on error saturation nonlinearities in nlms adaptation the effect of a saturation type error nonlinearity in the weight update equation in normalized least mean square nlms adaptation is investigated for system identification for a white gaussian data model nonlinear recursions are derived for the weight mean error and mean square deviation msd that include the effect of an error function erf saturation type nonlinearity on the error sequence driving the algorithm the nonlinear recursion for the msd is solved numerically and shown in excellent agreement with monte carlo simulations supporting the theoretical model assumptions the theory is extended to tracking a markov channel and accurately predicts the tracking behavior as well the saturation behavior of the algorithm is easily studied by varying a single parameter in the error function varying from a linear device to a hard limiter for the white data case the excess mean square error emse is simply related to the msd the tradeoff between the extent of error saturation steady state emse and algorithm convergence rate is studied using these results

generic singularities of nilpotent orbit closures according to a theorem of brieskorn and slodowy the intersection of the nilpotent cone of a simple lie algebra with a transverse slice to the subregular nilpotent orbit is a simple surface singularity at the opposite extremity of the poset of nilpotent orbits the closure of the minimal nilpotent orbit is also an isolated symplectic singularity called a minimal singularity for classical lie algebras kraft and procesi showed that these two types of singularities suffice to describe all generic singularities of nilpotent orbit closures specifically any such singularity is either a simple surface singularity a minimal singularity or a union of two simple surface singularities of type a 2k 1 in the present paper we complete the picture by determining the generic singularities of all nilpotent orbit closures in exceptional lie algebras up to normalization in a few cases we summarize the results in some graphs at the end of the paper in most cases we also obtain simple surface singularities or minimal singularities though often with more complicated branching than occurs in the classical types there are however six singularities that do not occur in the classical types three of these are unibranch non normal singularities an sl 2 c variety whose normalization is a 2 an sp 4 c variety whose normalization is a 4 and a two dimensional variety whose normalization is the simple surface singularity a 3 in addition there are three 4 dimensional isolated singularities each appearing once we also study an intrinsic symmetry action on the singularities extending slodowy s work for the singularity of the nilpotent cone at a point in the subregular orbit

l espace symetrique de drinfeld et correspondance de langlands locale ii we study the geometry and the cohomology of the tamely ramified cover of drinfeld s p adic symmetric space over a p adic field k for this tame level we prove in a purely local way most of a conjecture of harris on the form of the ell adic cohomologies as well as the torsion freeness of the integral cohomology in this paper we also compute the ell adic cohomology of coxeter deligne lusztig variety associated to mathrm gl d and some results of independent interest on the coefficient systems over the bruhat tits building associated to mathrm gl d k have been established

cuspidal ell modular representations of p adic classical groups for a classical group over a non archimedean local field of odd residual characteristic p we construct all cuspidal representations over an arbitrary algebraically closed field of characteristic different from p as representations induced from a cuspidal type we also give a fundamental step towards the classification of cuspidal representations identifying when certain cuspidal types induce to equivalent representations this result is new even in the case of complex representations finally we prove that the representations induced from more general types are quasi projective a crucial tool for extending the results here to arbitrary irreducible representations

weight monodromy conjecture for p adically uniformized varieties the aim of this paper is to prove the weight monodromy conjecture deligne s conjecture on the purity of monodromy filtration for varieties p adically uniformized by the drinfeld upper half spaces of any dimension the ingredients of the proof are to prove a special case of the hodge standard conjecture and apply a positivity argument of steenbrink m saito to the weight spectral sequence of rapoport zink as an application by combining our results with the results of schneider stuhler we compute the local zeta functions of p adically uniformized varieties in terms of representation theoretic invariants we also consider a p adic analogue by using the weight spectral sequence of mokrane

adaptive filter performance with nonlinearities in the correlation multiplier it is well known that the correlation multiplier used to form the update signal in adaptive transversal filters need not be a true multiplier by using an approximate multiplier such as a sign bit only multiplier implementation can be made less costly in this paper we derive expressions for the convergence rate and misalignment noise of adaptive transversal filters with arbitrary correlation multiplier non linearities the analysis shows any such nonlinearities to always harm performance and quantifies the penalty suffered sign bit only multiplication suffers a significant penalty and power of two multiplication is suggested as a better alternative its performance is almost equal to that of a true multiplier and in a digital implementation at least it is only slightly more difficult to realize than a sign bit only multiplier the theory is developed in a way emphasizing physical understanding and has been verified to be in good agreement with simulation

convergence of infinite products of stochastic matrices a graphical decomposition criterion this technical note presents a convergence criterion for infinite products of stochastic matrices which is based on graphical decomposition of the associated graphs we show that if the associated graphs of a set of stochastic matrices share a common graphical decomposition and the corresponding reduced graphs are rooted then any infinite products of the given set of stochastic matrices is convergent specifically we propose a numerical algorithm for finding the common graphical decomposition of the associated graphs which has been proved to be polynomial time fast the proposed criterion can be applied directly to a series of classical results in distributed coordination algorithm

computing green functions in small characteristic abstract let g q be a finite group of lie type over a field with q elements where q is a prime power the green functions of g q as defined by deligne and lusztig are known in almost all cases by work of beynon spaltenstein lusztig und shoji open cases exist for groups of exceptional type e 6 2 e 7 e 8 in small characteristics we propose a general method for dealing with these cases which proceeds by a reduction to the case where q is a prime and then uses computer algebra techniques in this way all open cases in type e 6 2 e 7 are solved as well as at least one particular open case in type e 8

green functions and character sheaves purely combinatorial way using earlier ideas of p hall in the general case they were introduced 3 in terms of l adic cohomology as values of certain virtual representations of r o t is a maximal torus defined over fq at unipotent elements the characters of rg 0 at arbitrary elements were then expressible in a simple form in terms of green functions of g and of smaller groups one drawback of the definition of 3 was that it did not allow one to compute the green functions except in some simple cases another definition of green functions was proposed by springer first in terms of trigonometric sums on the lie algebra and later in geometrical terms 17 this definition was applicable only in large characteristic and in that case it was identified with the definition in 3 by springer 17 and kazhdan 10 in 12 i observed that green functions for gln can be redefined in terms of intersection cohomology this led me to a new definition of green functions

on the nonexistence of quadratic lyapunov functions for consensus algorithms we provide an example proving that there exists no quadratic lyapunov function for a certain class of linear agreement consensus algorithms a fact that had been numerically verified in we also briefly discuss sufficient conditions for the existence of such a lyapunov function

application de hodge tate duale d un groupe de lubin tate immeuble de bruhat tits du groupe lineaire et filtrations de ramification

on error saturation nonlinearities in lms adaptation the effect of a saturation type error nonlinearity in the weight update equation in least mean squares lms adaptation is investigated for a white gaussian data model nonlinear difference equations are derived for the eight first and second moments which include the effect of an error function erf saturation type nonlinearity on the error sequence driving the algorithm a nonlinear difference equation for the mean norm is explicitly solved using a differential equation approximation and integration by quadratures the steady state second moment weight behavior is evaluated exactly for the erf nonlinearity using the above results the tradeoff between the extent of error saturation steady state excess mean square error and rate of algorithm convergence is studied the tradeoff shows that 1 starting with a sign detector the convergence rate is increased by nearly a factor of two for each additional bit and 2 as the number of bits is increased further the additional bit by very little in convergence speed asymptotically approaching the behavior of the linear algorithm

on the decomposition numbers of the finite general linear groups ii let g gl q q a prime power and let r be an odd prime not dividing q let s be a semisimple element of g of order prime to r and assume that r divides qdeg x 1 for all elementary divisors a of s relating representations of certain hecke algebras over symmetric groups with those of g we derive a full classification of all modular irreducible modules in the r block bh of g with semisimple part s the decomposition matrix d of bs may be partly described in terms of the decomposition matrices of the symmetric groups corresponding to the hecke algebras above moreover d is lower unitriangular this applies in particular to all r blocks of g if r divides q 1 thus in this case the r decomposition matrix of g is lower unitriangular introduction the modular representation theory of finite groups of lie type defined over a field of characteristic p is naturally divided into the cases of equal characteristic r p and unequal characteristic r p this paper begins the study of decomposition numbers in the unequal characteristic case of the finite general linear groups when r 2 let g be the full linear group of degree n over gf q and 2 r be a prime not dividing q let s c g be semisimple and consider the geometric conjugacy class s g of irreducible characters corresponding to the g conjugacy class of s using basic properties of the deligne lusztig operators introduced in 7 we will determine a parabolic subgroup p ps of g and a cuspidal irreducible character of x of p such that s g is just the set of constituents of xg the induced character let r r k be an r modular system for g and m a kp module affording x then end kg m is called the hecke algebra of m compare 5 and has been calculated in a more general context by r b howlett and g i lehrer in 12 it turns out that end kg m k w the hecke algebra of w where w wj denotes the weyl group of cg s the centralizer of s in g compare 1 2 4 13 in particular k w has a basis tw iw c w such that the structure constants of the multiplication are all contained in r c k so let r w be the r order in k w generated by wtiw ew and r w r r r w choosing a special rp lattice s in m and using the classification of the r blocks of rg given by p fong and b srinivasan in received by the editors july 25 1983 and in revised form october 18 1983 may 23 1984 and september 1 1984 1980 mathematics subject classification primary 20c20 secondary 20g40 this work was supported by the deutsche forschungsgemeinschaft 1985 american mathematical society 0002 9947 85 1 00 25 per page

persistent flows in deterministic chains this paper studies the role of persistent flows in the convergence of infinite backward products of stochastic matrices of deterministic chains over networks with nonreciprocal interactions between agents an arc describing the interaction strength between two agents is said to be persistent if its weight function has an infinite l 1 norm convergence of the infinite backward products to a rank one matrix of a deterministic chain of stochastic matrices is equivalent to achieving consensus at the node states we discuss two balance conditions on the interactions between agents which generalize the arc balance and cut balance conditions in the literature respectively the proposed conditions require that such a balance should be satisfied over each time window of a fixed length instead of at each time instant we prove that in both cases global consensus is reached if and only if the persistent graph which consists of all the persistent arcs contains a directed spanning tree the convergence rates of the system to consensus are also provided in terms of the interactions between agents having taken place the results are obtained under a weak condition without assuming the existence of a positive lower bound of all the nonzero weights of arcs and are compared with the existing results illustrative examples are provided to validate the results and show the critical importance of the nontrivial lower boundedness of the self confidence of the agents

distributed averaging with random network graphs and noises we consider a discrete time distributed averaging algorithm over multi agent networks with measurement noises and time varying random graphs each agent updates its state by a weighted sum of pairwise state differences between its neighbors and itself with both additive and multiplicative measurement noises the network structure is modeled by a sequence of time varying random digraphs which may be spatially and temporally dependent by stochastic lyapunov method and the combination of algebraic graph theory and martingale convergence theory we obtain sufficient conditions for stochastic approximation type algorithms to achieve mean square and almost sure average consensus we prove that all states of the agents converge to a common random variable whose mathematical expectation is the average of initial values in mean square and almost surely if the sequence of digraphs is conditionally balanced and uniformly conditionally jointly connected an upper bound of the variance of the limit random variable that is the mean square steady state error for stochastic average consensus is given quantitatively related to the weights the algorithm gain and the energy level of the noises

euler characteristics of the real points of certain varieties of algebraic tori let g be a complex connected reductive group which is defined over r let g be its lie algebra and t the variety of maximal tori of g for g r let t be the variety of tori in t whose lie algebra is orthogonal to with respect to the killing form we show using the fourier sato transform of conical sheaves on real vector bundles that the weighted euler characteristic see below of t r is zero unless is nilpotent in which case it equals 1 dimt 2 this is a real analogue of a result over finite fields which is connected with the steinberg representation of a reductive group

characters of finite reductive lie algebras abstract for any finite group of lie type g q deligne and lusztig p deligne g lusztig representations of reductive groups over finite fields ann of math 2 103 1976 103 161 defined a family of virtual q l characters r t g of g q such that any irreducible character of g q is an irreducible constituent of at least one of the r t g in this paper we study analogues of this result for characters of the finite reductive lie algebra g q where g lie g motivated by the results of e letellier fourier transforms of invariant functions on finite reductive lie algebras lecture notes in math vol 1859 springer verlag 2005 and g lusztig representations of reductive groups over finite rings represent theory 8 2004 1 14 we define two families r t g and r t g of virtual q l characters of g q we prove that they coincide when is in general position and that they differ in general we verify that any character of g q appears in some r t g we conjecture that this is also true if r t g is replaced by r t g

vanishing cycles for formal schemes let k be a non archimedean field and let x be a formal scheme locally finitely presented over the ring of integers k see 1 in this work we construct and study the vanishing cycles functor from the category of etale sheaves on the generic fibre x of x which is a k analytic space to the category of etale sheaves on the closed fibre xs of x which is a scheme over the residue field of k we prove that if x is the formal completion x of a scheme x finitely presented over k along the closed fibre then the vanishing cycles sheaves of x are canonically isomorphic to those of x as defined in sga7 exp xiii in particular the vanishing cycles sheaves of x depend only on x and any morphism x induces a homomorphism from the pullback of the vanishing cycles sheaves of x under s ys xs to those of y furthermore we prove that for each x one can find a nontrivial ideal of k such that if two morphisms x coincide modulo this ideal then the homomorphisms between the vanishing cycles sheaves induced by and coincide these facts were conjectured by p deligne in 1 we associate with a formal scheme x locally finitely presented over k a k analytic space x in the sense of ber1 and ber2 in 2 we find that the morphism y x which is induced by an etale morphism of formal schemes y x possesses a certain property morphisms of k analytic spaces with this property are called quasi etale and they give rise to a quasi etale site xqet of a k analytic space x there is a canonical morphism of sites xqet xet where xet is the etale site introduced in ber2 we show that the inverse image functor identifies the category of etale sheaves x et with a full subcategory of

convergence and performance analysis of the normalized lms algorithm with uncorrelated gaussian data it is demonstrated that the normalized least mean square nlms algorithm can be viewed as a modification of the widely used lms algorithm the nlms is shown to have an important advantage over the lms which is that its convergence is independent of environmental changes in addition the authors present a comprehensive study of the first and second order behavior in the nlms algorithm they show that the nlms algorithm exhibits significant improvement over the lms algorithm in convergence rate while its steady state performance is considerably worse

depth zero supercuspidal l packets and their stability in this paper we verify the local langlands correspondence for pure inner forms of unramied p adic groups and tame langlands parameters in general position for each such parameter we explicitly construct in a natural way a nite set l packet of depth zero supercuspidal representations of the appropriate p adic group and we verify some expected properties of this l packet in particular we prove with some conditions on the base eld that the appropriate sum of characters of the representations in our l packet is stable no proper subset of our l packets can form a stable combination our l packets are also consistent with the conjectures of b gross and d prasad on restriction from so2n 1 to so2n 24 these l packets are in general quite large for example sp2n has an l packet containing 2 n representations of which exactly two are generic in fact on a quasi split form eachl packet contains exactly one generic representation for every rational orbit of hyperspecial vertices in the reduced bruhattits building when the group has connected center every depth zero generic supercuspidal representation appears in one of these l packets we emphasize that there is nothing new about the representations we construct they are induced from deligne lusztig representations on subgroups of nite

a stabilization theorem for dynamics of continuous opinions abstract a stabilization theorem for processes of opinion dynamics is presented the theorem is applicable to a wide class of models of continuous opinion dynamics based on averaging like the models of hegselmann krause and weisbuch deffuant the analysis detects self confidence as a driving force of stabilization

formule de mackey pourqgrand soit g un groupe algebrique reductif connexe defini sur une cloture algebrique f du corps fini a p elements f ou p designe un nombre p premier soit f g a g un endomorphisme de frobenius relatif a une f structure sur g ou q est une puissance de p et f designe le sous corps q q de f a q elements on fixe un nombre premier l different de p et on note q une cloture algebrique du corps l adique q si p est un sous groupe l l parabolique de g et si l est un sous groupe de levi f stable de p g lusztig a construit un foncteur r k l a kg f entre les l p f f groupes de grothendieck des categories des q l modules et des q g l l modules respectivement appele foncteur d induction de lusztig ce fonc teur admet un adjoint r kg f a k l appele restriction de lusztig l p la formule de mackey pour l induction de lusztig decrit la composition d un foncteur d induction avec un foncteur de restriction de lusztig plus precisement si q est un autre sous groupe parabolique de g et si m est un sous groupe de levi f stable de q on appelle formule de mackey l egalite suivante

on approximations and ergodicity classes in random chains we study the limiting behavior of a random dynamic system driven by a stochastic chain our interest is in the chains that are not necessarily ergodic but are decomposable into ergodic classes to investigate the conditions under which the ergodic classes of a model can be identified we introduce and study an l1 approximation and infinite flow graph of the model we show that the l1 approximations of random chains preserve certain limiting behavior using the l1 approximations we show how the connectivity of the infinite flow graph is related to the structure of the ergodic groups of the model our main result of this paper provides conditions under which the ergodicity groups of the model can be identified by considering the connected components in the infinite flow graph we provide two applications of our main result to random networks namely broadcast over time varying networks and networks with random link failure

a recursive least m estimate algorithm for robust adaptive filtering in impulsive noise fast algorithm and convergence performance analysis this paper studies the problem of robust adaptive filtering in impulsive noise environment using a recursive least m estimate algorithm rlm the rlm algorithm minimizes a robust m estimator based cost function instead of the conventional mean square error function mse previous work has showed that the rlm algorithm offers improved robustness to impulses over conventional recursive least squares rls algorithm in this paper the mean and mean square convergence behaviors of the rlm algorithm under the contaminated gaussian impulsive noise model is analyzed a lattice structure based fast rlm algorithm called the huber prior error feedback least squares lattice h pef lsl algorithm is derived part of the h pef lsl algorithm was presented in icassp 2001 it has an order o n arithmetic complexity where n is the length of the adaptive filter and can be viewed as a fast implementation of the rlm algorithm based on the modified huber m estimate function and the conventional pef lsl adaptive filtering algorithm simulation results show that the transversal rlm and the h pef lsl algorithms have better performance than the conventional rls and other rls like robust adaptive algorithms tested when the desired and input signals are corrupted by impulsive noise furthermore the theoretical and simulation results on the convergence behaviors agree very well with each other

asymptotic stability of ltv systems with applications to distributed dynamic fusion we investigate the behavior of linear time varying ltv systems with randomly appearing sub stochastic system matrices motivated by dynamic fusion over mobile networks we develop conditions on the system matrices that lead to asymptotic stability of the underlying ltv system by partitioning the sequence of system matrices into slices we obtain the stability conditions in terms of slice lengths and introduce the notion of unbounded connectivity i e the time intervals over which the multi agent network is connected do not have to be bounded as long as they do not grow faster than a certain exponential rate we further apply the above analysis to derive the asymptotic behavior of a dynamic leader follower algorithm

deformation spaces of one dimensional formal modules and their cohomology abstract let m m be the formal scheme which represents the functor of deformations of a one dimensional formal module over f p equipped with a level m structure by work of boyer in equal characteristic and harris and taylor the l adic etale cohomology of the generic fibre m m of m m realizes simultaneously the local langlands and jacquet langlands correspondences the proofs given so far use drinfeld modular varieties or shimura varieties to derive this local result in this paper we show without the use of global moduli spaces that the jacquet langlands correspondence is realized by the euler poincare characteristic of the cohomology under a certain finiteness assumption on the cohomology groups it is shown that the correspondence is realized in only one degree one main ingredient of the proof consists in analyzing the boundary of the deformation spaces and in studying larger spaces which can be considered as compactifications of the spaces m m

green functions associated to complex reflection groups abstract green functions of classical groups are determined by the data from weyl groups and by certain combinatorial objects called symbols generalizing this we define green functions associated to complex reflection groups g e 1 n and study their combinatorial properties we construct hall littlewood functions and schur functions in our scheme and show that such green functions are obtained as a transition matrix between those two symmetric functions as in the case of gln

derived categories and deligne lusztig varieties ii this paper is a continuation and a completion of boro1 we extend the jordan decomposition of blocks we show that blocks of finite groups of lie type in non describing characteristic are morita equivalent to blocks of subgroups associated to isolated elements of the dual group the key new result is the invariance of the part of the cohomology in a given modular series of deligne lusztig varieties associated to a given levi subgroup under certain variations of parabolic subgroups we also show that the equivalence arises from a splendid rickard equivalence even in the setting of boro1 the finer homotopy equivalence was unknown as a consequence the equivalence preserves defect groups and categories of subpairs we finally determine when deligne lusztig induced representations of tori generate the derived category of representations

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

equivalences of tame blocks for p adic linear groups let p and ell be two distinct primes f a p adic field and n an integer we show that any level 0 block of the category of smooth overline mathbb z ell valued representations of mathrm gl n f is equivalent to the unipotent block of an appropriate product of mathrm gl n i f i more precisely we show that level 0 blocks of p adic general linear groups obey the functoriality principle for blocks introduced in dat contemp math 691 103 131 2017 the overall strategy is to use the jordan decomposition of blocks of finite general linear groups and the theory of coefficients systems on the relevant buildings as a bridge between the p adic and finite worlds to overcome the main technical difficulty we need fine properties of deligne lusztig cohomology proved in bonnafe et al ann math 185 2 609 670 2017

push sum on random graphs almost sure convergence and convergence rate in this paper we study the problem of achieving average consensus over a random time varying sequence of directed graphs by extending the class of so called push sum algorithms to such random scenarios provided that an ergodicity notion which we term the directed infinite flow property holds and the auxiliary states of agents are uniformly bounded away from zero infinitely often we prove the almost sure convergence of the evolutions of this class of algorithms to the average of initial states moreover for a random sequence of graphs generated using a so called time varying b irreducible probability matrix we establish convergence rates for the proposed push sum algorithm

linear consensus algorithms based on balanced asymmetric chains multi agent consensus algorithms with update steps based on so called balanced asymmetric chains are analyzed for such algorithms it is shown that i the empirical distribution of state values converges asymptotically and ii the occurrence of consensus or multiple consensus is directly related to the property of absolute infinite flow of the underlying update chain an example is provided to illustrate the novelty of the results

on characters and formal degrees of discrete series of affine hecke algebras of classical types we address two fundamental questions in the representation theory of affine hecke algebras of classical types one is an inductive algorithm to compute characters of tempered modules and the other is the determination of the constants in the formal degrees of discrete series in the form conjectured by reeder j reine angew math 520 37 93 2000 the former is completely different from the lusztig shoji algorithm shoji in invent math 74 239 267 1983 lusztig in ann math 131 355 408 1990 and it is more effective in a number of cases the main idea in our proof is to introduce a new family of representations which behave like tempered modules but for which it is easier to analyze the effect of parameter specializations our proof also requires a comparison of the c theoretic results of opdam delorme slooten solleveld j inst math jussieu 3 531 648 2004 arxiv 0909 1227 int math res not 2008 adv math 220 1549 1601 2009 acta math 205 105 187 2010 and the geometric construction from kato duke math j 148 305 371 2009 am j math 133 518 553 2011 ciubotaru and kato adv math 226 1538 1590 2011

on backward product of stochastic matrices we study the ergodicity of backward product of stochastic and doubly stochastic matrices by introducing the concept of absolute infinite flow property we show that this property is necessary for ergodicity of any chain of stochastic matrices by defining and exploring the properties of a rotational transformation for a stochastic chain then we establish that the absolute infinite flow property is equivalent to ergodicity for doubly stochastic chains furthermore we develop a rate of convergence result for ergodic doubly stochastic chains we also investigate the limiting behavior of a doubly stochastic chain and show that the product of doubly stochastic matrices is convergent up to a permutation sequence finally we apply the results to provide a necessary and sufficient condition for the absolute asymptotic stability of a discrete linear inclusion driven by doubly stochastic matrices

a necessary and sufficient condition for consensus over random networks we consider the consensus problem for stochastic discrete time linear dynamical systems the underlying graph of such systems at a given time instance is derived from a random graph process independent of other time instances for such a framework we present a necessary and sufficient condition for almost sure asymptotic consensus using simple ergodicity and probabilistic arguments this easily verifiable condition uses the spectrum of the average weight matrix finally we investigate a special case for which the linear dynamical system converges to a fixed vector with probability 1

convergence of type symmetric and cut balanced consensus seeking systems we consider continuous time consensus seeking systems whose time dependent interactions are cut balanced in the following sense if a group of agents influences the remaining ones the former group is also influenced by the remaining ones by at least a proportional amount models involving symmetric interconnections and models in which a weighted average of the agent values is conserved are special cases we prove that such systems always converge we give a sufficient condition on the evolving interaction topology for the limit values of two agents to be the same conversely we show that if our condition is not satisfied then these limits are generically different these results allow treating systems where the agent interactions are a priori unknown being for example random or determined endogenously by the agent values

on weight update saturation nonlinearities in lms adaptation the effect of a saturation type nonlinearity in the weight update equation in least mean square lms adaptation is investigated for a white gaussian data model nonlinear difference equations that include the effect of a 1 e sup ax saturation type nonlinearity on the update term driving the algorithm are derived for the weight first and second moments a nonlinear difference equation for the mean norm is explicitly solved using a differential equation approximation and integration by quadratures the steady state second moment weight behavior is evaluated approximately for the nonlinearity using these results the tradeoff between the extent of weight update saturation steady state excess mean square error and rate of algorithm convergence is studied for the same steady state misadjustment error the tradeoff results are discussed

generalized sarymsakov matrices within the set of stochastic indecomposable aperiodic sia matrices the class of sarymsakov matrices is the largest known subset that is closed under matrix multiplication and more critically whose compact subsets are all consensus sets this paper shows that a larger subset with these two properties can be obtained by generalizing the standard definition for sarymsakov matrices the generalization is achieved by introducing the notion of the sia index of a stochastic matrix whose value is 1 for sarymsakov matrices and then exploring those stochastic matrices with larger sia indices in addition to constructing the larger set this paper introduces another class of generalized sarymsakov matrices which contains matrices that are not sia and studies their products sufficient conditions are provided for an infinite product of matrices from this class converging to a rank one matrix finally as an application of the results just described and to confirm their usefulness a necessary and sufficient combinatorial condition the avoiding set condition for deciding whether or not a compact set of stochastic matrices is a consensus set is revisited in addition a necessary and sufficient combinatorial condition is established for deciding whether or not a compact set of doubly stochastic matrices is a consensus set

deligne lusztig restriction of gelfand graev characters abstract let g be a connected reductive algebraic group defined over a finite field f q in f digne g i lehrer j michel on gel fand graev characters of reductive groups with disconnected centre j reine angew math 491 1997 131 147 it is proved that the deligne lusztig restriction of a gelfand graev character of the finite group g f q is still a gelfand graev character however an ambiguity remains on the gelfand graev character obtained in this paper we describe the deligne lusztig restrictions of the gelfand graev characters of the finite group g f q using the theory of kostant slodowy transversal slices for the nilpotent orbits of the lie algebra of g

cohomology of sheaves on the building and r representations this article contains four parts the subject of the first one is to compare open compact subgroups of a reductive connected group g over a local non archimedean field associated to certain natural concave functions by the theory of bruhat tits bt1 we compare the groups which appear in the theory of unrefined minimal types by moy and prasad mp1 mp2 with those which appear in the theory of complex sheaves on the building x by schneider and stuhler ss schneider and stuhler give to special vertices a predominant role hiding in this way some symetry that we restaure we need all vertices in particular we describe how the groups vary along a geodesic starting from any point in a discussion with kutzko and with schneider it appeared that there are in the literature two different definitions for an iwahori subgroup the connected and the non connected as i was not aware of this and as there are may be other definitions i include here the unique decomposition property for the possible iwahori subgroups this part is entirely geometric and is certainly trivial for someone who is familiar with the theory of bruhat and tits

a unipotent support for irreducible representations 1 1 let g f be the group of fq rational points of a connected reductive algebraic group g defined over a finite field f throughout this paper we shall assume that the characteristic of the ground field is large the following is part of problem ii in l9 let p be an irreducible complex character of g f show that there is a unique umpotent class c in g which has the property that cga c cfqi p g 0 and has maximal dimension among classes with this property one of the results of this paper is a solution of this problem we also prove the following refinement if g e gf is such that tr g p 0 then the unipotent part of g lies in c or in a conjugacy class of dimension dim c we call c the unipotent support of p another map from the set of irreducible representations of gf to unipotent classes in g has been defined in l8 13 43 this was the composition of two maps one from irreducible representations of gf to a set of parameters in the langlands dual of g and one from this set of parameters to unipotent classes in g another conjectural definition of this map which did not pass through the langlands dual has been proposed by kawanaka kl k2 k3 in terms of generalized gelfand graev representations in analogy with real lie groups he uses the name wave front set for the unipotent class attached to a representation one of the results of this paper is a proof see section 11 of kawanaka s conjecture that his wave front set is well defined and that it coincides with the one defined in l8 this has been known earlier from the work of kawanaka in certain special cases we also show that the unipotent support of an irreducible representation coincides with the wave front set of the dual representation

cohomologie des varietes de deligne lusztig abstract we study the cohomology of deligne lusztig varieties with aim the construction of actions of hecke algebras on such cohomologies as predicted by the conjectures of broue malle and michel ultimately aimed at providing an explicit version of the abelian defect conjecture we develop the theory for varieties associated to elements of the braid monoid and partial compactifications of them we are able to compute the cohomology of varieties associated to possibly twisted rank 2 groups and powers of the longest element w 0 some indeterminacies remain for g 2 we use this to construct hecke algebra actions on the cohomology of varieties associated to w 0 or its square for groups of arbitrary rank in the subsequent work f digne j michel endomorphisms of deligne lusztig varieties nagoya j math 183 2006 we construct actions associated to more general regular elements and we study their traces on cohomology

base sizes for simple groups and a conjecture of cameron let g be a permutation group on a finite set a base for g is a subset b with pointwise stabilizer in g that is trivial we write b g for the smallest size of a base for g in this paper we prove that b g 6 if g is an almost simple group of exceptional lie type and is a primitive faithful g set an important consequence of this result when combined with other recent work is that b g 7 for any almost simple group g in a non standard action proving a conjecture of cameron the proof is probabilistic and uses bounds on fixed point ratios

on endoscopic transfer of deligne lusztig functions in this paper we prove the fundamental lemma for deligne lusztig functions namely for every deligne lusztig functionon a p adic group g we write down an explicit linear combinationh of deligne lusztig functions on an endoscopic group h such thatandh have matching orbital integrals in particular we prove a conjecture of kottwitz ko4 more precisely we do it under some mild restriction on p

exponential convergence of the discrete and continuous time altafini models this paper considers the discrete time version of altafini s model for opinion dynamics in which the interaction among a group of agents is described by a time varying signed digraph prompted by an idea from 3 exponential convergence of the system is studied using a graphical approach necessary and sufficient conditions for exponential convergence with respect to each possible type of limit states are provided specifically under the assumption of repeatedly jointly strong connectivity it is shown that 1 a certain type of two clustering will be reached exponentially fast for almost all initial conditions if and only if the sequence of signed digraphs is repeatedly jointly structurally balanced corresponding to that type of two clustering 2 the system will converge to zero exponentially fast for all initial conditions if and only if the sequence of signed digraphs is repeatedly jointly structurally unbalanced an upper bound on the convergence rate is provided the results are also extended to the continuous time altafini model

analysis of the normalized lms algorithm with gaussian inputs the lms adaptive filter algorithm requires a priori knowledge of the input power level to select the algorithm gain parameter for stability and convergence since the input power level is usually one of the statistical unknowns it is normally estimated from the data prior to beginning the adaptation process it is then assumed that the estimate is perfect in any subsequent analysis of the lms algorithm behavior in this paper the effects of the power level estimate are incorporated in a data dependent that appears explicitly within the algorithm the transient mean and second moment behavior of the modified lms nlms algorithm are evaluated taking into account the explicit statistical dependence of upon the input data the mean behavior of the algorithm is shown to converge to the wiener weight a constant coefficient matrix difference equation is derived for the weight fluctuations about the wiener weight the equation is solved for a white data covariance matrix and for the adaptive line enhancer with a single frequency input in steady state for small expressions for the misadjustment error are also presented it is shown for the white data covariance matrix case that the averaging of about ten data samples causes negligible degradation as compared to the lms algorithm in the ale application the steady state weight fluctuations are shown to be mode dependent being largest at the frequency of the input

a variant of the induction theorem for springer representations abstract let g be a simple algebraic group over c with the weyl group w for a unipotent element u g let b u be the variety of borel subgroups of g containing u let l be a levi subgroup of a parabolic subgroup of g with the weyl subgroup w l of w assume that u l and let b u l be a similar variety as b u for l for a certain choice of l u l and e 1 we describe the w modules n k mod e h 2 n b u for k 0 e 1 in terms of the w l module h b u l with some additional data which is a refinement of the induction theorem due to lusztig as an application we give an explicit formula for the values of green functions at root of unity in the case where u is a regular unipotent element in l

product of random stochastic matrices the paper deals with the convergence properties of the products of random row stochastic matrices the limiting behavior of such products is studied from a dynamical system point of view in particular by appropriately defining a dynamic associated with a given sequence of random row stochastic matrices we prove that the dynamics admits a class of time varying lyapunov functions including a quadratic one then we discuss a special class of stochastic matrices a class p which plays a central role in this work we then study cut balanced chains and using some geometric properties of these chains we characterize the stability of a subclass of cut balanced chains as a special consequence of this stability result we obtain an extension of a central result in the non negative matrix theory stating that for any aperiodic and irreducible row stochastic matrix a the limit limk ak exists and it is a rank one stochastic matrix we show that a generalization of this result holds not only for sequences of stochastic matrices but also for independent random sequences of such matrices

reaching a consensus in a dynamically changing environment a graphical approach this paper presents new graph theoretic results appropriate for the analysis of a variety of consensus problems cast in dynamically changing environments the concepts of rooted strongly rooted and neighbor shared are defined and conditions are derived for compositions of sequences of directed graphs to be of these types the graph of a stochastic matrix is defined and it is shown that under certain conditions the graph of a sarymsakov matrix and a rooted graph are one and the same as an illustration of the use of the concepts developed in this paper graph theoretic conditions are obtained which address the convergence question for the leaderless version of the widely studied vicsek consensus problem

resolutions for representations of reductive p adic groups via their buildings schneider stuhler and vigneras have used cosheaves on the affine bruhat tits building to construct natural projective resolutions of finite type for admissible representations of reductive p adic groups in characteristic not equal to p we use a system of idempotent endomorphisms of a representation with certain properties to construct a cosheaf and a sheaf on the building and to establish that these are acyclic and compute homology and cohomology with these coefficients this implies bernstein s result that certain subcategories of the category of representations are serre subcategories furthermore we also get results for convex subcomplexes of the building following work of korman this leads to trace formulas for admissible representations

on the optimum data nonlinearity in lms adaptation the effect of an arbitrary nonlinear operation on the data input to the weight update equation in the lms adaptive algorithm is investigated for a gaussian data model exact difference equations are derived for the weight first and second moments that include the effects of an arbitrary nonlinear operation on the data sequence the difference equations are used to obtain expressions for the transient behavior of the mean square error the mean square error is minimized over the choice of nonlinearity for a fixed transient behavior the best choice of nonlinearity is shown exactly to be of the form x 1 bx2 when the input data are white for an arbitrary data covariance matrix the optimum nonlinearity is shown to be linear when the product of the algorithm step size and input power is much less than unity

on ergodicity infinite flow and consensus in random models we consider the ergodicity and consensus problem for a discrete time linear dynamic model driven by random stochastic matrices which is equivalent to studying these concepts for the product of such matrices our focus is on the model where the random matrices have independent but time variant distribution we introduce a new phenomenon the infinite flow and we study its fundamental properties and relations with the ergodicity and consensus the central result is the infinite flow theorem establishing the equivalence between the infinite flow and the ergodicity for a class of independent random models where the matrices in the model have a common steady state in expectation and a feedback property for such models this result demonstrates that the expected infinite flow is both necessary and sufficient for the ergodicity the result is providing a deterministic characterization of the ergodicity which can be used for studying the consensus and average consensus over random graphs

theorie de lubin tate non abelienne et representations elliptiques non abelian lubin tate theory studies the cohomology of some moduli spaces for p divisible groups the broadest definition of which is due to rapoport zink aiming both at providing explicit realizations of local langlands functoriality and at studying bad reduction of shimura varieties in this paper we consider the most famous examples the so called drinfeld and lubin tate towers in the lubin tate case harris and taylor proved that the supercuspidal part of the cohomology realizes both the local langlands and jacquet langlands correspondences as conjectured by carayol recently boyer computed the remaining part of the cohomology and exhibited two defects first the representations of gl d which appear are of a very particular and restrictive form second the langlands correspondence is not realized anymore in this paper we study the cohomology complex in a suitable equivariant derived category and show how it encodes langlands correspondence for elliptic representations then we transfer this result to the drinfeld tower via an enhancement of a theorem of faltings due to fargues we deduce that deligne s weight monodromy conjecture is true for varieties uniformized by drinfeld s coverings of his symmetric spaces this completes the computation of local l factors of some unitary shimura varieties

generalized gelfand graev representations of exceptional simple algebraic groups over a finite field i introduction let ffi be an adjoint simple algebraic group of type e n 6 7 8 f 4 or g2 over an algebraically closed field k of characteristic p 0 we assume that 5 has a fixed fq rational structure for a finite subfield fq of k the purpose of this paper is to determine explicitly the values of the irreducible characters of g ffi fq at the unipotent elements when p is good 38 i 4 3 in this part i we shall do this only for large p and the full result will be proved in the forthcoming part ii after submitting the first version of the present paper the author was informed by lusztig that he solved analogous problems for classical groups using his theory of character sheaves and that he can also recover the result of this paper mentioned above our method depends upon 1 a parametrization of the irreducible characters of g and the determination of their multiplicities in deligne lusztig virtual representations lusztig 25 2 the computation of the green functions of g in large characteristic springer 36 7 1 shoji 33 beynon and spaltenstein 3 4 3 the determination of the values of generalized gelfand graev characters 20 of g in good characteristic see section 3 by 1 and 2 the uniform parts of the irreducible characters are already known explicitly in large characteristic this implies that in large characteristic our problem for groups of type e 6 o r e 7 has already been solved it should be mentioned here that the whole character table of the g2 group is also known by chang and ree 8 hence in the g2 case this paper gives just another approach to a part of the result of chang and ree if g is of type g2 f4 or e 8 the restriction of an irreducible character r of g to the set of unipotent elements can be written as a sum of its uniform part with a function of the form

l espace symetrique de drinfeld et correspondance de langlands locale i we study the geometry and the cohomology of the tamely ramified cover of drinfeld s p adic symmetric space over a p adic field k for this tame level we prove in a purely local way most of a conjecture of harris on the form of the ell adic cohomologies as well as the torsion freeness of the integral cohomology in this paper we also compute the ell adic cohomology of coxeter deligne lusztig variety associated to mathrm gl d and some results of independent interest on the coefficient systems over the bruhat tits building associated to mathrm gl d k have been established

on the convergence behavior of the lms and the normalized lms algorithms it is shown that the normalized least mean square nlms algorithm is a potentially faster converging algorithm compared to the lms algorithm where the design of the adaptive filter is based on the usually quite limited knowledge of its input signal statistics a very simple model for the input signal vectors that greatly simplifies analysis of the convergence behavior of the lms and nlms algorithms is proposed using this model answers can be obtained to questions for which no answers are currently available using other perhaps more realistic models examples are given to illustrate that even quantitatively the answers obtained can be good approximations it is emphasized that the convergence of the nlms algorithm can be speeded up significantly by employing a time varying step size the optimal step size sequence can be specified a priori for the case of a white input signal with arbitrary distribution

consensus over ergodic stationary graph processes in this technical note we provide a necessary and sufficient condition for convergence of consensus algorithms when the underlying graphs of the network are generated by an ergodic and stationary random process we prove that consensus algorithms converge almost surely if and only if the expected graph of the network contains a directed spanning tree our results contain the case of independent and identically distributed graph processes as a special case we also compute the mean and variance of the random consensus value that the algorithm converges to and provide a necessary and sufficient condition for the distribution of the consensus value to be degenerate

generalized springer correspondence and green functions for type b c graded hecke algebras this paper presents a combinatorial approach to the tempered representation theory of a graded hecke algebra h of classical type b or c with arbitrary parameters we present various combinatorial results which together give a uniform combinatorial description of what becomes the springer correspondence in the classical situation of equal parameters more precisely by using a general version of lusztig s symbols which describe the classical springer correspondence we associate to a discrete series representation of h with central character w0c a set w0c of w0 characters where w0 is the weyl group this set w0c is shown to parametrize the central characters of the generic algebra which specialize into w0c using the parabolic classification of the central characters of h t r on the one hand and a truncated induction of weyl group characters on the other hand we define a set w0c for any central character w0c of h t r and show that this property is preserved we show that in the equal parameter situation we retrieve the classical springer correspondence by considering a set u of partitions which replaces the unipotent classes of so2n 1 c and sp2n c and a bijection between u and the central characters of h t r we end with a conjecture which basically states that our generalized springer correspondence determines h t r exactly as the classical springer correspondence does in the equal label case in particular we conjecture that w0c indexes the modules in h t r with central character w0c in the following way a module m in h t r has a natural grading for the action of w0 and the w0 representation m in its top degree is irreducible when m runs through the modules in h t r with central character w0c m runs through w0c moreover still in analogy with the equal parameter case we conjecture that the w0 structure of the modules in h t r can be computed using generalized green functions

consensus and products of random stochastic matrices exact rate for convergence in probability we find the exact rate for convergence in probability of products of independent identically distributed symmetric stochastic matrices it is well known that if the matrices have positive diagonals almost surely and the support graph of the mean or expected value of the random matrices is connected the products of the matrices converge almost surely to the average consensus matrix and thus in probability in this paper we show that the convergence in probability is exponentially fast and we explicitly characterize the exponential rate of this convergence our analysis reveals that the exponential rate of convergence in probability depends only on the statistics of the support graphs of the random matrices further we show how to compute this rate for commonly used random models gossip and link failure with these models the rate is found by solving a min cut problem and hence it is easily computable finally as an illustration we apply our results to solving power allocation among networked sensors in a consensus innovations distributed detection problem