stochastic precoding for miso interference channels with channel mean feedback this work considers linear precoding strategies for multiple input single out miso interference channels with channel mean feedback at transmitters where the interference at each receiver is treated as additive noise the challenge here is that previous precoder designs with perfect channel state information csi at transmitters do not apply and new approaches are required based on the laplace transform order an altruistic non equilibrium strategy i e the stochastic zero forcing is first proposed under practical assumptions generalizing the traditional zero forcing which requires perfect csi interestingly the precoding matrices here are all rank one beamformers as in the traditional zero forcing the competitive use of the common physical media in miso interference channels is also formulated as a strategic noncooperative game in contrast to the perfect csi case with a unique rank one nash equilibrium with channel mean feedback the nash equilibria here are not necessarily rank one in general nevertheless when achieved by the rank one beamforming the equilibrium is unique and convenient for implementation accordingly the condition for beamforming to achieve the equilibrium is derived comparisons of the above two strategies reveal no overall dominance of one over the other thereby establishing stochastic zero forcing as an alternative to the nash equilibrium designs

spatial frequency signal alignment for opportunistic transmission in this paper we investigate opportunistic transmission based on signal alignment for multiple input multiple output mimo orthogonal frequency division multiplexing ofdm cognitive radio cr systems where both primary and secondary users have multiple antennas in the studied scenario primary users are transmitting based on ofdm and secondary users generate interference free transmission to the primary users by using both the spatial and frequency space leftover by the primary system moreover inter and intra interference among secondary users are considered as well the number of symbols that can be transmitted by each secondary user satisfying all interference free constraints is obtained precoding matrix design will be discussed for perfectly and partially aligned transmission two chordal distance based schemes called as exhaustive search algorithm and heuristic algorithm will be developed for each case compared to the traditional time division multiple access tdma scheme the proposed scheme can support more interference free symbols to be transmitted by secondary users simultaneously

asynchronous iterative water filling for gaussian frequency selective interference channels this paper considers the maximization of information rates for the gaussian frequency selective interference channel subject to power and spectral mask constraints on each link to derive decentralized solutions that do not require any cooperation among the users the optimization problem is formulated as a static noncooperative game of complete information to achieve the so called nash equilibria of the game we propose a new distributed algorithm called asynchronous iterative water filling algorithm in this algorithm the users update their power spectral density psd in a completely distributed and asynchronous way some users may update their power allocation more frequently than others and they may even use outdated measurements of the received interference the proposed algorithm represents a unified framework that encompasses and generalizes all known iterative water filling algorithms e g sequential and simultaneous versions the main result of the paper consists of a unified set of conditions that guarantee the global converge of the proposed algorithm to the unique nash equilibrium of the game

on the robustness of transmit beamforming beamforming is a simple transmit strategy that uses only one eigen direction in multiple input multiple output channels this simplicity makes beamforming a competitive strategy in practice but at the same time poses a doubt on the sensitivity of beamforming to the imperfectness of the channel state information at the transmitter csit this paper studies beamforming from the perspective of worst case robustness we show that beamforming can achieve the maximum received signal to noise ratio snr or guarantees a given received snr with the minimum transmit power in the worst channel within an elliptical uncertainty region defined by the weighted spectral norm this result further implies that beamforming has the ability to combat against the imperfectness of csit especially for small channel dimensions or small channel uncertainty

the dobrushin shlosman phase uniqueness criterion and applications to hard squares the rigorous dobrushin shlosman phase uniqueness criterion is reviewed then applied to the hard square model to prove that only a single phase exists at activityz 1 185 the criterion is violated for a five site by five site lattice cell atz 1 35557 but this does not imply phase nonuniqueness this work complements that of dobrushin kolafa and shlosman who proved phase uniqueness for allz 1 certain experimentally discovered regularities are presented as conjectures one for a more general problem and two for the application to hard squares even with these regularities however substantial further improvements in the algorithmic implementation of the criterion will be required before it can become a practical tool for locating phase transitions

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

agreement percolation and phase coexistence in some gibbs systems we extend some relations between percolation and the dependence of gibbs states on boundary conditions known for ising ferromagnets to other systems and investigate their general validity percolation is defined in terms of the agreement of a configuration with one of the ground states of the system this extension is studied via examples and counterexamples including the antiferromagnetic ising and hard core models on bipartite lattices potts models and many layered ising and continuum widom rowlinson models in particular our results on the hard square lattice model make rigorous observations made by hu and mak on the basis of computer simulations moreover we observe that the naturally defined clusters of the widom rowlinson model play for the wr model itself the same role that the clusters of the fortuin kasteleyn measure play for the ferromagnetic potts models the phase transition and percolation in this system can be mapped into the corresponding liquid vapor transition of a one component fluid

robust beamforming for cognitive multi antenna relay networks with bounded channel uncertainties in cognitive relay networks the interferences from secondary users sus and relays to primary users are constrained to be lower than a threshold the interference constraints are difficult to satisfy when the channel state information csi is imperfect in this paper we propose a robust beamforming scheme for the multi antenna non regenerative cognitive relay network where the multi antenna relay with imperfect csis helps the communication of single antenna su our objective is to design a robust beamforming scheme which maximizes the system capacity subject to transmit power constraint and interference constraints the bounded channel uncertainties are modeled using the worst case model the robust beamforming problem neglecting the correlation of channel uncertainties is reformulated as a convex semidefinite programming sdp by rank one relaxation this convex sdp is related with the worst case relay transmit power minimization problem which is further reformulated as a convex sdp whose rank one solution is proved to exist thus we propose the suboptimal solution to the robust beamforming problem which is found effectively by solving two convex sdps simulation results are provided to demonstrate the effectiveness of the proposed scheme

phase diagram of the two dimensional ising antiferromagnet computer assisted proof we study the phase diagram of the ising antiferromagnet on a square lattice in a neighbourhood of ground state critical pointsh 4 t 0 it leads to a question about the valuea c of the critical activity of the hard square lattice gas using a constructive criterion of uniqueness we prove thata c 1 and that the phase diagram of the antiferromagnet does not bulge near mentioned critical points it is a specific feature of this work that the proof was completed with the help of a computer

a competitive minimax approach to robust estimation of random parameters we consider the problem of estimating in the presence of model uncertainties a random vector x that is observed through a linear transformation h and corrupted by additive noise we first assume that both the covariance matrix of x and the transformation h are not completely specified and develop the linear estimator that minimizes the worst case mean squared error mse across all possible covariance matrices and transformations h in the region of uncertainty although the minimax approach has enjoyed widespread use in the design of robust methods we show that its performance is often unsatisfactory to improve the performance over the minimax mse estimator we develop a competitive minimax approach for the case where h is known but the covariance of x is subject to uncertainties and seek the linear estimator that minimizes the worst case regret namely the worst case difference between the mse attainable using a linear estimator ignorant of the signal covariance and the optimal mse attained using a linear estimator that knows the signal covariance the linear minimax regret estimator is shown to be equal to a minimum mse mmse estimator corresponding to a certain choice of signal covariance that depends explicitly on the uncertainty region we demonstrate through examples that the minimax regret approach can improve the performance over both the minimax mse approach and a plug in approach in which the estimator is chosen to be equal to the mmse estimator with an estimated covariance matrix replacing the true unknown covariance we then show that although the optimal minimax regret estimator in the case in which the signal and noise are jointly gaussian is nonlinear we often do not lose much by restricting attention to linear estimators

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

distributed power allocation with rate constraints in gaussian parallel interference channels this paper considers the minimization of transmit power in gaussian parallel interference channels subject to a rate constraint for each user to derive decentralized solutions that do not require any cooperation among the users we formulate this power control problem as a generalized nash equilibrium ne game we obtain sufficient conditions that guarantee the existence and nonemptiness of the solution set to our problem then to compute the solutions of the game we propose two distributed algorithms based on the single user water filling solution the sequential and the simultaneous iterative water filling algorithms wherein the users update their own strategies sequentially and simultaneously respectively we derive a unified set of sufficient conditions that guarantee the uniqueness of the solution and global convergence of both algorithms our results are applicable to all practical distributed multipoint to multipoint interference systems either wired or wireless where a quality of service in qos terms of information rate must be guaranteed for each link

robust optimization for amplify and forward mimo relaying from a worst case perspective in this paper we consider robust optimization of amplify and forward af multiple input multiple output mimo relay precoders in presence of deterministic imperfect channel state information csi when the csi uncertainty lies in a norm bounded region two widely used performance metrics mutual information mi and mean square error mse are adopted as design objectives according to the philosophy of worst case robustness the robust optimization problems with respect to maximizing the worst case mi and minimizing the worst case mse are formulated as maximin and minimax problems respectively due to the fact that these two problems do not have a concave convex or convex concave structure we cannot rely on the conventional saddle point theory to find the robust solutions nevertheless by exploiting majorization theory we show that the formulated maximin and minimax problems both admit saddle points we further analytically characterize the saddle points and provide closed form solutions to robust relay precoder designs interestingly we find that under both mi and mse metrics the robust relay optimization leads to a channel diagonalizing structure meaning that eigenmode transmission is optimal from the worst case robustness perspective the proposed robust designs can improve the spectral efficiency and reliability of af mimo relaying against csi uncertainties at the similar cost of computational complexity as the existing non robust schemes

completely analytic interactions with infinite values in this note we extend the notion of completely analytic interactions of gibbs random fields that is known for finite interactions with finite range to interactions that can have infinite values too we formulate a set of ten conditions on such interactions in terms of analyticity properties of the partition functions or correlation decay the main theorem states that all these conditions are equivalent therefore an interaction is called a completely analytic interaction if it satisfies one of these conditions

completely analytical interactions constructive description an interactionu is called a completely analytical ca interaction if it satisfies one of 12 given conditions formulated in terms of analyticity properties of the partition functions zv u or correlation decay or truncated correlation bounds or asymptotic behavior of ln zv u v the 12 conditions are presented together with part of the proof of their equivalence the main result of the paper is that each condition is constructive in the following sense instead of checking it in all finite volumesv v it is enough to consider only a finite amount of volumes with restricted size in particular the partition functions z v u for the complex perturbationsu ofu do not vanish for all v v and all with provided this is true only forv with diam v c and but with

multivariate nonnegative quadratic mappings in this paper we study several issues related to the characterization of specific classes of multivariate quadratic mappings that are nonnegative over a given domain with nonnegativity defined by a prespecified conic order in particular we consider the set cone of nonnegative quadratic mappings defined with respect to the positive semidefinite matrix cone and study when it can be represented by linear matrix inequalities we also discuss the applications of the results in robust optimization especially the robust quadratic matrix inequalities and the robust linear programming models in the latter application the implementational errors of the solution are taken into account and the problem is formulated as a semidefinite program

a robust maximin approach for mimo communications with imperfect channel state information based on convex optimization this paper considers a wireless communication system with multiple transmit and receive antennas i e a multiple input multiple output mimo channel the objective is to design the transmitter according to an imperfect channel estimate where the errors are explicitly taken into account to obtain a robust design under the maximin or worst case philosophy the robust transmission scheme is composed of an orthogonal space time block code ostbc whose outputs are transmitted through the eigenmodes of the channel estimate with an appropriate power allocation among them at the receiver the signal is detected assuming a perfect channel knowledge the optimization problem corresponding to the design of the power allocation among the estimated eigenmodes whose goal is the maximization of the signal to noise ratio snr is transformed to a simple convex problem that can be easily solved different sources of errors are considered in the channel estimate such as the gaussian noise from the estimation process and the errors from the quantization of the channel estimate among others for the case of gaussian noise the robust power allocation admits a closed form expression finally the benefits of the proposed design are evaluated and compared with the pure ostbc and nonrobust approaches

robust mimo cognitive radio via game theory cognitive radio cr systems improve the spectral efficiency by allowing the coexistence in harmony of primary users pus the legacy users with secondary users sus this coexistence is built on the premises that no su can generate interference higher than some prescribed limits against pus the system design based on perfect channel state information csi can easily end up violating the interference limits in a realistic situation where csi may be imperfect in this paper we propose a robust design of cr systems composed of multiple pus and multiple noncooperative sus in either single input single output siso frequency selective channels or more general multiple input multiple output mimo channels we formulate the design of the su network as a noncooperative game where the sus compete with each other over the resources made available by the pus by maximizing their own information rates subject to the transmit power and robust interference constraints following the philosophy of the worst case robustness we take explicitly into account the imperfectness of su to pu csi by adopting proper interference constraints that are robust with respect to the worst channel errors relying on the variational inequality theory we study the existence and uniqueness properties of the nash equilibria of the resulting robust games and devise totally asynchronous and distributed algorithms along with their convergency properties we also propose efficient numerical methods based on decomposition techniques to compute the robust transmit strategy for each su

distributed optimal beamformers for cognitive radios robust to channel uncertainties through spatial multiplexing and diversity multi input multi output mimo cognitive radio cr networks can markedly increase transmission rates and reliability while controlling the interference inflicted to peer nodes and primary users pus via beamforming the present paper optimizes the design of transmit and receive beamformers for ad hoc cr networks when cr to cr channels are known but cr to pu channels cannot be estimated accurately capitalizing on a norm bounded channel uncertainty model the optimal beamforming design is formulated to minimize the overall mean square error mse from all data streams while enforcing protection of the pu system when the cr to pu channels are uncertain even though the resultant optimization problem is non convex algorithms with provable convergence to stationary points are developed by resorting to block coordinate ascent iterations along with suitable convex approximation techniques enticingly the novel schemes also lend themselves naturally to distributed implementations numerical tests are reported to corroborate the analytical findings

robust minimum variance beamforming this paper introduces an extension of minimum variance beamforming that explicitly takes into account variation or uncertainty in the array response sources of this uncertainty include imprecise knowledge of the angle of arrival and uncertainty in the array manifold in our method uncertainty in the array manifold is explicitly modeled via an ellipsoid that gives the possible values of the array for a particular look direction we choose weights that minimize the total weighted power output of the array subject to the constraint that the gain should exceed unity for all array responses in this ellipsoid the robust weight selection process can be cast as a second order cone program that can be solved efficiently using lagrange multiplier techniques if the ellipsoid reduces to a single point the method coincides with capon s method we describe in detail several methods that can be used to derive an appropriate uncertainty ellipsoid for the array response we form separate uncertainty ellipsoids for each component in the signal path e g antenna electronics and then determine an aggregate uncertainty ellipsoid from these we give new results for modeling the element wise products of ellipsoids we demonstrate the robust beamforming and the ellipsoidal modeling methods with several numerical examples

lorentz positive maps and quadratic matrix inequalities with applications to robust miso transmit beamforming consider a unicast downlink beamforming optimization problem with robust signal to interference plus noise ratio constraints to account for imperfect channel state information at the base station in a multiple input single output miso communication system the convexity of this robust beamforming problem remains unknown a slightly conservative version of the robust beamforming problem is thus studied herein as a compromise it is in the form of a semi infinite second order cone program socp and more importantly it possesses an equivalent and explicit convex reformulation due to a linear matrix inequality lmi description of the cone of lorentz positive maps hence the conservative robust beamforming problem can be efficiently solved by an optimization solver additional robust shaping constraints can also be easily handled to control the amount of interference generated on other co existing users such as in cognitive radio systems

robust energy efficiency maximization in cognitive radio networks the worst case optimization approach energy efficiency ee is very crucial for future wireless communication systems especially for cognitive radio networks crns the ee performance relies on channel state information csi of channels besides the interference from secondary users sus to primary users pus also closely depends on csi in underlay crns however available works on ee usually assume that csi is perfect which is often inaccurate in practical systems thus in this paper we investigate the robust ee maximization problem in underlay crns with multiple sus and pus assuming csi error to be bounded we consider that all channels lie in some bounded uncertainty regions from the perspective of worst case optimization we formulate it as the max min problem with infinite constraint which is nontrivial even without this constraint this is because that the outer maximization problem is non convex and the inner minimization problem is a concave minimization problem known as np hard in general we propose a scheme to handle this problem via the fractional programming and global optimization techniques particularly we efficiently solve this problem in two special cases simulation results validate that our proposed scheme can improve the worst case ee of sus distinctly and strictly guarantee the quality of service qos of pus under all parameters uncertainties

a uniqueness condition for gibbs measures with application to the 2 dimensional ising antiferromagnet a uniqueness condition for gibbs measures is given this condition is stated in terms of absence of a certain type of percolation involving two independent realisations this result can be applied in certain concrete situations by comparison with ordinary percolation in this way we prove that the ising antiferromagnet on a square lattice has a unique gibbs measure if 4 h 1 2ln pc 1 pc whereh denotes the external magnetic field the inverse temperature andpc the critical probability for site percolation on that lattice sincepc is larger than 1 2 this extends a result by dobrushin kolafa and shlosman whose proof was computer assisted

a finite element implementation of the nonlocal granular rheology summary inhomogeneous flows involving dense particulate media display clear size effects in which the particle length scale has an important effect on flow fields hence nonlocal constitutive relations must be used in order to predict these flows recently a class of nonlocal fluidity models has been developed for emulsions and subsequently adapted to granular materials these models have successfully provided a quantitative description of experimental flows in many different flow configurations in this work we present a finite element based numerical approach for solving the nonlocal constitutive equations for granular materials which involve an additional non standard nodal degree of freedom the granular fluidity which is a scalar state parameter describing the susceptibility of a granular element to flow our implementation is applied to three canonical inhomogeneous flow configurations 1 linear shear with gravity 2 annular shear flow without gravity and 3 annular shear flow with gravity we verify our implementation demonstrate convergence and show that our results are mesh independent copyright 2016 john wiley sons ltd

statistically robust design of linear mimo transceivers the treatment of channel state information csi is critical in the design of mimo systems accurate csi at the transmitter is often not possible or may require high feedback rates herein we consider the robust design of linear mimo transceivers with perfect csi either at the transmitter or at both sides of the link the framework considers the design problem where the imperfect csi consists of the channel mean and covariance matrix or equivalently the channel estimate and the estimation error covariance matrix the robust transceiver design is based on a general cost function of the average mses as well as a design with individual mse based constraints in particular a lower bound of the average mse matrix is explored for the design when only the csi at the transmitter is imperfect under different csi conditions the proposed robust transceivers exhibit a similar structure to the transceiver designs for perfect csi but with a different equivalent channel and or noise covariance matrix

a fixed point equation for the high temperature phase of discrete lattice spin systems a fixed point equation on an infinite dimensional space is proposed as an alternative to the usual definition of the infinite volume limit in discrete lattice spin systems in the high temperature phase it is argued heuristically that the free energy and correlation functions one obtains by solving this equation agree with the usual definitions of these quantities a theorem is then proved that says that if a certain finite volume condition is satisfied then this fixed point equation has a solution and the resulting free energy is analytic in the parameters in the hamiltonian for particular values of the temperature this finite volume condition may be checked with the help of a computer the two dimensional ising model is considered as a test case and it is shown that the finite volume condition is satisfied for 0 77 critical

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

continuum theory of partially fluidized granular flows a continuum theory of partially fluidized granular flows is developed the theory is based on a combination of the equations for the flow velocity and shear stresses coupled with the order parameter equation which describes the transition between the flowing and static components of the granular system we apply this theory to several important granular problems avalanche flow in deep and shallow inclined layers rotating drums and shear granular flows between two plates we carry out quantitative comparisons between the theory and experiment

worst case robust mimo transmission with imperfect channel knowledge in this paper we consider robust transmit strategies against the imperfectness of the channel state information at the transmitter csit for multi input multi output mimo communication systems following a worst case deterministic model the actual channel is assumed to be inside an ellipsoid centered at a nominal channel the objective is to maximize the worst case received signal to noise ratio snr or to minimize the worst case chernoff bound of the error probability thus leading to a maximin problem moreover we also consider the qos problem as a complement of the maximin design which minimizes the transmit power consumption and meanwhile keeps the received snr above a given threshold for any channel realization in the ellipsoid it is shown that for a general class of power constraints both the maximin and qos problems can be equivalently transformed into convex problems or even further into semidefinite programs sdps thus efficiently solvable by the numerical methods the most interesting result is that the optimal transmit directions i e the eigenvectors of the transmit covariance are just the right singular vectors of the nominal channel under some mild conditions this result leads to a channel diagonalizing structure as in the cases of perfect csit and statistical csit with mean or covariance feedback and reduces the complicated matrix valued problem to a scalar power allocation problem then we provide the closed form solution to the resulting power allocation problem

gradient dependent plasticity formulation and algorithmic aspects a plasticity theory is proposed in which the yield strength not only depends on an equivalent plastic strain measure hardening parameter but also on the laplacian thereof the consistency condition now results in a differential equation instead of an algebraic equation as in conventional plasticity to properly solve the set of non linear differential equations the plastic multiplier is discretized in addition to the usual discretization of the displacements for appropriate boundary conditions this formulation can also be derived from a variational principle accordingly the theory is complete

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

regularity properties and pathologies of position space renormalization group transformations scope and limitations of gibbsian theory we reconsider the conceptual foundations of the renormalization group rg formalism and prove some rigorous theorems on the regularity properties and possible pathologies of the rg map our main results apply to local in position space rg maps acting on systems of bounded spins compact single spin space regarding regularity we show that the rg map defined on a suitable space of interactions formal hamiltonians is always single valued and lipschitz continuous on its domain of definition this rules out a recently proposed scenario for the rg description of first order phase transitions on the pathological side we make rigorous some arguments of griffiths pearce and israel and prove in several cases that the renormalized measure is not a gibbs measure for any reasonable interaction this means that the rg map is ill defined and that the conventional rg description of first order phase transitions is not universally valid for decimation or kadanoff transformations applied to the ising model in dimension d 3 these pathologies occur in a full neighborhood 0 h e of the low temperature part of the first order phase transition surface for block averaging transformations applied to the ising model in dimension d 2 the pathologies occur at low temperatures for arbitrary magnetic field strength pathologies may also occur in the critical region for ising models in dimension d 4 we discuss the heuristic and numerical evidence on rg pathologies in the light of our rigorous theorems in addition we discuss critically the concept of gibbs measure which is at the heart of present day classical statistical mechanics we provide a careful and we hope pedagogical overview of the theory of gibbsian measures as well as the less familiar non gibbsian measures emphasizing the distinction between these two objects and the possible occurrence of the latter in different physical situations we give a rather complete catalogue of the known examples of such occurrences the main message of this paper is that despite a well established tradition gibbsiannessshould not be taken for granted

robust mmse precoding in mimo channels with pre fixed receivers in this paper we design robust precoders under the minimum mean square error mmse criterion for different types of channel state information csi in multiple input multiple output mimo channels we consider low complexity pre fixed receivers that may adapt to the channel but are oblivious to the existence of a precoder at the transmitter in particular three types of csi are taken into account i perfect csi ii statistical csi in the form of mean feedback and iii deterministic imperfect csi assuming that the actual channel is within the neighborhood of a nominal channel which leads to the worst case robust design that is the focus of this paper interestingly it is found that under some mild conditions the optimal transmit directions i e the left singular vectors of the precoder are equal to the right singular vectors of the channel the channel mean and the nominal channel for perfect csi statistical csi and the worst case design respectively consequently the matrix valued problems can be simplified to scalar power allocation problems that either admit closed form solutions or can be efficiently solved by the proposed algorithm

partially ordered models we provide a formal definition and study the basic properties of partially ordered random fields porf these systems were proposed to model textures in image processing and to represent independence relations between random variables in statistics in the latter case they are known as bayesian networks our random fields are a generalization of probabilistic cellular automata pca and their theory has features intermediate between that of discrete time processes and the theory of statistical mechanical lattice fields its proper definition is based on the notion of partially ordered specification pos in close analogy to the theory of gibbs measures this paper contains two types of results first we present the basic elements of the general theory of porfs basic geometrical issues definition in terms of conditional probability kernels extremal decomposition extremality and triviality reconstruction starting from single site kernels relations between pom and gibbs fields second we prove three uniqueness criteria that correspond to the criteria known as uniform boundedness dobrushin uniqueness and disagreement percolation in the theory of gibbs measures

design of cognitive radio systems under temperature interference constraints a variational inequality 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 a novel nash equilibrium ne problem to model concurrent communications of cognitive secondary users who compete against each other to maximize their information rate the formulation contains constraints on the transmit power and possibly spectral masks as well as aggregate interference tolerable at the primary users receivers the coupling among the strategies of the players due to the interference constraints presents a new challenge for the analysis of this class of nash games that cannot be addressed using the game theoretical models proposed in the literature for this purpose we need the framework given by the more advanced theory of finite dimensional variational inequalities vi this provides us with all the mathematical tools necessary to analyze the proposed ne problem e g existence and uniqueness of the solution and to devise alternative distributed algorithms along with their convergence properties

formulation and finite element implementation of a multiplicative model of coupled poro plasticity at finite strains under fully saturated conditions in this paper we present the formulation and numerical analysis of a finite deformation model of coupled poro plasticity fully saturated conditions are assumed the model is based on a multiplicative decomposition of the deformation gradient in elastic and plastic parts together with an additive elastoplastic decomposition of the fluid content the final relations describing the evolution of the different fields are then obtained in the thermodynamic framework furnished by the principle of maximum plastic dissipation the particular case of an associated drucker prager model in effective stresses is considered as a model example a complete characterization of the dissipative structure of the problem of evolution is described through the derivation of an a priori stability estimate we describe in detail the finite element implementation of the model in the context of staggered algorithms for the solution of the physically coupled problem finally we present representative numerical simulations to illustrate the features of the proposed models in particular the case of strain localization in globally undrained conditions is studied in the proposed framework