in semantic categories e g streets highways coasts are projected closed together the performance of the spatial envelope model shows that specific information about object shape or identity is not a requirement for scene categorization and that modeling a holistic representation of the scene informs about its probable semantic category

singularly perturbed nonlinear dirichlet problems with a general nonlinearity let be a bounded domain in r n n 3 with a boundary c 2 we consider the following singularly perturbed nonlinear elliptic problem on e 2 u u f u 0 u 0 on u 0 on where the nonlinearity f is of subcritical growth under rather strong conditions on f it has been known that for small e 0 there exists a mountain pass solution u e of above problem which exhibits a spike layer near a maximum point of the distance function d from as e 0 in this paper we construct a solution u e of above problem which exhibits a spike layer near a maximum point of the distance function under certain conditions on f which we believe to be almost optimal

supervised matrix factorization hashing for cross modal retrieval the target of cross modal hashing is to embed heterogeneous multimedia data into a common low dimensional hamming space which plays a pivotal part in multimedia retrieval due to the emergence of big multimodal data recently matrix factorization has achieved great success in cross modal hashing however how to effectively use label information and local geometric structure is still a challenging problem for these approaches to address this issue we propose a cross modal hashing method based on collective matrix factorization which considers both the label consistency across different modalities and the local geometric consistency in each modality these two elements are formulated as a graph laplacian term in the objective function leading to a substantial improvement on the discriminative power of latent semantic features obtained by collective matrix factorization moreover the proposed method learns unified hash codes for different modalities of an instance to facilitate cross modal search and the objective function is solved using an iterative strategy the experimental results on two benchmark data sets show the effectiveness of the proposed method and its superiority over state of the art cross modal hashing methods

remarks on a brezis nirenberg s result in this note we revisit the equation with sobolev critical exponent which is firstly studied by brezis nirenberg in 4 p u u u p 2u u 2 2u in u h01 where rn is a bounded smooth domain n 3 2 0 r we show that for any m n there exists m 0 such that p has m solutions for any r 0 and every 0 m when n 4 0 we show that there is 0 0 such that problem p has a nontrivial solution for every 0 moreover we get multiple sign changing solutions for problem p

full space local topology extraction for cross modal retrieval with the ever increasing availability of various kinds of multimedia data cross modal retrieval which enables information retrieval from various types of data given various types of query has become a research hotspot hashing based techniques have been developed to solve this problem however most previous works cannot capture the shared underlying structure of real world multimodal data which degrades their retrieval performances in this paper we propose a novel hashing method based on the extraction of the common manifold structure shared among different feature spaces to faithfully represent the common structure two kinds of local topology information are exploited in our method local angles are incorporated within the extraction of local topology of each feature space which is then used to learn a common intermediate subspace after heterogeneous features being embedded into this subspace local similarities are exploited to extract the local topology between different feature spaces and learn compact hamming embeddings to facilitate cross modal retrieval the proposed method is referred to as full space local topology extraction for hashing extensive comparisons with other state of the art methods on three benchmark multimedia data sets demonstrate the superiority of our proposed method in terms of retrieval recall and search accuracy

singular perturbed kirchhoff type problem with critical exponent abstract in the present paper we consider the following kirchhoff type problem with critical exponent e 2 a e b r 3 u 2 d x u v x u f u in r 3 u h 1 r 3 by variational methods we show the existence of the positive solutions concentrating around global minima of the potential v x as e 0 we do not need the monotonicity of the function f 3

uniqueness and nondegeneracy of the ground state for a quasilinear schrodinger equation with a small parameter abstract we study least energy solutions of a quasilinear schrodinger equation with a small parameter we prove that the ground state is nondegenerate and unique up to translations and phase shifts using bifurcation theory

multiplicity of sign changing solutions for kirchhoff type equations abstract we are concerned with sign changing solutions to nonlocal perturbation of the nonlinear schrodinger equation in the whole r 3 by using the method of invariant sets of descending flow we prove the existence of multiple sign changing solutions provided the perturbation is sufficiently small

np completeness of sensor selection problems arising in partially observed discrete event systems we consider the three properties of diagnosability normality and observability of discrete event systems in each case we consider the problem of finding an observable event set with minimum cardinality such that the property under consideration holds we prove that these search problems are computationally hard by showing that the corresponding decision problems are np complete

positive solutions for the kirchhoff type problem involving general critical growth part i existence theorem involving general critical growth abstract in this paper we consider the following kirchhoff type problem a r 3 u 2 d x b r 3 u 2 d x u b u f u in r 3 u h 1 r 3 u 0 in r 3 where 0 is a parameter a b are positive constants and f reaches the critical growth without the ambrosetti rabinowitz condition we prove the existence of positive solutions for the kirchhoff type problem with a general critical nonlinearity we also study the asymptotics of solutions as 0 numerical solutions for related problems will be discussed in the second part

existence of semiclassical ground state solutions for a generalized choquard equation abstract in this paper we study a generalized quasilinear choquard equation e p p u v x u p 2 u e n r n q y f u y x y q x f u in r n where p is the p laplacian operator 1 p n v and q are two continuous real functions on r n 0 n f s is the primate function of f s and e is a positive parameter under suitable assumptions on p and f we establish a new concentration behavior of solutions for the quasilinear choquard equation by variational methods the results are also new for the semilinear case p 2

standing waves with a critical frequency for nonlinear schrodinger equations this paper is concerned with the existence and qualitative property of standing wave solutions for the nonlinear schrodinger equation with e being a critical frequency in the sense that we show that there exists a standing wave which is trapped in a neighbourhood of isolated minimum points of v and whose amplitude goes to 0 as moreover depending upon the local behaviour of the potential function v x near the minimum points the limiting profile of the standing wave solutions will be shown to exhibit quite different characteristic features this is in striking contrast with the non critical frequency case which has been extensively studied in recent years

semiclassical analysis for pseudo relativistic hartree equations abstract in this paper we study the semiclassical limit for the pseudo relativistic hartree equation e 2 m 2 u v u i u p u p 2 u in r n where m 0 2 p 2 n n 1 v r n r is an external scalar potential i x c n x n is a convolution kernel c n is a positive constant and n 1 p n n for n 3 p 2 our equation becomes the pseudo relativistic hartree equation with coulomb kernel

hashing on nonlinear manifolds learning based hashing methods have attracted considerable attention due to their ability to greatly increase the scale at which existing algorithms may operate most of these methods are designed to generate binary codes preserving the euclidean similarity in the original space manifold learning techniques in contrast are better able to model the intrinsic structure embedded in the original high dimensional data the complexities of these models and the problems with out of sample data have previously rendered them unsuitable for application to large scale embedding however in this paper how to learn compact binary embeddings on their intrinsic manifolds is considered in order to address the above mentioned difficulties an efficient inductive solution to the out of sample data problem and a process by which nonparametric manifold learning may be used as the basis of a hashing method are proposed the proposed approach thus allows the development of a range of new hashing techniques exploiting the flexibility of the wide variety of manifold learning approaches available it is particularly shown that hashing on the basis of t distributed stochastic neighbor embedding outperforms state of the art hashing methods on large scale benchmark data sets and is very effective for image classification with very short code lengths it is shown that the proposed framework can be further improved for example by minimizing the quantization error with learned orthogonal rotations without much computation overhead in addition a supervised inductive manifold hashing framework is developed by incorporating the label information which is shown to greatly advance the semantic retrieval performance

standing waves for nonlinear schrodinger equations with a general nonlinearity for elliptic equations e2 u v x u f u 0 x rn n 3 we develop a new variational approach to construct localized positive solutions which concentrate at an isolated component of positive local minimum points of v as e 0 under conditions on f which we believe to be almost optimal

on codiagnosability and coobservability with dynamic observations codiagnosability and coobservability in discrete event systems where observations are dynamic are considered instead of having a fixed set of observable events the observation of an event is dynamic trace dependent in this paper a procedure is developed to transform the problem of coobservability to the problem of codiagnosability in the context of dynamic observations this proves that problems of coobservability are transformable to problems of codiagnosability and enables us to leverage the large literature available for codiagnosability to solve problems of coobservability furthermore in the case of dynamic observations the known polynomial complexity tests for the property of codiagnosability based on verifier automata with fixed observable event set s are no longer directly applicable a new testing procedure is developed that can handle transition based dynamic observations and remains of polynomial complexity in the state space of the system this new testing procedure employs a covering of the state space of the system based on cluster automata which enhances its computational efficiency based on cluster automata a new type of verifier automaton is built called the c verifier for verification of codiagnosability as an application of the above mentioned transformation the c verifier becomes a unified method for verifying both codiagnosability and coobservability

minimizing the cardinality of an events set for supervisors of discrete event dynamical systems in this paper we study sufficient observation and work spaces for supervisors of a class of discrete event dynamical systems deds we use finite state automata to model a deds the finite automata generates a formal language defined over the set of events in the deds a supervisor is a feedback system that observes a generated trace of events and dynamically disables or enables a subset of controllable events such that the closed loop system behaves as desired we model the desired behavior of the deds by a sublanguage defined over the set of events a sufficient observation space is a collection of events whose observation by a supervisor is enough to realize a given desired behavior a sufficient work space is a sufficient observation space such that the control action of the supervisor is limited to only the controllable elements of the work space we construct algorithms to evaluate a sufficient work or observation space the reduction of work or observation spaces results in reducing the number of event detectors communication and command channels between the supervisor and the plant

on most permissive observers in dynamic sensor activation problems we consider the problem of dynamic sensor activation for fault diagnosis of discrete event systems modeled by finite state automata under the constraint that any fault must be diagnosed within no more than k 1 events after its occurrence a property called k diagnosability we begin by defining an appropriate notion of information state for the problem and defining dynamic versions of the projection operator and information state evolution we continue by showing that the problem can be reduced to that of state disambiguation then we define the most permissive observer mpo structure that contains all the solutions to the problem and we prove results showing that maintaining the k diagnosability property is equivalent to satisfying the extended specification of the state disambiguation problem we then prove a monotonicity property of the extended specification and show that this allows us to reduce our information state which in turn allows us to significantly reduce the complexity of our solution putting all of our results together we obtain a mpo with a size complexity of o 2 x k 2 x 2 e compared with o 2 x 2 k 2 e for the previous approach where x and e are respectively the sets of states and events of the automaton to diagnose finally we provide an algorithm for constructing the most permissive observer and demonstrate its scalability through simulation