robust stability and stabilisation of 2d discrete state delayed systems abstract in this paper we first present sufficient stability and robust stability conditions for discrete linear state delayed 2d systems in terms of linear matrix inequalities all results are obtained with fornasini marchesini delay model but appropriate transformation to the corresponding roesser form is provided as well generalisation to the multiple state delayed case is also given then the stabilisation and robust stabilisation using static state feedback are studied stabilising feedback gain matrices are constructed based on the solutions of certain linear matrix inequalities an numerical example is used to illustrate the effectiveness of the approach

learnability with respect to fixed distributions consider a first order typed language with semantics s for expressions and types adding subtyping means that a partial order on types is defined and that the typing rules are extended to the effect that expression e has type t whenever e has type s and s t we show how to adapt the semantics s in a simple set theoretic way obtaining a semantics s that satisfies in addition to some obvious requirements also the property that s s is included in s t whenever s t

distribution dependent sample complexity of large margin learning we obtain a tight distribution specific characterization of the sample complexity of large margin classification with l2 regularization we introduce the margin adapted dimension which is a simple function of the second order statistics of the data distribution and show distribution specific upper and lower bounds on the sample complexity both governed by the margin adapted dimension of the data distribution the upper bounds are universal and the lower bounds hold for the rich family of sub gaussian distributions with independent features we conclude that this new quantity tightly characterizes the true sample complexity of large margin classification to prove the lower bound we develop several new tools of independent interest these include new connections between shattering and hardness of learning new properties of shattering with linear classifiers and a new lower bound on the smallest eigenvalue of a random gram matrix generated by sub gaussian variables our results can be used to quantitatively compare large margin learning to other learning rules and to improve the effectiveness of methods that use sample complexity bounds such as active learning

hz algebra spectra are differential graded algebras we show that the homotopy theory of differential graded algebras coincides with the homotopy theory of h algebra spectra namely we construct quillen equivalences between the quillen model categories of unbounded differential graded algebras and h algebra spectra we also construct quillen equivalences between the differential graded modules and module spectra over these algebras we use these equivalences in turn to produce algebraic models for rational stable model categories we show that basically any rational stable model category is quillen equivalent to modules over a differential graded algebra with many objects

uniqueness of the multiplicative cyclotomic trace abstract making use of the theory of noncommutative motives we characterize the topological dennis trace map as the unique multiplicative natural transformation from algebraic k theory to topological hochschild homology thh and the cyclotomic trace map as the unique multiplicative lift through topological cyclic homology tc moreover we prove that the space of all multiplicative structures on algebraic k theory is contractible we also show that the algebraic k theory functor from small stable categories to spectra is lax symmetric monoidal which in particular implies that e n ring spectra give rise to e n 1 ring algebraic k theory spectra along the way we develop a multiplicative morita theory establishing a symmetric monoidal equivalence between the category of small idempotent complete stable categories and the morita localization of the category of spectral categories

homotopical algebraic geometry i topos theory this is the rst of a series of papers devoted to lay the foundations of algebraic geometry in homotopical and higher categorical contexts in this rst part we investigate a notion of higher topos for this we use s categories i e simplicially enriched categories as models for certain kind of 1 categories and we develop the notions of s topologies s sites and stacks over them we prove in particular that for an s category t endowed with an s topology there exists a model category of stacks over t generalizing the model category structure on simplicial presheaves over a grothendieck site of a joyal and r jardine we also prove some analogs of the relations between topologies and localizing subcategories of the categories of presheaves by proving that there exists a one to one correspodence between s topologies on an s category t and certain left exact bouseld localizations of the model category of pre stacks on t based on the above results we study the notion of model topos introduced by c rezk and we relate it to our model categories of stacks over s sites in the second part of the paper we present a parallel theory where s categories s topologies and s sites are replaced by model categories model topologies and model sites we prove that a canonical way to pass from the theory of stacks over model sites to the theory of stacks over s sites is provided by the simplicial localization construction of dwyer and kan as an example of application we propose a denition of etale k theory of ring spectra extending the etale k theory of commutative rings

a cellular nerve for higher categories abstract we realise joyal cell category as a dense subcategory of the category of categories the associated cellular nerve of an category extends the well known simplicial nerve of a small category cellular sets like simplicial sets carry a closed model structure in quillen s sense with weak equivalences induced by a geometric realisation functor more generally there exists a dense subcategory a of the category of a algebras for each operad a in batanin s sense whenever a is contractible the resulting homotopy category of a algebras i e weak categories is equivalent to the homotopy category of compactly generated spaces

learning with prior information a notion of learnability is introduced referred to as learnability with prior information w p i this notion is weaker than the standard notion of probably approximately correct pac learnability a property called dispersability is introduced and it is shown that dispersability plays a key role in the study of learnability w p i specifically dispersability of a function class is always a sufficient condition for the function class to be learnable moreover in the case of concept classes dispersability is also a necessary condition for learnability w p i thus in the case of learnability w p i the dispersability property plays a role similar to the finite metric entropy condition in the case of pac learnability with a fixed distribution next the notion of learnability w p i is extended to the distribution free d f situation and it is shown that a property called d f dispersability is always a sufficient condition for d f learnability w p i and is also a necessary condition for d f learnability in the case of concept classes the approach to learning introduced in the paper is believed to be significant in all problems where a nonlinear system has to be designed based on data this includes direct inverse control and system identification

supervised learning and co training co training under the conditional independence assumption is among the models which demonstrate how radically the need for labeled data can be reduced if a huge amount of unlabeled data is available in this paper we explore how much credit for this saving must be assigned solely to the extra assumptions underlying the co training model to this end we compute general almost tight upper and lower bounds on the sample size needed to achieve the success criterion of pac learning in the realizable case within the model of co training under the conditional independence assumption in a purely supervised setting the upper bounds lie significantly below the lower bounds for pac learning without co training thus co training saves labeled data even when not combined with unlabeled data on the other hand the saving is much less radical than the known savings in the semi supervised setting

replacing model categories with simplicial ones in this paper we show that model categories of a very broad class can be replaced up to quillen equivalence by simplicial model categories

simplicial structures on model categories and functors we produce a highly structured way of associating a simplicial category to a model category which improves on work of dwyer and kan and answers a question of hovey we show that model categories satisfying a certain axiom are quillen equivalent to simplicial model categories a simplicial model category provides higher order structure such as composable mapping spaces and homotopy colimits we also show that certain homotopy invariant functors can be replaced by weakly equivalent simplicial or continuous functors this is used to show that if a simplicial model category structure exists on a model category then it is unique up to simplicial quillen equivalence

on autoequivalences of the infty 1 category of infty operads we study the infty 1 category of autoequivalences of infty operads using techniques introduced by toen lurie and barwick and schommer pries we prove that this infty 1 category is a contractible infty groupoid our calculation is based on the model of complete dendroidal segal spaces introduced by cisinski and moerdijk similarly we prove that the infty 1 category of autoequivalences of non symmetric infty operads is the discrete monoidal category associated to mathbf z 2 mathbf z we also include a computation of the infty 1 category of autoequivalences of infty n categories based on rezk s theta n spaces

a uniqueness theorem for stable homotopy theory roughly speaking the stable homotopy category of algebraic topology is obtained from the homotopy category of topological spaces by inverting the suspension functor yielding a linear approximation to the homotopy category of spaces the isomorphism classes of objects in the stable homotopy category represent the generalized cohomology theories defined by the eilenberg steenrod axioms es45 without the dimension axiom which distinguishes ordinary from generalized cohomology theories the first construction of the full stable homotopy category was given by boardman b69 nowadays manymodels for the stable homotopy category are known most of which have the additional structure of a closed model category in the sense of quillen q67 in m83 h r margolis introduced a short list of axioms and conjectured that they characterize the stable homotopy category up to an equivalence of categories in theorem 3 2 we prove that these axioms do uniquely specify the stable homotopy category whenever there is some underlying quillen model category we also prove amore structured version theuniqueness theorembelow which states that the model category of spectra itself is uniquely determined by certain equivalent conditions up to so called quillen equivalence of

input output finite region stability and stabilization for discrete 2 d fornasini marchesini models abstract this paper establishes input output finite region stability i o frs and stabilization analysis methods to investigate the transient behavior of output signals for discrete two dimensional 2 d fornasini marchesini fm models for 2 d systems with two classes of input signals by building special recursive formulas sufficient i o frs conditions are formulated in terms of solvability of linear matrix inequalities lmis furthermore aiming at designing static state feedback controllers i o finite region stabilization issues are analyzed for the corresponding 2 d systems and sufficient conditions are reported to guarantee i o frs of the closed loop systems to conclude the paper we provide some numerical examples to confirm the validity of the proposed methods

a metric entropy bound is not sufficient for learnability the authors prove by means of a counterexample that it is not sufficient for probably approximately correct pac learning under a class of distributions to have a uniform bound on the metric entropy of the class of concepts to be learned this settles a conjecture of benedek and itai 1991

probably approximate learning over classes of distributions this paper presents algorithms that construct approximations to sets and functions on the reals from randomly chosen sample points the model that is analyzed is a generalization of the paradigm of probably approximate learning proposed by valiant previously necessary and sufficient conditions for learning sets were established for the case when the class of sampling distributions is finite and for the case when the class of sampling distributions is the set of all possible distributions here sufficient conditions are obtained for learning sets and functions over general classes of sampling distributions the results for functions are with respect to general metrics for measuring the distance between two functions

topological hypercovers and 1 realizations we show that if u is a hypercover of a topological space x then the natural map hocolim u x is a weak equivalence this fact is used to construct topological realization functors for the 1 homotopy theory of schemes over real and complex fields in an appendix we also prove a theorem about computing homotopy colimits of spaces that are not cofibrant

pac learning with generalized samples and an applicaiton to stochastic geometry an extension of the standard probably approximately correct pac learning model that allows the use of generalized samples is introduced a generalized sample is viewed as a pair consisting of a functional on the concept class together with the value obtained by the functional operating on the unknown concept it appears that this model can be applied to a number of problems in signal processing and geometric reconstruction to provide sample size bounds under a pac criterion a specific application of the generalized model to a problem of curve reconstruction is considered and some connections with a result from stochastic geometry are discussed

learning by canonical smooth estimation ii learning and choice of model complexity this paper analyzes the properties of a procedure for learning from examples this canonical learner is based on a canonical error estimator developed in part i in learning problems one can observe data that consists of labeled sample points and the goal is to find a model or hypothesis from a set of candidates that will accurately predict the labels of new sample points the expected mismatch between a hypothesis prediction and the actual label of a new sample point is called the hypothesis generalization error we compare the canonical learner with the traditional technique of finding hypotheses that minimize the relative frequency based empirical error estimate it is shown that for a broad class of learning problems the set of cases for which such empirical error minimization works is a proper subset of the cases for which the canonical learner works we derive bounds to show that the number of samples required by these two methods is comparable we also address the issue of how to determine the appropriate complexity for the class of candidate hypotheses

learnability and the vapnik chervonenkis dimension valiant s learnability model is extended to learning classes of concepts defined by regions in euclidean space e n the methods in this paper lead to a unified treatment of some of valiant s results along with previous results on distribution free convergence of certain pattern recognition algorithms it is shown that the essential condition for distribution free learnability is finiteness of the vapnik chervonenkis dimension a simple combinatorial parameter of the class of concepts to be learned using this parameter the complexity and closure properties of learnable classes are analyzed and the necessary and sufficient conditions are provided for feasible learnability

the homotopy theory of dg categories and derived morita theory the main purpose of this work is to study the homotopy theory of dg categories up to quasi equivalences our main result is a description of the mapping spaces between two dg categories c and d in terms of the nerve of a certain category of c d bimodules we also prove that the homotopy category ho dg cat possesses internal hom s relative to the derived tensor product of dg categories we use these two results in order to prove a derived version of morita theory describing the morphisms between dg categories of modules over two dg categories c and d as the dg category of c d bi modules finally we give three applications of our results the first one expresses hochschild cohomology as endomorphisms of the identity functor as well as higher homotopy groups of the classifying space of dg categories i e the nerve of the category of dg categories and quasi equivalences between them the second application is the existence of a good theory of localization for dg categories defined in terms of a natural universal property our last application states that the dg category of continuous morphisms between the dg categories of quasi coherent resp perfect complexes on two schemes resp smooth and proper schemes is quasi equivalent to the dg category of quasi coherent resp perfect complexes on their product

are all localizing subcategories of stable homotopy categories coreflective abstract we prove that in a triangulated category with combinatorial models every localizing subcategory is coreflective and every colocalizing subcategory is reflective if a certain large cardinal axiom vop nka s principle is assumed true it follows that under the same assumptions orthogonality sets up a bijective correspondence between localizing subcategories and colocalizing subcategories the existence of such a bijection was left as an open problem by hovey palmieri and strickland in their axiomatic study of stable homotopy categories and also by neeman in the context of well generated triangulated categories

stability analysis of stochastic delayed systems with an application to multi agent systems this technical note is concerned with the stability problem of stochastic delayed systems by using a more general halanay type inequality with time varying coefficients a new comparison principle of the proposed halanay type inequality is developed to ensure the stability of stochastic delayed systems the p th moment stability p th moment asymptotic stability and p th moment exponential stability are investigated by means of the proposed general halanay type inequality two examples including one of the consensus of multi agent systems with time varying topologies and transmission delays are presented to demonstrate the effectiveness of the proposed results

robust h_ infty filtering for two dimensional uncertain linear discrete time varying systems a krein space based method a robust h infty filtering algorithm is proposed for two dimensional 2 d linear uncertain time varying systems in this study the considered 2 d systems are subject to unknown inputs measurement noises and time varying modeling uncertainties to appropriately deal with the system uncertainties a new problem formulation of robust h infty filter design for 2 d uncertain systems is first presented by introducing an alternative indefinite quadratic performance function in lieu of the standard h infty performance index then the robust 2 d h infty filter design is converted to an optimization problem of finding the positive minimum of the new indefinite quadratic performance function under certain conditions by relating this quadratic form to a specific 2 d state space model in krein space the krein space estimation theory is used to solve the reformulated optimization problem a recursive robust 2 d time varying h infty filter and its explicit condition for the existence are obtained through projection techniques in 2 d krein space one thermal process plant is used to illustrate the effectiveness of the proposed filter

finite region dissipative dynamic output feedback control for 2 d fm systems with missing measurements abstract this paper focuses on the finite region dissipative dynamic output feedback control problem for a class of discrete time two dimensional 2 d fornasini marchesini fm systems with missing measurements firstly the definitions of finite region boundedness frb and finite region t s r dissipativity are introduced for 2 d fm systems secondly sufficient conditions on the frb and finite region t s r dissipativity of the resultant closed loop 2 d systems are obtained by the construction of the lyapunov function and the special recursive formulas thirdly based on the decoupling technique the desired dynamic output feedback controller design method for the considered 2 d systems is further provided in the end an example of the metal rolling process is given to show the effectiveness of the proposed design results

derived equivalences induced by big cotilting modules abstract we prove that given a grothendieck category g with a tilting object of finite projective dimension the induced triangle equivalence sends an injective cogenerator of g to a big cotilting module moreover every big cotilting module can be constructed like that in an essentially unique way we also prove that the triangle equivalence is at the base of an equivalence of derivators which in turn is induced by a quillen equivalence with respect to suitable abelian model structures on the corresponding categories of complexes

improved lower bounds for learning from noisy examples this paper presents a general information theoretic approach for obtaining lower bounds on the number of examples required for probably approximately correct pac learning in the presence of noise this approach deals directly with the fundamental information quantities avoiding a bayesian analysis the technique is applied to several different models illustrating its generality and power the resulting bounds add logarithmic factors to or improve the constants in previously known lower bounds

smart pac learners the pac learning model is distribution independent in the sense that the learner must reach a learning goal with a limited number of labeled random examples without any prior knowledge of the underlying domain distribution in order to achieve this one needs generalization error bounds that are valid uniformly for every domain distribution these bounds are almost tight in the sense that there is a domain distribution which does not admit a generalization error being significantly smaller than the general bound note however that this leaves open the possibility to achieve the learning goal faster if the underlying distribution is simple informally speaking we say a pac learner l is smart if for a vast majority of domain distributions d l does not require significantly more examples to reach the learning goal than the best learner whose strategy is specialized to d in this paper focusing on sample complexity and ignoring computational issues we show that smart learners do exist this implies at least from an information theoretical perspective that full prior knowledge of the domain distribution or access to a huge collection of unlabeled examples does for a vast majority of domain distributions not significantly reduce the number of labeled examples required to achieve the learning goal

left fibrations and homotopy colimits for a small category mathbf a we prove that the homotopy colimit functor from the category of simplicial diagrams on mathbf a to the category of simplicial sets over the nerve of mathbf a establishes a left quillen equivalence between the projective or reedy model structure on the former category and the covariant model structure on the latter we compare this equivalence to a quillen equivalence in the opposite direction previously established by lurie from our results we deduce that a categorical equivalence of simplicial sets induces a quillen equivalence on the corresponding over categories equipped with the covariant model structures also we show that a version of quillen s theorem a for infty categories easily follows

lmi stability conditions for 2d roesser models this note is devoted to the stability analysis of linear two dimensional systems described by continuous discrete or mixed roesser models commonly used polynomial based tests of stability are reduced to that of solving a set of linear matrix inequalities the main contribution is that the approach is very general and the criteria under certain hypothesis are not conservative

combinatorial model categories have presentations abstract we show that every combinatorial model category is quillen equivalent to a localization of a diagram category where diagram category means diagrams of simplicial sets this says that every combinatorial model category can be built from a category of generators and a set of relations

universal homotopy theories abstract begin with a small category c the goal of this short note is to point out that there is such a thing as a universal model category built from c we describe applications of this to the study of homotopy colimits the dwyer kan theory of framings sheaf theory and the homotopy theory of schemes

homotopical and operator algebraic twisted k theory using the framework for multiplicative parametrized homotopy theory introduced in joint work with c schlichtkrull we produce a multiplicative comparison between the homotopical and operator algebraic constructions of twisted k theory both in the real and complex case we also improve several comparison results about twisted k theory of c algebras to include multiplicative structures our results can also be interpreted in the infty categorical setup for parametrized spectra

stochastic stability analysis for 2 d roesser systems with multiplicative noise this paper is concerned with the robust stochastic stability analysis for two dimensional 2 d discrete state multiplicative noisy systems smnss in the roesser form we first derive a new sufficient condition under which linear discrete 2 d smnss are 2 d robustly stochastically stable the underlying problem can then be recast as a convex problem expressed by linear matrix inequalities which can be facilitated using existing numerical algorithms we then apply the obtained result to examine the 2 d robust stochastic stability for 2 d digital filters in the roesser form with random coefficient variation and saturation overflow arithmetic based on free weighting matrices and diagonally dominant matrices an illustrative example is presented to verify the usefulness and potential of the proposed results

modules over motivic cohomology abstract for fields of characteristic zero we show that the homotopy category of modules over the motivic ring spectrum representing motivic cohomology is equivalent to voevodsky s big category of motives the proof makes use of some highly structured models for motivic stable homotopy theory motivic spanier whitehead duality the homotopy theories of motivic functors and of motivic spaces with transfers as introduced from ground up in this paper working with rational coefficients we extend the equivalence for fields of characteristic zero to all perfect fields by employing the techniques of alterations and homotopy purity in motivic homotopy theory

some contributions to fixed distribution learning theory we consider some problems in learning with respect to a fixed distribution we introduce two new notions of learnability these are probably uniformly approximately correct puac learnability which is a stronger requirement than the widely studied pac learnability and minimal empirical risk mer learnability which is a stronger requirement than the previously defined notions of solid or potential learnability it is shown that although the motivations for defining these two notions of learnability are entirely different these two notions are in fact equivalent to each other and in turn equivalent to a property introduced here referred to as the shrinking width property it is further shown that if the function class to be learned has the property that empirical means converge uniformly to their true values then all of these learnability properties hold in the course of proving conditions for these forms of learnability we also obtain a new estimate for the vc dimension of a collection of sets obtained by performing boolean operations on a given collection this result is of independent interest we consider both the case in which there is an underlying target function as well as the case of model free or agnostic learning finally we consider the issue of representation of a collection of sets by its subcollection of equivalence classes it is shown by example that by suitably choosing representatives of each equivalence class it is possible to affect the property of uniform convergence of empirical probabilities

topological equivalences for differential graded algebras we investigate the relationship between differential graded algebras dgas and topological ring spectra every dga c gives rise to an eilenberg mac lane ring spectrum denoted hc if hc and hd are weakly equivalent then we say c and d are topologically equivalent quasi isomorphic dgas are topologically equivalent but we produce explicit counterexamples of the converse we also develop an associated notion of topological morita equivalence using a homotopical version of tilting

sample size lower bounds in pac learning by algorithmic complexity theory this paper focuses on a general setup for obtaining sample size lower bounds for learning concept classes under fixed distribution laws in an extended pac learning framework these bounds do not depend on the running time of learning procedures and are information theoretic in nature they are based on incompressibility methods drawn from kolmogorov complexity and algorithmic probability theories

on a fat small object argument abstract good colimits introduced by j lurie generalize transfinite composites and provide an important tool for understanding cofibrant generation in locally presentable categories we will explore the relation of good colimits to transfinite composites further and show in particular how they eliminate the use of large objects in the usual small object argument

on the sample complexity of pac learning half spaces against the uniform distribution we prove an spl omega d spl epsiv 1 spl epsiv log1 spl delta lower bound on the pac probably approximately correct learning sample complexity of learning half spaces against the uniform distribution on the unit ball in r sup d

distributed h state estimation for stochastic delayed 2 d systems with randomly varying nonlinearities over saturated sensor networks in this paper the distributed h state estimation problem is investigated for the two dimensional 2 d time delay systems the target plant is characterized by the generalized fornasini marchesini 2 d equations where both stochastic disturbances and randomly varying nonlinearities rvns are considered the sensor measurement outputs are subject to saturation restrictions due to the physical limitations of the sensors based on the available measurement outputs from each individual sensor and its neighboring sensors the main purpose of this paper is to design distributed state estimators such that not only the states of the target plant are estimated but also the prescribed h disturbance attenuation performance is guaranteed by defining an energy like function and utilizing the stochastic analysis as well as the inequality techniques sufficient conditions are established under which the augmented estimation error system is globally asymptotically stable in the mean square and the prescribed h performance index is satisfied furthermore the explicit expressions of the individual estimators are also derived finally numerical example is exploited to demonstrate the effectiveness of the results obtained in this paper

k theory and the bridge from motives to noncommutative motives abstract in this work we present a new approach to the theory of noncommutative motives and use it to explain the different flavors of algebraic k theory of schemes and dg categories the work is divided into three main parts in the first part we use the techniques of higher algebra developed in 63 to provide a universal characterization for the symmetric monoidal 1 category underlying the motivic stable a 1 homotopy theory of morel voevodsky 107 67 more precisely given a symmetric monoidal model category v together with an object x v we characterize the underlying symmetric monoidal 1 category of the symmetric monoidal model category sp v x introduced by hovey in 43 by means of a universal property amongst symmetric monoidal 1 categories this characterization trivializes the problem of finding motivic monoidal realizations in the second part we introduce a new approach to the theory of noncommutative motives by constructing a stable motivic homotopy theory for the noncommutative spaces of kontsevich 56 55 54 the key ingredient is a notion of nisnevich topology in the noncommutative setting compatible with the classical notion this compatibility together with the universal property proved in the first part ensures the existence of a canonical monoidal map from the stable motivic theory of morel voevodsky towards these new noncommutative motives that allow us to compare the two theories in the last part of this paper we explain how this bridge can be used to explain the various flavors of algebraic k theory of dg categories more precisely we prove that the non connective k theory of dg categories introduced by schlichting 82 is the non commutative nisnevich sheafification of connective algebraic k theory then we prove that its further non commutative a 1 localization is a tensor unit in our noncommutative motives as a corollary we obtain a precise proof for an original conjecture of kontsevich claiming that k theory gives the correct mapping spaces in noncommutative motives our major application is the discovery of a canonical factorization of our motivic bridge through the 1 category of modules over the commutative algebra object representing homotopy invariant algebraic k theory of schemes the results in 77 imply that this bridge is fully faithful over a field k with resolutions of singularities so that at the motivic level no information below k theory is lost by passing to the noncommutative world

on homotopy varieties given an algebraic theory t a homotopy t algebra is a simplicial set where all equations from t hold up to homotopy all homotopy t algebras form a homotopy variety we will give a characterization of homotopy varieties analogous to the characterization of varieties

k theory and derived equivalences we show that if two rings have equivalent derived categories then they have the same algebraic k theory similar results are given for g theory and for a large class of abelian categories

brief paper finite time control of discrete time linear systems analysis and design conditions in this paper we deal with some finite time control problems for discrete time time varying linear systems first we provide necessary and sufficient conditions for finite time stability these conditions require either the computation of the state transition matrix of the system or the solution of a certain difference lyapunov inequality then we address the design problem the proposed conditions allow us to find output feedback controllers which stabilize the closed loop system in the finite time sense all these conditions can be expressed in terms of lmis and therefore are numerically tractable as shown in the example included in the paper

brief paper h filtering for 2d markovian jump systems this paper is concerned with the problem of h filtering for 2d discrete markovian jump systems the mathematical model of 2d jump systems is established upon the well known roesser model our attention is focused on the design of a full order filter which guarantees the filtering error system to be mean square asymptotically stable and has a prescribed h disturbance attenuation performance sufficient conditions for the existence of a desired filter are established in terms of linear matrix inequalities lmis and the corresponding filter design is cast into a convex optimization problem which can be efficiently solved by using commercially available numerical software a numerical example is provided to illustrate the effectiveness of the proposed design method

monoidal uniqueness of stable homotopy theory we show that the monoidal product on the stable homotopy category of spectra is essentially unique this strengthens work of this author with schwede on the uniqueness of models of the stable homotopy theory of spectra also the equivalences constructed here give a unified construction of the known equivalences of the various symmetric monoidal categories of spectra s modules w spaces orthogonal spectra simplicial functors with symmetric spectra as an application we show that with an added assumption about underlying model structures margolis axioms uniquely determine the stable homotopy category of spectra up to monoidal equivalence

primary operations in differential cohomology abstract we characterize primary operations in differential cohomology via stacks and illustrate by differentially refining steenrod squares and steenrod powers explicitly this requires a delicate interplay between integral rational and mod p cohomology as well as cohomology with u 1 coefficients and differential forms along the way we develop computational techniques in differential cohomology including a kunneth decomposition that should also be useful in their own right and point to applications to higher geometry and mathematical physics

orbispaces orthogonal spaces and the universal compact lie group this paper identifies the homotopy theories of topological stacks and orbispaces with unstable global homotopy theory at the same time we provide a new perspective by interpreting it as the homotopy theory of spaces with an action of the universal compact lie group the upshot is a novel way to construct and study genuine cohomology theories on stacks orbifolds and orbispaces defined from stable global homotopy types represented by orthogonal spectra the universal compact lie group which is neither compact nor a lie group is a well known object namely the topological monoid mathcal l of linear isometric self embeddings of mathbb r infty the underlying space of mathcal l is contractible and the homotopy theory of mathcal l spaces with respect to underlying weak equivalences is just another model for the homotopy theory of spaces however the monoid mathcal l contains copies of all compact lie groups in a specific way and we define global equivalences of mathcal l spaces by testing on corresponding fixed points we establish a global model structure on the category of mathcal l spaces and prove it to be quillen equivalent to the global model category of orthogonal spaces and to the category of orbispaces i e presheaves of spaces on the global orbit category

dissipativity analysis and synthesis for discrete time t s fuzzy stochastic systemswith time varying delay this paper is concerned with the problems of dissipativity analysis and synthesis for discrete time takagi sugeno fuzzy systems with stochastic perturbation and time varying delay first a novel model transformation method is introduced to pull the time varying delay uncertainty out of the original system consequently the transformed model is composed of a linear time invariant system and a norm bounded uncertain subsystem by using this model transformation method combined with the lyapunov krasovskii technique sufficient conditions of the dissipativity are established then a fuzzy controller is designed to guarantee the dissipative performance of the closed loop system finally three examples are presented one shows the effectiveness of model transformation method the second performs the comparison with alternative approaches and the third illustrates the applicability of the proposed dissipative control methods

frobenius and the derived centers of algebraic theories we show that the derived center of the category of simplicial algebras over every algebraic theory is homotopically discrete with the abelian monoid of components isomorphic to the center of the category of discrete algebras for example in the case of commutative algebras in characteristic p this center is freely generated by frobenius our proof involves the calculation of homotopy coherent centers of categories of simplicial presheaves as well as of bousfield localizations numerous other classes of examples are discussed

computational limitations on learning from examples the computational complexity of learning boolean concepts from examples is investigated it is shown for various classes of concept representations that these cannot be learned feasibly in a distribution free sense unless r np these classes include a disjunctions of two monomials b boolean threshold functions and c boolean formulas in which each variable occurs at most once relationships between learning of heuristics and finding approximate solutions to np hard optimization problems are given

finite time stabilization of high order stochastic nonlinear systems in strict feedback form this paper deals with the problem of finite time stabilization for a class of high order stochastic nonlinear systems in strict feedback form by using ito s formula mathematical induction and backstepping design method a novel state feedback controller is constructed to guarantee that the closed loop high order nonlinear system has a unique solution and the solution of the closed loop high order nonlinear system is finite time stable a systematic design algorithm is developed for the construction of the backstepping controller finally the effectiveness of the state feedback controller is illustrated by two examples

the importance of convexity in learning with squared loss we show that if the closure of a function class f under the metric induced by some probability distribution is not convex then the sample complexity for agnostically learning f with squared loss using only hypotheses in f is spl omega ln 1 spl delta spl epsiv sup 2 where 1 spl delta is the probability of success and spl epsiv is the required accuracy in comparison if the class f is convex and has finite pseudodimension then the sample complexity is o 1 spl epsiv ln 1 spl epsiv ln 1 b if a nonconvex class f has finite pseudodimension then the sample complexity for agnostically learning the closure of the convex hull of f is o 1 spl epsiv 1 spl epsiv ln 1 spl epsiv ln 1 spl delta hence for agnostic learning learning the convex hull provides better approximation capabilities with little sample complexity penalty