clustering in neutral ecology the neutral ecology model assumes that all organisms in the same trophic level have the same death duplication migration and mutation rates and are subjected to a zero sum rule we show by exact analytical methods that under the assumption of this model organisms tend to aggregate and form clusters at dimensions less than or equal to 2 cluster size grows in average and one specie will dominate the whole ecosystem if enough time is allocated at dimension d 3 or higher an equilibrium is reached and cluster sizes are distributed as a power law

numerical methods for the generalized zakharov system we present two numerical methods for the approximation of the generalized zakharov system zs the first one is the time splitting spectral tssp method which is explicit time reversible and time transverse in variant if the generalized zs is keeps the same decay rate of the wave energy as that in the generalized zs gives exact results for the plane wave solution and is of spectral order accuracy in space and second order accuracy in time the second one is to use a local spectral method the discrete singular convolution dsc for spatial derivatives and the fourth order runge kutta rk4 for time integration which is of high the same as spectral order accuracy in space and can be applied to deal with general boundary conditions in order to test accuracy and stability we compare these two methods with other existing methods fourier pseudospectral method fps and wavelet galerkin method wg for spatial derivatives combining with the rk4 for time integration as well as the standard finite difference method fd for solving the zs with a solitary wave solution furthermore extensive numerical tests are presented for plane waves solitary wave collisions in 1d as well as a 2d problem of the generalized zs numerical results show that tssp and dsc are spectralorder accuracy in space and much more accurate than fd and for stability tssp requires k o h dsc rk4 requires k o h2 for fixed acoustic speed where k is the time step and h is the spatial mesh size

functions analytic on the half plane as quantum mechanical states a transform between the state space of one dimensional quantum mechanical systems and a direct sum of two spaces of square integrable functions analytic on the open upper half plane is constructed it gives a representation of usual quantum mechanics on which the free evolution is trivial and the representation of canonical transformation very simple generalizations to higher dimensions are also discussed

the efficiency of resource allocation mechanisms for budget constrained users we study the efficiency of mechanisms for allocating a divisible resource given scalar signals submitted by all users such a mechanism decides the fraction of the resource that each user will rec

a wavelet or lifting scheme based imputation method summary the paper proposes a new approach to imputation using the expected sparse representation of a surface in a wavelet or lifting scheme basis our method incorporates a bayesian mixture prior for these wavelet coefficients into a gibbs sampler to generate a complete posterior distribution for the variable of interest intuitively the estimator operates by borrowing strength from those observed neighbouring values to impute at the unobserved sites we demonstrate the strong performance of our estimator in both one and two dimensional imputation problems where we also compare its application with the standard imputation techniques of kriging and thin plate splines

mean field stochastic theory for species rich assembled communities a dynamical model of an ecological community is analyzed within a mean field approximation in which one of the species interacts with the combination of all of the other species in the community within this approximation the model may be formulated as a master equation describing a one step stochastic process the stationary distribution is obtained in closed form and is shown to reduce to a log series or log normal distribution depending on the values that the parameters describing the model take on a hyperbolic relationship between the connectance of the matrix of interspecies interactions and the average number of species exists for a range of parameter values the time evolution of the model at short and intermediate times is analyzed using van kampen s approximation which is valid when the number of individuals in the community is large good agreement with numerical simulations is found the large time behavior and the approach to the stationary state is obtained by solving the equation for the generating function of the probability distribution the analytical results which follow from the analysis are also in good agreement with direct simulations of the model

analytical solution of a neutral model of biodiversity the unified neutral model of biodiversity proposed by s hubbell is solved analytically the distributions of species abundance in the metacommunity and in a local community are calculated exactly as a function of speciation and migration rates and of the size of the community in the limit of large population sizes the densities of species of given relative abundance are found to be given by universal functions depending only on two parameters

a system performance approach to osnr optimization in optical networks this paper studies a constrained optical signal to noise ratio osnr optimization problem in optical networks from the perspective of system performance a system optimization problem is formulated with the objective of achieving an osnr target for each channel while satisfying the total power constraint in order to establish existence of a unique optimal solution the conditions are derived which can be used as a basis for an admission control scheme the original problem is then converted to a relaxed system problem by using a barrier function and solved by a distributed iterative algorithm next the system optimization framework developed is compared to the game theoretic one in 1 the effects of parameters in both formulations are investigated to study efficiency of nash equilibria in the osnr game and pricing mechanisms affecting overall system performance the theoretical analysis is supported by numerical simulations and experiments conducted on an optical fiber link

optimized wavelet denoising for self similar alpha stable processes we investigate the performance of wavelet shrinkage methods for the denoising of symmetric alpha stable text s alpha text s self similar stochastic processes corrupted by additive white gaussian noise awgn where alpha is tied to the sparsity of the process the wavelet transform is assumed to be orthonormal and the shrinkage function minimizes the mean square approximation error mmse estimator we derive the corresponding formula for the expected value of the averaged estimation error we show that the predicted mmse is a monotone function of a simple criterion that depends on the wavelet and the statistical parameters of the process using the calculus of variations we then optimize this criterion to find the best performing wavelet within the extended family of meyer wavelets which are bandlimited these are compared with the daubechies wavelets which are compactly supported in time we find that the wavelets that are shorter in time in particular the haar basis are better suited to denoise the sparser processes say alpha while the bandlimited ones including the held and shannon wavelets offer the best performance for alpha 1 6 the limit corresponding to the gaussian case fbm with alpha 2

design of regular nonseparable bidimensional wavelets using grobner basis techniques the design of two dimensional 2 d filter banks yielding orthogonality and linear phase filters and generating regular wavelet bases is a difficult task involving the algebraic properties of multivariate polynomials using cascade forms implies dealing with nonlinear optimization we turn the issue of optimizing the orthogonal linear phase cascade from kovacevic and vetterli 1992 into a polynomial problem and solve it using grobner basis techniques and computer algebra this leads to a complete description of maximally flat wavelets among the orthogonal linear phase family proposed by kovacevic and vetterli we obtain up to five degrees of flatness for a 16 spl times 16 filter bank whose sobolev exponent is 2 11 making this wavelet the most regular orthogonal linear phase nonseparable wavelet to the authors knowledge

wavelet sampling and localization schemes for the radon transform in two dimensions two theorems are presented for wavelet decompositions of the two dimensional radon transform the rst theorem establishes an upper error bound in l 2 norm between the radon transform and its wavelet approximation whose coecients at dierent scales are estimated from radon data acquired at corresponding sampling rates the second theorem gives an estimate of the accuracy of a local image reconstructed from localized radon data at multiple levels these results show how to design a multilevel sampling and localization strategy for parallel beam scanning by using wavelet regularity and vanishing moment characteristics clarify the interaction between the wavelet structure and the essential bandwidth of an object image and provide guidelines for wavelet local tomography

transcale control for a class of discrete stochastic systems based on wavelet packet decomposition abstract in this paper a wavelet packet decomposition wpd based real time transcale linear quadratic gaussian lqg tracking control algorithm is given for a class of discrete stochastic systems which is developed with the state space models of wavelet packet coefficients at the coarsest scale decomposition layer established by haar wpd the wpd based transcale control algorithm provides a compromise between performance index and computational efficiency compared with the conventional lqg tracking control algorithm and it is an improvement of the wavelet transform based algorithm previously proposed simulation results are presented to demonstrate the effectiveness of the proposed algorithm

linearly convergent away step conditional gradient for non strongly convex functions we consider the problem of minimizing the sum of a linear function and a composition of a strongly convex function with a linear transformation over a compact polyhedral set jaggi and lacoste julien an affine invariant linear convergence analysis for frank wolfe algorithms nips 2013 workshop on greedy algorithms frank wolfe and friends 2014 show that the conditional gradient method with away steps employed on the aforementioned problem without the additional linear term has a linear rate of convergence depending on the so called pyramidal width of the feasible set we revisit this result and provide a variant of the algorithm and an analysis based on simple linear programming duality arguments as well as corresponding error bounds this new analysis a enables the incorporation of the additional linear term and b depends on a new constant that is explicitly expressed in terms of the problem s parameters and the geometry of the feasible set this constant replaces the pyramidal width which is difficult to evaluate

designing network protocols for good equilibria designing and deploying a network protocol determines the rules by which end users interact with each other and with the network we consider the problem of designing a protocol to optimize the equilibrium behavior of a network with selfish users we consider network cost sharing games where the set of nash equilibria depends fundamentally on the choice of an edge cost sharing protocol previous research focused on the shapley protocol in which the cost of each edge is shared equally among its users we systematically study the design of optimal cost sharing protocols for undirected and directed graphs single sink and multicommodity networks and different measures of the inefficiency of equilibria our primary technical tool is a precise characterization of the cost sharing protocols that induce only network games with pure strategy nash equilibria we use this characterization to prove among other results that the shapley protocol is optimal in directed graphs and that simple priority protocols are essentially optimal in undirected graphs

transforms associated to square integrable group representations i general results let g be a locally compact group which need not be unimodular let x u x x g be an irreducible unitary representation of g in a hilbert space h u assume that u is square integrable i e that there exists in h u at least one nonzero vector g such that u x g g 2 dx we give here a reasonably self contained analysis of the correspondence associating to every vector f h u the function u x g f on g discussing its isometry characterization of the range inversion and simplest interpolation properties this correspondence underlies many properties of generalized coherent states

the price of anarchy under nonlinear and asymmetric costs in this paper we characterize the price of anarchy i e the inefficiency between user and system optimal solutions when costs are nonseparable asymmetric and nonlinear generalizing earlier work that has addressed the price of anarchy under separable costs the results in this paper apply primarily to nonatomic games such as the traffic equilibrium problem but also in competitive multiperiod pricing and competitive supply chain settings the bounds established in this paper are tight and explicitly account for the degree of asymmetry and nonlinearity of the cost function we first provide a proof method for problems with a positive definite jacobian matrix subsequently we use ideas from semidefinite optimization in order to account for problems with a positive semidefinite jacobian matrix where the first approach does not apply this latter connection also provides a different application of semidefinite optimization

on the variational equilibrium as a refinement of the generalized nash equilibrium we are concerned with a class of games in which the players strategy sets are coupled by a shared constraint a widely employed solution concept for such generalized nash games is the generalized nash equilibrium gne the variational equilibrium ve facchinei kanzow 2007 is a specific kind of gne characterized by the solution of the variational inequality formed from the common constraint and the mapping of the gradients of player objectives our contribution is a theory that provides sufficient conditions for ensuring that the existence of a gne implies the existence of a ve in such an instance the ve is said to be a refinement of the gne for certain games these conditions are shown to be necessary this theory rests on a result showing the equality of the brouwer degree of two suitably defined functions whose zeros are the gne and ve respectively this theory has a natural extension to the primal dual space of strategies and lagrange multipliers corresponding to the shared constraint our results unify some known results pertaining to such equilibria and provide mathematical substantiation for ideas that were known to be appealing to economic intuition

a new class of biorthogonal wavelet systems for image transform coding we construct general biorthogonal coifman wavelet systems a new class of compactly supported biorthogonal wavelet systems with vanishing moments equally distributed for a scaling function and wavelet pair a time domain design method is employed and closed form expressions for the impulse responses and the frequency responses of the corresponding dual filters are derived the resulting filter coefficients are all dyadic fractions which is an attractive feature in the realization of multiplication free discrete wavelet transform even ordered systems in this family are symmetric which correspond to linear phase dual filters in particular three filterbanks fbs in this family are systematically verified to have competitive compression potential to the 9 7 tap biorthogonal wavelet fb by cohen et al 1992 which is currently the most widely used one in the field of wavelet transform coding in addition the proposed fb s have much smaller computational complexity in terms of floating point operations required in transformation and therefore indicate a better tradeoff between compression performance and computational complexity

multiresolution modeling and estimation of multisensor data this paper presents a multiresolution multisensor data fusion scheme for dynamic systems to be observed by several sensors of different resolutions a state projection equation is introduced to associate the states of a system at each resolution with others this projection equation together with the state transition equation and the measurement equations at each of the resolutions construct a continuous time model of the system the model meets the requirements of kalman filtering in discrete time the state transition is described at the finest resolution and the sampling frequencies of sensors decrease successively by a factor of two in resolution we can build a discrete model of the system by using a linear projection operator to approximate the state space projection this discrete model satisfies the requirements of discrete kalman filtering which actually offers an optimal estimation algorithm of the system in time invariant case the stability of the kalman filter is analyzed and a sufficient condition for the filtering stability is given a markov process based example is given to illustrate and evaluate the proposed scheme of multiresolution modeling and estimation with multiple sensors

selfish routing in capacitated networks according to wardrop s first principle agents in a congested network choose their routes selfishly a behavior that is captured by the nash equilibrium of the underlying noncooperative game a nash equilibrium does not optimize any global criterion per se and so there is no apparent reason why it should be close to a solution of minimal total travel time i e the system optimum in this paper we offer positive results on the efficiency of nash equilibria in traffic networks in contrast to prior work we present results for networks with capacities and for latency functions that are nonconvex nondifferentiable and even discontinuous the inclusion of upper bounds on arc flows has early been recognized as an important means to provide a more accurate description of traffic flows in this more general model multiple nash equilibria may exist and an arbitrary equilibrium does not need to be nearly efficient nonetheless our main result shows that the best equilibrium is as efficient as in the model without capacities moreover this holds true for broader classes of travel cost functions than considered hitherto

on the least asymmetric wavelets the asymmetry of daubechies 1988 1992 scaling functions and wavelets can be diminished by minimizing a special second moment in time for the wavelet generating discrete time filter the moment is involved in an uncertainty relation for discrete time signals other measures of asymmetry are addressed as well and corresponding results are compared

multiscale poisson data smoothing summary the paper introduces a framework for non linear multiscale decompositions of poisson data that have piecewise smooth intensity curves the key concept is conditioning on the sum of the observations that are involved in the computation of a given multiscale coefficient within this framework most classical wavelet thresholding schemes for data with additive homoscedastic noise can be used any family of wavelet transforms orthogonal biorthogonal or second generation can be incorporated in this framework our second contribution is to propose a bayesian shrinkage approach with an original prior for coefficients of this decomposition as such the method combines the advantages of the haar fisz transform with wavelet smoothing and bayesian multiscale likelihood models with additional benefits such as extendability towards arbitrary wavelet families simulations show an important reduction in average squared error of the output compared with the present techniques of anscombe or fisz variance stabilization or multiscale likelihood modelling

inefficiency of nash equilibria it is shown that nash equilibria of smooth games generally tend to be inefficient in the pareto sense

design of price mechanisms for network resource allocation via price of anarchy we study the design of price mechanisms for communication network problems in which a user s utility depends on the amount of flow she sends through the network and the congestion on each link depends on the total traffic flows over it the price mechanisms are characterized by a set of axioms that have been adopted in the cost sharing games and we search for the price mechanisms that provide the minimum price of anarchy we show that given the non decreasing and concave utilities of users and the convex quadratic congestion costs in each link if the price mechanism cannot depend on utility functions the best achievable price of anarchy is 4 3 2 sqrt 2 approx 31 4 thus the popular marginal cost pricing with price of anarchy less than 1 3 33 3 is nearly optimal we also investigate the scenario in which the price mechanisms can be made contingent on the users preference profile while such information is available

pricing with markups in industries with increasing marginal costs we study a game that models a market in which heterogeneous producers of perfect substitutes make pricing decisions in a first stage followed by consumers that select a producer that sells at lowest price as opposed to cournot or bertrand competition producers select prices using a supply function that maps prices to production levels solutions of this type of models are normally referred to as supply function equilibria we consider a market where producers convex costs functions are proportional to each other depending on the efficiency of each particular producer we provide necessary and sufficient conditions for the existence of an equilibrium that uses simple supply functions that replicate the cost structure we then specialize the model to monomial cost functions with exponent q 0 which allows us to reinterpret the simple supply functions as a markup applied to the production cost we prove that an equilibrium for the markups exists if and only if the number of producers in the market is strictly larger than 1 q and if an equilibrium exists it is unique the main result for monomials is that the equilibrium nearly minimizes the total production cost when the market is competitive the result holds because when there is enough competition markups are bounded thus preventing prices to be significantly distorted from costs focusing on the case of linear unit cost functions on the production quantities we characterize the equilibrium accurately and refine the previous result to establish an almost tight bound on the worst case inefficiency of equilibria finally we derive explicitly the producers best response for series parallel networks with linear unit cost functions extending our previous result to more general topologies we prove that a unique equilibrium exists if and only if the network that captures the market structure is 3 edge connected for non series parallel markets we provide an example that does not admit an equilibrium on markups

nonlocal image restoration with bilateral variance estimation a low rank approach simultaneous sparse coding ssc or nonlocal image representation has shown great potential in various low level vision tasks leading to several state of the art image restoration techniques including bm3d and lssc however it still lacks a physically plausible explanation about why ssc is a better model than conventional sparse coding for the class of natural images meanwhile the problem of sparsity optimization especially when tangled with dictionary learning is computationally difficult to solve in this paper we take a low rank approach toward ssc and provide a conceptually simple interpretation from a bilateral variance estimation perspective namely that singular value decomposition of similar packed patches can be viewed as pooling both local and nonlocal information for estimating signal variances such perspective inspires us to develop a new class of image restoration algorithms called spatially adaptive iterative singular value thresholding saist for noise data saist generalizes the celebrated bayesshrink from local to nonlocal models for incomplete data saist extends previous deterministic annealing based solution to sparsity optimization through incorporating the idea of dictionary learning in addition to conceptual simplicity and computational efficiency saist has achieved highly competent often better objective performance compared to several state of the art methods in image denoising and completion experiments our subjective quality results compare favorably with those obtained by existing techniques especially at high noise levels and with a large amount of missing data

ito volterra optimal state estimation with continuous multirate randomly sampled and delayed measurements the optimal filter for continuous linear stochastic time varying systems described by the itocirc volterra equations with discontinuous measure is derived with an appropriately selected measure the result is applicable to a wide range of observation processes including the hybrid case of observations formed by an arbitrary combination of continuous and discrete measurements which may be sampled with a priori unknown changing and possibly random rates and delays the simultaneous presence of continuous and sampled measurements causes impulsive discontinuity in the inputs of the optimal filter equations which leads to a discontinuous change in state estimates every time a sampled measurement becomes available using the theory of vibrosolutions the explicit and unique expressions for the jumps in state estimates and estimation error covariance are derived several examples illustrate the procedure of modeling hybrid measurement systems by selecting an appropriate discontinuous measure we further show that the itocirc volterra model and the main result of the paper can be specialized to several important cases including state space systems for which we recover several known state estimation results and derive a novel optimal filter for continuous ltv systems with an arbitrary combination of continuous and delayed sampled measurements this optimal filter updates the state estimates for incoming measurements as soon as they become available and does not require prior knowledge of sampling instants and delays which makes it applicable when deterministic and random changes in sampling and delays are present several computational examples demonstrate the implementation of the developed filter and compare its performance to the traditional alternatives using monte carlo simulations

optimal pyramidal and subband decompositions for hierarchical coding of noisy and quantized images optimal hierarchical coding is sought for progressive or scalable image transmission by minimizing the variance of the error difference between the original image and its lower resolution renditions the optimal according to the above criterion pyramidal and subband image coders are determined for images subject to corruption by quantization or transmission noise given arbitrary analysis filters and assuming adequate knowledge of the noise statistics optimal synthesis filters are found the optimal analysis filters are subsequently determined leading to formulas for globally optimal structures for pyramidal and subband image decompositions experimental results illustrate the implementation and performance of the optimal coders

improved transient signal detection using a wavepacket based detector with an extended translation invariant wavelet transform this paper presents the theory of m band extended translation invariant eti wavelet transforms the eti generalizes the translation invariant wavelet transform of weiss 1933 it is shown that iteration of the eti in a tree structure provides a signal decomposition into an orthonormal wavepacket basis other properties such as translation invariance and invertibility of the transform are proven the theory is then applied to transient signal detection through development of a family of translation invariant wavepacket based detectors this family of detectors provides improved the performance over previously defined wavepacket based detectors a performance analysis is conducted roc curves generated by monte carlo simulation are presented indicating the detector performance the detector performance is demonstrated to be independent of the signal translation

potential games are necessary to ensure pure nash equilibria in cost sharing games we consider the problem of designing distribution rules to share welfare cost or revenue among individually strategic agents there are many known distribution rules that guarantee the existence of a pure nash equilibrium in this setting e g the shapley value and its weighted variants however a characterization of the space of distribution rules that guarantees the existence of a nash equilibrium is unknown our work provides an exact characterization of this space for a specific class of scalable and separable games that includes a variety of applications such as facility location routing network formation and coverage games given arbitrary local welfare functions x1d568 we prove that a distribution rule guarantees equilibrium existence for all games i e all possible sets of resources agent action sets etc if and only if it is equivalent to a generalized weighted shapley value on some ground welfare functions x1d568 which can be distinct from x1d568 however if budget balance is required in

wavelet based linear system modeling and adaptive filtering it is shown how linear time varying systems can be modeled in several different ways by discrete time wavelets or more generally by some set of functions interpretation of physical meanings possible efficiency and other characteristics of the modeling are considered system identification minimizing the mean square output error is studied optimal coefficients and the corresponding minimum mean square error are found and they are in general time varying least mean square adaptive filtering algorithms are derived for on line filtering and system identification theoretically and by simulations the advantages of using wavelet based filtering are shown separation of adaptation effects from unknown time varying system behavior and fast convergence adaptive coefficients estimated by a recursive least square algorithm can tend toward constants even in the case of time varying systems time invariant system identification and adaptive filtering is given as a special case of the general time varying setting

continuous probabilistic approach to species dynamics in hubbell s zero sum local community in this paper a continuous probabilistic approach formulated using kolmogorov fokker planck forward and backward models is applied to hubbell s zero sum neutral theory for species dynamics in local community using this technique the probability density of species abundance distribution of the first passage time to extinction or fixation and probability of extinction are defined the resulting values for the distribution of the first passage time to extinction are verified by the simulation study of hubbell s zero sum neutral model for the local community based on the sensitivity analysis for the continuous probabilistic models the realistic classification of local communities subject to their diversity and species dynamics is proposed with respect to the immigration probability the species metacommunity relative abundance and the size of local community doi 10 1103 physreve 74 021902 pacs numbers 87 23 cc 02 50 r the main goals of biodiversity study are to explain and quantify the distribution abundance and dynamics of living organisms in ecological communities these questions are also of central theoretical and practical importance in conservation biology and ecosystem management 1 2 since understanding the mechanisms of species abundance dynamics is of high concern in viability analysis species abundance relationships have long been studied by ecologists who defined them as species commonness and rarity in ecological communities 1 3 4 these relationships are usually described by species abundance distributions which show the number of species as the functions of their observed abundances early studies on species abundance relationships were focused on finding distributions that could fit well empirical data among the proposed distributions were the log series 5 and the log normal 6 later the preference was given to modeling species abundance relationships using one or another ecological theory of community organization using this approach the broken stick model was proposed by macarthur 7 8 the log normal patterns of species abundances were explained using the niche preemption model 9 11 and using the dynamic population model with gompertz density dependence 12 the gamma type of abundance distribution including fisher s log series the extended gamma distribution and macarthur s broken stick model was elucidated using the dynamic approach with logistic density dependence 13

multirate interacting multiple model filtering for target tracking using multirate models a multirate interacting multiple model mrimm tracking algorithm has been developed the algorithm is based on a reformulation of the interacting multiple model imm filter under the assumption that each model operates at an update rate proportional to the model s assumed dynamics a set of multirate models is derived based on the geometrical interpretation of a discrete wavelet transform a wavelet transform is used to generate equivalent multirate measurements which exhibit the additional property of lower equivalent measurement noise for low rate data using this filtering approach the mrimm algorithm significantly outperforms a full rate imm filter when no manoeuvres occur and performs comparably with the imm filter when manoeuvres occur with a certain amount of computational savings this approach also has the advantages of improved sensitivity for manoeuvre detection

optimal cost sharing for resource selection games joint use of resources with usage dependent cost raises the question who pays how much we study cost sharing in resource selection games where the strategy spaces are either singletons or bases of a matroid defined on the ground set of resources our goal is to design cost sharing protocols so as to minimize the resulting price of anarchy and price of stability we investigate three classes of protocols basic protocols guarantee the existence of at least one pure nash equilibrium separable protocols additionally require that the resulting cost shares only depend on the set of players on a resource uniform protocols are separable and require that the cost shares on a resource may not depend on the instance that is they remain the same even if new resources are added to or removed from the instance we find optimal basic and separable protocols that guarantee the price of stability and price of anarchy to grow logarithmically in the number of players except for the case of matroid games induced by separable protocols where the price of anarchy grows linearly with the number of players for uniform protocols we show that the price of anarchy is unbounded even for singleton games

distributed welfare games game theoretic tools are becoming a popular design choice for distributed resource allocation algorithms a central component of this design choice is the assignment of utility functions to the individual agents the goal is to assign each agent an admissible utility function such that the resulting game possesses a host of desirable properties including scalability tractability and existence and efficiency of pure nash equilibria in this paper we formally study this question of utility design on a class of games termed distributed welfare games we identify several utility design methodologies that guarantee desirable game properties irrespective of the specific application domain lastly we illustrate the results in this paper on two commonly studied classes of resource allocation problems coverage problems and coloring problems

social optima in mean field lqg control centralized and decentralized strategies we study a class of linear quadratic gaussian lqg control problems with n decision makers where the basic objective is to minimize a social cost as the sum of n individual costs containing mean field coupling the exact socially optimal solution determining a particular pareto optimum requires centralized information for each agent and has high implementational complexity as an alternative we subsequently exploit a mean field structure in the centralized optimal control problem to develop decentralized cooperative optimization so that each agent only uses its own state and a function which may be computed offline the resulting set of strategies asymptotically achieves the social optimum as n a key feature in this scheme is to let each agent optimize a new cost as the sum of its own cost and another component capturing its social impact on all other agents we also discuss the relationship between the decentralized cooperative solution and the so called nash certainty equivalence based solution presented in previous work on mean field lqg games

adaptive transient solution of nonuniform multiconductor transmission lines using wavelets this paper presents a highly adaptive algorithm for the transient simulation of nonuniform interconnects loaded with arbitrary nonlinear and dynamic terminations the discretization of the governing equations is obtained through a weak formulation using biorthogonal wavelet bases as trial and test functions it is shown how the multiresolution properties of wavelets lead to very sparse approximations of the voltages and currents in typical transient analyzes a simple yet effective time space adaptive algorithm capable of selecting the minimal number of unknowns at each time iteration is described numerical results show the high degree of adaptivity of the proposed scheme

quantum field theory in ninety minutes on presente divers aspects de la theorie quantique des champs la theorie p 2 a 2 dimensions la theorie 3 4 a 3 dimensions la theorie de yang mills a 4 dimensions

the laplacian pyramid as a compact image code we describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions the representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space pixel to pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself the result is a net data compression since the difference or error image has low variance and entropy and the low pass filtered image may represented at reduced sample density further data compression is achieved by quantizing the difference image these steps are then repeated to compress the low pass image iteration of the process at appropriately expanded scales generates a pyramid data structure the encoding process is equivalent to sampling the image with laplacian operators of many scales thus the code tends to enhance salient image features a further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression fast algorithms are described for coding and decoding

equilibrium existence and uniqueness in network games with additive preferences a directed network game of imperfect strategic substitutes with heterogeneous players is analyzed we consider concave additive separable utility functions that encompass the quasi linear ones it is found that pure strategy nash equilibria verify a non linear complementarity problem by requiring appropriate concavity in the utility functions the existence of an equilibrium point is shown and equilibrium uniqueness is established with a p matrix then it appears that previous ndings on network structure and sparsity hold for many more games

interpolating wavelet collocation method of time dependent maxwell s equations characterization of electrically large optical waveguide discontinuities biorthogonal interpolating wavelets have been applied to electromagnetic field modeling through the wavelet collocation method in time domain yielding a versatile first principle algorithm for the solution of time dependent maxwell s equations with inhomogeneous media the resulting scheme maintains high accuracy while by virtue of its sub gridding capability significant reduction of the computational expenditure has been obtained the proposed method has been applied to the analysis of two dimensional dielectric waveguide discontinuities particularly for the modeling of electrically large optical waveguides where the dimension of the analyzed structure is much larger than the wavelength of the highest frequency content of the transmitted signal the proposed method has been proven to be highly efficient compared to the standard finite difference method

ondelettes and phase cell cluster expansions a vindication y meyer has recently developed a particularly useful o n basis forl2 r d expansions using this basis i e expansions into ondelettes or wavelets have yielded important new results in soft and hard analysis the expansion into ondelettes of a boson scalar field naturally leads to phase cell cluster expansions a formalism already developed by the authors using other related bases adoption of ondelettes expansions into the phase cell program gives improvements of some extant results and excises an early error

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

a block spin construction of ondelettes part i lemarie functions using block spin assignments we construct anl2 orthonormal basis consisting of dyadic scalings and translates of just a finite number of functions these functions have exponential localization and for even values of a construction parameterm one can make them classcm 1 with vanishing moments up to orderm inclusive such a basis has an important application to phase cell cluster expansions in quantum field theory

phase space localization theorem for ondelettes it is proven that an orthonormal basis of ondelettes can never have exponential localization in both position space and momentum space

polytope conditioning and linear convergence of the frank wolfe algorithm it is well known that the gradient descent algorithm converges linearly when applied to a strongly convex function with lipschitz gradient in this case the algorithm s rate of convergence is determined by the condition number of the function in a similar vein it has been shown that a variant of the frank wolfe algorithm with away steps converges linearly when applied to a strongly convex function with lipschitz gradient over a polytope in a nice extension of the unconstrained case the algorithm s rate of convergence is determined by the product of the condition number of the function and a certain condition number of the polytope we shed new light on the latter type of polytope conditioning in particular we show that previous and seemingly different approaches to define a suitable condition measure for the polytope are essentially equivalent to each other perhaps more interesting they can all be unified via a parameter of the polytope that formalizes a key premise linked to the algorithm s line

special paraunitary matrices cayley transform and multidimensional orthogonal filter banks we characterize and design multidimensional md orthogonal filter banks using special paraunitary matrices and the cayley transform orthogonal filter banks are represented by paraunitary matrices in the polyphase domain we define special paraunitary matrices as paraunitary matrices with unit determinant we show that every paraunitary matrix can be characterized by a special paraunitary matrix and a phase factor therefore the design of paraunitary matrices and thus of orthogonal filter banks becomes the design of special paraunitary matrices which requires a smaller set of nonlinear equations moreover we provide a complete characterization of special paraunitary matrices in the cayley domain which converts nonlinear constraints into linear constraints our method greatly simplifies the design of md orthogonal filter banks and leads to complete characterizations of such filter banks

lattice structures for optimal design and robust implementation of two channel perfect reconstruction qmf banks a lattice structure and an algorithm are presented for the design of two channel qmf quadrature mirror filter banks satisfying a sufficient condition for perfect reconstruction the structure inherently has the perfect reconstruction property while the algorithm ensures a good stopband attenuation for each of the analysis filters implementations of such lattice structures are robust in the sense that the perfect reconstruction property is preserved in spite of coefficient quantization the lattice structure has the hierarchical property that a higher order perfect reconstruction qmf bank can be obtained from a lower order perfect reconstruction qmf bank simply by adding more lattice sections several numerical examples are provided in the form of design tables

scale free avalanche dynamics in the stock market abstract self organized criticality soc has been claimed to play an important role in many natural and social systems in the present work we empirically investigate the relevance of this theory to stock market dynamics avalanches in stock market indices are identified using a multi scale wavelet filtering analysis designed to remove gaussian noise from the index here new methods are developed to identify the optimal filtering parameters which maximize the noise removal the filtered time series is reconstructed and compared with the original time series a statistical analysis of both high frequency nasdaq e mini futures and daily dow jones data is performed the results of this new analysis confirm earlier results revealing a robust power law behaviour in the probability distribution function of the sizes duration and laminar times between avalanches this power law behaviour holds the potential to be established as a stylized fact of stock market indices in general while the memory process implied by the power law distribution of the laminar times is not consistent with classical models for soc we note that a power law distribution of the laminar times cannot be used to rule out self organized critical behaviour

multiresolutional distributed filtering an algorithm for optimal and dynamic multiresolutional distributed filtering is derived the wavelet transform is utilized as a bridge linking signals at different resolution levels the algorithm can be employed for dynamic multisensor data fusion

efficiency of scalar parameterized mechanisms we consider the problem of allocating a fixed amount of an infinitely divisible resource among multiple competing fully rational users we study the efficiency guarantees that are possible when we restrict to mechanisms that satisfy certain scalability constraints motivated by large scale communication networks in particular we restrict attention to mechanisms where users are restricted to one dimensional strategy spaces we first study the efficiency guarantees possible when the mechanism is not allowed to price differentiate we study the worst case efficiency loss ratio of the utility associated with a nash equilibrium to the maximum possible utility and show that kelly s proportional allocation mechanism minimizes the efficiency loss when users are price anticipating we then turn our attention to mechanisms where price differentiation is permitted using an adaptation of the vickrey clarke groves class of mechanisms we construct a class of mechanisms with one dimensional strategy spaces where nash equilibria are fully efficient these mechanisms are shown to be fully efficient even in general convex environments under reasonable assumptions our results highlight a fundamental insight in mechanism design when the pricing flexibility available to the mechanism designer is limited restricting the strategic flexibility of bidders may actually improve the efficiency guarantee

efficiency loss in a network resource allocation game we explore the properties of a congestion game in which users of a congested resource anticipate the effect of their actions on the price of the resource when users are sharing a single resource we establish that the aggregate utility received by the users is at least 3 4 of the maximum possible aggregate utility we also consider extensions to a network context where users submit individual payments for each link in the network they may wish to use in this network model we again show that the selfish behavior of the users leads to an aggregate utility that is no worse than 3 4 of the maximum possible aggregate utility we also show that the same analysis extends to a wide class of resource allocation systems where end users simultaneously require multiple scarce resources these results form part of a growing literature on the price of anarchy i e the extent to which selfish behavior affects system efficiency

wavelet transform based adaptive filters analysis and new results in this paper the wavelet transform is used in an adaptive filtering structure the coefficients of the adaptive filter are updated by the help of the least mean square lms algorithm first the wavelet transform based adaptive filter wtaf is described and it is analyzed for its wiener optimal solution then the performance of the wtaf is studied by the help of learning curves for three different convergence factors 1 constant convergence factor 2 time varying convergence factor and 3 exponentially weighted convergence factor the exponentially weighted convergence factor is proposed to introduce scale based variation to the weight update equation it is shown for two different sets of data that the rate of convergence increases significantly for all three wtaf structures as compared to that of time domain lms the high convergence rates of the wtaf give us reason to expect that it will perform well in tracking rapid changes in a signal

competition and efficiency in congested markets we study the efficiency of oligopoly equilibria oe in congested markets the motivating examples are the allocation of network flows in a communication network or of traffic in a transportation network we show that increasing competition among oligopolists can reduce efficiency measured as the difference between users willingness to pay and delay costs we characterize a tight bound of 5 6 on efficiency in pure strategy equilibria when there is zero latency at zero flow and a tight bound of 2 2 2 with positive latency at zero flow these bounds are tight even when the numbers of routes and oligopolists are arbitrarily large

three modeling paradigms in mathematical programming celebrating the sixtieth anniversary since the zeroth international symposium on mathematical programming was held in 1949 this paper discusses several promising paradigms in mathematical programming that have gained momentum in recent years but have yet to reach the main stream of the field these are competition dynamics and hierarchy the discussion emphasizes the interplay between these paradigms and their connections with existing subfields including disjunctive equilibrium and nonlinear programming and variational inequalities we will describe the modeling approaches mathematical formulations and recent results of these paradigms and sketch some open mathematical and computational challenges arising from the resulting optimization and equilibrium problems our goal is to elucidate the need for a systematic study of these problems and to inspire new research in the field

symmetry based scalable lossless compression of 3d medical image data we propose a novel symmetry based technique for scalable lossless compression of 3d medical image data the proposed method employs the 2d integer wavelet transform to decorrelate the data and an intraband prediction method to reduce the energy of the sub bands by exploiting the anatomical symmetries typically present in structural medical images a modified version of the embedded block coder with optimized truncation ebcot tailored according to the characteristics of the data encodes the residual data generated after prediction to provide resolution and quality scalability performance evaluations on a wide range of real 3d medical images show an average improvement of 15 in lossless compression ratios when compared to other state of the art lossless compression methods that also provide resolution and quality scalability including 3d jpeg2000 jpeg2000 and h 264 avc intra coding

painless nonorthogonal expansions in a hilbert space h discrete families of vectors hj with the property that f j hj f hj for every f in h are considered this expansion formula is obviously true if the family is an orthonormal basis of h but also can hold in situations where the hj are not mutually orthogonal and are overcomplete the two classes of examples studied here are i appropriate sets of weyl heisenberg coherent states based on certain non gaussian fiducial vectors and ii analogous families of affine coherent states it is believed that such quasiorthogonal expansions will be a useful tool in many areas of theoretical physics and applied mathematics