shape optimization of shell structures based on nurbs description using automatic differentiation the consolidation of the link among four fields in computational mathematics and mechanics is the main objective of this work surfaces based on nurbs non uniform rational b spline mathematical optimization the finite element method fem in structural analysis and automatic differentiation ad are applied in shape optimization of shells this problem is performed taking into account the fact that material and mechanical characteristics influence both the structural shape and the thickness variation in order to obtain the best performance with respect to a specific criterium some techniques were implemented to modify the shell geometry conserving the same parameterization without a new finite element mesh generation the shape modification is carried out using an optimization code based on the data obtained by a finite element analysis and gradients evaluation in this work the optimization procedure is performed using an sqp sequential quadratic programming algorithm where the variables are the control points in homogeneous coordinates the knot vectors and the thickness the functional value is determined by the fem and gradients are evaluated using ad some examples are analyzed and discussed as a consequence of the shape optimization shells with high structural performance and aesthetically beautiful shapes can be obtained copyright 2011 john wiley sons ltd

exact energy and momentum conserving algorithms for general models in nonlinear elasticity implicit time integration schemes that inherit the conservation laws of total energy linear and angular momentum are considered for initial boundary value problems in finite deformation elastodynamics conserving schemes are constructed for general hyperelastic material models both compressible and incompressible and are formulated in a way that is independent of spatial discretization three numerical examples for ogden type material models implemented using a finite element discretization in space are given to illustrate the performance of the proposed schemes these examples show that relative to the standard implicit mid point rule the conserving schemes exhibit superior numerical stability properties without a compromise in accuracy

robust comparative statics of risk changes the standard method for establishing the comparative statics of risk changes in optimization problems has been confined to comparing unique interior solutions relying on strong assumptions about payoff functions and decision variables we propose a simple and intuitive approach that hinges on considerably weaker assumptions merging insights from the monotone comparative statics literature with insights from the risk apportionment literature we show that the ranking of simple lottery pairs is all that is needed for establishing the comparative statics of risk changes we use this approach to analyze the comparative statics of nth degree stochastic dominance shifts in a general setting with one and with multiple decision variables and we show how these results can be applied to generalize the classical theories of precautionary saving self protection and others this paper was accepted by james smith decision analysis

a modified split radix fft with fewer arithmetic operations recent results by van buskirk have broken the record set by yavne in 1968 for the lowest exact count of real additions and multiplications to compute a power of two discrete fourier transform dft here we present a simple recursive modification of the split radix algorithm that computes the dft with asymptotically about 6 fewer operations than yavne matching the count achieved by van buskirk s program generation framework we also discuss the application of our algorithm to real data and real symmetric discrete cosine transforms where we are again able to achieve lower arithmetic counts than previously published algorithms

efficient computation of fourier inversion for finite groups let g be a finite group and let s be a complex valued function on g if is a matrix representation of g of dimension d then the fourier transform of f at g if is defined to be the matrix f s g f s s let r be a complete set of inequivalent irreducible matrix representations of g the fourier transform of f with respect to r is defined as the set of matrices f r recovery of f from its fourier transform may be accomplished via the fourier inversion formula f s g d trace f s 1

on the formulation of high frequency dissipative time stepping algorithms for nonlinear dynamics part ii second order methods we present in this paper the formulation of a new high frequency dissipative time stepping algorithm for nonlinear elastodynamics that is second order accurate in time the new scheme exhibits unconditional energy dissipation and momentum conservation and thus the given name of energy dissipative momentum conserving second order scheme edmc 2 leading also to the conservation of the relative equilibria of the underlying physical system the unconditional character of these properties applies not only with respect to the time step size but equally important with respect to the considered elastic potential moreover the dissipation properties are fully controlled through an algorithmic parameter reducing to existing fully conserving schemes if desired the design of the new algorithm is described in detail including a complete analysis of its dissipation conservation properties in the fully nonlinear range of finite elasticity to motivate the different constructions that lead to the dissipative properties of the final scheme the same arguments are used first in the construction of new linear time stepping algorithms for the system of linear elastodynamics including first and second order schemes the new schemes exhibit a rigorous decay of the physical energy with the second order schemes formulated in a general two stage formula accommodating the aforementioned control parameter in the dissipation of the energy a complete spectral analysis of the new schemes is presented in this linear range to evaluate their different numerical properties in particular the dissipative character of the proposed schemes in the high frequency range is fully demonstrated in fact it is shown that the new second order scheme is l stable most remarkably the extension of these ideas to the nonlinear range is accomplished avoiding the use of multi stage formulae given the freedom gained in using general nonlinear relations while preserving the conservation laws of the momenta and the corresponding relative equilibria several representative numerical simulations are presented in the context of nonlinear elastodynamics to evaluate the performance of the newly proposed schemes

spectral analysis for discrete longitudinal data abstract we develop a fourier type of analysis for data consisting of many short strings x 1 x 2 x n with x i x i 1 x ip the paper offers an approach testing and residual analysis based on a group theoretic decomposition of the sample space this is illustrated on a physical chance type data set where it is natural to allow each string to have its own parameter i i d coin tossing with parameter varying from string to string the usual model is rejected

fast generalized fourier transforms abstract let g be a f inite group then ls g the linear complexity of a suitable wedderburn transform corresponding to g is smaller than 2 g 2 we improve this trivial upper bound by showing that ls g is smaller than min s t l t g 7 q t g 3 2 where the minimum is taken over all towers t g n g n 1 g 0 1 of subgroups of g gn and where q t resp s t is the maximum resp sum of all indices gi 1 gi corresponding to t and l t n is the length of the tower a similar upper bound is valid for the linear complexity of the inverse of such a wedderburn transform for symmetric groups our technique yields the stronger estimate ls sn 0 sn log3 sn

aggregating the single crossing property the single crossing property plays a crucial role in economic theory yet there are important instances where the property cannot be directly assumed or easily derived difficulties often arise because the property cannot be aggregated the sum or convex combination of two functions with the single crossing property need not have that property we introduce a new condition characterizing when the single crossing property is stable under aggregation and also identify sufficient conditions for the preservation of the single crossing property under multidimensional aggregation we use our results to establish properties of objective functions convexity logsupermodularity the monotonicity of optimal decisions under uncertainty and the existence of monotone equilibria in bayesian games

operator calculus approach to orthogonal polynomial expansions using techniques of operational calculus we show how to compute the generalized fourier coefficients for the meixner classes of orthogonal polynomials in particular krawtchouk polynomials are discussed in detail including an algorithm for computing krawtchouk transforms

the algebraic approach to the discrete cosine and sine transforms and their fast algorithms it is known that the discrete fourier transform dft used in digital signal processing can be characterized in the framework of the representation theory of algebras namely as the decomposition matrix for the regular module mathbb c z n mathbb c x x n 1 this characterization provides deep insight into the dft and can be used to derive and understand the structure of its fast algorithms in this paper we present an algebraic characterization of the important class of discrete cosine and sine transforms as decomposition matrices of certain regular modules associated with four series of chebyshev polynomials then we derive most of their known algorithms by pure algebraic means we identify the mathematical principle behind each algorithm and give insight into its structure our results show that the connection between algebra and digital signal processing is stronger than previously understood

strategic information transmission this paper develops a model of strategic communication in which a better informed sender s sends a possibly noisy signal to a receiver r who then takes an action that determines the welfare of both we characterize the set of bayesian nash equilibria under standard assumptions and show that equilibrium signaling always takes a strikingly simple form in which s partitions the support of the scalar variable that represents his private information and introduces noise into his signal by reporting in effect only which element of the partition his observation actually lies in we show under further assumptions that before s observes his private information the equilibrium whose partition has the greatest number of elements is pareto superior to all other equilibria and that if agents coordinate on this equilibrium r s equilibrium expected utility rises when agents preferences become more similar since r bases his choice of action on rational expectations this establishes a sense in which equilibrium signaling is more informative when agents preferences are more similar

fast fourier transforms for symmetric groups theory and implementation recently it has been proved that a fourier transform for the symmetric group s based on young s seminormal form can be evaluated in less than 0 5 n3 n2 n arithmetic operations we look at this algorithm in more detail and show that it allows an efficient software implementation using appropriate data structures we also describe a similarly efficient algorithm for the inverse fourier transform we compare the time and memory requirements of our program to those of other existing implementations

computing irreducible representations of supersolvable groups recently it has been shown that the ordinary irreducible represen tations of a supersolvable group g of order n given by a power commutator presentation can be constructed in time 0 n2 log we present an improved algorithm with running time 0 n log

efficient computation of the fourier transform on finite groups let g be a finite group f g c a function and p an ir reducible representation of g the fourier transform is defined as f p eseeg f s p s direct computation for all irreducible representations involves order igi operations we derive fast algorithms and develop them for the symmetric group sn there n 2 is reduced to nf nf al2 where a is the constant for matrix multiplication 2 38 as of this writing variations of the algorithm allow efficient computation for small representations a practical version of the algorithm is given on sn numerical evidence is presented to show a speedup by a factor of 100 for n 9 department of mathematics harvard university cambridge massachusetts 02138 department of mathematics columbia university new york new york 10027 this content downloaded from 157 55 39 153 on mon 19 sep 2016 04 53 00 utc all use subject to http about jstor org terms

on the computational complexity of the general discrete fourier transform abstract in this paper the complexity of computing the general discrete fourier transform over group algebras of finite groups is studied starting with a short introduction to known results the complexity gains of a new algorithm derived from clifford s theorem are discussed applying these results to the class of finite solvable groups new upper bounds also for the complexity of the underlying group algebras are derived

a nurbs based finite element model applied to geometrically nonlinear elastodynamics using a corotational approach summary a numerical model to deal with nonlinear elastodynamics involving large rotations within the framework of the finite element based on nurbs non uniform rational b spline basis is presented a comprehensive kinematical description using a corotational approach and an orthogonal tensor given by the exact polar decomposition is adopted the state equation is written in terms of corotational variables according to the hypoelastic theory relating the jaumann derivative of the cauchy stress to the eulerian strain rate the generalized method g method and generalized energy momentum method with an additional parameter gemm are employed in order to obtain a stable and controllable dissipative time stepping scheme with algorithmic conservative properties for nonlinear dynamic analyses the main contribution is to show that the energy momentum conservation properties and numerical stability may be improved once a nurbs based fem in the spatial discretization is used also it is shown that high continuity can postpone the numerical instability when gemm with consistent mass is employed likewise increasing the continuity class yields a decrease in the numerical dissipation a parametric study is carried out in order to show the stability and energy budget in terms of several properties such as continuity class spectral radius and lumped as well as consistent mass matrices copyright 2015 john wiley sons ltd

relations between young s natural and the kazhdan lusztig representations of sn abstract our main result here is that under a suitable order of standard tableaux the classical representation of sn introduced by young in the collected papers of alfred young 1873 1940 univ of toronto press toronto qsa iv and usually referred as the natural representattion the the more recently discovered invent math 53 1979 165 184 kazhdan lusztig k l representation are related by an upper triangular integral matrix with unit diagonal elements we have been led to this discovery by a numerical exploration we noted it in each of the irreducible representations of sn up to n 6 the calculations in these cases were carried out by constructing the corresponding kazhdan lusztig graphs from tables m goresky tables of kazhdan lusztig polynomials unpublished of k l polynomials to extend the calculations to n 7 we have used graphs obtained by means of an algorithm given by lascoux and schutzenberger polynomes de kazhdan lusztig pour les grassmanniennes preprint remarkably the same property holds also for these graphs these findings appear to confirm the assertion made by these authors that their algorithm does indeed yield k l graphs for the case of hook shapes we have obtained an explicit construction of the transforming matrices a result which was also suggested by our numerical data for general shapes the transforming matrices are less explicit and our proof is based on certain properties of the kazhdan lusztig representations given in their article invent math 53 1979 165 184 and on a purely combinatorial construction of the natural representation

separation of variables and the computation of fourier transforms on finite groups ii we present a general diagrammatic approach to the construction of efficient algorithms for computing the fourier transform of a function on a finite group by extending work which connects bratteli diagrams to the construction of fast fourier transform algorithms we make explicit use of the path algebra connection to the construction of gel fand tsetlin bases and work in the setting of quivers we relate this framework to the construction of a configuration space derived from a bratteli diagram in this setting the complexity of an algorithm for computing a fourier transform reduces to the calculation of the dimension of the associated configuration space our methods give improved upper bounds for computing the fourier transform for the general linear groups over finite fields the classical weyl groups and homogeneous spaces of finite groups while also recovering the best known algorithms for the symmetric group

on the formulation of high frequency dissipative time stepping algorithms for nonlinear dynamics part i low order methods for two model problems and nonlinear elastodynamics abstract we present in this paper the development of a class of time stepping algorithms for nonlinear elastodynamics that exhibits the controllable numerical dissipation in the high frequency range required for the robust solution of the resulting numerically stiff systems to motivate and illustrate better the developments in this general case we present first the formulation and analysis of these methods for two simple model problems namely we consider a nonlinear elastic spring mass system and a simplified model of thin elastic beams as it is discussed in detail in this paper the conservation by the numerical algorithm of the momenta and corresponding relative equilibria of these characteristic hamiltonian systems with symmetry is of the main importance these conservation properties lead for a fixed and finite time step to a correct qualitative picture of the phase space where the discrete dynamics takes place even in the presence of the desired and controlled numerical dissipation of the energy this situation is contrasted with traditional dissipative numerical schemes which are shown through rigorous analyses to not only lose their dissipative character in the general nonlinear range but also the aforementioned conservation properties thus leading to a qualitatively distorted approximation of the phase dynamics the key for a successful algorithm in this context is the incorporation of the numerical dissipation in the internal modes of the motion while not affecting the group motions of the systems the algorithms presented in this work accomplish these goals the focus in this first part is given to first order methods representative numerical simulations ranging from applications in nonlinear structural dynamics to nonlinear continuum three dimensional elastodynamics are presented in the context of the finite element method to illustrate these ideas and results

formulation and analysis of conserving algorithms for frictionless dynamic contact impact problems this paper presents the formulation of conserving time stepping algorithms for frictionless dynamic contact of solids a new class of finite element methods is proposed for the solution of these problems that exhibit the same conservation laws as the underlying continuum dynamical system the proposed methods are based on a penalty regularization of the constrained contact problem and lead to full conservation of the total energy of the system including the regularization penalty potential during persistent contact and restoration of the original energy upon release both linear and angular momenta are conserved by the scheme furthermore the newly developed methods have the ability to enforce the associated constraints in the velocity besides the impenetrability constraint in the displacements while preserving the conservation restoration properties of the final numerical scheme a modification of these schemes is described that assures positive energy dissipation if desired even in the highly nonlinear setting of contact impact problems leading to contact schemes with high frequency energy dissipation representative numerical simulations are presented illustrating the performance of the proposed numerical schemes

an energy stable generalized α method for the swift hohenberg equation abstract we propose a second order accurate energy stable time integration method that controls the evolution of numerical instabilities introducing numerical dissipation in the highest resolved frequencies our algorithm further extends the generalized method and provides control over dissipation via the spectral radius we derive the first and second laws of thermodynamics for the swift hohenberg equation and provide a detailed proof of the unconditional energy stability of our algorithm finally we present numerical results to verify the energy stability and its second order accuracy in time

seminormal representations of weyl groups and iwahori hecke algebras the purpose of this paper is to describe a general procedure for computing analogues of young s seminormal representations of the symmetric groups the method is to generalize the jucys murphy elements in the group algebras of the symmetric groups to arbitrary weyl groups and iwahori hecke algebras the combinatorics of these elements allow one to compute irreducible representations explicitly and often very easily in this paper we do these computations for weyl groups and iwahori hecke algebras of types a n b n d n g 2 although these computations are within reach for types f 4 e 6 and e 7 we shall in view of the length of the current paper postpone this to another work in reading this paper i would suggest that the reader begin with 3 the symmetric group case and go back and pick up the generalities from 1 and 2 as they are needed this will make the motivation for the material in the earlier sections much more clear and the further examples in the later sections very easy the realization that the jucys murphy elements for weyl groups and iwahori hecke algebras come from the very natural central elements in 2 1 and proposition 2 4 is one of the main points of this paper there is a simple concrete connection proposition 2 8 between jucys murphy type elements in iwahori hecke algebras and jucys murphy elements in group algebras of weyl groups i know that the analogues of the jucys murphy elements in weyl groups of types b and d will be new to some of the experts and known to others these jucys murphy elements for types b and d are not new similar elements appear in the paper of cherednik 7 but i was not able to recognize them there until they were pointed out to me by m nazarov i extend my thanks to him for this some people were asking me for jucys murphy elements in type g 2 as late as june 1995 in july 1995 i was told that it was not known how to quantize the elements of cherednik that is to find analogues of them in the iwahori hecke algebras of types b and d of course this had been done already in 1974 by hoefsmit i have chosen to state my results in terms of the general mechanism of path algebras which i have defined in 1 this is a technique which i learned from h wenzl during our work on the paper 30 it is a well known method in several fields with many dif ferent terminologies i shall mention here only a few of the

on the limits of communication in multidimensional cheap talk a comment we analyze a cheap talk game a la crawford and sobel in a multidimensional state and policy space a feature of the multidimensional state space is that communication on one dimension often reveals information on others we show how this feature imposes bounds on communication

design of energy conserving algorithms for frictionless dynamic contact problems this paper proposes a formulation of dynamic contact problems which enables exact algorithmic conservation of linear momentum angular momentum and energy in finite element simulations it is seen that a lagrange multiplier enforcement of an appropriate contact rate constraint produces these conservation properties a related method is presented in which a penalty regularization of the aforementioned rate constraint is utilized this penalty method sacrifices the energy conservation property but is dissipative under all conditions of changing contact so that the global algorithm remains stable notably it is also shown that augmented lagrangian iteration utilizing this penalty kernel reproduces the energy conserving i e lagrange multiplier solution to any desired degree of accuracy the result is a robust stable method even in the context of large deformations as is shown by some representative numerical examples in particular the ability of the formulation to produce accurate results where more traditional integration schemes fail is emphasized by the numerical simulations 1997 by john wiley sons ltd

fast fourier transforms for finite inverse semigroups abstract we extend the theory of fast fourier transforms on finite groups to finite inverse semigroups we use a general method for constructing the irreducible representations of a finite inverse semigroup to reduce the problem of computing its fourier transform to the problems of computing fourier transforms on its maximal subgroups and a fast zeta transform on its poset structure we then exhibit explicit fast algorithms for particular inverse semigroups of interest specifically for the rook monoid and its wreath products by arbitrary finite groups

selecting cheap talk equilibria there are typically multiple equilibrium outcomes in the crawford sobel cs model of strategic information transmission this paper identifies a simple condition on equilibrium payoffs called nits no incentive to separate that selects among cs equilibria under a commonly used regularity condition only the equilibrium with the maximal number of induced actions satisfies nits we discuss various justifications for nits including perturbed cheap talk games with nonstrategic players or costly lying we also apply nits to other models of cheap talk illustrating its potential beyond the cs framework

a ribbon hopf algebra approach to the irreducible representations of centralizer algebras the brauer birman wenzl and type a iwahori hecke algebras abstract we show how the ribbon hopf algebra structure on the drinfel d jimbo quantum groups of types a b c and d can be used to derive formulas giving explicit realizations of the irreducible representations of the iwahori hecke algebras of type a and the birman wenzl algebras we use this derivation to give explicit realizations of the irreducible representations of the brauer algebras as well the derivation is accomplished by way of a combination of techniques from operator algebras quantum groups and the theory of 3 manifold invariants although our applications are in the cases of the quantum groups of types a b c and d most of the aspects of our approach apply in the general setting of ribbon hopf algebras

nash codes for noisy channels this paper studies the stability of communication protocols that deal with transmission errors we consider a coordination game between an informed sender and an uninformed receiver who communicate over a noisy channel the sender s strategy called a code maps states of nature to signals the receiver s best response is to decode the received channel output as the state with highest expected receiver payoff given this decoding an equilibrium or nash code results if the sender encodes every state as prescribed we show two theorems that give sufficient conditions for nash codes first a receiver optimal code defines a nash code a second more surprising observation holds for communication over a binary channel which is used independently a number of times a basic model of information transmission under a minimal monotonicity requirement for breaking ties when decoding which holds generically every code is a nash code

the efficient computation of fourier transforms on the symmetric group this paper introduces new techniques for the efficient computation of fourier transforms on symmetric groups and their homogeneous spaces we replace the matrix multiplications in clausen s algorithm with sums indexed by combinatorial objects that generalize young tableaux and write the result in a form similar to horner s rule the algorithm we obtain computes the fourier transform of a function on s n in no more than 3 4n n 1 s n multiplications and the same number of additions analysis of our algorithm leads to several combinatorial problems that generalize path counting we prove corresponding results for inverse transforms and transforms on homogeneous spaces

a new solution procedure for application of energy conserving algorithms to general constitutive models in nonlinear elastodynamics abstract this paper develops a novel solution strategy for temporal discretization of initial value problems in nonlinear elastodynamics enabling exact energy and momentum conservation for a spatially discretized problem this new energy momentum algorithm fits into the general framework established by simo and tarnow z angew math phys 43 1992 757 however in contrast to the presentation given in that reference the current approach extends the critical stress update formula to encompass generic stored energy functions for the hyperelastic continuum in a manner which also allows for quadratically convergent newton raphson solution of the nonlinear algorithmic equations numerical examples using a neo hookean material model are given to illustrate the excellent performance of the proposed scheme not only is the new algorithm guaranteed to be second order accurate and unconditionally stable in the fully nonlinear regime as are other energy momentum strategies but also the approach advocated is demonstrated to be more robust and versatile than its predecessors

the base size of a primitive diagonal group abstract a base b for a finite permutation group g acting on a set is a subset of with the property that only the identity of g can fix every point of b we prove that a primitive diagonal group g has a base of size 2 unless the top group of g is the alternating or symmetric group acting naturally in which case the minimal base size of g is determined up to two possible values we also prove that the minimal base size of g satisfies a well known conjecture of pyber moreover we prove that if the top group of g does not contain the alternating group then the proportion of pairs of points that are bases for g tends to 1 as g tends to infinity a similar result for the case when the degree of the top group is fixed is given

isotone equilibrium in games of incomplete information an isotone pure strategy equilibrium exists in any game of incomplete information in which each player s action set is a finite sublattice of multidimensional euclidean space types are multidimensional and atomless and each player s interim expected payoff function satisfies two nonprimitive conditions whenever others adopt isotone pure strategies i single crossing in own action and type and ii quasi supermodularity in own action conditions i ii are satisfied in supermodular and log supermodular games given affiliated types and in games with independent types in which each player s ex post payoff satisfies supermodularity in own action and nondecreasing differences in own action and type this result is applied to provide the first proof of pure strategy equilibrium existence in the uniform price auction when bidders have multi unit demand nonprivate values and independent types

some lower and upper complexity bounds for generalized fourier transforms and their inverses for 2 leqq c leqq infty the c linear complexity l c a of a complex matrix a is defined as the minimal number of additions subtractions and multiplications by complex constants of absol

multi agent inference in social networks a finite population learning approach when people in a society want to make inference about some parameter each person may want to use data collected by other people information data exchange in social networks is usually costly so to make reliable statistical decisions people need to weigh the benefits and costs of information acquisition conflicts of interests and coordination problems will arise in the process classical statistics does not consider people s incentives and interactions in the data collection process to address this imperfection this work explores multi agent bayesian inference problems with a game theoretic social network model motivated by our interest in aggregate inference at the societal level we propose a new concept finite population learning to address whether with high probability a large fraction of people in a given finite population network can make good inference serving as a foundation this concept enables us to study the long run trend of aggregate inference quality as population grows supp

the computational complexity to evaluate representations of general linear groups we describe a fast algorithm to evaluate irreducible matrix representations of complex general linear groups rm gl m with respect to a symmetry adapted basis gelfand tsetlin basis this is complemented by a lower bound which shows that our algorithm is optimal up to a factor m 2 with regard to nonscalar complexity our algorithm can be used for the fast evaluation of special functions for instance we obtain an o ell log ell algorithm to evaluate all associated legendre functions of degree ell as a further application we obtain an algorithm to evaluate immanants which is faster than previous algorithms due to hartmann and barvinok

the hamiltonian structure of nonlinear elasticity the material and convective representations of solids rods and plates it is our belief that a thorough understanding of the mathematical underpinnings of elasticity is crucial to its analytical and numerical implementation for example in the analysis of rotating structures the coupling of the equations for geometrically inexact models obtained by linearization or other approximations with those for rotating rigid bodies can easily lead to misleading artificial softening effects that can significantly alter numerical results see simo and vuquoc 1986c especially equations 3 and 5 in this paper we consider fully nonlinear geometrically exact models for rods plates and shells which take into account shear and torsion as well as the usual bending effects in traditional rod and plate models these models can be obtained either from the three dimensional theory by a systematic use of projection methods see e g antman 1972 and naghdi 1972 or by a direct approach within the context of cosserat continuum remarkably the two approaches lead to essentially the same form of the governing field equations in the present context we have chosen as a model problem a particular rod model which may be regarded as an extension of the classical kirchhoff love model see love 1944 to include shear deformations as in

certifiable pre play communication full disclosure this article asks when communication with certifiable information leads to complete information revelation we consider bayesian games augmented by a pre play communication phase in which announcements are made publicly we first characterize the augmented games in which there exists a fully revealing sequential equilibrium with extremal beliefs i e any deviation is attributed to a single type of the deviator next we define a class of games for which existence of a fully revealing equilibrium is equivalent to a richness property of the evidence structure this characterization enables us to provide different sets of sufficient conditions for full information disclosure that encompass and extend all known results in the literature and are easily applicable we use these conditions to obtain new insights in games with strategic complementarities voting with deliberation and persuasion games with multidimensional types

the quasi partition algebra abstract we introduce the quasi partition algebra q p k n as a centralizer algebra of the symmetric group this algebra is a subalgebra of the partition algebra and inherits many similar combinatorial properties we construct a basis for q p k n give a formula for its dimension in terms of the bell numbers and describe a set of generators for q p k n as a complex algebra in addition we give the dimensions and indexing set of its irreducible representations we also provide the bratteli diagram for the tower of quasi partition algebras constructed by letting k range over the positive integers

learning sets in state dependent signalling game forms a characterization we consider repeated game forms with incomplete information and state dependent signalling structure we study the information a player can learn about the state of nature through a communication procedure in a way robust to unilateral deviations more precisely we say that playeri can distinguish state from state if there exists a strategy profile such that if is the true state and at most one player deviates from the profile then playeri will know after a finite number of stages that is not the true state the learning set of playeri at is the set of states that playeri cannot distinguish from it corresponds to the information playeri can learn in a way immune against unilateral deviations if the state is and players communicate through the game form for a finite number of stages this notion was introduced in a joint paper with t tomala renault and tomala 2000 we provide here a general characterization of the learning sets

randomized quantization and source coding with constrained output distribution this paper studies fixed rate randomized vector quantization under the constraint that the quantizer s output has a given fixed probability distribution a general representation of randomized quantizers that includes the common models in the literature is introduced via appropriate mixtures of joint probability measures on the product of the source and reproduction alphabets using this representation and results from optimal transport theory the existence of an optimal minimum distortion randomized quantizer having a given output distribution is shown under various conditions for sources with densities and the mean square distortion measure it is shown that this optimum can be attained by randomizing quantizers having convex codecells for stationary and memoryless source and output distributions a rate distortion theorem is proved providing a single letter expression for the optimum distortion in the limit of large blocklengths

fourier theoretic probabilistic inference over permutations permutations are ubiquitous in many real world problems such as voting ranking and data association representing uncertainty over permutations is challenging since there are n possibilities and typical compact and factorized probability distribution representations such as graphical models cannot capture the mutual exclusivity constraints associated with permutations in this paper we use the low frequency terms of a fourier decomposition to represent distributions over permutations compactly we present kronecker conditioning a novel approach for maintaining and updating these distributions directly in the fourier domain allowing for polynomial time bandlimited approximations low order fourier based approximations however may lead to functions that do not correspond to valid distributions to address this problem we present a quadratic program defined directly in the fourier domain for projecting the approximation onto a relaxation of the polytope of legal marginal distributions we demonstrate the effectiveness of our approach on a real camera based multi person tracking scenario

energy conserving and decaying algorithms in non linear structural dynamics a generalized formulation of the energy momentum methodwill be developed within the framework of the generalizedmethodwhich allows at the same time guaranteed conservation or decay of total energy and controllable numerical dissipation of unwanted high frequency response furthermore the latter algorithm will be extended by the consistently integrated constraints of energy and momentum conservation originally derived for the constraint energy momentum algorithm the goal of this general approach of implicit energyconserving and decaying time integration schemes is to compare these algorithms on the basis of an equivalent notation by the means of an overall algorithmic design and hence to investigate their numerical properties numerical stability and controllable numerical dissipation of high frequencies will be studied in application to non linear structural dynamics among the methods considered will be the newmark method the classical methods the energy momentum methodwith and without numerical dissipation the constraint energymomentum algorithm and the constraint energy method copyright 1999 john wiley sons ltd

monotone comparative statics the authors derive a necessary and sufficient condition for the solution set of an optimization problem to be monotonic in the parameters of the problem in addition they develop practical methods for checking the condition and demonstrate its applications to the classical theories of the competitive firm the monopolist the bertrand oligopolist consumer and growth theory game theory and general equilibrium analysis copyright 1994 by the econometric society

communication equilibria in repeated games with incomplete information correlated equilibria in the sense of aumann i e normal form correlated equilibria are studied in two person infinitely repeated games with lack of information on one side extensions of the solution concept are introduced several of which are shown to be payoff equivalent in the model under consideration a normal form correlated equilibrium is a nash equilibrium of the game where each player gets a private output from a correlation device before the beginning of the original game an r device r 0 1 is a communication device receiving an input from each player before every stage t 1 r and selecting a pair of outputs one for each player at every stage t 1 2 according to a memory dependent transition probability an r communication equilibrium is a nash equilibrium of the game extended by means of an r device let c resp dr r 0 1 be the set of normal form correlated resp r communication equilibrium payoffs d0 is the set of extensive form correlated equilibrium payoffs achieved by means of an autonomous device acting only by sending a stream of outputs to each player and d is the set of all communication equilibrium payoffs corresponding to communication devices which can receive inputs at every stage even arbitrarily large the paper characterizes the different sets and investigate whether they coincide

on the existence of monotone pure strategy equilibria in bayesian games we extend and strengthen both athey s 2001 and mcadams 2003 results on the existence of monotone pure strategy equilibria in bayesian games we allow action spaces to be compact locally complete metrizable semilatttices and can handle both a weaker form of quasisupermodularity than is employed by mcadams and a weaker single crossing property than is required by both athey and mcadams our proof which is based upon contractibility rather than convexity of best reply sets demonstrates that the only role of single crossing is to help ensure the existence of monotone best replies finally we do not require the milgrom weber 1985 absolute continuity condition on the joint distribution of types

constraint energy momentum algorithm and its application to non linear dynamics of shells abstract a modified time integration method is developed for non linear structural dynamics combining controllable algorithmic dissipation of higher modes and at the same time conservation of energy as well as linear and angular momentum although these features seem to be actually inconsistent numerical stability with large time steps for dynamic buckling and snap through problems as well as for dynamical systems with smooth solutions is guaranteed arbitrary implicit one step time integration schemes with newmark approximations are suitable for use as basic algorithms for the proposed method the desired conservation attributes are obtained if the basic algorithm is augmented by energy and momentum constraints the potential of the suggested algorithm is demonstrated by selected applications to non linear dynamics of shell structures

fast fourier transforms for the rook monoid we define the notion of the fourier transform for the rook monoid also called the symmetric inverse semigroup and provide two efficient divide and conquer algorithms fast fourier transforms or ffts for computing it this paper marks the first extension of group ffts to nongroup semigroups

generalized energy momentum method for non linear adaptive shell dynamics in the present study a generalization of the energy momentum method denoted by generalized energy momentum method applied to the non linear dynamics of shells will be developed within the framework of the generalized a method this algorithmic environment contains the unconditionally stable energy momentum method and its numerically damped version as well as the classical newmark and a methods as special cases in order to control the size of the time steps of the integration scheme with respect to accuracy and eaciency an adaptive time stepping procedure based on local a posteriori error estimation will be improved for non linear dynamical systems and applied to the proposed class of algorithms the spatial discretization is realized by an eight noded finite shell element of reissner mindlin type including an extensible shell director field permitting the application of three dimensional material laws the original formulation of this finite element will be developed for non linear dynamic analysis and adapted for the employment within the introduced energy conserving decaying time integration scheme 1999 elsevier science s a all rights reserved

asymptotic values for degrees associated with strips of young diagrams abstract the sums s l n occur in the representations of the symmetric and the general linear groups in combinatorics and in pi algebras we give asymptotic values for these sums

convex stochastic dominance in bayesian localization filtering and controlled sensing pomdps this paper provides conditions on the observation probability distribution in bayesian localization and optimal filtering so that the conditional mean estimate satisfies convex stochastic dominance convex dominance allows us to compare the unconditional mean square error between two optimal bayesian state estimators over arbitrary time horizons instead of using brute force monte carlo computations the proof uses two key ideas from microeconomics namely integral precision dominance and aggregation of single crossing the convex dominance result is then used to give sufficient conditions so that the optimal policy of a controlled sensing two state partially observed markov decision process pomdp is lower bounded by a myopic policy numerical examples are presented where the shannon capacity of the observation distribution using one sensor dominates that of another and convex dominance holds but blackwell dominance does not hold these illustrate the usefulness of the main result in localization filtering and controlled sensing applications

the hidden subgroup problem and quantum computation using group representations the hidden subgroup problem is the foundation of many quantum algorithms an efficient solution is known for the problem over abelian groups employed by both simon s algorithm and shor s factoring and discrete log algorithms the nonabelian case however remains open an efficient solution would give rise to an efficient quantum algorithm for graph isomorphism we fully analyze a natural generalization of the algorithm for the abelian case to the nonabelian case and show that the algorithm determines the normal core of a hidden subgroup in particular normal subgroups can be determined we show however that this immediate generalization of the abelian algorithm does not efficiently solve graph isomorphism

a co rotational element time integration strategy for non linear dynamics new procedures are proposed for implicit dynamic analysis using the finite element method the main aim is to give stable solutions with significant rigid body motions in particular rotations in contrast to most conventional approaches the time integration strategy is closely linked to the element technologies with the latter involving a form of co rotational procedure for the undamped situation one of the solution procedures leads to an algorithm that exactly conserves energy when constant external forces are applied i e with gravity loading

seismic data interpolation using a fast generalized fourier transform we have found a fast and efficient method for the interpolation of nonstationary seismic data the method uses the fast generalized fourier transform fgft to identify the space wavenumber evolution of nonstationary spatial signals at each temporal frequency the nonredundant nature of fgft renders a big computational advantage to this interpolation method a least squares fitting scheme is used next to retrieve the optimal fgft coefficients representative of the ideal interpolated data for randomly sampled data on a regular grid we seek a sparse representation of fgft coefficients to retrieve the missing samples in addition to interpolate the regularly sampled seismic data at a given frequency we use a mask function derived from the fgft coefficients of the low frequencies synthetic and real data examples can be used to examine the performance of the method

variational multiscale residual based turbulence modeling for large eddy simulation of incompressible flows we present an les type variational multiscale theory of turbulence our approach derives completely from the incompressible navier stokes equations and does not employ any ad hoc devices such as eddy viscosities we tested the formulation on forced homogeneous isotropic turbulence and turbulent channel flows in the calculations we employed linear quadratic and cubic nurbs a dispersion analysis of simple model problems revealed nurbs elements to be superior to classical finite elements in approximating advective and diffusive processes which play a significant role in turbulence computations the numerical results are very good and confirm the viability of the theoretical framework

an explicit time integration method for structural dynamics using septuple b spline functions in this paper an explicit time integration method with three parameters is proposed for structural dynamics using periodic septuple b spline interpolation polynomial functions in this way by use of septuple bsplines the authors have proceeded to solve the de of motion governing a single dof system and later the presented method has been generalized for a multiple dof system in the proposed method a direct recursive formula for response of the system was formulated on the basis of septuple b spline interpolation approximation in terms of the specific requirements of this proposed method two initialization approaches are given for initial calculation one is called direct initialization and the other is indirect initialization the stability analysis of the proposed method illustrates that by use of adjustable parameters a highfrequency response can be damped out without inducing excessive algorithmic damping in important low frequency modes the computational accuracy and efficiency of the proposed method is demonstrated with three numerical examples and the results from the proposed method are compared with those from some of the existent numerical methods such as the newmark and wilsonmethods the compared results show that the proposed method has high accuracy with low time consumption copyright 2013 john wiley sons ltd

e factor of representations of classical groups abstract we let g be the isometry group of a nondegenerate symmetric or skew symmetric form h on a space v over some local or global field k i e g u v h we let lg be the l group of go the identity component of g and r be the natural representation of this group we develop here a theory of l functions and e factors attached to this r in particular we develop a theory of local and global zeta integrals for such g we use very special intertwining operators therein we require an analysis of the proper normalization of such operators with such techniques we determine the correct e factors associated to local representations the issue of the correct local l factor is discussed

on optimal rules of persuasion a speaker wishes to persuade a listener to accept a certain request the conditions under which the request is justified from the listener s point of view depend on the values of two aspects the values of the aspects are known only to the speaker and the listener can check the value of at most one a mechanism specifies a set of messages that the speaker can send and a rule that determines the listener s response namely which aspect he checks and whether he accepts or rejects the speaker s request we study mechanisms that maximize the probability that the listener accepts the request when it is justified and rejects the request when it is unjustified given that the speaker maximizes the probability that his request is accepted we show that a simple optimal mechanism exists and can be found by solving a linear programming problem in which the set of constraints is derived from what we call the l principle

computational complexity and communication coordination in two player games the main contribution of this paper is the development and application of cryptographic techniques to the design of strategic communication mechanisms one of the main assumptions in cryptography is the limitation of the computational power available to agents we introduce the concept of limited computational complexity and by borrowing results from cryptography we construct a communication protocol to establish that every correlated equilibrium of a two person game with rational payoffs can be achieved by means of computationally restricted unmediated communication this result provides an example in game theory where limitations of computational abilities of players are helpful in solving implementation problems more specifically it is possible to construct mechanisms with the property that profitable deviations are too complicated to compute

fast fourier transforms for metabelian groups let g be a finite group then l s g the minimal number of arithmetic operations to evaluate a fourier transform corresponding to g is smaller than 2 cdot g 2 the fast fourier transform algorithms improve this trivial upper bound by showing that for a cyclic group g l s g leqq c cdot g cdot log g this last result is extended to metabelian groups and it is shown that these groups also have fast inverse fourier transforms in particular there are fast algorithms for the inverse fourier transforms for dihedral and generalized quaternion groups as well as for all groups of square free order