shannon meets nash on the interference channel the interference channel is the simplest communication scenario where multiple autonomous users compete for shared resources we combine game theory and information theory to define the notion of a nash equilibrium region of the interference channel the notion is game theoretic it captures the selfish behavior of each user as they compete the notion is also information theoretic it allows each user to use arbitrary communication strategies as it optimizes its own performance we give an exact characterization of the nash equilibrium region of the two user linear deterministic interference channel and an approximate characterization of the nash equilibrium region of the two user gaussian interference channel to within 1 bit s hz

a commutative algebra on degenerate cp1 and macdonald polynomials we introduce a unital associative algebra a associated with degenerate cp1 we show that a is a commutative algebra and whose poincare series is given by the number of partitions thereby we can regard a as a smooth degeneration limit of the elliptic algebra introduced by feigin and odesskii int math res notices 11 531 1997 then we study the commutative family of the macdonald difference operators acting on the space of symmetric functions a canonical basis is proposed for this family by using a and the heisenberg representation of the commutative family studied by shiraishi commun math phys 263 439 2006 it is found that the ding iohara algebra lett math phys 41 183 1997 provides us with an algebraic framework for the free field construction an elliptic deformation of our construction is discussed showing connections with the drinfeld quasi hopf twisting leningrad math j 1 1419 1990 in the sence of babelon bernard billey phys lett b 375 89 1996 the ruijsenaar

inverting the shapovalov form abstract we provide an explicit formula for the inversion of the shapovalov form associated to irreducible verma modules this formula implies that the singularities of the inverse are all simple poles

game theoretic opportunistic spectrum sharing strategy selection for cognitive mimo multiple access channels this paper studies opportunistic spectrum sharing strategy i e quantized precoding strategy selection for cognitive multiple input multiple output multiple access channels with limited feedback under interference power constraint and maximum transmission stream number constraint we put forward a game theoretic framework to model the precoding strategy selection behaviors of the secondary users under the specified constraints first we prove the formulated discrete game is a potential game which possesses at least one feasible pure strategy nash equilibrium the feasibility and optimality of the nash equilibrium are also analyzed then we prove that the solution to the sum rate maximization problem constitutes a feasible pure strategy nash equilibrium of our formulated game furthermore we design two algorithms the iterative precoding strategy selection algorithm based on the best response rule is designed to attain a feasible nash equilibrium the modified algorithm is designed to improve the sum rate performance simulation results show that our designed algorithms can achieve optimal or near optimal sum rate performance with low complexity

mimo cognitive radio a game theoretical approach the concept of cognitive radio cr has recently received great attention from the research community as a promising paradigm to achieve efficient use of the frequency resource by allowing the coexistence of licensed primary and unlicensed secondary users in the same bandwidth in this paper we propose and analyze a totally decentralized approach based on game theory to design cognitive mimo transceivers who compete with each other to maximize their information rate the formulation incorporates constraints on the transmit power as well as null and or soft shaping constraints on the transmit covariance matrix so that the interference generated by secondary users be confined within the temperature interference limit required by the primary users we provide a unified set of conditions that guarantee the uniqueness and global asymptotic stability of the nash equilibrium of all the proposed games through totally distributed and asynchronous algorithms interestingly the proposed algorithms overcome the main drawback of classical waterfilling based algorithms the violation of the temperature interference limit and they have the desired features required for cr applications such as low complexity distributed implementation robustness against missing or outdated updates of the users and fast convergence behavior

extensions of thickened verma modules of the virasoro algebra abstract let g denote the virasoro lie algebra h its cartan subalgebra and s h the symmetric algebra on h in this paper we consider thickened verma modules m which are u g s h bimodules satisfying m s h c m where m is the usual verma module with highest weight h we determine ext 1 m m to be s h s h where is up to a c algebra automorphism of s h a product of irreducible factors of the determinant of the shapovalov matrix this result provides a conceptual explanation of the factorization of the shapovalov determinant and implies that the inverse of the shapovalov matrix has only simple poles

analyticity of nekrasov partition functions we prove that the k theoretic nekrasov instanton partition functions have a positive radius of convergence in the instanton counting parameter and are holomorphic functions of the coulomb parameters in a suitable domain we discuss the implications for the agt correspondence and the analyticity of the norm of gaiotto states for the deformed virasoro algebra the proof is based on random matrix techniques and relies on an integral representation of the partition function due to moore nekrasov and shatashvili which we also prove

the evolution of conventions the author shows how a group of individuals can learn to play a coordination game without any common knowledge and with only a small amount of rationality the game is repeated many times by different players each player chooses an optimal reply based on incomplete information about what other players have done in the past occasionally they make mistakes when the likelihood of mistakes is very small typically one coordination equilibrium will be played almost all of the time over the long run this stochastically stable equilibrium can be computed analytically using a general theorem the author proves on perturbed markov processes copyright 1993 by the econometric society

crystallization of deformed virasoro algebra ding iohara miki algebra and 5d agt correspondence in this paper we consider the q 0 limit of the deformed virasoro algebra and that of the level 1 2 representation of the ding iohara miki algebra moreover 5d agt correspondence in this limit is discussed this specialization corresponds to the limit from macdonalds functions to hall littlewood functions using the theory of hall littlewood functions some problems are solved for example the simplest case of 5d agt conjectures is proven in this limit and we obtain a formula for the 4 point correlation function of a certain operator

the mimo iterative waterfilling algorithm this paper considers the noncooperative maximization of mutual information in the vector gaussian interference channel in a fully distributed fashion via game theory this problem has been widely studied in a number of works during the past decade for frequency selective channels and recently for the more general multiple input multiple output mimo case for which the state of the art results are valid only for nonsingular square channel matrices surprisingly these results do not hold true when the channel matrices are rectangular and or rank deficient matrices the goal of this paper is to provide a complete characterization of the mimo game for arbitrary channel matrices in terms of conditions guaranteeing both the uniqueness of the nash equilibrium and the convergence of asynchronous distributed iterative waterfilling algorithms our analysis hinges on new technical intermediate results such as a new expression for the mimo waterfilling projection valid also for singular matrices a mean value theorem for complex matrix valued functions and a general contraction theorem for the multiuser mimo watefilling mapping valid for arbitrary channel matrices the quite surprising result is that uniqueness convergence conditions in the case of tall possibly singular channel matrices are more restrictive than those required in the case of full rank fat channel matrices we also propose a modified game and algorithm with milder conditions for the uniqueness of the equilibrium and convergence and virtually the same performance in terms of nash equilibria of the original game

strong approximations of k th records and k th record times by wiener processes we develop several strong approximations for k th records and k th record times by wiener processes our main result is that it is possible to approximate by the same wiener process up to the almost sure rate o log j where j stands for the index of the observations the k th records the logarithms of the k th record times and the logarithms of the k th interrecord times we also provide some limiting weak laws and obtain berry esseen type theorems for k th record times

optimized signaling for mimo interference systems with feedback the system mutual information of a multiple input multiple output mimo system with multiple users which mutually interfere is considered perfect channel state information is assumed to be known to both transmitters and receivers asymptotic performance analysis shows that the system mutual information changes behavior as the interference becomes sufficiently strong in particular beamforming is the optimum signaling for all users when the interference is large we propose several numerical approaches to decide the covariance matrices of the transmitted signals and compare their performance in terms of the system mutual information we model the system as a noncooperative game and perform iterative water filling to find the nash equilibrium distributively a centralized global approach and a distributed iterative approach based on the gradient projection method are also proposed numerical results show that all proposed approaches give better performance than the standard signaling which is optimum for the case without interference both the global and the iterative gradient projection methods are shown to outperform the nash equilibrium significantly

asymptotic variability analysis for a two stage tandem queue part ii the law of the iterated logarithm abstract a strong form of the law of the iterated logarithm lil is established for a two stage tandem queue the concerned lil with a stronger mathematical form is a later generalization of levy s lil and it quantifies the magnitude of asymptotic stochastic fluctuations of stochastic processes compensated by their deterministic fluid limits the lils are established in twelve cases covering three regimes the underloaded critically loaded and overloaded divided by traffic intensity of the two stages for five processes the queue length workload busy idle and departure processes all the lils are expressed into some simple analytic functions of the primitive data the first and second moments of the interarrival and service times the proofs are based on a fluid approximation and a strong approximation which approximate discrete performance processes with their expected mean values and reflected brownian motions respectively

quantum scr w algebras and elliptic algebras we define a quantum open image in new window algebra associated to mathfrak s mathfrak l n as an associative algebra depending on two parameters for special values of the parameters this algebra becomes the ordinary open image in new window algebra of mathfrak s mathfrak l n or theq deformed classical open image in new window algebra algebra of mathfrak s mathfrak l n we construct free field realizations of the quantum open image in new window algebra and the screening currents we also point out some interesting elliptic structures arising in these algebras in particular we show that the screening currents satisfy elliptic analogues of the drinfeld relations in open image in new window

capacity of a multiple antenna fading channel with a quantized precoding matrix given a multiple input multiple output mimo channel feedback from the receiver can be used to specify a transmit precoding matrix which selectively activates the strongest channel modes here we analyze the performance of random vector quantization rvq in which the precoding matrix is selected from a random codebook containing independent isotropically distributed entries we assume that channel elements are independent and identically distributed i i d and known to the receiver which relays the optimal rate maximizing precoder codebook index to the transmitter using b bits we first derive the large system capacity of beamforming rank one precoding matrix as a function of b where large system refers to the limit as b and the number of transmit and receive antennas all go to infinity with fixed ratios rvq for beamforming is asymptotically optimal i e no other quantization scheme can achieve a larger asymptotic rate we subsequently consider a precoding matrix with arbitrary rank and approximate the asymptotic rvq performance with optimal and linear receivers matched filter and minimum mean squared error mmse numerical examples show that these approximations accurately predict the performance of finite size systems of interest given a target spectral efficiency numerical examples show that the amount of feedback required by the linear mmse receiver is only slightly more than that required by the optimal receiver whereas the matched filter can require significantly more feedback

asymptotic variability analysis for a two stage tandem queue part i the functional law of the iterated logarithm abstract a functional law of the iterated logarithm lil and its corresponding lil are established for a two stage tandem queue the functional lil and the lil limits quantify the magnitude of asymptotic stochastic fluctuations of stochastic processes compensated by their deterministic fluid limits in two forms the functional and numerical respectively the earliest functional lil and lil concerned are both developed for brownian motion by volker strassen and levy respectively we establish the functional lils and their corresponding lils in twelve cases covering three regimes divided by the traffic intensity the underloaded critically loaded and overloaded for five processes the queue length workload busy idle and departure processes by the primitive data of the first and second moments of the interarrival and service times all the functional lils are expressed into some compact sets of continuous functions and all the corresponding lils are some analytic functions the proofs are based on the fluid approximation and the strong approximation of the queueing system with the fluid approximation characterizing the expected values of the performance functions and the strong approximation approximating discrete performance processes with reflected brownian motions a companion paper asymptotic variability analysis for a two stage tandem queue part ii the law of the iterated logarithm develops another different version of lil which is a later generalization of levy s lil and also quantifies the magnitude of the asymptotic stochastic fluctuations of the performance functions

five dimensional su 2 agt conjecture and recursive formula of deformed gaiotto state this paper deals with the five dimensional pure su 2 alday gaiotto tachikawa agt conjecture proposed by awata and yamada j high energy phys 1001 125 2010 we give a conjecture on a recursive formula for the inner product of the deformed gaiotto state we also show that the k theoretic pure su 2 nekrasov partition function satisfies the same recursion relation therefore the five dimensional agt conjecture is reduced to our conjectural recursive formula

optimal linear precoding strategies for wideband noncooperative systems based on game theory part i nash equilibria in this two part paper we propose a decentralized strategy based on a game theoretic formulation to find out the optimal precoding multiplexing matrices for a multipoint to multipoint communication system composed of a set of wideband links sharing the same physical resources i e time and bandwidth we assume as optimality criterion the achievement of a nash equilibrium and consider two alternative optimization problems 1 the competitive maximization of mutual information on each link given constraints on the transmit power and on the spectral mask imposed by the radio spectrum regulatory bodies and 2 the competitive maximization of the transmission rate using finite order constellations under the same constraints as above plus a constraint on the average error probability in this first part of the paper we start by showing that the solution set of both noncooperative games is always nonempty and contains only pure strategies then we prove that the optimal precoding multiplexing scheme for both games leads to a channel diagonalizing structure so that both matrix valued problems can be recast in a simpler unified vector power control game with no performance penalty thus we study this simpler game and derive sufficient conditions ensuring the uniqueness of the nash equilibrium interestingly although derived under stronger constraints incorporating for example spectral mask constraints our uniqueness conditions have broader validity than previously known conditions finally we assess the goodness of the proposed decentralized strategy by comparing its performance with the performance of a pareto optimal centralized scheme to reach the nash equilibria of the game in part ii we propose alternative distributed algorithms along with their convergence conditions

conformal symmetry in two dimensions an explicit recurrence formula for the conformal partial wave amplitude an explicit recurrence relation for the conformal block functions is presented this relation permits one to evaluate thex expansion of these functions order by order and appropriate for numerical calculations

optimal linear precoding strategies for wideband non cooperative systems based on game theory part ii algorithms in this two part paper we address the problem of finding the optimal precoding multiplexing scheme for a set of noncooperative links sharing the same physical resources e g time and bandwidth we consider two alternative optimization problems p l the maximization of mutual information on each link given constraints on the transmit power and spectral mask and p 2 the maximization of the transmission rate on each link using finite order constellations under the same constraints as in p l plus a constraint on the maximum average error probability on each link aiming at finding decentralized strategies we adopted as optimality criterion the achievement of a nash equilibrium and thus we formulated both problems p l and p 2 as strategic noncooperative matrix valued games in part i of this two part paper after deriving the optimal structure of the linear transceivers for both games we provided a unified set of sufficient conditions that guarantee the uniqueness of the nash equilibrium in this part ii of the paper we focus on the achievement of the equilibrium and propose alternative distributed iterative algorithms that solve both games specifically the new proposed algorithms are the following 1 the sequential and simultaneous iterative waterfilling based algorithms incorporating spectral mask constraints and 2 the sequential and simultaneous gradient projection based algorithms establishing an interesting link with variational inequality problems our main contribution is to provide sufficient conditions for the global convergence of all the proposed algorithms which although derived under stronger constraints incorporating for example spectral mask constraints have a broader validity than the convergence conditions known in the current literature for the sequential iterative waterfilling algorithm

kiefer s theorem via the hungarian construction a proof of kiefer s theorem estimating the difference between the empirical and quantile processes is given by appealing to the hungarian construction

strong approximation of extended renewal processes we develop a strong approximation approach to extended multidimensional renewal theory the consequences of this approximation are a bahadur kiefer type representation of the renewal process in terms of partial sums strassen and chung type laws of the iterated logarithm we also give a characterization of the renewal process by four classes of deterministic curves in the sense of revesz 1982 we generalize our results to the case of non independent and or nonidentically distributed random vectors

the deformed virasoro algebra at roots of unity we discuss some aspects of the representation theory of the deformed virasoro algebra virpq in particular we give a proof of the formula for the kac determinant and then determine the center of virp q for q a primitive nth root of unity we derive explicit expressions for the generators of the center in the limit t qp 1 and elucidate the connection to the hall littlewood symmetric functions furthermore we argue that for the algebra describes gentile statistics of order n 1 i e a situation in which at most n 1 particles can occupy the same state

energy efficient spectrum sharing strategy selection for cognitive mimo interference channels in this paper we propose a promising discrete game theoretic framework for distributed energy efficient discrete spectrum sharing strategy selection i e joint discrete power control and multimode precoding strategy selection with limited feedback for cognitive mimo interference channels given the competitive nature the secondary users are assumed to be selfish and noncooperative each of whom attempts to maximize its individual energy efficiency under a minimum data rate constraint and an interference power constraint a mechanism for shutting down links is proposed to reduce interference and save energy a payoff function is designed to guarantee the feasibility of the pure strategy nash equilibrium with no need to know the infeasible strategy profiles a spectrum sharing strategy profile is said to be feasible if the stated constraints are satisfied otherwise the spectrum sharing strategy profile is said to be infeasible i e they may not satisfy the interference power constraint and minimum data rate constraint in advance we then investigate the existence and the feasibility of the pure strategy nash equilibrium and further devise a pricing based distributed algorithm for spectrum strategy selection the proposed algorithm is proved to converge to a feasible pure strategy nash equilibrium under specific conditions moreover by studying the relationship between our proposed game and the social optimum we find that the pricing mechanism can result in pareto improvement and lead to better convergence for the proposed distributed algorithm numerical results show that our designed algorithm significantly outperforms the random selection algorithm and the pricing mechanism has a dramatic effect in improving the system performance