asymptotic equivalence of nonparametric regression and white noise the principal result is that under conditions to any nonparametric regression problem there corresponds an asymptotically equivalent sequence of white noise with drift problems and conversely this asymptotic equivalence is in a global and uniform sense any normalized risk function attainable in one problem is asymptotically attainable in the other with the difference in normalized risks converging to zero uniformly over the entire parameter space the results are constructive a recipe is provided for producing these asymptotically equivalent procedures some implications and generalizations of the principal result are also discussed

on the minimum stable commutation time for switching nonlinear systems real systems are often driven by switching reference signals which affect dynamics and or equilibrium points this technical note addresses the computation of upper bounds of the minimum commutation time ensuring stability for switching nonlinear systems specifically we consider the cases of constant and variable equilibrium point of interest for polynomial systems and for a class of non polynomial systems we hence propose upper bounds of the sought minimum commutation time by adopting homogeneous polynomial lyapunov functions for the former case and polynomial lyapunov functions for the latter one which can be computed via linear matrix inequaltiy optimizations for given lyapunov functions

characterization and computation of disturbance invariant sets for constrained switched linear systems with dwell time restriction this paper introduces the concept and characterization of disturbance dwell time invariance ddt invariance and constraint admissible ddt invariance caddt invariance for constrained systems with additive disturbance under dwell time switching using the characterization necessary and sufficient conditions for ddt invariance and algorithms for the computation of the minimal and maximal constraint admissible convex ddt invariant sets are provided numerical examples of such sets for several systems are also provided

construction of surfaces of general type from elliptic surfaces via q gorenstein smoothing we present methods to construct interesting surfaces of general type via mathbb q gorenstein smoothing of a singular surface obtained from an elliptic surface by applying our methods to special enriques surfaces we construct new examples of a minimal surface of general type with p g 0 pi 1 mathbb z 2 mathbb z and k2 4

asymptotic equivalence for nonparametric regression with multivariate and random design we show that nonparametric regression is asymptotically equivalent in le cam s sense to a sequence of gaussian white noise experiments as the number of observations tends to infinity we propose a general constructive framework based on approximation spaces which allows asymptotic equivalence to be achieved even in the cases of multivariate and random design

exceptional collections of line bundles on the beauville surface abstract we construct quasi phantom admissible subcategories in the derived category of coherent sheaves on the beauville surface s these quasi phantoms subcategories appear as right orthogonals to subcategories generated by exceptional collections of maximal possible length 4 on s we prove that there are exactly 6 exceptional collections consisting of line bundles up to a twist and these collections are spires of two helices

a converse lyapunov theorem for nonlinear switched systems abstract in this paper we present a converse lyapunov theorem for uniform asymptotic stability of switched nonlinear systems its proof is a simple consequence of some results on converse lyapunov theorems for systems with bounded disturbances obtained by lin et al siam j control optim 34 1996 124 160 once an association of the switched system with a nonlinear system with disturbances is established

on the derived category of the classical godeaux surface abstract we construct an exceptional sequence of length 11 on the classical godeaux surface x which is the z 5 z quotient of the fermat quintic surface in p 3 this is the maximal possible length of such a sequence on this surface which has grothendieck group z 11 z 5 z in particular the result answers kuznetsov s nonvanishing conjecture which concerns hochschild homology of an admissible subcategory in the negative the sequence carries a symmetry when interpreted in terms of the root lattice of the simple lie algebra of type e 8 we also produce explicit nonzero objects in the right orthogonal to the exceptional sequence

brief paper control design with guaranteed ultimate bound for perturbed systems we present a new control design method for perturbed multiple input systems which guarantees any desired componentwise ultimate bound on the system state the method involves eigenvalue eigenvector assignment by state feedback and utilises a componentwise bound computation procedure this procedure directly takes into account both the system and perturbation structures by performing componentwise analysis thus avoiding the need for bounds on the norm of the perturbation the perturbation description adopted can accommodate numerous types of uncertainties including uncertain time delays in the feedback loop we apply the method to an example taken from the literature to illustrate its simplicity and generality

rodeo sparse greedy nonparametric regression we present a greedy method for simultaneously performing local bandwidth selection and variable selection in nonparametric regression the method starts with a local linear estimator with large bandwidths and incrementally decreases the bandwidth of variables for which the gradient of the estimator with respect to bandwidth is large the method called rodeo regularization of derivative expectation operator conducts a sequence of hypothesis tests to threshold derivatives and is easy to implement under certain assumptions on the regression function and sampling density it is shown that the rodeo applied to local linear smoothing avoids the curse of dimensionality achieving near optimal minimax rates of convergence in the number of relevant variables as if these variables were isolated in advance

exceptional collections on dolgachev surfaces associated with degenerations abstract dolgachev surfaces are simply connected minimal elliptic surfaces with p g q 0 and of kodaira dimension 1 these surfaces are constructed by logarithmic transformations of rational elliptic surfaces in this paper we explain the construction of dolgachev surfaces via q gorenstein smoothing of singular rational surfaces with two cyclic quotient singularities this construction is based on the paper 25 also some exceptional bundles on dolgachev surfaces associated with q gorenstein smoothing have been constructed based on the idea of hacking 12 in the case if dolgachev surfaces were of type 2 3 we describe the picard group and present an exceptional collection of maximal length finally we prove that the presented exceptional collection is not full hence there exists a nontrivial phantom category in the derived category

stability criteria for switched and hybrid systems the study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems the objective of this paper is to outline some of these problems to review progress made in solving them in a number of diverse communities and to review some problems that remain open an important contribution of our work is to bring together material from several areas of research and to present results in a unified manner we begin our review by relating the stability problem for switched linear systems and a class of linear differential inclusions closely related to the concept of stability are the notions of exponential growth rates and converse lyapunov theorems both of which are discussed in detail in particular results on common quadratic lyapunov functions and piecewise linear lyapunov functions are presented as they represent constructive methods for proving stability and also represent problems in which significant progress has been made we also comment on the inherent difficulty in determining stability of switched systems in general which is exemplified by np hardness and undecidability results we then proceed by considering the stability of switched systems in which there are constraints on the switching rules through both dwell time requirements and state dependent switching laws also in this case the theory of lyapunov functions and the existence of converse theorems are reviewed we briefly comment on the classical lur e problem and on the theory of stability radii both of which contain many of the features of switched systems and are rich sources of practical results on the topic finally we present a list of questions and open problems which provide motivation for continued research in this area

an lmi approach for h analysis and control of discrete time piecewise affine systems in this paper we investigate some analysis and control problems for discrete time hybrid systems in the piece wise affine form by using arguments from the dissipativity theory for non linear systems we show that h x analysis and synthesis problems can be formulated and solved via linear matrix inequalities by taking into account the switching structure of the considered system in this paper we address the generalized problem of controlling hybrid systems whose switching structure does not depend only on the state but also on the control input

switched systems with average dwell time computation of the robust positive invariant set abstract in this paper computational results of robust positive invariant rpi sets for switched systems with amplitude bounded persistent additive disturbance and average dwell time adt switching are developed towards this end new idea for facilitating the analysis of the adt switching signal is conceptualized by a series of predefined stages and sufficient conditions for the existence of an adt rpi set of the considered systems are established by utilizing the structure characteristics at each stage of the adt switching signal an exact computational algorithm of the adt rpi set of the considered system is developed the effectiveness of the proposed algorithms are illustrated by a numerical example

constraint admissible state sets for switched systems with average dwell time abstract the exact computational problem of constrained admissible average dwell time caadt contractive set and caadt invariant set for discrete time switched systems with and without persistent amplitude bounded additive disturbance is investigated in this paper the considered switching signal satisfies average dwell time adt and is discussed in terms of stage which is both length based and sequence based for the first time two more general criteria are established for checking the existence of the average dwell time adt contractive set and the adt invariant set of the considered system by assuming the value of stage length is taken from an arbitrary finite set a detailed discussion is included to identify a proper value for stage length by taking the computational complexity and the conservatism of the designed finite step computational algorithms of the caadt contractive set and the caadt invariant set into consideration some characteristics of the admissible caadt contractive set and caadt invariant set are derived an illustrative example illustrates the effectiveness of the developed results

equivalence theory for density estimation poisson processes and gaussian white noise with drift this paper establishes the global asymptotic equivalence between a poisson process with variable intensity and white noise with drift under sharp smoothness conditions on the unknown function this equivalence is also extended to density estimation models by poissonization the asymptotic equivalences are established by constructing explicit equivalence mappings the impact of such asymptotic equivalence results is that an investigation in one of these nonparametric models automatically yields asymptotically analogous results in the other models

stability analysis of switched systems using variational principles an introduction many natural and artificial systems and processes encompass several modes of operation with a different dynamical behavior in each mode switched systems provide a suitable mathematical model for such processes and their stability analysis is important for both theoretical and practical reasons we review a specific approach for stability analysis based on using variational principles to characterize the most unstable solution of the switched system we also discuss a link between the variational approach and the stability analysis of switched systems using lie algebraic considerations both approaches require the use of sophisticated tools from many different fields of applied mathematics the purpose of this paper is to provide an accessible and self contained review of these topics emphasizing the intuitive and geometric underlying ideas

brief paper on the algebraic characterization of invariant sets of switched linear systems in this paper a suitable lasalle principle for continuous time linear switched systems is used to characterize invariant sets and their associated switching laws an algorithm to determine algebraically these invariants is proposed the main novelty of our approach is that we require no dwell time conditions on the switching laws by not focusing on restricted control classes we are able to describe the asymptotic properties of the considered switched systems observability analysis of a flying capacitor converter is proposed as an illustration

adaptive estimation of a quadratic functional by model selection we consider the problem of estimating s 2 when s belongs to some separable hilbert space and one observes the gaussian process y t langles t rangle sigmal t for all t epsilon mathbb h where l is some gaussian isonormal process this framework allows us in particular to consider the classical gaussian sequence model for which mathbb h l 2 mathbb n and l t sum lambda geq1 t lambda varepsilon lambda where varepsilon lambda lambda geq1 is a sequence of i i d standard normal variables our approach consists in considering some at most countable families of finite dimensional linear subspaces of mathbb h the models and then using model selection via some conveniently penalized least squares criterion to build new estimators of s 2 we prove a general nonasymptotic risk bound which allows us to show that such penalized estimators are adaptive on a variety of collections of sets for the parameter s depending on the family of models from which they are built in particular in the context of the gaussian sequence model a convenient choice of the family of models allows defining estimators which are adaptive over collections of hyperrectangles ellipsoids l p bodies or besov bodies we take special care to describe the conditions under which the penalized estimator is efficient when the level of noise sigma tends to zero our construction is an alternative to the one by efroimovich and low for hyperrectangles and provides new results otherwise

computation of maximal safe sets for switching systems the problem of determining maximal safe sets and hybrid controllers is computationally intractable because of the mathematical generality of hybrid system models given the practical and theoretical relevance of the problem finding implementable procedures that could at least approximate the maximal safe set is important to this end we begin by restricting our attention to a special class of hybrid systems switching systems we exploit the structural properties of the graph describing the discrete part of a switching system to develop an efficient procedure for the computation of the safe set this procedure requires the computation of a maximal controlled invariant set we then restrict our attention to linear discrete time systems for which there is a wealth of results available in the literature for the determination of maximal controlled invariant sets however even for this class of systems the computation may not converge in a finite number of steps we then propose to compute inner approximations that are controlled invariant and for which a procedure that terminates in a finite number of steps can be obtained a tight bound on the error can be given by comparing the inner approximation with the classical outer approximation of the maximal controlled invariant set our procedure is applied to the idle speed regulation problem in engine control to demonstrate its efficiency

nonconservative lifted convex conditions for stability of discrete time switched systems under minimum dwell time constraint in this note a novel conception called virtual clock which is defined by an artificial timer over a finite cycle is introduced for stability analysis of discrete time switched linear systems under minimum dwell time constraint two necessary and sufficient conditions associated with a virtual clock with a sufficient length are proposed to ensure the global uniform asymptotic stability of discrete time switched linear systems for the two nonconservative stability criteria the lifted version maintains the convexity in system matrices based on the lifted convex conditions the extensions to ell 2 gain computation and mathcal h infty control problems are presented in the sequel in particular a novel virtual clock dependent controller is designed which outperforms the traditional mode dependent and common gain controllers several numerical examples are provided to illustrate our theoretic results

uniform tube based stabilization of switched linear systems with mode dependent persistent dwell time in this note the stabilization problem for a class of discrete time switched linear systems with additive disturbances is investigated the considered switching signals are of mode dependent persistent dwell time mpdt property and the disturbances are assumed to be amplitude bounded by constructing a quasi time varying qtv lyapunov function a qtv stabilizing controller is designed for the nominal system such that the resulting closed loop system is globally uniformly asymptotically stable in the presence of bounded additive disturbances a mpdt robust positive invariant set is determined for the error system between the nominal system and disturbed system a concept of generalized robust positive invariant grpi set under admissible mpdt switching is further proposed for the error system it is demonstrated that the disturbed system is also asymptotically stable in the sense of converging to the mpdt grpi set that can be regarded as the cross section of a uniform tube of the disturbed system a numerical example is provided to verify the theoretical findings

hybrid system stability and robustness verification using linear matrix inequalities this paper addresses issues concerning exponential stability and robustness of hybrid systems stability conditions using lyapunov techniques are given the search for the lyapunov functions is formulated as a linear matrix inequality lmi problem for hybrid systems with affine as well as non linear vector fields it is shown how the lyapunov approach most advantageously also can be used to guarantee stability despite the presence of model uncertainties several examples are given to illustrate the theory

a constructive approach to reachability realization of discrete time switched linear systems this paper studies the reachability of discrete time switched linear systems a new constructive approach to designing switching sequences is developed so that not only the reachable subspace is realized but also the required number of switchings is reduced significantly detailed comparison between the obtained result and that reported in the open literature is also made which verifies the advantage of the proposed approach

tight conditions for consistency of variable selection in the context of high dimensionality we address the issue of variable selection in the regression model with very high ambient dimension textit i e when the number of variables is very large the main focus is on the situation where the number of relevant variables called intrinsic dimension and denoted by d is much smaller than the ambient dimension d without assuming any parametric form of the underlying regression function we get tight conditions making it possible to consistently estimate the set of relevant variables these conditions relate the intrinsic dimension to the ambient dimension and to the sample size the procedure that is provably consistent under these tight conditions is based on comparing quadratic functionals of the empirical fourier coefficients with appropriately chosen threshold values the asymptotic analysis reveals the presence of two quite different re gimes the first regime is when d is fixed in this case the situation in nonparametric regression is the same as in linear regression textit i e consistent variable selection is possible if and only if log d is small compared to the sample size n the picture is different in the second regime d to infty as n to infty where we prove that consistent variable selection in nonparametric set up is possible only if d log log d is small compared to log n we apply these results to derive minimax separation rates for the problem of variable selection

on the moduli space of diffeomorphic algebraic surfaces in this paper we show that the number of deformation types of complex structures on a fixed smooth oriented four manifold can be arbitrarily large the examples that we consider in this paper are locally simple abelian covers of rational surfaces the proof involves the algebraic description of rational blowdowns classical brill noether theory and deformation theory of normal flat abelian covers

optimal adaptive estimation of a quadratic functional minimax mean squared error estimates of quadratic functionals of smooth functions have been constructed for a variety of smoothness classes in contrast to many nonparametric function estimation problems there are both regular and irregular cases in the regular cases the minimax mean squared error converges at a rate proportional to the inverse of the sample size whereas in the irregular case much slower rates are the rule we investigate the problem of adaptive estimation of a quadratic functional of a smooth function when the degree of smoothness of the underlying function is not known it is shown that estimators cannot achieve the minimax rates of convergence simultaneously over two parameter spaces when at least one of these spaces corresponds to the irregular case a lower bound for the mean squared error is given which shows that any adaptive estimator which is rate optimal for the regular case must lose a logarithmic factor in the irregular case on the other hand we give a rather simple adaptive estimator which is sharp for the regular case and attains this lower bound in the irregular case moreover we explicitly describe a subset of functions where our adaptive estimator loses the logarithmic factor and show that this subset is relatively small

on nodal enriques surfaces and quartic double solids we consider the class of singular double coverings x rightarrow mathbb p 3 ramified in the degeneration locus d of a family of 2 dimensional quadrics these are precisely the quartic double solids constructed by artin and mumford as examples of unirational but nonrational conic bundles with such a quartic surface d one can associate an enriques surface s which is the factor of the blowup of d by a natural involution acting without fixed points such enriques surfaces are known as nodal enriques surfaces or reye congruences we show that the nontrivial part of the derived category of coherent sheaves on this enriques surface s is equivalent to the nontrivial part of the derived category of a minimal resolution of singularities of x

exceptional collections and the neron severi lattice for surfaces abstract we work out properties of smooth projective varieties x over a not necessarily algebraically closed field k that admit collections of objects in the bounded derived category of coherent sheaves d b x that are either full exceptional or numerically exceptional of maximal length our main result gives a necessary and sufficient condition on the neron severi lattice for a smooth projective surface s with o s 1 to admit a numerically exceptional collection of maximal length consisting of line bundles as a consequence we determine exactly which complex surfaces with p g q 0 admit a numerically exceptional collection of maximal length another consequence is that a minimal geometrically rational surface with a numerically exceptional collection of maximal length is rational

bayes and empirical bayes multiplicity adjustment in the variable selection problem this paper studies the multiplicity correction effect of standard bayesian variable selection priors in linear regression our first goal is to clarify when and how multiplicity correction happens automatically in bayesian analysis and to distinguish this correction from the bayesian ockham s razor effect our second goal is to contrast empirical bayes and fully bayesian approaches to variable selection through examples theoretical results and simulations considerable differences between the two approaches are found in particular we prove a theorem that characterizes a surprising aymptotic discrepancy between fully bayes and empirical bayes this discrepancy arises from a different source than the failure to account for hyperparameter uncertainty in the empirical bayes estimate indeed even at the extreme when the empirical bayes estimate converges asymptotically to the true variable inclusion probability the potential for a serious difference remains

computations of mode dependent dwell times for discrete time switching system given a system that switches among n linear subsystems this paper shows an approach that computes n dwell times one for each of the subsystems such that the overall system is stable under switching signals that respect the dwell times the dwell times are obtained progressively starting from the groups of all pairwise switching systems and increasing the size of the group by one for each step in each progressive step a bisection search algorithm is used to obtain the mode dependent dwell times for that step when the final step is reached the n mode dwell times are obtained these dwell times are smaller in terms of their sum than an existing approach in recent literature for all the examples considered in this paper

asymptotic approximation of nonparametric regression experiments with unknown variances asymptotic equivalence results for nonparametric regression experiments have always assumed that the variances of the observations are known in practice however the variance of each observation is generally considered to be an unknown nuisance parameter we establish an asymptotic approximation to the nonparametric regression experiment when the value of the variance is an additional parameter to be estimated or tested this asymptotically equivalent experiment has two components the first contains all the information about the variance and the second has all the information about the mean the result can be extended to regression problems where the variance varies slowly from observation to observation

derived categories of surfaces isogenous to a higher product abstract let s c d g be a surface isogenous to a higher product of unmixed type with p g q 0 g z 3 2 we construct exceptional sequences of line bundles of maximal length on s as a consequence we find new examples of quasiphantom categories

asymptotic statistical equivalence for scalar ergodic diffusions for scalar diffusion models with unknown drift function asymptotic equivalence in the sense of le cam s deficiency between statistical experiments is considered under long time asymptotics a local asymptotic equivalence result is established with an accompanying sequence of simple gaussian shift experiments corresponding globally asymptotically equivalent experiments are obtained as compound experiments the results are extended in several directions including time discretisation an explicit transformation of decision functions from the gaussian to the diffusion experiment is constructed

control of systems integrating logic dynamics and constraints this paper proposes a framework for modeling and controlling systems described by interdependent physical laws logic rules and operating constraints denoted as mixed logical dynamical mld systems these are described by linear dynamic equations subject to linear inequalities involving real and integer variables mld systems include linear hybrid systems finite state machines some classes of discrete event systems constrained linear systems and nonlinear systems which can be approximated by piecewise linear functions a predictive control scheme is proposed which is able to stabilize mld systems on desired reference trajectories while fulfilling operating constraints and possibly take into account previous qualitative knowledge in the form of heuristic rules due to the presence of integer variables the resulting on line optimization procedures are solved through mixed integer quadratic programming miqp for which efficient solvers have been recently developed some examples and a simulation case study on a complex gas supply system are reported

derived categories of keum s fake projective planes abstract we conjecture that derived categories of coherent sheaves on fake projective n spaces have a semi orthogonal decomposition into a collection of n 1 exceptional objects and a category with vanishing hochschild homology we prove this for fake projective planes with non abelian automorphism group such as keum s surface then by passing to equivariant categories we construct new examples of phantom categories with both hochschild homology and grothendieck group vanishing

mode identifying time estimation and switching delay tolerant control for switched systems in this paper an elementary time unit etu method is proposed to study the problem of estimating the admissible delay in the identification of the active mode in the analysis and design of switched systems the activation interval of a subsystem is considered to consist of a finite time number of segments called etus by which a novel class of time scheduled lyapunov function is used to estimate the admissible delay in mode identification for switched systems further the etu method is applied for switching delay tolerant control problem and a class of time scheduled state feedback controllers are designed to achieve the exponentially stability several numerical examples are presented to validate the theoretic findings

some comments on cp i study the typical configuration of a cp plot when the number of variables in the regression problem is large and there are many weak effects i show that a particular configuration that is very commonly seen can arise in a simple way i give a formula by means of which the risk incurred by the minimum cp rule can be estimated

brief paper stability results for linear parameter varying and switching systems in this paper stabilizability problems for discrete and continuous time linear systems with switching or polytopic uncertainties are dealt with both state feedback and full information controllers are considered possibly with an integral action several cases will be analyzed depending on the control the uncertainty and the presence of uncertainties in the input matrix a complete overview of the stabilizability implications among these different cases will be given

a numerical technique for the stability analysis of linear switched systems in this paper the ray gridding approach a new numerical technique for the stability analysis of linear switched systems is presented it is based on uniform partitions of the state space in terms of ray directions which allow refinable families of polytopes of adjustable complexity to be examined for invariance in this framework the existence of a polyhedral lyapunov function that is common to a family of asymptotically stable subsystems can be checked efficiently via simple iterative algorithms the technique can be used to prove the stability of switched linear systems classes of linear time varying systems and linear differential lnclusions we also present preliminary results on another related problem namely the construction of multiple polyhedral lyapunov functions for the specification of stabilizing switching sequences for a switched system constructed from a family of stable linear subsystems

high dimensional ising model selection using l1 regularized logistic regression we consider the problem of estimating the graph associated with a binary ising markov random field we describe a method based on l1 regularized logistic regression in which the neighborhood of any given node is estimated by performing logistic regression subject to an l1 constraint the method is analyzed under high dimensional scaling in which both the number of nodes p and maximum neighborhood size d are allowed to grow as a function of the number of observations n our main results provide sufficient conditions on the triple n p d and the model parameters for the method to succeed in consistently estimating the neighborhood of every node in the graph simultaneously with coherence conditions imposed on the population fisher information matrix we prove that consistent neighborhood selection can be obtained for sample sizes n d3log p with exponentially decaying error when these same conditions are imposed directly on the sample matrices we show that a reduced sample size of n d2log p suffices for the method to estimate neighborhoods consistently although this paper focuses on the binary graphical models we indicate how a generalization of the method of the paper would apply to general discrete markov random fields

brief paper the minimal disturbance invariant set outer approximations via its partial sums this paper is concerned with outer approximations of the minimal disturbance invariant set mdis of a discrete time linear system with an additive set bounded disturbance the k step disturbance reachable sets minkowski partial sums are inner approximations of mdis that converge to mdis enlarged by a suitable scaling they can lead to outer approximations of mdis three families of approximations each based on partial sums are considered theoretical properties of the families are proved and interrelated algorithmic questions including error bounds are addressed the results are illustrated by computational data from several examples

criteria of asymptotic stability of differential and difference inclusions encountered in control theory abstract for a class of differential inclusions to which many of the practically important control systems can be reduced necessary and sufficient conditions for asymptotic stability of the zero solution are established by the method of lyapunov functions similar results are obtained for the corresponding class of difference inclusions

stability analysis and control synthesis for switched systems a switched lyapunov function approach this paper addresses the problem of stability analysis and control synthesis of switched systems in the discrete time domain the approach followed in this paper looks at the existence of a switched quadratic lyapunov function to check asymptotic stability of the switched system under consideration two different linear matrix inequality based conditions allow to check the existence of such a lyapunov function the first one is classical while the second is new and uses a slack variable which makes it useful for design problems these two conditions are proved to be equivalent for stability analysis investigating the static output feedback control problem we show that the second condition is in this case less conservative the reduction of the conservatism is illustrated by a numerical evaluation

exceptional bundles associated to degenerations of surfaces in 1981 j wahl described smoothings of surface quotient singularities with no vanishing cycles w81 5 9 1 given a smoothing of a projective surface x of this type we construct an associated exceptional vector bundle on the nearby fiber y in the case h2 0 y h1 y 0 if y p2 we show that our construction establishes a bijective correspondence between the possible degenerate surfaces x and exceptional bundles on y modulo a natural equivalence relation if y is of general type then our construction establishes a connection between components of the boundary of the moduli space of surfaces deformation equivalent to y and exceptional bundles on y let n a be positive integers such that a n and a n 1 consider the cyclic quotient singularity

on robust stability and set invariance of switched linear parameter varying systems in this paper we address the problem of robust stability and set invariance of switched linear parameter varying lpv systems affected by bounded disturbances a switched lpv system is a collection of single lpv subsystems with a switching rule that decides which subsystem is active at each time this framework is useful for lpv systems with large parameter variation range for which it may be difficult to assess or guarantee stability over the whole parameter range our first contribution is to derive a result for a single lpv system that extends and generalises previous work for switched systems our second and main contribution is to apply this seed result in the derivation of dwell time type conditions on the switched lpv switching rule which ensure robust closed loop stability and set invariance of the trajectories of the switched lpv system across the whole parameter range as an application of the results we consider the problem of reference tracking for lpv systems using switched lpv state fe

an improved method of ultimate bound computation for linear switched systems with bounded disturbances in this note an improved method of ultimate bound computation for a linear switched system under arbitrary switching is presented an ultimate bound for a linear switched system can be computed by solving a class of linear matrix inequalities the effectiveness of the obtained results is illustrated by numerical examples

brief paper componentwise ultimate bound and invariant set computation for switched linear systems we present a novel ultimate bound and invariant set computation method for continuous time switched linear systems with disturbances and arbitrary switching the proposed method relies on the existence of a transformation that takes all matrices of the switched linear system into a convenient form satisfying certain properties the method provides ultimate bounds and invariant sets in the form of polyhedral and or mixed ellipsoidal polyhedral sets is completely systematic once the aforementioned transformation is obtained and provides a new sufficient condition for practical stability we show that the transformation required by our method can easily be found in the well known case where the subsystem matrices generate a solvable lie algebra and we provide an algorithm to seek such transformation in the general case an example comparing the bounds obtained by the proposed method with those obtained from a common quadratic lyapunov function computed via linear matrix inequalities shows a clear advantage of the proposed method in some cases

lie algebraic stability criteria for switched systems it was recently shown that a family of exponentially stable linear systems whose matrices generate a solvable lie algebra possesses a quadratic common lyapunov function which implies that the corresponding switched linear system is exponentially stable for arbitrary switching in this paper we prove that the same properties hold under the weaker condition that the lie algebra generated by given matrices can be decomposed into a sum of a solvable ideal and a subalgebra with a compact lie group the corresponding local stability result for nonlinear switched systems is also established moreover we demonstrate that if a lie algebra fails to satisfy the above condition then it can be generated by a family of stable matrices such that the corresponding switched linear system is not stable relevant facts from the theory of lie algebras are collected at the end of the paper for easy reference

brief paper discrete time switching linear system with constraints characterization and computation of invariant sets under dwell time consideration this paper introduces the concepts of dwell time invariant contractive dt invariant contractive set constraint admissible dt invariant contractive cadt invariant contractive set for a discrete time switching system under dwell time switching main contributions of this paper include a characterization for a dt contractive set an algorithm for the computation of the maximal cadt invariant set a necessary and sufficient condition for asymptotic stability of the origin of switching systems under dwell time switching and computation of the minimal dwell time needed for asymptotic stability of the origin

almost sure estimation and synthesis of ultimate bounds for discrete time markov jump linear systems this paper is concerned with the problems of almost sure ultimate bound estimation and controller design for markov jump linear systems with bounded stochastic disturbances by utilising a lyapunov based scheme proposed in this paper an almost sure estimation of ellipsoidal ultimate bound eub of the system is obtained through tractable matrix inequalities on the basis of the estimation results the problem of designing mode dependent state feedback controllers that make the closed loop system admit a prescribed ellipsoid as an eub is considered the obtained results on estimation and synthesis are then extended to the case of systems with deficient mode information finally a practical example in dc motor devices is presented to demonstrate the applicability of the obtained results

brief paper modal and transition dwell time computation in switching systems a set theoretic approach we consider a plant the dynamics of which switch among a family of systems each of these systems has a single stable equilibrium point we assume that a constraint region for the state is assigned and we consider the problem of finding suitable limitations on the commutation speed in order to avoid constraints violations even in the absence of state measurements we introduce the concepts of modal and transition dwell times which lead to the definition of dwell time vector and dwell time graph represented by a proper matrix respectively the former imposes a minimum permanence time on a discrete mode before commuting the latter imposes the minimum permanence time on the current mode before switching to a specific new one both dwell time vector and dwell time graph can be computed via set theoretic techniques when the systems share a single equilibrium state stability can be assured as a special case finally under the assumption of affine dynamics non conservative values are achieved

derived categories of burniat surfaces and exceptional collections we construct an exceptional collection varupsilon of maximal possible length 6 on any of the burniat surfaces with k x 2 6 a 4 dimensional family of surfaces of general type with p g q 0 we also calculate the dg algebra of endomorphisms of this collection and show that the subcategory generated by this collection is the same for all burniat surfaces the semiorthogonal complement mathcal a of varupsilon is an almost phantom category it has trivial hochschild homology and k 0 mathcal a mathbb z 2 6

necessary and sufficient condition for stability of switched uncertain linear systems under dwell time constraint in this technical note a necessary and sufficient stability criterion for switched linear systems under dwell time constraint is proposed by employing a class of time scheduled homogeneous polynomial lyapunov functions with a sufficiently large degree the key feature of this nonconservative condition lies in its convexity in the system matrices which explicitly facilitates its further extension to uncertain systems then in order to obtain numerically testable condition a family of lmi conditions are presented with the aid of the idea of dividing the dwell time interval into a finite number of segments it is proved that the non conservativeness can be maintained with a sufficiently large interval dividing parameter in the end the result is straightforwardly extended to the uncertain case in virtue of the convexity in the system matrices numerical examples are presented to illustrate our findings

stability and stabilizability of switched linear systems a survey of recent results during the past several years there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems this paper aims to briefly survey recent results in this field first the stability analysis for switched systems is reviewed we focus on the stability analysis for switched linear systems under arbitrary switching and we highlight necessary and sufficient conditions for asymptotic stability after a brief review of the stability analysis under restricted switching and the multiple lyapunov function theory the switching stabilization problem is studied and a variety of switching stabilization methods found in the literature are outlined then the switching stabilizability problem is investigated that is under what condition it is possible to stabilize a switched system by properly designing switching control laws note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature a necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here

high dimensional variable selection this paper explores the following question what kind of statistical guarantees can be given when doing variable selection in high dimensional models in particular we look at the error rates and power of some multi stage regression methods in the first stage we fit a set of candidate models in the second stage we select one model by cross validation in the third stage we use hypothesis testing to eliminate some variables we refer to the first two stages as screening and the last stage as cleaning we consider three screening methods the lasso marginal regression and forward stepwise regression our method gives consistent variable selection under certain conditions

a simply connected surface of general type with p g 0 and k 2 2 in this paper we construct a simply connected minimal complex surface of general type with pg 0 and k2 2 using a rational blow down surgery and a gorenstein smoothing theory

bounds and invariant sets for a class of switching systems with delayed state dependent perturbations we present a novel method to compute componentwise transient bounds componentwise ultimate bounds and invariant regions for a class of switching continuous time linear systems with perturbation bounds that may depend nonlinearly on a delayed state the main advantage of the method is its componentwise nature i e the fact that it allows each component of the perturbation vector to have an independent bound and that the bounds and sets obtained are also given componentwise this componentwise method does not employ a norm for bounding either the perturbation or state vectors avoids the need for scaling the different state vector components in order to obtain useful results and may also reduce conservativeness in some cases the present paper builds upon and extends to switching systems with delayed state dependent perturbations previous results by the authors in this sense the contribution is three fold the derivation of the aforementioned extension the elucidation of the precise relationship between the class of switching linear systems to which the proposed method can be applied and those that admit a common quadratic lyapunov function a question that was left open in our previous work and the derivation of a technique to compute a common quadratic lyapunov function for switching linear systems with perturbations bounded componentwise by affine functions of the absolute value of the state vector components in this latter case we also show how our componentwise method can be combined with standard techniques in order to derive bounds possibly tighter than those corresponding to either method applied individually

kernel meets sieve post regularization confidence bands for sparse additive model we develop a novel procedure for constructing confidence bands for components of a sparse additive model our procedure is based on a new kernel sieve hybrid estimator that combines two most popula

height of exceptional collections and hochschild cohomology of quasiphantom categories we define the normal hochschild cohomology of an admissible subcategory of the derived category of coherent sheaves on a smooth projective varietyx a graded vector space which controls the restriction morphism from the hochschild cohomology of x to the hochschild cohomology of the orthogonal complement of this admissible subcategory when the subcategory is generated by an exceptional collection we define a new invariant the height and show that the orthogonal to an exceptional collection of height h in the derived category of a smooth projective varietyx has the same hochschild cohomology asx in degrees up to h 2 we use this to describe the second hochschild cohomology of quasiphantom categories in the derived categories of some surfaces of general type we also give necessary and sufficient conditions for the fullness of an exceptional collection in terms of its height and of its normal hochschild cohomology

stability analysis and l1 gain characterization for switched positive systems under dwell time constraint abstract this paper deals with the problems of stability analysis and l 1 gain characterization for continuous time switched systems consisting of positive subsystems with the aid of a discretized copositive lyapunov function a sufficient condition ensuring the asymptotic stability of continuous time switched positive systems under dwell time constraint is obtained which can be checked via linear programming furthermore the conservatism of the proposed approach is studied and the result with least conservatism in the framework of discretized copositive lyapunov function is obtained the result is then extended to l 1 gain characterization for switched positive systems with a prescribed dwell time an unweighted l 1 gain can be computed via solving a linear programming problem a numerical example and a practical traffic example are given to illustrate our results