on witten s proof of the positive energy theorem this paper gives a mathematically rigorous proof of the positive energy theorem using spinors this completes and simplifies the original argument presented by edward witten we clarify the geometric aspects of this argument and prove the necessary analytic theorems concerning the relevant dirac operator

on the invariant mass conjecture in general relativity an asymptotic symmetries theorem is proved under certain hypotheses on the behaviour of the metric at spatial infinity this implies that the einstein von freud adm mass can be invariantly assigned to an asymptotically flat four dimensional end of an asymptotically empty solution of einstein equations if the metric is a no radiation metric or if the end is defined in terms of a collection of boost type domains

cauchy problems of semilinear pseudo parabolic equations abstract this paper concerns with the cauchy problems of semilinear pseudo parabolic equations after establishing the necessary existence uniqueness and comparison principle for mild solutions which are also classical ones provided that the initial data are appropriately smooth we investigate large time behavior of solutions it is shown that there still exist the critical global existence exponent and the critical fujita exponent for pseudo parabolic equations and that these two critical exponents are consistent with the corresponding semilinear heat equations

positivity of the bondi energy we give a new proof that the bondi momentum is time like and future directed this is done by extending a theorem showing the existence of solutions of witten s equation on a complete asymptotically flat surface to the case where the surface is asyptotically hyperbolic and spans a cut s of i by choosing appropriate boundary conditions the positivity of the bondi energy is also shown for the case where the surface is no longer free of inner boundaries but is internally bounded by the union of a finite number of marginally trapped surfaces this argument also applies to the case of asymptotically flat surfaces

a strictly positive mass theorem we show that the adm 4 momentum of an isolated gravitational system spatially asymptotically flat spacetime satisfying the dominant energy condition cannot be null like unless it is flat together with the positive mass theorem this implies that the adm 4 momentum of an isolated gravitational system must be strictly time like

global existence nonexistence and asymptotic behavior of solutions for the cauchy problem of semilinear heat equations abstract in this paper we study the cauchy problem of semilinear heat equations by introducing a family of potential wells we first prove the invariance of some sets and isolating solutions then we obtain a threshold result for the global existence and nonexistence of solutions finally we discuss the asymptotic behavior of the solution

kernelized locality sensitive hashing fast retrieval methods are critical for many large scale and data driven vision applications recent work has explored ways to embed high dimensional features or complex distance functions into a low dimensional hamming space where items can be efficiently searched however existing methods do not apply for high dimensional kernelized data when the underlying feature embedding for the kernel is unknown we show how to generalize locality sensitive hashing to accommodate arbitrary kernel functions making it possible to preserve the algorithm s sublinear time similarity search guarantees for a wide class of useful similarity functions since a number of successful image based kernels have unknown or incomputable embeddings this is especially valuable for image retrieval tasks we validate our technique on several data sets and show that it enables accurate and fast performance for several vision problems including example based object classification local feature matching and content based retrieval

existence theorem for solutions of witten s equation and nonnegativity of total mass we prove that given an asymptotically flat in a very weak sense initial data set there always exists a spinor field that satisfies witten s equation and that becomes constant at infinity thus we fill a gap in witten s arguments on the nonnegativity of the total mass of an isolated system when measured at spatial infinity we also include a review of witten s argument

addendum to global existence and finite time blow up for a class of semilinear pseudo parabolic equations j func anal 264 12 2013 2732 2763 abstract in this remark we correct the proof of the asymptotic behavior of solution for the initial boundary value problem of semilinear pseudo parabolic equations with critical initial energy obtained in xu and su 2013 1

critical and sup critical initial energy finite time blowup phenomena for the fourth order wave equations with nonlinear strain term abstract this paper is devoted to the blowup phenomena for a class of fourth order wave equation with nonlinear strain term first for the model equation with strain structure we prove the finite time blowup of solution for the critical initial energy i e e 0 d then the finite time blowup and the upper bound of the blowup time are established for the sup critical initial energy i e e 0 0

a weakly nonlinear analysis of elasto plastic microstructure models at certain critical values of the hardening modulus the governing equations of elasto plastic flow may lose their hyperbolicity and exhibit two modes of ill posedness shear band and flutter ill posedness these modes of ill posedness are characterized by the uncontrolled growth of modes at infinitely fine scales which ultimately violates the continuum assumption in previous work l an and a peirce siam j appl math 54 1994 pp 708 730 a continuum model accounting for microscale deformations was built linear analysis demonstrated the regularizing effect of the microstructure and provided a relationship between the width of the localized instabilities and the microlength scale in this paper a weakly nonlinear analysis is used to explore the immediate post critical behavior of the solutions for both one dimensional and anti plane shear models post critical deformations in the plastic regions are shown to be governed by the boussinesq equation one of the completely integrable pdes having so

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

global existence and blow up of solution for semilinear hyperbolic equation with logarithmic nonlinearity abstract in this paper we consider the semilinear wave equation with logarithmic nonlinearity by modifying and using potential well combined with logarithmic sobolev inequality we derive the global existence and infinite time blow up of the solution at low energy level e 0 d then these results are extended in parallel to the critical case e 0 d besides with additional assumptions on initial data the infinite time blow up result is given with arbitrary positive initial energy e 0 0

distributed adaptive binary quantization for fast nearest neighbor search hashing has been proved an attractive technique for fast nearest neighbor search over big data compared with the projection based hashing methods prototype based ones own stronger power to generate discriminative binary codes for the data with complex intrinsic structure however existing prototype based methods such as spherical hashing and k means hashing still suffer from the ineffective coding that utilizes the complete binary codes in a hypercube to address this problem we propose an adaptive binary quantization abq method that learns a discriminative hash function with prototypes associated with small unique binary codes our alternating optimization adaptively discovers the prototype set and the code set of a varying size in an efficient way which together robustly approximate the data relations our method can be naturally generalized to the product space for long hash codes and enjoys the fast training linear to the number of the training data we further devise a distributed framework for the large scale learning which can significantly speed up the training of abq in the distributed environment that has been widely deployed in many areas nowadays the extensive experiments on four large scale up to 80 million data sets demonstrate that our method significantly outperforms state of the art hashing methods with up to 58 84 performance gains relatively

the isometry groups of asymptotically flat asymptotically empty space times with timelike adm four momentum we give a complete classification of all connected isometry groups together with their actions in the asymptotic region in asymptotically flat asymptotically vacuum space times with timelike adm four momentum

evolutionary compact embedding for large scale image classification effective dimensionality reduction is a classical research area for many large scale analysis tasks in computer vision several recent methods attempt to learn either graph embedding or binary hashing for fast and accurate applications in this paper we propose a novel framework to automatically learn the task specific compact coding called evolutionary compact embedding ece which can be regarded as an optimization algorithm combining genetic programming gp and a boosting trick as an evolutionary computation methodology gp can solve problems inspired by natural evolution without any prior knowledge of the solutions in our evolutionary architecture each bit of ece is iteratively computed using a binary classification function which is generated through gp evolving by jointly minimizing its empirical risk with the adaboost strategy on a training set we address this as greedy optimization leading to small hamming distances for similar samples and large distances for dissimilar samples we then evaluate ece on four image datasets usps digital hand writing cmu pie face cifar 10 tiny image and sun397 scene showing the accurate and robust performance of our method for large scale image classification

the mass of an asymptotically flat manifold we show that the mass of an asymptotically flat n manifold is a geometric invariant the proof is based on harmonic coordinates and to develop a suitable existence theory results about elliptic operators with rough coefficients on weighted sobolev spaces are summarised some relations between the mass scalar curvature and harmonic maps are described and the positive mass theorem for n dimensional spin manifolds is proved

killing vectors in asymptotically flat space times ii asymptotically translational killing vectors and the rigid positive energy theorem in higher dimensions we show that the borderline cases in the proof of the positive energy theorem for initial data sets on spin manifolds in dimensions n 3 are only possible for initial data arising from embeddings in minkowski space time

maximal hypersurfaces in stationary asymptotically flat spacetimes existence of maximal hypersurfaces and of foliations by maximal hypersurfaces is proven in two classes of asymptotically flat spacetimes which possess a one parameter group of isometries whose orbits are timelike near infinity the first class consists of strongly causal asymptotically flat spacetimes which contain no black hole or white hole but may contain ergoregions where the killing orbits fail to be timelike the second class of spacetimes possess a black hole and a white hole with the black and white hole horizons intersecting in a compact 2 surfaces

killing vectors in asymptotically flat space times i asymptotically translational killing vectors and the rigid positive energy theorem we study killing vector fields in asymptotically flat space times we prove the following result implicitly assumed in the uniqueness theory of stationary black holes if the conditions of the rigidity part of the positive energy theorem are met then in such space times there are no asymptotically null killing vector fields except if the initial data set can be embedded in minkowski space time we also give a proof of the nonexistence of nonsingular in an appropriate sense asymptotically flat space times that satisfy an energy condition and that have a null adm four momentum under conditions weaker than previously considered

the classification of static electro vacuum space times containing an asymptotically flat spacelike hypersurface with compact interior we show that static electro vacuum black hole space times containing an asymptotically flat spacelike hypersurface with compact interior and with both degenerate and non degenerate components of the event horizon do not exist this is done by a careful study of the near horizon geometry of degenerate horizons which allows us to eliminate the last restriction of the static electro vacuum no hair theory

multiview alignment hashing for efficient image search hashing is a popular and efficient method for nearest neighbor search in large scale data spaces by embedding high dimensional feature descriptors into a similarity preserving hamming space with a low dimension for most hashing methods the performance of retrieval heavily depends on the choice of the high dimensional feature descriptor furthermore a single type of feature cannot be descriptive enough for different images when it is used for hashing thus how to combine multiple representations for learning effective hashing functions is an imminent task in this paper we present a novel unsupervised multiview alignment hashing approach based on regularized kernel nonnegative matrix factorization which can find a compact representation uncovering the hidden semantics and simultaneously respecting the joint probability distribution of data in particular we aim to seek a matrix factorization to effectively fuse the multiple information sources meanwhile discarding the feature redundancy since the raised problem is regarded as nonconvex and discrete our objective function is then optimized via an alternate way with relaxation and converges to a locally optimal solution after finding the low dimensional representation the hashing functions are finally obtained through multivariable logistic regression the proposed method is systematically evaluated on three data sets 1 caltech 256 2 cifar 10 and 3 cifar 20 and the results show that our method significantly outperforms the state of the art multiview hashing techniques

on potential wells and applications to semilinear hyperbolic equations and parabolic equations abstract in this paper we generalize the family of potential wells to the initial boundary value problem of semilinear hyperbolic equations and parabolic equations u tt u f u x t 0 u x 0 u 0 x u t x 0 u 1 x x u x t 0 x t 0 and u t u f u x t 0 u x 0 u 0 x x u x t 0 x t 0 not only give a threshold result of global existence and nonexistence of solutions but also obtain the vacuum isolating of solutions finally we prove the global existence of solutions for above problem with critical initial conditions i u 0 0 e 0 d or i u 0 0 j u 0 d so payne and sattinger s results are generalized and improved in essential

additive logistic regression a statistical view of boosting boosting is one of the most important recent developments in classification methodology boosting works by sequentially applying a classification algorithm to reweighted versions of the training data and then taking a weighted majority vote of the sequence of classifiers thus produced for many classification algorithms this simple strategy results in dramatic improvements in performance we show that this seemingly mysterious phenomenon can be understood in terms of well known statistical principles namely additive modeling and maximum likelihood for the two class problem boosting can be viewed as an approximation to additive modeling on the logistic scale using maximum bernoulli likelihood as a criterion we develop more direct approximations and show that they exhibit nearly identical results to boosting direct multiclass generalizations based on multinomial likelihood are derived that exhibit performance comparable to other recently proposed multiclass generalizations of boosting in most situations and far superior in some we suggest a minor modification to boosting that can reduce computation often by factors of 10 to 50 finally we apply these insights to produce an alternative formulation of boosting decision trees this approach based on best first truncated tree induction often leads to better performance and can provide interpretable descriptions of the aggregate decision rule it is also much faster computationally making it more suitable to large scale data mining applications

query adaptive hash code ranking for large scale multi view visual search hash based nearest neighbor search has become attractive in many applications however the quantization in hashing usually degenerates the discriminative power when using hamming distance ranking besides for large scale visual search existing hashing methods cannot directly support the efficient search over the data with multiple sources and while the literature has shown that adaptively incorporating complementary information from diverse sources or views can significantly boost the search performance to address the problems this paper proposes a novel and generic approach to building multiple hash tables with multiple views and generating fine grained ranking results at bitwise and tablewise levels for each hash table a query adaptive bitwise weighting is introduced to alleviate the quantization loss by simultaneously exploiting the quality of hash functions and their complement for nearest neighbor search from the tablewise aspect multiple hash tables are built for different data views as a joint index over which a query specific rank fusion is proposed to rerank all results from the bitwise ranking by diffusing in a graph comprehensive experiments on image search over three well known benchmarks show that the proposed method achieves up to 17 11 and 20 28 performance gains on single and multiple table search over the state of the art methods

sequential compact code learning for unsupervised image hashing effective hashing for large scale image databases is a popular research area attracting much attention in computer vision and visual information retrieval several recent methods attempt to learn either graph embedding or semantic coding for fast and accurate applications in this paper a novel unsupervised framework termed evolutionary compact embedding ece is introduced to automatically learn the task specific binary hash codes it can be regarded as an optimization algorithm that combines the genetic programming gp and a boosting trick in our architecture each bit of ece is iteratively computed using a weak binary classification function which is generated through gp evolving by jointly minimizing its empirical risk with the adaboost strategy on a training set we address this as greedy optimization by embedding high dimensional data points into a similarity preserved hamming space with a low dimension we systematically evaluate ece on two data sets sift 1m and gist 1m showing the effectiveness and the accuracy of our method for a large scale similarity search

proof of the positive mass theorem ii the positive mass theorem states that for a nontrivial isolated physical system the total energy which includes contributions from both matter and gravitation is positive this assertion was demonstrated in our previous paper in the important case when the space time admits a maximal slice here this assumption is removed and the general theorem is demonstrated abstracts of the results of this paper appeared in 11 and 13

the boost problem in general relativity we show that any asymptotically flat initial data for the einstein field equations have a development which includes complete spacelike surfaces boosted relative to the initial surface furthermore the asymptotic fall off is preserved along these boosted surfaces and there exists a global system of harmonic coordinates on such a development we also extend former results on global solutions of the constraint equations by virtue of this extension the constraint and evolution parts of the problem fit together exactly several theorems are given which concern the behaviour in the large of general classes of linear and quasilinear differential systems this paper contains in addition a systematic exposition of the functional spaces employed

hetero manifold regularisation for cross modal hashing recently cross modal search has attracted considerable attention but remains a very challenging task because of the integration complexity and heterogeneity of the multi modal data to address both challenges in this paper we propose a novel method termed hetero manifold regularisation hmr to supervise the learning of hash functions for efficient cross modal search a hetero manifold integrates multiple sub manifolds defined by homogeneous data with the help of cross modal supervision information taking advantages of the hetero manifold the similarity between each pair of heterogeneous data could be naturally measured by three order random walks on this hetero manifold furthermore a novel cumulative distance inequality defined on the hetero manifold is introduced to avoid the computational difficulty induced by the discreteness of hash codes by using the inequality cross modal hashing is transformed into a problem of hetero manifold regularised support vector learning therefore the performance of cross modal search can be significantly improved by seamlessly combining the integrated information of the hetero manifold and the strong generalisation of the support vector machine comprehensive experiments show that the proposed hmr achieve advantageous results over the state of the art methods in several challenging cross modal tasks

effect of aggregation on population recovery modeled by a forward backward pseudoparabolic equation in this paper we study the equation u t u f u u t f u in a bounded domain of r d d 1 with homogeneous boundary conditions of the neumann type as a model of aggregating population with a migration rate determined by and total birth and mortality rates characterized by f we will show that the aggregating mechanism induced by u allows the survival of a species in danger of extinction numerical simulations suggest that the solutions stabilize asymptotically in time to a not necessarily homogeneous stationary solution this is shown to be the case for a particular version of the function u

latent structure preserving hashing aiming at efficient similarity search hash functions are designed to embed high dimensional feature descriptors to low dimensional binary codes such that similar descriptors will lead to binary codes with a short distance in the hamming space it is critical to effectively maintain the intrinsic structure and preserve the original information of data in a hashing algorithm in this paper we propose a novel hashing algorithm called latent structure preserving hashing lsph with the target of finding a well structured low dimensional data representation from the original high dimensional data through a novel objective function based on nonnegative matrix factorization nmf with their corresponding kullback leibler divergence of data distribution as the regularization term via exploiting the joint probabilistic distribution of data lsph can automatically learn the latent information and successfully preserve the structure of high dimensional data to further achieve robust performance with complex and nonlinear data in this paper we also contribute a more generalized multi layer lsph ml lsph framework in which hierarchical representations can be effectively learned by a multiplicative up propagation algorithm once obtaining the latent representations the hash functions can be easily acquired through multi variable logistic regression experimental results on three large scale retrieval datasets i e sift 1m gist 1m and 500 k tinyimage show that ml lsph can achieve better performance than the single layer lsph and both of them outperform existing hashing techniques on large scale data

hyperbolic and parabolic equations with several opposite sign source at critical initial energy level in heat and vibrating systems abstract we study semilinear hyperbolic equations and parabolic equations with several opposite sign source terms under the dirichlet boundary condition in heat and vibrating systems for the above problems we prove the global nonexistence of solution and give the sharp conditions at critical energy level furthermore we prove that the existence of global solution of parabolic equation vanishes to zero as time goes to infinity which is different from the behavior of solution of the hyperbolic equation

equality in the spacetime positive mass theorem we affirm the rigidity conjecture of the spacetime positive mass theorem in dimensions less than eight namely if an asymptotically flat initial data set satisfies the dominant energy condition and has e p then e p 0 where e p is the adm energy momentum vector the dimensional restriction can be removed if we assume the positive mass inequality holds previously the result was only known for spin manifolds beig and chru ciel in j math phys37 4 1939 1961 1996 chru ciel and maerten in j math phys 47 2 2006

fourth order wave equations with nonlinear strain and source terms abstract in this paper we study the initial boundary value problem for fourth order wave equations with nonlinear strain and source terms first we introduce a family of potential wells and prove the invariance of some sets and vacuum isolating of solutions then we obtain a threshold result of global existence and nonexistence finally we discuss the global existence of solutions for the problem with critical initial condition i u 0 0 e 0 d so the esquivel avila s results are generalized and improved

global existence and finite time blow up for a class of semilinear pseudo parabolic equations abstract in this paper we study a class of semilinear pseudo parabolic equations by introducing a family of potential wells we prove the invariance of some sets global existence nonexistence and asymptotic behavior of solutions with initial energy j u 0 d moreover we obtain finite time blow up with high initial energy j u 0 d by comparison principle

global existence blow up and extinction for a class of thin film equation abstract in this paper we use the modified method of potential wells to study the properties of solutions for a class of higher order nonlinear parabolic equations with p laplace term u x p 2 u x x and nonlocal source u q 1 u 1 u q 1 u d x global existence uniqueness blow up in finite time and asymptotic behavior of solutions will be proved under different initial conditions furthermore a numerical example is given to illustrate the blow up of solutions in finite time

global solutions and finite time blow up for fourth order nonlinear damped wave equation in this paper we study the initial boundary value problem and global well posedness for a class of fourth order wave equations with a nonlinear damping term and a nonlinear source term which was introduced to describe the dynamics of a suspension bridge the global existence decay estimate and blow up of solution at both subcritical e 0 0 in this paper we study the initial boundary value problem and global well posedness for a class of fourth order wave equations with a nonlinear damping term and a nonlinear source term which was introduced to describe the dynamics of a suspension bridge the global existence decay estimate and blow up of solution at both subcritical e 0 0

a class of fourth order wave equations with dissipative and nonlinear strain terms we study the initial boundary value problem for a class of fourth order wave equations with dissipative and nonlinear strain terms by introducing a family of potential wells we not only obtain the invariant sets and vacuum isolating of solutions but also give some threshold results of global existence and nonexistence of solutions