a variational analysis of the toda system on compact surfaces in this paper we consider the following toda system of equations on a compact surface we will give existence results by using variational methods in a noncoercive case a key tool in our analysis is a new moser trudinger type inequality under suitable conditions on the center of mass and the scale of concentration of the two components u1 and u2 2012 wiley periodicals inc

sharp estimates for solutions of multi bubbles in compact riemann surfaces in this paper we consider a sequence of multibubble solutions u k of the equation 0 1 0 u k k he uk f m he u k d 1 0 in m where h is a c 2 positive function in a compact riemann surface m and k is a constant satisfying lim k k 8m for some positive integer m 1 we prove among other things that k 8m 2 m m j 1h 1 p k j 0 log h p k j 8m 2k p k j k j e k j o e k j where p k j are centers of the bubbles of u k and k j are the local maxima of u k after adding a constant this yields a uniform bound of solutions as k converges to 8m from below provided that 0 log h p k j 8m 2k p k j 0 it generalizes a previous result due to ding jost li and wang 18 and nolasco and tarantello 31 which says that any sequence of minimizers u k is uniformly bounded if k 0 for any maximum point p of the sum of 2 log h and the regular part of the green function where k is the gaussian curvature of m the analytic work of this paper is the first step toward computing the topological degree of 0 1 which was initiated by li 24

a priori estimates and uniqueness for some mean field equations abstract we consider the classical solutions of v e v in where is a bounded open set in r 2 this equation is related to geometry and several fields of physics and has significant applications in the theory of plasma we derive some uniqueness results and a priori estimate by using the classical isoperimetric inequality and the blow up analysis

a singular sphere covering inequality uniqueness and symmetry of solutions to singular liouville type equations we derive a singular version of the sphere covering inequality which was recently introduced in gui and moradifam invent math https doi org 10 1007 s00222 018 0820 2 2018 suitable for treating singular liouville type problems with superharmonic weights as an application we deduce new uniqueness results for solutions of the singular mean field equation both on spheres and on bounded domains as well as new self contained proofs of previously known results such as the uniqueness of spherical convex polytopes first established in luo and tian proc am math soc 116 4 1119 1129 1992 furthermore we derive new symmetry results for the spherical onsager vortex equation

finite time stabilization of linear time varying continuous systems in this technical note the problem of finite time stabilization of linear time varying continuous systems is considered necessary and sufficient conditions based upon the solution to some lyapunov differential matrix equations are proposed for particular cases of interest from these conditions the design of time varying state feedback controller guaranteeing the finite time closed loop stability is presented numerical experiments illustrate the potentialities of the approach

stabilization of uncertain systems via linear control this note considers the problem of stabilizing a linear dynamical system whose state equation includes a time varying uncertain parameter vector q cdot given the dynamics dot x t a q t x t b q t u t and a bounding set q for the values q t the objective is to choose a control law u t p x t guaranteeing uniform asymptotic stability for all admissible variations of q cdot our results differ from previous work in one fundamental way that is we show that when working with linear controllers it is possible to dispense with all assumptions on b cdot which have been made by previous authors e g see 1 9 this elimination of hypotheses on b cdot is accomplished roughly as follows the system sigma underline underline delta a q b q is shown to be equivalent to another system sigma underline underline delta a q b as far as stabilization is concerned since b is a constant matrix independent of q the desired result is readily obtained

mean field equation of liouville type with singular data topological degree we consider the following mean field equation gv h ev mh ev 1 4 j 1n j qj 1 on m where m is a compact riemann surface with volume 1 h is a positive c1 function on m and and j are constants satisfying j 1 in this paper we derive the topological degree counting formula for noncritical values of we also give several applications of this formula including existence of the curvature 1 metric with conic singularities doubly periodic solutions of electroweak theory and a special case of self gravitating strings 2015 wiley periodicals inc

statistical learning methods in linear algebra and control problems the example of finite time control of uncertain linear systems abstract in this paper we show how some difficult linear algebra problems can be approximately solved using statistical learning methods we illustrate our results by considering the state and output feedback finite time robust stabilization problems for linear systems subject to time varying norm bounded uncertainties and to unknown disturbances in the state feedback case the paper provides a sufficient condition for finite time stabilization in the presence of time varying disturbances such condition requires the solution of a linear matrix inequality lmi feasibility problem which is by now a standard application of linear algebraic methods in the output feedback case however we end up with a bilinear matrix inequality bmi problem which we tackle by resorting to a statistical approach

singular mean field equations on compact riemann surfaces for a general class of elliptic pde s in mean field form on compact riemann surfaces with exponential nonlinearity we address the question of the existence of solutions with concentrated nonlinear term which in view of the applications are physically of definite interest in the model we also include the possible presence of singular sources in the form of dirac masses which makes the problem more difficult to attack

existence and multiplicity result for the singular toda system abstract we consider the toda system on a compact surface g u 1 2 1 h 1 e u 1 h 1 e u 1 d v g 1 2 h 2 e u 2 h 2 e u 2 d v g 1 4 j 1 j 1 j p j 1 u 2 2 2 h 2 e u 2 h 2 e u 2 d v g 1 1 h 1 e u 1 h 1 e u 1 d v g 1 4 j 1 j 2 j p j 1 where h i are smooth positive functions i are positive real parameters p j are given points on and i j are numbers greater than 1 we give existence and multiplicity results using variational and morse theoretical methods it is the first existence result when some of the i j s are allowed to be negative

an improved geometric inequality via vanishing moments with applications to singular liouville equations we consider a class of singular liouville equations on compact surfaces motivated by the study of electroweak and self dual chern simons theories the gaussian curvature prescription with conical singularities and onsager s description of turbulence we analyse the problem of existence variationally and show how the angular distribution of the conformal volume near the singularities may lead to improvements in the moser trudinger inequality and in turn to lower bounds on the euler lagrange functional we then discuss existence and non existence results

randomized algorithms for probabilistic robustness with real and complex structured uncertainty there has been a growing interest in developing randomized algorithms for probabilistic robustness of uncertain control systems unlike classical worst case methods these algorithms provide probabilistic estimates assessing for instance if a certain design specification is met with a given probability one of the advantages of this approach is that the robustness margins can be often increased by a considerable amount at the expense of a small risk in this sense randomized algorithms may be used by the control engineer together with standard worst case methods to obtain additional useful information the applicability of these probabilistic methods to robust control is presently limited by the fact that the sample generation is feasible only in very special cases which include systems affected by real parametric uncertainty bounded in rectangles or spheres sampling in more general uncertainty sets is generally performed through overbounding at the expense of an exponential rejection rate in the paper randomized algorithms for stability and performance of linear time invariant uncertain systems described by a general m spl delta configuration are studied in particular efficient polynomial time algorithms for uncertainty structures spl delta consisting of an arbitrary number of full complex blocks and uncertain parameters are developed

elliptic functions green functions and the mean field equations on tori we show that the green functions on flat tori can have either 3 or 5 critical points only there does not seem to be any direct method to attack this problem instead we have to employ sophisticated non linear partial differential equations to study it we also study the distribution of number of critical points over the moduli space of flat tori through deformations the functional equations of special theta values provide important inequalities which lead to a solution for all rhombus tori the general picture is also emerged though some of the necessary technicality is still to de developed 1 introduction and statement of results the study of geometric or analytic problems on two dimensional tori is the same as the study of problems on r 2 with doubly periodic data such situations occur naturally in sciences and mathematics since early days the mathematical foundation of elliptic functions was subsequently devel oped in the 19th century it turns out that these special functions are rather deep objects by themselves tori of different shape may result in very dif ferent behavior of the elliptic functions and their associated objects arith metic on elliptic curves is perhaps the eldest and the most vivid example in this paper we show that this is also the case for certain non linear par tial differential equations indeed researches on doubly periodic problems in mathematical physics or differential equations often restrict the study to rectangular tori for simplicity this leaves the impression that the theory for general tori may resemble much the same way as for the rectangular case however this turns out to be false we will show that the solvability of themean field equation dependson the shape of the green function which in turn depends on the geometry of the tori in an essential way recall that the green function g z w on a flat torus t c z 1 z 2 is the unique function on t t which satisfies zg z w w z 1 t

finite time stabilization of linear time varying systems by piecewise constant feedback most existing methods for finite time stabilizing controller design of linear time varying systems involve solving differential linear matrix equations due to the non convexity of the problem it requires a high computational burden this paper proposes a numerical method to solve finite time stabilization problems successive approximations are performed to estimate the evolution of system states accordingly a gain switched state feedback controller can be obtained by solving a sequence of linear matrix inequalities lmis based optimization problems the proposed algorithm is used to design the mass spring system and the autopilot system of the btt missile comparison with existing methods is given and the simulation results show the effectiveness of the proposed method

on a convex parameter space method for linear control design of uncertain systems this paper presents a new procedure for continuous and discrete time linear control systems design it consists of the definition of a convex programming problem in the parameter space that when solved provides the feedback gain one of the most important features of the procedure is that additional design constraints are easily incorporated in the original formulation yielding solutions to problems that have raised a great deal of interest within the last few years this is precisely the case of the decentralized control problem and the quadratic stabilizability problem of uncertain systems with both dynamic and input uncertain matrices in this last case necessary and sufficient conditions for the existence of a linear stabilizing gain are provided and to the authors knowledge this is one of the first numerical procedures able to handle and solve this interesting design problem for high order continuous time or discrete time linear models the theory is illustrated by examples

moser trudinger trace inequalities sharp constants in exponential inequalities involving a general class of measures in domains are exhibited in the limiting case of the sobolev embedding theorem a comprehensive approach is presented yielding as special instances trace inequalities on o on smooth submanifolds of o of arbitrary dimension and also on fractal subsets of o and recovering in particular the classical moser trudinger inequality

a no reference optical flow based quality evaluator for stereoscopic videos in curvelet domain most of the existing 3d video quality assessment 3d vqa svqa methods only consider spatial information by directly using an image quality evaluation method in addition a few take the motion information of adjacent frames into consideration in practice one may assume that a single data view is unlikely to be sufficient for effectively learning the video quality therefore integration of multi view information is both valuable and necessary in this paper we propose an effective multi view feature learning metric for blind stereoscopic video quality assessment bsvqa which jointly focuses on spatial information temporal information and inter frame spatio temporal information in our study a set of local binary patterns lbp statistical features extracted from a computed frame curvelet representation are used as spatial and spatio temporal description and the local flow statistical features based on the estimation of optical flow are used to describe the temporal distortion subsequently a support vector regression svr is utilized to map the feature vectors of each single view to subjective quality scores finally the scores of multiple views are pooled into the final score according to their contribution rate experimental results demonstrate that the proposed metric significantly outperforms the existing metrics and can achieve higher consistency with subjective quality assessment

existence and non existence results for the su 3 singular toda system on compact surfaces we consider the su 3 singular toda system on a compact surface g u1 2 1 h1eu1 h1eu1dvg 1 2 h2eu2 h2eu2dvg 1 4 m 1m 1m pm 1 u2 2 2 h2eu2 h2eu2dvg 1 1 h1eu1 h1eu1dvg 1 4 m 1m 2m pm 1 where hi are smooth positive functions on i r pm and im 1 we give both existence and non existence results under some conditions on the parameters i and im existence results are obtained using variational methods which involve a geometric inequality of new type non existence results are obtained using blow up analysis and localized poho aev type identities

brief probabilistic solutions to some np hard matrix problems during recent years it has been shown that a number of problems in matrix theory are np hard including robust nonsingularity robust stability robust positive semidefiniteness robust bounded norm state feedback stabilization with structural and norm constraints etc in this paper we use standard bounds on empirical probabilities as well as recent results from statistical learning theory on the vc dimension of families of sets defined by a finite number of polynomial inequalities to show that for each of the above problems as well as for still more general and more difficult problems there exists a polynomial time randomized algorithm that can provide a yes or no answer to arbitrarily small levels of accuracy and confidence

qualitative properties of solutions to some nonlinear elliptic equations in r 2 o introduction elliptic equations in this paper we investigate properties of the solutions to the au r x e u x x r 2 for functions r x which are positive near infinity equations of this kind arise from a variety of situations such as from prescribing gaussian curvature in geometry i 2 and from combustion theory in physics 3 recently a series ofworks have been sought to understand the existence and the qualitative properties of the solutions of ni i 5 and ni cheng 4 1 considered the case where r x is nonpositive mcowen 6 1 and aviles 7 investigated the situation where r x 0 in some order as ixl in our previous paper 1 we consider a special case where r is a constant we proved that the solutions are radially symmetric and hence classified all the solutions in this paper we consider more general functions r x first we obtain the asymptotic behavior of the solution near infinity consequently we prove that all the solutions satisfy an identity which is somewhat of a generalization of the well known kazdan warner condition finally using the asymptotic behavior together with the further development of the method employed in our previous paper i 1 we show that all the solutions are radially symmetric provided r is radially symmetric and nonincreasing this part can be viewed as the completion of 1 throughout this paper we assume that the function r x is positive near infinity in 1 we study the asymptotic behavior of the solution u x of let fl 1 2n r2 r x e dx under some appropriate conditions we show that the solutions approach

a general existence result for the toda system on compact surfaces in this paper we consider the following toda system of equations on a compact surface u1 2 1 h1eu1 h1eu1dvg 1 2 h2eu2 h2eu2dvg 1 u1 4 j 1m 1 j pj 1 u2 2 2 h2eu2 h2eu2dvg 1 1 h1eu1 h1eu1dvg 1 u2 4 j 1m 2 j pj 1 which is motivated by the study of models in non abelian chern simons theory here h1 h2h1 h2 are smooth positive functions 1 2 1 2 two positive parameters pipi points of the surface and 1 i 2 j 1 i 2 j non negative numbers we prove a general existence result using variational methods the same analysis applies to the following mean field equation u 1 heu heudvg 1 2 he u he udvg 1 which arises in fluid dynamics

probabilistic robustness analysis explicit bounds for the minimum number of samples in this paper we study robustness analysis of control systems affected by bounded uncertainty motivated by the difficulty to perform this analysis when the uncertainty enters into the plant coefficients in a nonlinear fashion we study a probabilistic approach in this setting the uncertain parameters q are random variables bounded in a set q and described by a multivariate density function f q we then pose the following question given a performance level what is the probability that this level is attained the main content of this paper is to derive explicit bounds for the number of samples required to estimate this probability with a certain accuracy and confidence a priori specified it is shown that the number obtained is inversely proportional to these thresholds and it is much smaller than that of classical results finally we remark that the same approach can be followed to study several problems in a control system context for example we can evaluate the worst case h norm of the sensitivity function of multi input multi output systems or compute when the robustness margin is of interest

non degeneracy and uniqueness of solutions to singular mean field equations on bounded domains abstract the aim of this paper is to complete the program initiated in 51 23 and then carried out by several authors concerning non degeneracy and uniqueness of solutions to mean field equations in particular we consider mean field equations with general singular data on non smooth domains the argument is based on the alexandrov bol inequality and on the eigenvalues analysis of linearized singular liouville type problems

conformal deformation of metrics on s 2 soit d un domaine lisse de s 2 et k une fonction lisse definie sur d alors pour que le probleme aux limites de neumann u k exp 2u 1 sur d u n 0 sur d ait une solution u on a a quand aire d max x d k x 0

technical communique finite time control of linear systems subject to parametric uncertainties and disturbances in this paper we consider finite time control problems for linear systems subject to time varying parametric uncertainties and to exogenous constant disturbances the main result provided is a sufficient condition for robust finite time stabilization via state feedback it can be applied to problems with both non zero initial conditions and unknown constant disturbances this condition is then reduced to a feasibility problem involving linear matrix inequalities lmis a detailed example is presented to illustrate the proposed methodology

a special class of stationary flows for two dimensional euler equations a statistical mechanics description we consider the canonical gibbs measure associated to an vortex system in a bounded domain at inverse temperature widetilde beta and prove that in the limitn widetilde beta n n 1 where 8 here denotes the vorticity intensity of each vortex the one particle distribution function n nx x converges to a superposition of solutions of the following mean field equation left begin array 20 c varrho beta x frac e beta psi mathop smallint limits lambda e beta psi delta psi varrho beta in lambda psi partial lambda 0 end array right

two dimensional euler flows with concentrated vorticities for a planar model of euler flows proposed by tur and yanovsky 2004 we construct a family of velocity fields w e for a fluid in a bounded region with concentrated vorticities e for e 0 small more precisely given a positive integer and a sufficiently small complex number a we find a family of stream functions e which solve the liouville equation with dirac mass source e e 2 e e 4 pa e in e 0 on for a suitable point p p a e the vorticities e e concentrate in the sense that 1 e 4 pa e 8 1 j 1 pa e a j 0 as e 0 j 1 where the satellites a 1 a 1 denote the complex 1 roots of a the point p a e lies close to a zero point of a vector field explicitly built upon derivatives of order 1 of the regular part of green s function of the domain

asymptotic blow up analysis for singular liouville type equations with applications abstract we generalize the pointwise estimates obtained in 2 19 and 34 concerning blow up solutions of the liouville type equation u x 2 w x e u in with r 2 open and bounded 1 and w any lipschitz continuous function which satisfies 0 a w b we focus to the case left open in 2 and 34 where the parameter n whose analysis is much more involved as we need to resolve the difficulty of a genuinely non radial behaviour of blow up solutions in the worst situation there is no chance in general to resolve the profile in the form of a solution of a liouville equation in r 2 instead we need to adopt iterated blow up arguments next we refine our blow up analysis to cover a class of planar liouville type problems see 1 27 1 28 below arising from the study of cosmic strings cfr 28 35 in this context we are able to distinguish between a single blow up radial profile and the case of multiple blow up profiles typical of non radial solutions as a consequence we obtain a radial symmetry result which is interesting in itself but also contributes towards the sharp solvability issue for the planar problem 1 27 1 28

np hardness of some linear control design problems we show that some basic linear control design problems are np hard implying that unless p np they cannot be solved by polynomial time algorithms the problems that we consider include simultaneous stabilization by output feedback stabilization by state or output feedback in the presence of bounds on the elements of the gain matrix and decentralized control these results are obtained by first showing that checking the existence of a stable matrix in an interval family of matrices is np hard

local binary features for texture classification local binary patterns lbp have emerged as one of the most prominent and widely studied local texture descriptors truly a large number of lbp variants has been proposed to the point that it can become overwhelming to grasp their respective strengths and weaknesses and there is a need for a comprehensive study regarding the prominent lbp related strategies new types of descriptors based on multistage convolutional networks and deep learning have also emerged in different papers the performance comparison of the proposed methods to earlier approaches is mainly done with some well known texture datasets with differing classifiers and testing protocols and often not using the best sets of parameter values and multiple scales for the comparative methods very important aspects such as computational complexity and effects of poor image quality are often neglected in this paper we provide a systematic review of current lbp variants and propose a taxonomy to more clearly group the prominent alternatives merits and demerits of the various lbp features and their underlying connections are also analyzed we perform a large scale performance evaluation for texture classification empirically assessing forty texture features including thirty two recent most promising lbp variants and eight non lbp descriptors based on deep convolutional networks on thirteen widely used texture datasets the experiments are designed to measure their robustness against different classification challenges including changes in rotation scale illumination viewpoint number of classes different types of image degradation and computational complexity the best overall performance is obtained for the median robust extended local binary pattern mrelbp feature for textures with very large appearance variations fisher vector pooling of deep convolutional neural networks is clearly the best but at the cost of very high computational complexity the sensitivity to image degradations and computational complexity are among the key problems for most of the methods considered highlightsa taxonomy and comprehensive survey of lbp variants characteristics of and connections between lbp variants are provided a comprehensive experimental evaluation of 32 lbp methods comparison of 32 lbp variants with 8 deep convnets features evaluation of robustness to rotation illumination scale and noise changes comparison of computational complexity of forty variants

adams inequalities on measure spaces abstract in 1988 adams obtained sharp moser trudinger inequalities on bounded domains of r n the main step was a sharp exponential integral inequality for convolutions with the riesz potential in this paper we extend and improve adams results to functions defined on arbitrary measure spaces with finite measure the riesz fractional integral is replaced by general integral operators whose kernels satisfy suitable and explicit growth conditions given in terms of their distribution functions natural conditions for sharpness are also given most of the known results about moser trudinger inequalities can be easily adapted to our unified scheme we give some new applications of our theorems including sharp higher order moser trudinger trace inequalities sharp adams moser trudinger inequalities for general elliptic differential operators scalar and vector valued for sums of weighted potentials and for operators in the cr setting

multi view intact space learning it is practical to assume that an individual view is unlikely to be sufficient for effective multi view learning therefore integration of multi view information is both valuable and necessary in this paper we propose the multi view intact space learning misl algorithm which integrates the encoded complementary information in multiple views to discover a latent intact representation of the data even though each view on its own is insufficient we show theoretically that by combing multiple views we can obtain abundant information for latent intact space learning employing the cauchy loss a technique used in statistical learning as the error measurement strengthens robustness to outliers we propose a new definition of multi view stability and then derive the generalization error bound based on multi view stability and rademacher complexity and show that the complementarity between multiple views is beneficial for the stability and generalization misl is efficiently optimized using a novel iteratively reweight residuals irr technique whose convergence is theoretically analyzed experiments on synthetic data and real world datasets demonstrate that misl is an effective and promising algorithm for practical applications

on a class of elliptic problems in r symmetry and uniqueness results in the plane r 2 we classify all solutions for an elliptic problem of liouville type involving a radial weight function as a consequence we clarify the origin of the non radially symmetric solutions for the given problem as established by chanillo and kiessling for a more general class of liouville type problems we show that rather than radial symmetry the solutions always inherit the invariance of the problem under inversion with respect to suitable circles this symmetry result is derived with the help of a shrinking sphere method

generic multiplicity for a scalar field equation on compact surfaces we prove generic multiplicity of solutions for a scalar field equation on compact surfaces via morse inequalities in particular our result improves significantly the multiplicity estimate which can be deduced from the degree counting formula in chen and lin 2003 12 related results are derived for the prescribed q curvature equation

classification and nondegeneracy of su n 1 toda system with singular sources we consider the following toda system open image in new window where i 1 0 is dirac measure at 0 and the coefficients a ij form the standard tri diagonal cartan matrix in this paper i we completely classify the solutions and obtain the quantization result sum j 1 n a ij int mathbb r 2 e u j dx 4 pi 2 gamma i gamma n 1 i quad forall 1 leq i leq n this generalizes the classification result by jost and wang for i 0 forall 1 leq i leq n ii we prove that if i i 1 j for all 1 i j n then any solution u i is radially symmetric w r t 0 iii we prove that the linearized equation at any solution is non degenerate these are fundamental results in order to understand the bubbling behavior of the toda system

uniqueness and symmetry results for solutions of a mean field equation on 2 via a new bubbling phenomenon motivated by the study of gauge field vortices we consider a mean field equation on the standard two sphere involving a dirac distribution supported at a point p of s 2 as needed for the applications we show that solutions concentrate exactly at p for some limiting value of a given parameter we use this fact to obtain symmetry about the axis op and uniqueness property for the solution the presence of the dirac measure makes such a task particularly delicate indeed we need to rule out the possibility that after blow up in a suitable scale the solution sequence may admit a double peak profile described in terms of appropriate limiting problems for instance we need to account for the presence of non axially symmetric solutions in such limiting problems in this process we establish a symmetry result about a maximal circle through p and its antipodal point p that applies to more general situations where the full axial symmetry cannot be expected

sharp existence results for mean field equations with singular data abstract let be a simply connected open and bounded domain in r 2 we are concerned with the nonlinear elliptic problem 0 1 v 8 e v e v 4 j 1 m j p j in v 0 on where j 0 p j denotes the dirac mass with singular point p j and p 1 p m we provide necessary and sufficient conditions for the existence of solutions to 0 1 our result is the two dimensional version of the sharp existence nonexistence result obtained in druet 2002 13 for elliptic equations with critical exponent in dimension 3 in particular we prove that the set m is open where for a given 1 m 0 0 m p 1 p m problem 0 1 has a solution

supercritical mean field equations on convex domains and the onsager s statistical description of two dimensional turbulence we are motivated by the study of the microcanonical variational principle within onsager s description of two dimensional turbulence in the range of energies where the equivalence of statistical ensembles fails we obtain sufficient conditions for the existence and multiplicity of solutions for the corresponding mean field equation on convex and thin enough domains in the supercritical with respect to the moser trudinger inequality regime this is a brand new achievement since existence results in the supercritical region were previously known only on multiply connected domains we then study the structure of these solutions by the analysis of their linearized problems and we also obtain a new uniqueness result for solutions of the mean field equation on thin domains whose energy is uniformly bounded from above finally we evaluate the asymptotic expansion of those solutions with respect to the thinning parameter and combining it with all the results obtained so far we solve the microcanonical variational principle in a small range of supercritical energies where the entropy is shown to be concave

multiresolution gray scale and rotation invariant texture classification with local binary patterns presents a theoretically very simple yet efficient multiresolution approach to gray scale and rotation invariant texture classification based on local binary patterns and nonparametric discrimination of sample and prototype distributions the method is based on recognizing that certain local binary patterns termed uniform are fundamental properties of local image texture and their occurrence histogram is proven to be a very powerful texture feature we derive a generalized gray scale and rotation invariant operator presentation that allows for detecting the uniform patterns for any quantization of the angular space and for any spatial resolution and presents a method for combining multiple operators for multiresolution analysis the proposed approach is very robust in terms of gray scale variations since the operator is by definition invariant against any monotonic transformation of the gray scale another advantage is computational simplicity as the operator can be realized with a few operations in a small neighborhood and a lookup table experimental results demonstrate that good discrimination can be achieved with the occurrence statistics of simple rotation invariant local binary patterns

existence of conformal metrics with constant q curvature given a compact four dimensional manifold we prove existence of conformal metrics with constant q curvature under generic assumptions the problem amounts to solving a fourth order nonlinear elliptic equation with variational structure since the corresponding euler functional is in general unbounded from above and from below we employ topological methods and min max schemes jointly with the compactness result of 35

a sup inf inequality for some nonlinear elliptic equations involving exponential nonlinearities let u be a solution of the equation u v x eu in a domain r2 where 0 a v b and v is lipschitz continuous we prove that sup u can be controlled in terms of inf u more precisely supku inf u c a b k v l for any compact subset k this extends an earlier result of shafrir who obtained a similar conclusion when v 1

some open problems in matrix theory arising in linear systems and control control theory has long provided a rich source of motivation for developments in matrix theory accordingly we discuss some open problems in matrix theory arising from theoretical and practical issues in linear systems theory and feedback control the problems discussed include robust stability matrix exponent induced norms stabilizability and pole assignability and nonstandard matrix equations a substantial number of references are included to acquaint matrix theorists with problems and trends in this application area feedback control theory has long provided a rich source of motivation for developments in matrix theory the purpose of this paper is to discuss several open problems in matrix theory that arise from theoretical and practical issues in feedback control theory and the associated area of linear systems theory many of these problems are remarkably simple to state are of intense interest in control theory and applications and yet remain unsolved besides leading to the resolution of these problems it is hoped that this paper will help to stimulate increased interaction between matrix and control theorists accord

global asymptotic linearisation of the pole placement map a closed form solution for the constant output feedback problem abstract the problem of pole assignment by constant output feedback controllers is studied for minimal systems described by a proper transfer function matrix g s r m p s with mcmillan degree n a new method is presented based on asymptotic linearisation around a degenerate point of the pole placement map related to the problem the essence of the present approach is to reduce the multilinear nature of the problem to one of solving a linear set of equations and this is achieved without losing any of the degrees of freedom in the controller the solution is given in closed form in terms of a one parameter family of static feedback compensators for which the closed loop poles approach the required ones as 0 conditions for the generic as well as exact solvability of the arbitrary pole placement problem are given in terms of the numbers m p n and the rank of a new system invariant the d restricted plucker matrix it is shown that the method works generically when mp n which along with the boundary case mp n is the best possible condition as far as the number of states of the open loop system is concerned for achieving arbitrary pole placement via constant output feedback

total least squares for affinely structured matrices and the noisy realization problem structured rank deficient matrices arise in many applications in signal processing system identification and control theory the author discusses the structured total least squares stls problem which is the problem of approximating affinely structured matrices i e matrices affine in the parameters by similarly structured rank deficient ones while minimizing an l sub 2 error criterion it is shown that the optimality conditions lead to a nonlinear generalized singular value decomposition which can be solved via an algorithm that is inspired by inverse iteration next the author concentrates on the so called l sub 2 optimal noisy realization problem which is equivalent with approximating a given data sequence by the impulse response of a finite dimensional time invariant linear system of a given order this can be solved as a structured total least squares problem it is shown with some simple counter examples that classical algorithms such as the steiglitz mcbride 1965 iterative quadratic maximum likelihood and cadzow s 1988 iteration do not converge to the optimal l sub 2 solution despite misleading claims in the literature

improved sample complexity estimates for statistical learning control of uncertain systems probabilistic methods and statistical learning theory have been shown to provide approximate solutions to difficult control problems unfortunately the number of samples required in order to guarantee stringent performance levels may be prohibitively large this paper introduces bootstrap learning methods and the concept of stopping times to drastically reduce the bound on the number of samples required to achieve a performance level we then apply these results to obtain more efficient algorithms which probabilistically guarantee stability and robustness levels when designing controllers for uncertain systems

on avoiding vertexization of robustness problems the approximate feasibility concept for a large class of robustness problems with uncertain parameter vector q confined to a box q there are many papers providing results along the following lines the desired performance specification is robustly satisfied for all q spl isin q if and only if it is satisfied at each vertex q sup i of q since the number of vertices of q explodes combinatorically with the dimension of q the computation associated with the implementation of such results is often intractable the main point of this paper is to introduce a new approach to such problems aimed at alleviation of this computational complexity problem to this end the notion of approximate feasibility is introduced and the theory which follows from this definition is vertex free

weighted barycentric sets and singular liouville equations on compact surfaces given a closed surface we prove a general existence result for some elliptic pde with exponential nonlinearities and negative dirac deltas extending a theory recently obtained for the regular case this is done by global methods since the associated euler functional might be unbounded from below we define a new model space generalizing the so called space of formal barycenters and characterizing up to homotopy equivalence its low sublevels as a result the analytic problem is reduced to a topological one concerning the contractibility of this model space to this aim we prove a new functional inequality in the spirit of chen and li 1991 11 and then employ a min max scheme based on conical construction jointly with the blow up analysis in bartolucci and montefusco 2007 4 after bartolucci and tarantello 2002 brezis and merle 1991 and this study is motivated by abelian chern simons theory in self dual regime or from the problem of prescribing the gaussian curvature with conical singularities generalizing a problem raised in kazdan and warner 1974 24

semiclassical limit of liouville field theory liouville field theory lft for short is a two dimensional model of random surfaces which is for instance involved in 2d string theory or in the description of the fluctuations of metrics in 2d liouville quantum gravity this is a probabilistic model that consists in weighting the classical free field action with an interaction term given by the exponential of a gaussian multiplicative chaos the main input of our work is the study of the semiclassical limit of the theory which is a prescribed asymptotic regime of lft of interest in physics literature see cite witten and references therein we derive exact formulas for the laplace transform of the liouville field in the case of flat metric on the unit disk with dirichlet boundary conditions as a consequence we prove that the liouville field concentrates on the solution of the classical liouville equation with explicit negative scalar curvature we also characterize the leading fluctuations which are gaussian and massive and establish a large deviation principle though considered as an ansatz in the whole physics literature it seems that it is the first rigorous probabilistic derivation of the semiclassical limit of lft on the other hand we carry out the same analysis when we further weight the liouville action with heavy matter operators this procedure appears when computing the n points correlation functions of lft

a quantization property for blow up solutions of singular liouville type equations abstract motivated by the study of self dual vortices in gauge field theory cf vortices and monopoles birkhauser boston 1980 solitons in field theory and nonlinear analysis monographs in mathematics springer new york 2001 we consider a concentrating solution sequence u k satisfying u k z 2 k v k z e u k in b 1 z 2 k v k z e u k z 0 weakly in the sense of measures in b 1 where i k r k ii v k c 0 1 b 1 0 a v k b and v k a in b 1 we prove that necessarily 8 n 8 1 8 z the result is sharp as shown by explicit examples and should be compared with that obtained by li shafrir ind univ math j 43 4 1994 1255 concerning the situation where k 0 k n

intelligent reversible watermarking and authentication hiding depth map information for 3d cameras in this paper we propose an application for 3d cameras by reversibly hiding the depth map in the corresponding 2d images the proposed technique is prospective in cameras capable of capturing simultaneously the 2d image and resultant depth map of an object 3d cameras equipped with self embedding capability can serve two additional purposes protection of the captured image and secure transmission of its depth map the reversible watermarking in addition to other features guarantees the lossless recovery of an original image and separation of its depth map when required for this purpose a reversible watermarking scheme based on genetic algorithm ga has been proposed which computes suitable threshold for each block of coefficients in the wavelet domain thus a tradeoff is made between watermark imperceptibility and capacity using ga the threshold map is embedded in addition to the actual payload and thus the proposed approach does not require histogram pre processing in order to avoid overflow underflow the same threshold map has been used for authentication purpose by correlating it with the low frequency coefficients of the 2d transformed image further to exploit the inherent redundancy in the depth map which is the actual payload in this case lossless compression has been employed before its embedding similarly besides secret key based permutation a cryptographic layer is overlaid on the watermarking layer for security purposes experiments conducted on images and depth maps obtained using a 3d camera and an optical microscopic system validate the proposed concept

large margin multi viewinformation bottleneck in this paper we extend the theory of the information bottleneck ib to learning from examples represented by multi view features we formulate the problem as one of encoding a communication system with multiple senders each of which represents one view of the data based on the precise components filtered out from multiple information sources through a bottleneck a margin maximization approach is then used to strengthen the discrimination of the encoder by improving the code distance within the frame of coding theory the resulting algorithm therefore inherits all the merits of the ib principle and coding theory it has two distinct advantages over existing algorithms namely that our method finds a tradeoff between the accuracy and complexity of the multi view model and that the encoded multi view data retains sufficient discrimination for classification we also derive the robustness and generalization error bound of the proposed algorithm and reveal the specific properties of multi view learning first the complementarity of multi view features guarantees the robustness of the algorithm second the consensus of multi view features reduces the empirical rademacher complexity of the objective function enhances the accuracy of the solution and improves the generalization error bound of the algorithm the resulting objective function is solved efficiently using the alternating direction method experimental results on annotation classification and recognition tasks demonstrate that the proposed algorithm is promising for practical applications

topological degree for a mean field equation on riemann surfaces we consider the following mean field equations 0 1 where m is a compact riemann surface with volume 1 h is a positive continuous function on m is a real number 0 2 and where is a bounded smooth domain h is a c1 positive function on and based on our previous analytic work 14 we prove among other things that the degree counting formula for 0 1 is given by for 8m 8 m 1 2003 wiley periodicals inc

prescribing curvature on compact surfaces with conical singularities we study the berger nirenberg problem on surfaces with conical singularities i e we discuss conditions under which a function on a riemann surface is the gaussian curvature of some conformal metric with a prescribed set of singularities of conical types

blow up analysis for su 3 toda system abstract using the method of symmetrization and the rescaling we study non compact solution sequence to the su 3 toda system in non abelian relativistic self dual gauge theory i e the quantization of the total mass and classification of the singular limit

output feedback pole placement with dynamic compensators derives a new rank condition which guarantees the arbitrary pole assignability of a given system by dynamic compensators of degree at most q by using this rank condition the authors establish several new sufficiency conditions which ensure the arbitrary pole assignability of a generic system the authors proofs also come with a concrete numerical procedure to construct a particular compensator which assigns a given set of closed loop poles

probabilistic robust design with linear quadratic regulators in this paper we study robust design of uncertain systems in a probabilistic setting by means of linear quadratic regulators lqr we consider systems affected by random bounded nonlinear uncertainty so that classical optimization methods based on linear matrix inequalities cannot be used without conservatism the approach followed here is a blend of randomization techniques for the uncertainty together with convex optimization for the controller parameters in particular we propose an iterative algorithm for designing a controller which is based upon subgradient iterations at each step of the sequence we first generate a random sample and then we perform a subgradient step for a convex constraint defined by the lqr problem the main result of the paper is to prove that this iterative algorithm provides a controller which quadratically stabilizes the uncertain system with probability one in a finite number of steps in addition at a fixed step we compute a lower bound of the probability that a quadratically stabilizing controller is found