control for safety specifications of systems with imperfect information on a partial order in this paper we consider the control problem for uncertain systems with imperfect information in which an output of interest must be kept outside an undesired region the bad set in the output space the state input output and disturbance spaces are equipped with partial orders the system dynamics are either input output order preserving with output in r2 or given by the parallel composition of input output order preserving dynamics each with scalar output we provide necessary and sufficient conditions under which an initial set of possible system states is safe that is the corresponding outputs are steerable away from the bad set with open loop controls a closed loop control strategy is explicitly constructed which guarantees that the current set of possible system states as obtained from an estimator generates outputs that never enter the bad set the complexity of algorithms that check safety of an initial set of states and implement the control map is quadratic with the dimension of the state space the algorithms are illustrated on two application examples a ship maneuver to avoid an obstacle and safe navigation of an helicopter among buildings

representations of semisimple lie algebras in prime characteristic and the noncommutative springer resolution we prove most of lusztig s conjectures on the canonical basis in homology of a springer ber the conjectures predict that this basis controls numerics of representations of the lie algebra of a semisimple algebraic group over an algebraically closed eld of positive characteristic we check this for almost all characteristics to this end we construct a noncommutative resolution of the nilpotent cone which is derived equivalent to the springer resolution on the one hand this noncommutative resolution is closely related to the positive characteristic derived localization equivalences obtained earlier by the present authors and rumynin on the other hand it is compatible with the t structure arising from an equivalence with the derived category of perverse sheaves on the ane ag variety of the langlands dual group this equivalence established by arkhipov and the rst author ts the framework of local geometric langlands duality the latter compatibility allows one to apply frobenius purity theorem to deduce the desired properties of the basis we expect the noncommutative counterpart of the springer resolution to be of independent interest from the perspectives of algebraic geometry and geometric langlands duality

fourier transforms and frobenius eigenvalues for finite coxeter groups abstract lusztig s classification of the unipotent characters of a finite chevalley or steinberg group involves a certain non abelian fourier transformation we construct analogous transformations for the suzuki and ree groups based on a set of axioms derived from lusztig s theory of character sheaves we also determine fourier matrices for the spetses in the sense of broue michel and the second author associated with twisted dihedral groups this completes the determination of fourier matrices for all spetses associated with finite coxeter groups we end by collecting common properties of these fourier matrices and the eigenvalues of frobenius of character sheaves and unipotent characters

character sheaves v this paper is part of a series s 131 devoted to the study of a class g of irreducible perverse sheaves called character sheaves on a connected reductive algebraic group g the numbering of chapters sections and references will continue that of s 131 this paper is a step towards the classification of character sheaves on g one of the main results is the following one under certain assumptions there is a natural surjective map with finite fibers from g to the set of all pairs 9 c up to conjugacy by the weyl group where 9 is a tame local system on the maximal torus and c is a two sided cell in the stabilizer w of 9 in the weyl group the assumptions made on g are

categorification of induced cell modules and the rough structure of generalised verma modules this paper presents categorifications of right cell modules and induced cell modules for hecke algebras of finite weyl groups fit type a we show that these categorifications depend only on the isomorphism class of the cell module not on the cell itself our main application is multiplicity formulas for parabolically induced modules over a reductive lie algebra of type a which finally determines the so called rough structure of generalised verma modules on the way we present several categorification results and give a positive answer to kostant s problem from a joseph kostant s problem goldie rank and the gelfand kirillov conjecture invent math 56 3 1980 191 213 in many cases we also present a general setup of decategorification precategorification and categorification

applications of transportation theory to statistical problems abstract the two dimensional controlled selection problem and the problem of maximizing the overlap of old and new primary sampling units after restratification and change of selection probabilities have been studied for several decades but have never been completely solved until now using transportation theory complete solutions are obtained here for these and other problems the solution to the controlled selection problem is based on a specific transportation model that was originally developed in a previous paper by cox and ernst 1982 to solve completely the controlled rounding problem namely the problem of optimally rounding real valued entries in a two way tabular array to adjacent integer values in a manner that preserves the tabular additive structure of the array this model is also applied to other statistical problems such as raking and statistical disclosure for frequency count tabulations and microdata

the exotic robinson schensted correspondence abstract we study the action of the symplectic group on pairs of a vector and a flag considering the irreducible components of the conormal variety we obtain an exotic analogue of the robinson schensted correspondence conjecturally the resulting cells are related to exotic character sheaves

statistical disclosure in two dimensional tables general tables abstract confidentiality protection of data published in tables is a major problem for statistical offices to obtain full cooperation of the respondents it is required that information of individual respondents with a confidential character is kept from being disclosed one method to avoid disclosure is the method of cell suppression in which the values of a number of statistical cells are not published but are suppressed from publication we discuss the method of cell suppression in general two dimensional tables in which row totals and column totals are always published the values of the sensitive cells are replaced by a cross x usually additional suppressions are necessary to prevent the values of the sensitive cells from being calculated from the row or column totals because of these additional suppressions useful information gets lost we want to minimize the loss of information by making the best choice for the additional suppressions therefore we introduce and compare the performance o

monotonicity properties for the viable control of discrete time systems this paper deals with the control of nonlinear systems in the presence of state and control constraints for discrete time dynamics in finite dimensional spaces the viability kernel is known to play a basic role for the analysis of such problems and the design of viable control feedbacks unfortunately this kernel may display very nonregular geometry and its computation is not an easy task in general in the present paper we show how monotonicity properties of both dynamics and constraints allow for relevant analytical upper and lower approximations of the viability kernel through weakly and strongly invariant sets an example on fish harvesting management illustrates some of the assertions

controlled rounding and cell perturbation statistical disclosure limitation methods for tabular data rounding methods are common techniques in many statistical offices to protect sensitive information when publishing data in tabular form classical versions of these methods do not consider protection levels while searching patterns with minimum information loss and therefore typically the so called auditing phase is required to check the protection of the proposed patterns this paper presents a mathematical model for the whole problem of finding a protected pattern with minimum loss of information and proposes a branch and cut algorithm to solve it it also describes a new methodology closely related to the classical controlled rounding methods but with several advantages the new methodology is named cell perturbation and leads to a different optimization problem which is simpler to solve than the previous problem this paper presents a cutting plane algorithm for finding an exact solution of the new problem which is a pattern guaranteeing the same protection level requirements but with smaller loss of information when compared with the classical controlled rounding optimal patterns the auditing phase is unnecessary on the solutions generated by the two algorithms the paper concludes with computational results on real world instances and discusses a modification in the objective function to guarantee statistical properties in the solutions

cells in affine weyl groups and tensor categories abstract in this paper we construct a tensor or monoidal category for any two sided cell in a finite or affine weyl group the isomorphism classes of simple objects of this category correspond to the elements of the two sided cell the tensor product arises by a certain truncation procedure from the standard convolution of perverse sheaves on a flag manifold which imitates geometrically the definition of the ring j given in g lusztig j algebra 109 1987 536 548 similarly we construct for any left cell a tensor category in which the isomorphism classes of simple objects correspond to the elements in the left cell intersected with its inverse a right cell this contains as a special case the category of equivariant perverse sheaves on an affine grassmannian which as a consequence of g lusztig asterisque 101 102 1983 208 209 is a tensor category for convolution without truncation closely related to the tensor category of representations of the group dual in the sense of langlands to the group which gives rise to the affine grassmannian but our construction can be specialized in other ways and it gives a conjectural realization of the tensor category of representations of the reductive quotient of the centralizer of any unipotent element of the langlands dual group

obtaining cell counts for contingency tables from rounded conditional frequencies abstract we present an integer linear programming formulation and solution procedure for determining the tightest bounds on cell counts in a multi way contingency table given knowledge of a corresponding derived two way table of rounded conditional probabilities and the sample size the problem has application in statistical disclosure limitation which is concerned with releasing useful data to the public and researchers while also preserving privacy and confidentiality previous work on this problem invoked the simplifying assumption that the conditionals were released as fractions in lowest terms rather than the more realistic and complicated setting of rounded decimal values that is treated here the proposed procedure finds all possible counts for each cell and runs fast enough to handle moderately sized tables

the character sheaves on the group compactification abstract we give a definition of character sheaves on the group compactification which is equivalent to lusztig s definition in g lusztig parabolic character sheaves ii mosc math j 4 4 2004 869 896 we also prove some properties of the character sheaves on the group compactification

quasisplit hecke algebras and symmetric spaces let g k be a symmetric pair over an algebraically closed field of characteristic different from 2 and let be an automorphism with square 1 of g preserving k in this paper we consider the set of pairs o l where o is a stable k orbit on the flag manifold of g and l is an irreducible k equivariant local system on o which is fixed by given two such pairs o l o l with o in the closure o of o the multiplicity space of l in a cohomology sheaf of the intersection cohomology of o with coefficients in l restricted to o carries an involution induced by and we are interested in computing the dimensions of its 1 and 1 eigenspaces we show that this computation can be done in terms of a certain module structure over a quasisplit hecke algebra on a space spanned by the pairs o l as above

experiments based parameter identification on the gpu for cooperative systems abstract in this paper we describe how to enhance experimental parameter identification for cooperative systems using the gpu this kind of identification is necessary for example in the area of developing robust controllers and observers based on available measurement data first we point out which parts of the general global optimization based parameter identification procedure can be parallelized and compare it to the experiments based technique after that we illustrate the principle and its implementation with the help of a close to life textbook example finally we demonstrate how the gpu based experimental parameter identification works for identifying experimentally the parameters of the reduced order temperature model for the distributed heating system this is an important step towards working with uncertain models in the context of solid oxide fuel cells

remarks on computing irreducible characters 0 1 let g be a connected reductive algebraic group defined over a finite field fq and let g fq be the finite group of all fq rational points of g we would like to present here a strategy for computing the character table of g fq under the assumption that p the characteristic of fq is sufficiently large we can assume that g has a simply connected derived group indeed in the general case we can find a connected reductive group g with simply connected derived group and a surjective homomorphism f g g whose kernel is a central torus such that g and f are defined over fq then the character table

a unified mathematical programming framework for different statistical disclosure limitation methods this paper concerns statistical disclosure control methods to minimize information loss while keeping small the disclosure risk from different data snoopers this issue is of primary importance in practice for statistical agencies when publishing data it is assumed that the sensitive data have been identified by practitioners in the statistical offices and the paper addresses the secondary problem of protecting these data with different methods all defined in a unified mathematical framework a common definition of protection is used in four different methodologies two integer linear programming models described in the literature for the cell suppression methodology are extended to work also for the controlled rounding methodology in addition two relaxed variants are presented using two associated linear programming models called partial cell suppression and partial controlled rounding respectively a final discussion shows how to combine the four methods and how to implement a cutting plane approach for the exact and heuristic resolution of the combinatorial problems in practice this approach was implemented in argus a software package of disclosure limitation tools

robust controlled invariance for monotone systems the robust controlled invariance describes the ability to maintain using suitable control actions the state of a system in a set for any value of the disturbances by considering a class of monotone systems and a multidimensional interval as target set we obtain a simple characterization of the robust controlled invariance we then give a method to stabilize the state into a robust controlled invariant interval when it is initialized outside of the target set these results are applied to a model for the temperature control in an intelligent building equipped with automated underfloor air distribution ufad and implemented in a small scale experimental ufad flat

local cohomology of modules of covariants abstract let g be a connected reductive algebraic group over an algebraically closed field of characteristic zero and let w u be two finite dimensional representations of g in this paper we compute the local cohomology of u sw g provided a certain relatively weak technical condition is true

controlled rounding of tabular data controlled rounding is a procedure that perturbs tabular data collected from respondents in such a way as to preserve the anonymity of the respondents while maintaining the integrity of the data the three dimensional controlled rounding problem is np complete this paper describes a binary tree search algorithm for solving three dimensional problems based on linear programming techniques computational results obtained from tests with over 31 000 randomly generated tables and 292 real life tables have shown that this algorithm can effectively find controlled roundings when they exist or determine that no solution exists the computational results also demonstrate that the running time of the search algorithm can be cut in half by using a heuristic for initializing the simplex basis for the linear programming problems

topological generation of exceptional algebraic groups abstract let g be a simple algebraic group over an algebraically closed field k and let c 1 c t be non central conjugacy classes in g in this paper we consider the problem of determining whether there exist g i c i such that g 1 g t is zariski dense in g first we establish a general result which shows that if is an irreducible subvariety of g t then the set of tuples in generating a dense subgroup of g is either empty or dense in in the special case c 1 c t by considering the dimensions of fixed point spaces we prove that this set is dense when g is an exceptional algebraic group and t 5 assuming k is not algebraic over a finite field in fact for g g 2 we only need t 4 and both of these bounds are best possible as an application we show that many faithful representations of exceptional algebraic groups are generically free we also establish new results on the topological generation of exceptional groups in the special case t 2 which have applications to random generation of finite exceptional groups of lie type in particular we prove a conjecture of liebeck and shalev on the random r s generation of exceptional groups

box invariance in biologically inspired dynamical systems a dynamical system is box invariant if there exists a box shaped positively invariant region we show that box invariance can be checked in cubic time for linear and affine systems and that it remains decidable for classes of nonlinear systems of interest with polynomial structure we present results on the robustness of box invariance for linear systems using spectral properties of metzler matrices we also present sufficient conditions for establishing box invariance of switched and hybrid systems in general we argue that box invariance is a characteristic of many biologically inspired dynamical models

characteristic cycles for the loop grassmannian and nilpotent orbits x which is a linear combination of closures of conormal bundles to submanifolds of x intuitively the microlocal multiplicities c me asurethesingularity of at in settings related to representation theory a group g acts on x is g equivariant and the microlocal multiplicities play a significant but only partially understood role in representation theory see ro sv abv and kasa e g in this paper we compute microlocal multiplicities for certain cases of interest in representation theory let g be a connected reductive group with loop group lg and let p bethesubgroup of lg consisting of loops with positive fourier coefficients then p orbits on theloop grassmannian lg p correspond to the irreducible representations l of thedual re ductivegroup g for dominant weights and of a torus of

survey paper set invariance in control the properties of positively invariant sets are involved in many different problems in control theory such as constrained control robustness analysis synthesis and optimization in this paper we provide an overview of the literature concerning positively invariant sets and their application to the analysis and synthesis of control systems

a constructive procedure for unbiased controlled rounding abstract it is often necessary to round values in a two way statistical table that is replace each value by an adjacent integer multiple of an appropriately chosen integer rounding base such is the case when statistical data are to be presented in increments such as personal income presented in multiples of 1 000 or retail sales in units of 1 million or when counts must be adjusted prior to release to reduce the risk of statistical disclosure cox mcdonald and nelson 1986 it is desirable that the rounded array also be additive along rows and columns and to the grand total a table satisfying these conditions is called a controlled rounding of the original table if as is often the case entries that are already integer multiples of the base must remain unchanged the controlled rounding is said to be zero restricted controlled rounding is an important adjunct to statistical methods for adjusting contingency tables such as iterative proportional fitting ireland and kullback 1968 because suc

asymptotic tracking for constrained monotone systems this note addresses tracking control of nonlinear discrete time monotone systems subject to input and state constraints forcing saturation on a previously designed controller may in general lead to destabilization or at least result in constraint violation and performance losses hereby it is shown that for a certain class of nonlinear monotone systems it is possible to design a static nonlinear output feedback which saturated among suitable state dependent bounds is able to guarantee constraint satisfaction and asymptotic tracking of piecewise constant references with a moderate online computational burden simulation experiments concerning the synthesis of a protein demonstrate the effectiveness of the proposed control strategy