dilemma solving by the coevolution of networks and strategy in a 2 2 game a 2 ifmmode times else texttimes fi 2 game model implemented by a coevolution mechanism of both networks and strategy inspired by the work of zimmermann and eguiluz phys rev e72 056118 2005 is established network adaptation is the manner in which an existing link between two agents is destroyed and how a new one is established to replace it the strategy is defined as whether an agent offers cooperation c or defection d both the networks and strategy are synchronously renovated in a simulation time step a series of numerical experiments considering various 2 ifmmode times else texttimes fi 2 game structures reveals that the proposed coevolution mechanism can solve dilemmas in several game classes the effect of solving a dilemma means mutual cooperation reciprocity r reciprocity which is brought about by emerging several cooperative hub agents who have plenty of links this effect can be primarily observed in game classes of the prisoner s dilemma and stag hunt the coevolution mechanism however seems counterproductive for game classes of leader and hero where the alternating reciprocity st reciprocity is meaningful

on the error probability of coded frequency hopped spread spectrum multiple access systems a simple exact calculation is presented of the probability distribution of the number of hits in a block of n symbols in a frequency hopped spread spectrum multiple access communication system while the sequence of hits is not markovian there is an underlying markovian structure that allows the probability distribution of the number of hits to be calculated in a recursive fashion knowing the probability distribution of the number of hits makes it possible to calculate the probability of error for a system employing error correcting codes for several different types of receivers including receivers with both errors and erasures the numerical results show that both the approximation obtained by assuming the actual sequence of hits is markovian and the approximation obtained by assuming the hits are independent are very good when the number of frequency slots is not too small less than five calculations show that assuming the independence of hits gives an error probability accurate to within 1 of the actual error probability assuming the hits are markovian gives error probabilities which are accurate to within 0 001

symbol by symbol map demodulation of cpm and psk signals on rayleigh flat fading channels demodulation using the symbol by symbol maximum a posteriori probability map algorithm is presented the algorithm is derived for the case of continuous phase modulation cpm signals transmitted over rayleigh flat fading channels and a corresponding receiver structure is specified it is shown that the map algorithm requires computing for each trellis branch the sum of the products of the weights of all paths through the trellis which pass through that branch and that this generic computational problem can be solved efficiently by an approach that uses a forward and backward recursion through the trellis simulation results are presented which show both the hard and soft decision performance of the map receiver to be robust even in the presence of fade rates of up to 30 of the symbol rate the application of the receiver concept to phase shift keying psk signals is also discussed and then evaluated via simulation the concept of joint demodulation and decoding using iterative processing techniques is introduced it is shown that the map receiver is well suited for iterative processing applications due to its use of a priori symbol probabilities and its production of optimal soft decisions simulation results for the reception of quaternary psk qpsk show that the bit error rate ber performance of the iterative map receiver can approach that of a receiver operating with perfect knowledge of the fading process

noncoherent decorrelative detection for nonorthogonal multipulse modulation over the multiuser gaussian channel this paper introduces the problem of noncoherent detection for nonorthogonal multipulse modulation in the context of the synchronous multiuser gaussian channel each user sends an m ary information symbol by transmitting one of m possibly nonorthogonal waveforms furthermore the m signals of one user are allowed to be correlated with the signals of all other users a key idea proposed here is that of a noncoherent decorrelative receiver front end like its counterpart in single pulse modulation this front end eliminates multiuser interference it therefore reduces the multiuser detection problem into decoupled single user problems over equivalent noise enhanced single user channels each equivalent single user channel is rather general and can be described as one where the waveforms employed are not only correlated but are also of unequal energies several new results pertaining to the design and analysis of optimum and suboptimum noncoherent detectors for this single user channel are obtained in the multiuser channel these detectors constitute the post decorrelative processing units for each user

nd convolutional codes i performance analysis a noncoherent coded system which incorporates convolutional codes in conjunction of multiple symbol noncoherent detection is presented in this two part paper where part i focuses on the performance analysis of the system and part ii deals with the structural properties of the underlying convolutional codes these convolutional codes are referred to as nd convolutional codes it is shown that nd convolutional codes provide a general framework for various noncoherent coding systems including differential systems two models of the carrier phase are examined and the relationships between them is established for the first one the carrier phase remains constant for l channels signals whereas for the second one it unvaries throughout the transmission period the regular structure of nd codes facilitates the evaluation of a simple upper bound on the pairwise and bit error probabilities as well as a simple expression for the generalized cutoff rate the exponential rate of the error probability which is the single parameter governing the error performance at large signal to noise ratios is identified via large deviations techniques this parameter leads to the interesting conclusion that increasing l does not necessarily monotonically improve the error performance of the noncoherent system the same conclusion is reached by examining upper bounds and computer simulation results of several interesting examples these examples also reveal that optimal codes for coherent detection are not necessarily optimal for noncoherent detection and a search for good codes some of which are tabulated in part ii of the paper is required

the use of the fourier bessel series in calculating error probabilities for digital communication systems using the theory of spherical symmetric random vectors one can find an expression for the error probability of a wide variety of digital communications systems these expressions however are in the form of bessel integrals which are usually difficult to solve in this paper we show how the fourier bessel series can be used to solve the integrals numerically the calculation error is found to depend on two series parameters which can be manipulated to make the error arbitrarily small two examples are used to show the utility of the technique in the first the probability of error for a cpsk communications system operating in gaussian noise and cochannel interference is found in the second the error performance for a multilevel ask communications system operating in the same corrupting environment is determined the fourier bessel series technique is a valuable practical tool for solving these and other signal detection problems

breaking the symmetry between interaction and replacement in evolutionary dynamics on graphs we study the evolution of cooperation modeled as symmetric 2 2 games in a population whose structure is split into an interaction graph defining who plays with whom and a replacement graph specifying evolutionary competition we find it is always harder for cooperators to evolve whenever the two graphs do not coincide in the thermodynamic limit the dynamics on both graphs is given by a replicator equation with a rescaled payoff matrix in a rescaled time analytical results are obtained in the pair approximation and for weak selection their validity is confirmed by computer simulations

extinction properties of solutions for a class of fast diffusive p laplacian equations abstract we consider the extinction properties of solutions for the homogeneous dirichlet boundary value problem for the p laplacian equation u t div u p 2 u u q u r with 1 p 2 q 1 and r 0 for 0 it is known that r p 1 is the critical extinction exponent for the weak solution for 0 we show that r p 1 is still the critical extinction exponent when q 1 moreover the precise decay estimates of solutions before the occurrence of the extinction are derived however extinction can always occur when 0 q r 1

adaptive non orthogonal mfsk m ary frequency shift keying mfsk using one or more orthogonal tones per symbol has been in use in non coherent systems for quite some time we present an alternate system for non coherent systems using non orthogonal tones spread non uniformly throughout the bandwidth which outperforms the equivalent orthogonal tone system we demonstrate that from a theoretical capacity point of view the same bit rate could be achieved by the proposed system with as much as 2 5 db lower signal to noise ratio snr for some practical configurations we demonstrate as much as 2 db of gain we present the performance with maximum likelihood ml receivers as well as least squares ls receivers as well as lower complexity receivers based on compressed sensing cs we also demonstrate that such a non orthogonal system may be used to increase the spectral efficiency of the overall system by adapting the spectral efficiency in response to the link snr such an adaptive non orthogonal mfsk system requires estimation of the snr or e s n 0 and we present both the cramer rao lower bound crlb as well as maximum likelihood ml estimators which attain the crlb for both data aided da snr estimation as well as non data aided nda snr estimation

mixing protocols in the public goods game if interaction partners in social dilemma games are not selected randomly from the population but are instead determined by a network of contacts it has far reaching consequences for the evolutionary dynamics selecting partners randomly leads to a well mixed population where pattern formation is essentially impossible this rules out important mechanisms that can facilitate cooperation most notably network reciprocity in contrast if interactions are determined by a lattice or a network then the population is said to be structured where cooperators can form compact clusters that protect them from invading defectors between these two extremes however there is ample middle ground that can be brought about by the consideration of temporal networks mobility or other coevolutionary processes the question that we here seek to answer is when does mixing on a lattice actually lead to well mixed conditions to that effect we use the public goods game on a square lattice and we consider nearest neighbor and random mixing with different frequencies as well as a mix of both mixing protocols not surprisingly we find that nearest neighbor mixing requires a higher frequency than random mixing to arrive at the well mixed limit the differences between the two mixing protocols are most expressed at intermediate mixing frequencies whilst at very low and very high mixing frequencies the two almost converge we also find a near universal exponential growth of the average size of cooperator clusters as their fraction increases from zero to one regardless of whether this increase is due to increasing the multiplication factor of the public goods decreasing the frequency of mixing or gradually shifting the mixing from random to nearest neighbors

stochastic dynamics of invasion and fixation we study evolutionary game dynamics in finite populations we analyze an evolutionary process which we call pairwise comparison for which we adopt the ubiquitous fermi distribution function from statistical mechanics the inverse temperature in this process controls the intensity of selection leading to a unified framework for evolutionary dynamics at all intensities of selection from random drift to imitation dynamics we derive a simple closed formula that determines the feasibility of cooperation in finite populations whenever cooperation is modeled in terms of any symmetric two person game in contrast with previous results the present formula is valid at all intensities of selection and for any initial condition we investigate the evolutionary dynamics of cooperators in finite populations and study the interplay between intensity of selection and the remnants of interior fixed points in infinite populations as a function of a given initial number of cooperators showing how this interplay strongly affects the approach to fixation of a given trait in finite populations leading to counterintuitive results at different intensities of selection

on the capacity of the wiener phase noise channel bounds and capacity achieving distributions in this paper the capacity of the additive white gaussian noise awgn channel affected by time varying wiener phase noise is investigated tight upper and lower bounds on the capacity of this channel are developed the upper bound is obtained by using the duality approach and by considering a specific distribution over the output of the channel in order to lower bound the capacity first a family of capacity achieving input distributions is found by solving a functional optimization of the channel mutual information then lower bounds on the capacity are obtained by drawing samples from the proposed distributions through monte carlo simulations the proposed capacity achieving input distributions are circularly symmetric non gaussian and the input amplitudes are correlated over time the evaluated capacity bounds are tight for a wide range of signal to noise ratio snr values and thus they can be used to quantify the capacity specifically the bounds follow the well known awgn capacity curve at low snr while at high snr they coincide with the high snr capacity result available in the literature for the phase noise channel

enhancement of cooperation in highly clustered scale free networks we study the effect of clustering on the organization of cooperation by analyzing the evolutionary dynamics of the prisoner s dilemma on scale free networks with a tunable value of clustering we find on the one hand that a high value of the clustering coefficient produces an overall enhancement of cooperation in the network even for a very high temptation to defect on the other hand high clustering homogenizes the process of invasion of degree classes by defectors decreasing the chances of survival of low densities of cooperators in the network

optimal partial decision combining in diversity systems the optimal partial decision combiner is derived and its performance is analyzed and compared to majority voting and selection diversity using binary noncoherent frequency shift keying on a rayleigh faded additive white gaussian noise channel the degradation in the probability of bit error is evaluated when the channel state estimate is imperfect due to parameter quantization awgn and cochannel interference it is demonstrated that the optimal partial decision combiner can provide a simple means for improving performance on channels with limited cochannel interference

towards effective payoffs in the prisoner s dilemma game on scale free networks we study the transition towards effective payoffs in the prisoner s dilemma game on scale free networks by introducing a normalization parameter guiding the system from accumulated payoffs to payoffs normalized with the connectivity of each agent we show that during this transition the heterogeneity based ability of scale free networks to facilitate cooperative behavior deteriorates continuously eventually collapsing with the results obtained on regular graphs the strategy donations and adaptation probabilities of agents with different connectivities are studied results reveal that strategies generally spread from agents with larger towards agents with smaller degree however this strategy adoption flow reverses sharply in the fully normalized payoff limit surprisingly cooperators occupy the hubs even if the averaged cooperation level due to partly normalized payoffs is moderate

non extinction and critical exponent for a polytropic filtration equation abstract this paper is concerned with the homogeneous dirichlet boundary value problem of a polytropic filtration equation with reaction sources we will show the non extinction property of non trivial solutions and determine the critical fujita exponent for the problem

extinction behavior of solutions for a quasilinear parabolic system with nonlocal sources this paper deals with the extinction properties of solutions for a quasilinear parabolic system u t div u p 2 u v x t dx v t div v q 2 v u x t dx with zero dirichlet boundary conditions in a smooth bounded domain r n n 1 where 1 p q 2 and 0 by using the comparison principle and energy estimate methods we obtain the sufficient conditions of extinction solutions

cooperation for volunteering and partially random partnerships competition among cooperative defective and loner strategies is studied by considering an evolutionary prisoner s dilemma game for different partnerships in this game each player can adopt one of its coplayer s strategy with a probability depending on the difference of payoffs coming from games with the corresponding coplayers our attention is focused on the effects of annealed and quenched randomness in the partnership for fixed number of coplayers it is shown that only the loners survive if the four coplayers are chosen randomly mean field limit on the contrary on the square lattice all the three strategies are maintained by the cyclic invasions resulting in a self organizing spatial pattern if the fixed partnership is described by a regular small world structure then a homogeneous oscillation occurs in the population dynamics when the measure of quenched randomness exceeds a threshold value similar behavior with higher sensitivity to the randomness is found if temporary partners are substituted for the standard ones with some probability at each step of iteration

adaptive networks coevolution of disease and topology d epartement de physique de g enie physique et d optique universit e laval qu ebec qu ebec canada g1v 0a6 dated september 13 2010 adaptive networks have been recently introduced in the context of disease propagation on complexnetworks they account for the mutual interaction between the network topology and the states ofthe nodes until now existing models have been analyzed using low complexity analytic formalisms revealing nevertheless some novel dynamical features however current methods have failed toreproduce with accuracy the simultaneous time evolution of the disease and the underlying networktopology in the framework of the adaptive sis model of gross et al phys rev lett 96 208701 2006 we introduce an improved compartmental formalism able to handle this coevolutionarytask successfully with this approach we analyze the interplay and outcomes of both dynamicalelements process and structure on adaptive networks featuring di erent degree distributions at theinitial stage

m ary phase coding for the noncoherent awgn channel this work considers coded m ary phase shift keying mpsk schemes with noncoherent detection a class of block codes called module phase codes is described the algebraic framework used for describing these codes relies on elements from module theory which are discussed along with a method for constructing such codes for noncoherent detection it is shown that differential encoding may be viewed as a specific code from a particular class of module phase codes two classes of codes that achieve significant coding gain with respect to coherent detection of uncoded mpsk are presented in the first class of module phase codes the coding gain is achieved at the expense of bandwidth expansion in the second class however the coding gain is achieved at the expense of signal constellation expansion without expanding bandwidth finally an integrated demodulation decoding technique based on a modification of information set decoding is presented it is shown that this reduced complexity suboptimal decoding strategy performs nearly as well as maximum likelihood decoding

memory based snowdrift game on networks we present a memory based snowdrift game mbsg taking place on networks we found that when a lattice is taken to be the underlying structure the transition of spatial patterns at some critical values of the payoff parameter is observable for both four and eight neighbor lattices the transition points as well as the styles of spatial patterns can be explained by local stability analysis in sharp contrast to previously reported results cooperation is promoted by the spatial structure in the mbsg interestingly we found that the frequency of cooperation of the mbsg on a scale free network peaks at a specific value of the payoff parameter this phenomenon indicates that properly encouraging selfish behaviors can optimally enhance the cooperation the memory effects of individuals are discussed in detail and some nonmonotonous phenomena are observed on both lattices and scale free networks our work may shed some new light on the study of evolutionary games over networks

nonlocal kirchhoff problems extinction and non extinction of solutions abstract in this paper we discuss the extinction and non extinction properties of solutions for the following fractional p kirchhoff problem u t m u s p p p s u u r 2 u u q 2 u x t 0 u 0 x t r n 0 u x 0 u 0 x x where u s p is the gagliardo seminorm of u r n is a bounded domain with lipschitz boundary p s is the fractional p laplacian with 0 s 1 p 2 m 0 0 is a continuous function 1 q 2 r 1 and 0 under suitable assumptions we obtain the extinction of solutions to get more precisely decay estimates of solutions we develop the gagliardo nirenberg inequality moreover the non extinction property of solutions is also investigated

evolutionary prisoner s dilemma game on newman watts networks maintenance of cooperation was studied for a two strategy evolutionary prisoner s dilemma game where the players are located on a one dimensional chain and their payoff comes from games with the nearest and next nearest neighbor interactions the applied host geometry makes it possible to study the impacts of two conflicting topological features the evolutionary rule involves some noise affecting the strategy adoptions between the interacting players using monte carlo simulations and the extended versions of dynamical mean field theory we determined the phase diagram as a function of noise level and a payoff parameter the peculiar feature of the diagram is changed significantly when the connectivity structure is extended by extra links as suggested by newman and watts

a differentially coherent pn code acquisition receiver for cdma systems new differentially coherent detectors for acquisition of direct sequence spread spectrum signals are introduced these detectors are alternatives to the noncoherent detectors that have been considered almost exclusively in the past the proposed detectors are suitable for commercial code division multiple access cdma systems which operate with a relatively large noise floor and provide a surprisingly large signal to noise ratio snr improvement over the noncoherent detectors of approximately 5 db under the random code sequence assumption an exact analysis of the differentially coherent detection performance for both full period correlation fpc and partial period correlation ppc is carried out the detector performance in terms of detection and false alarm probabilities for both partial and full period correlations is investigated and the results are compared with those of classical noncoherent detection the mean acquisition time for both single dwell and multiple dwell acquisition schemes are compared with their noncoherent counterparts

co evolving prisoner s dilemma performance indicators and analytic approaches understanding the intrinsic relation between the dynamical processes in a co evolving network and the necessary ingredients in formulating a reliable theory is an important question and a challenging task using two slightly different definitions of performance indicator in the context of a co evolving prisoner s dilemma game it is shown that very different cooperative levels result and theories of different complexity are required to understand the key features when the payoff per opponent is used as the indicator case a non cooperative strategy has an edge and dominates in a large part of the parameter space formed by the cutting and rewiring probability and the strategy imitation probability when the payoff from all opponents is used case b cooperative strategy has an edge and dominates the parameter space two distinct phases one homogeneous and dynamical and another inhomogeneous and static emerge and the phase boundary in the parameter space is studied in detail a simple theory assuming an average competing environment for cooperative agents and another for non cooperative agents is shown to perform well in case a the same theory however fails badly for case b it is necessary to include more spatial correlation into a theory for case b we show that the local configuration approximation which takes into account of the different competing environments for agents with different strategies and degrees is needed to give reliable results for case b the results illustrate that formulating a proper theory requires both a conceptual understanding of the effects of the adaptive processes in the problem and a delicate balance between simplicity and accuracy

hawks and doves on small world networks we explore the hawk dove game on networks with topologies ranging from regular lattices to random graphs with small world networks in between this is done by means of computer simulations using several update rules for the population evolutionary dynamics we find the overall result that cooperation is sometimes inhibited and sometimes enhanced in those network structures with respect to the mixing population case the differences are due to different update rules and depend on the gain to cost ratio we analyze and qualitatively explain this behavior by using local topological arguments

channel coding with multilevel phase signals a coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth this is achieved by channel coding with expanded sets of multilevel phase signals in a manner which increases free euclidean distance soft maximum likelihood ml decoding using the viterbi algorithm is assumed following a discussion of channel capacity simple hand designed trellis codes are presented for 8 phase shift keying psk and 16 quadrature amplitude shift keying qask modulation these simple codes achieve coding gains in the order of 3 4 db it is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals which we call mapping by set partitioning based on a new distance measure between binary code sequences which efficiently lower bounds the euclidean distance between the corresponding channel signal sequences a search procedure for more powerful codes is developed codes with coding gains up to 6 db are obtained for a variety of multilevel phase modulation schemes simulation results are presented and an example of carrier phase tracking is discussed

degree mixing in multilayer networks impedes the evolution of cooperation traditionally the evolution of cooperation has been studied on single isolated networks yet a player especially in human societies will typically be a member of many different networks and those networks will play different roles in the evolutionary process multilayer networks are therefore rapidly gaining on popularity as the more apt description of a networked society with this motivation we here consider two layer scale free networks with all possible combinations of degree mixing wherein one network layer is used for the accumulation of payoffs and the other is used for strategy updating we find that breaking the symmetry through assortative mixing in one layer and or disassortative mixing in the other layer as well as preserving the symmetry by means of assortative mixing in both layers impedes the evolution of cooperation we use degree dependent distributions of strategies and cluster size analysis to explain these results which highlight the importance of hubs and the preservation of symmetry between multilayer networks for the successful resolution of social dilemmas

extinction and positivity for the evolution p laplacian equation in rn abstract the aim of this paper is to discuss extinction and positivity for the solution of the initial boundary value problem of evolution p laplacian equation it is proved that the weak solution will be extincted for 1 p 2 and will be positive for p 2 for large t

symbol insertion a low complexity joint peak power reduction and forward error correction for single carrier systems in this paper we present a new modulation code named symbol insertion si that simultaneously achieves both peak to average power ratio papr reduction and forward error correction for pulse shaped single carrier systems in a low complexity manner based on the fact that papr highly depends on the successive phase patterns of discrete complex symbols the proposed code controls phase shifts by inserting a redundant symbol between consecutive information bearing symbols at the receiver by viewing the inserted symbols as parities we exploit them for error correction we show that when the si is used as an inner code of serially concatenated codes its error rate performance is close to those of conventional capacity approaching codes the proposed system thus becomes favorable if the amount of papr reduction is taken into account furthermore the si with a rotationally invariant insertion scheme can accommodate itself to noncoherent detection

generalized kelvin voigt equations with p laplacian and source absorption terms abstract this study considers the blow up in finite time and large time behavioral properties of solutions to the initial boundary value problem for generalized kelvin voigt equations with p laplacian and source absorption terms v t v v p div d v q 2 d v t d v p 2 d v v m 2 v div v x t 0 x t q t where d v 1 2 v v t is the rate of the strain tensor v x t is the velocity field p x t is the pressure is the viscosity kinematic coefficient and is the viscosity relaxation coefficient the coefficient and the exponents p m are given constants two different cases are considered in the case where 0 with an absorption term we prove that the solutions of the associated problem exhibit exponential and power decay and in the case where 0 with nonlinear source term the solutions blow up in a finite time under suitable assumptions on the exponents p q m and the coefficients with certain initial data

evolutionary prisoner s dilemma game on hierarchical lattices an evolutionary prisoner s dilemma pd game is studied with players located on a hierarchical structure of layered square lattices the players can follow two strategies d defector and c cooperator and their income comes from pd games with the neighbors the adoption of one of the neighboring strategies is allowed with a probability dependent on the payoff difference monte carlo simulations are performed to study how the measure of cooperation is affected by the number of hierarchical levels q and by the temptation to defect according to the simulations the highest frequency of cooperation can be observed at the top level if the number of hierarchical levels is low q 4 for larger q however the highest frequency of cooperators occurs in the middle layers the four level hierarchical structure provides the highest average total income for the whole community

phase transitions in a coevolving snowdrift game with costly rewiring we propose and study a dissatisfied adaptive snowdrift game with a payoff parameter r that incorporates a cost for rewiring a connection an agent facing adverse local environment may switch action without a cost or rewire an existing link with a cost a so as to attain a better competing environment detailed numerical simulations reveal nontrivial and nonmonotonic dependence of the frequency of cooperation and the densities of different types of links on a and r a theory that treats the cooperative and noncooperative agents separately and accounts for spatial correlation up to neighboring agents is formulated the theory gives results that are in good agreement with simulations the frequency of cooperation f c is enhanced suppressed at high rewiring cost relative to that at low rewiring cost when r is small large for a given value of r there exists a critical value of the rewiring cost below which the system evolves into a phase of frozen dynamics with isolated noncooperative agents segregated from a cluster of cooperative agents and above which the system evolves into a connected population of mixed actions with continual dynamics the phase boundary on the a text ensuremath r phase space that separates the two phases with distinct structural population and dynamical properties is mapped out the phase diagram reveals that as a general feature for small r small a the disconnected and segregated phase can survive over a wider range of a r

spectrally efficient noncoherent communication this paper considers noncoherent communication over a frequency nonselective channel in which the time varying channel gain is unknown a priori but is approximately constant over a coherence interval unless the coherence interval is large coherent communication which requires explicit channel estimation and tracking prior to detection incurs training overhead which may be excessive especially for multiple antenna communication in contrast noncoherent detection may be viewed as a generalized likelihood ratio test glrt which jointly estimates the channel and the data and hence does not require separate training the main results in this paper are as follows 1 we develop a signal space criterion for signal and code design for noncoherent communication in terms of the distances of signal points from the decision boundaries 2 the noncoherent metric thus obtained is used to guide the design of signals for noncoherent communication that are based on amplitude phase constellations these are significantly more efficient than conventional differential phase shift keying psk especially at high signal to noise ratio snr also known results on the high snr performance of multiple symbol demodulation of differential psk are easily inferred from the noncoherent metric 3 the glrt interpretation is used to obtain near optimal low complexity implementations of noncoherent block demodulation in particular this gives an implementation of multiple symbol demodulation of differential psk which is of linear complexity in the block length and whose degradation from the exact exponential complexity implementation can be made as small as desired

spatial social dilemmas dilution mobility and grouping effects with imitation dynamics abstract we present an extensive systematic study of the prisoner s dilemma and snowdrift games on a square lattice under a synchronous noiseless imitation dynamics we show that for both the occupancy of the network and the random mobility of the agents there are intermediate values that may increase the amount of cooperators in the system and new phases appear we analytically determine the transition lines between these phases and compare with the mean field prediction and the observed behavior on a square lattice we point out which are the more relevant microscopic processes that entitle cooperators to invade a population of defectors in the presence of mobility and discuss the universality of these results

cooperation in the noisy case prisoner s dilemma game on two types of regular random graphs we have studied an evolutionary prisoner s dilemma game with players located on two types of random regular graphs with a degree of 4 the analysis is focused on the effects of payoffs and noise temperature on the maintenance of cooperation when varying the noise level and or the highest payoff the system exhibits a second order phase transition from a mixed state of cooperators and defectors to an absorbing state where only defectors remain alive for the random regular graph and bethe lattice the behavior of the system is similar to those found previously on the square lattice with nearest neighbor interactions although the measure of cooperation is enhanced by the absence of loops in the connectivity structure for low noise the optimal connectivity structure is built up from randomly connected triangles

noncoherent hybrid ds sfh spread spectrum multiple access communications the performance of noncoherent reception in synchronous and asynchronous hybrid direct sequence slow frequency hopped spread spectrum multiple access communication systems operating through additive white gaussian noise channels is investigated systems with binary and m ary frequency shift keying modulation and noncoherent demodulation as well as systems with differential phase shift keying modulation and differentially coherent demodulation are examined and their probability of error is evaluated for random frequencyhopping patterns and signature sequences the multiple access capability of noncoherent hybrid spread spectrum is shown to be superior to that of noncoherent purely frequency hopped spread spectrum and inferior to that of noncoherent purely directsequence spread spectrum for systems with the same bandwidth expansion comparison of hybrid systems with coherent and noncoherent demodulation shows a considerable loss in the performance of the noncoherent systems

pilot symbol assisted coded transmission over the block noncoherent awgn channel in this paper pilot symbol assisted transmission in conjunction with high performance coding over the block independent noncoherent additive white gaussian noise channel is investigated several approximate iterative receivers are proposed which either perform carrier phase estimation separately from detection or joint carrier phase estimation decoding in an iterative fashion the performance of the proposed receivers is analyzed using density evolution the power allocation to the pilot symbol is quantified and it is shown that an optimal allocation scheme exists that minimizes the overall information bit signal to noise ratio required for error free communication this optimal power allocation which could be utilized in code design is found to be sensitive to the channel coherence interval as well as to the particular receiver used in addition a simple upper bound on the performance of any receiver that performs joint iterative carrier phase estimation and detection is derived the obtained results are compared with the simulated performance of the proposed receivers

eigenproblems of large powers of the laplacian in bounded domains we present a method for computing the spectrum of large powers of the laplacian in a bounded domain restricting ourselves to the one and three dimensional cases since it does not seem possible to obtain information on the eigenvalues directly from the transcendental equation that gives the spectrum we introduce a wallis inspired method we obtain the expansion of the eigenfunction and the eigenvalues in power series where the inverse of the power at which the laplacian is raised plays the role of the small parameter we compare these eigenvalues to those obtained through a simple variational approach and remark that the latter offers an excellent approximation to the exact result

multiple symbol differential detection of mpsk a differential detection technique for mpsk multiple phase shift keying which uses a multiple symbol observation interval is presented and its performance is analyzed and simulated the technique makes use of maximum likelihood sequence estimation of the transmitted phases rather than symbol by symbol detection as in the conventional differential detection thus the performance of this multiple symbol detection scheme fills the gap between conventional two symbol observation differentially coherent detection of mpsk and ideal coherent of mpsk with differential encoding the amount of improvement gained over conventional differential detection depends on the number of phases m and the number of additional symbol intervals added to the observation what is particularly interesting is that substantial performance improvement can be obtained for only one or two additional symbol intervals of observation the analysis and simulation results presented are for uncoded mpsk

capacity and coding for the block independent noncoherent awgn channel communication over the noncoherent additive white gaussian noise awgn channel is considered where the transmitted signal undergoes a phase rotation unknown to the transmitter and the receiver the effects of phase dynamics are explicitly taken into account by considering a block independent model for the phase process the unknown phase is constant for a block of n complex symbols and independent from block to block in the first part of the paper the capacity achieving input distribution is characterized in particular it is shown that the maximizing density has circular symmetry is discrete in amplitude with infinite number of mass points and always has a mass point at zero furthermore asymptotic expressions and bounds for the capacity are derived based on these results the capacity is evaluated through numerical optimizations for unconstrained and modulation constrained input distributions in the second part of this paper inspired by the capacity results two classes of coding and modulation schemes are proposed for fast and moderate phase dynamics in the case of fast phase dynamics i e small n optimized modulation alphabets are designed having exponential complexity with n at the demodulator in the case of moderate phase dynamics i e moderate values of n specially designed modulation alphabets are utilized that have linear complexity with n these alphabets are used together with optimized irregular low density parity check ldpc codes simulation results show that these codes can achieve close to capacity performance with moderate complexity and outperform the best known codes so far

turbo decoding of concatenated channel coding and trellis shaping for peak power controlled single carrier systems trellis shaping ts has found its application in the peak power control of band limited single carrier signals our recent work has demonstrated that a well designed ts can control the symbol transitions such that the output signal has almost constant envelope which significantly alleviates the linearity requirement of power amplifiers compared to transmission without constellation shaping however the ts involves signal constellation expansion exclusively for peak power control therefore unlike trellis coded modulation tcm that increases the minimum euclidean distances med the ts decreases the med thus incurring the increase in signal to noise power ratio snr required for achieving a certain error rate in this letter in order to overcome this drawback we propose a serial concatenation of coding and shaping together with an effective decoding algorithm that utilizes the memory effect i e error correcting capability of the shaped symbols the achievable performance of the proposed system is analyzed in terms of the average mutual information the simulation results demonstrate that the iterative decoding of the proposed concatenated system with outer convolutional codes and inner trellis shaping offers a significant performance gain

probability of error in frequency hop spread spectrum multiple access communication systems with noncoherent reception expressions are developed for the probability of error for asynchronous frequency hop spread spectrum multiple access networks using markov hopping patterns and binary frequency shift keying bfsk with one symbol transmitted per hop the expressions are exact when there is one interfering user and orthogonal bfsk is used they provide excellent approximations when there are more than one interfering user it is also shown that the error probability when markov hopping patterns are used is a good approximation to the error probability when memoryless hopping patterns are used by computing the channel capacity and the associated throughput a simple hard decision receiver is shown to perform much better than a receiver using perfect side information to erase the symbols transmitted on hops that were hit when all the users have the same power and one binary symbol is transmitted per hop

on the performance evaluation of trellis codes generating function techniques for analyzing the error event and the bit error probabilities for trellis codes are considered the conventional state diagram approach for linear codes where the number of states is equal to the number of trellis states cannot be applied directly to arbitrary trellis codes and instead a state diagram where the number of states is equal to the square of the number of trellis states must be used it is shown that for an interesting class of trellis codes a modified generating function can be defined for which the number of states em is equal to the number of trellis states the class of codes considered includes trellis codes of rate r n 1 n based upon set partitioning whenever the first partition breaks the signal constellation into two subsets which have the same configuration matrix i e the same ordered set of mutual distances the complexity of calculating this modified generating function is the same as for the ordinary generating function of a convolutional code with the same number of trellis states bounds on the performance of some interesting codes are given based upon this method

a novel frequency hopping spread spectrum multiple access network using m ary orthogonal walsh sequence keying a novel frequency hop spread spectrum multiple access network employing m ary orthogonal walsh sequence keying with noncoherent demodulation is proposed the transmitted walsh sequence is overlaid by a user specific pseudonoise sequence to reduce the effect of multiple access hits two gaussian approximations for the multiple access interference from both the dehopped slot and its neighboring slots are developed and are used to analyze the performance of the proposed network for synchronous and asynchronous hopping under nonfading and rayleigh fading channels the effect of imperfect hop timing synchronization at the receiver is also analyzed it is shown that the proposed network offers significantly improved network throughput compared to networks based on traditional m ary frequency shift keying modulation

ncfsk bit error rate with unsynchronized slowly fading interferers an expression for the bit error rate ber of noncoherent frequency shift keying with a nonfaded desired signal in the presence of n rayleigh faded unsynchronized cochannel interferers uccis and additive white gaussian noise is first derived this result can be used to obtain the ber for a faded desired signal for a large number of uccis numerical evaluation of this expression can be quite time consuming an approximate method that yields fairly accurate results is thus described numerical results show that for a rician faded desired signal with a strong specular component in an interference limited environment the ber decreases slightly with n whereas for a rayleigh faded desired signal the ber varies very little with n a comparison to the ber performance with synchronized cochannel interferers is also provided

the performance of trellis coded nonorthogonal noncoherent fsk in noise and jamming the performance of trellis coded fsk modulation with noncoherent detection is presented as applicable to a frequency hopped spread spectrum communication system or a conventional fsk system nonorthogonal tone spacing is considered as a parameter to control bandwidth occupancy of the hopped signal and to allow an increased number of users soft decision decoding with a maximum metric decoder is employed the metrics considered are the energy metric with and without perfect jammer state information as well as a practical self normalized metric that compensates for jamming or interference performance analyses for full and partial band and both noise and multitone jammings are presented for nonorthogonal tone spacing the signals are correlated and so chernoff bounds on the pairwise error probability for energy detectors with correlated signals are presented and evaluated these bounds supplement earlier performance estimates for trellis coded fsk to assess the tightness of the bounds simulations have been carried out with results that come within 1 to 3 db of the bounds system performance is evaluated for 2 4 and 8 state trellis codes with tone spacings of 1 3t 1 2t 2 3t and 1 t hz

extinction and non extinction for a p laplacian equation with nonlinear source abstract in this paper we deal with the extinction of solutions of the initial boundary value problem of the p laplacian equation u t div u p 2 u u q in a bounded domain of r n with n 2 for 1 p 2 we show that q p 1 is the critical exponent of extinction for the weak solution furthermore for 1 p 2 and q p 1 we prove that the extinction and non extinction of the solution depends strongly on the first eigenvalue of the problem div p 2 p 2 in 0

coding for the discretely phase ambiguous additive white gaussian channel communication over the additive white gaussian channel subject to a discrete phase ambiguity at the receiver is considered when this phase ambiguity is considered as a discretely distributed random variable the channel is termed the acoherent additive white gaussian aawg channel it is shown that the optimum decoder for the aawg channel is not practically implementable and a suboptimum decoder that is asymptotically optimum at high signal to noise ratio is developed the low signal to noise ratio performance of the suboptimum decoder is also examined by considering the structural possibilities for this decoder it is shown that one implementation leads to rotationally invariant codes other implementations based on a rotationally disjoint property lead to a variety of solutions that offer a general framework for communication over this channel some of these solutions use a parallel receiver configuration various solutions are compared in terms of implementation and performance

capacity of frequency hop spread spectrum multiple access communication systems the information theoretic capacity is considered in order to account for independent encoding and decoding and private to the sender and receiver hopping patterns an interference channel model is adopted with k sender receiver pairs with the ith receiver only interested in the message transmitted by the ith sender both synchronous and asynchronous hopping patterns are investigated although the channel exhibits memory in the latter case it is possible to compute the capacity region the asymptotic normalized sum capacity is also computed

on the capacity of the blockwise incoherent mpsk channel the capacity of m ary phase shift keying mpsk over an additive white gaussian noise awgn channel with carrier phase unknown but constant over l symbols is investigated it is shown that capacity achieving channel inputs are uniformly distributed and independent mpsk symbols capacity over a range of signal to noise ratio snr and l is presented for binary phase shift keying bpsk and quaternary phase shift keying qpsk upper and lower easy to compute bounds on capacity are derived it is proven that for large l the coherent capacity is approached an analytic asymptotic expression for low l spl middot snr is derived exhibiting the expected quadratic dependence on the snr

multiuser demodulation and iterative decoding for frequency hopped networks demodulation and decoding for frequency hopped spread spectrum multiple access fh ssma systems have been traditionally conducted by conventional single user noncollaborative demodulation and error and erasure correcting decoding techniques in this paper we study the demodulation and decoding aspects of collaborative multiuser reception for fh ssma and propose methods which increase the number of users the system can support in particular we propose and analyze the optimum maximum a priori probability demodulation of multiple symbols or type and the use of iterative multiuser decoding after the demodulation since hits from one or two other users are the most likely hit events in fh ssma the joint demodulation of two or of three users is performed based on likelihood ratio tests m ary frequency shift keying modulation with noncoherent demodulation and reed solomon codes with hard decision minimum distance decoding are used in the fh ssma system results are derived for both synchronous and asynchronous frequency hop systems the performance of the proposed multiuser detector in additive white gaussian noise and flat rayleigh fading channels is evaluated scenarios when all simultaneous users or only a subset of them are collaboratively demodulated and decoded are simulated

long time extinction of solutions of some semilinear parabolic equations we study the long time behavior of solutions of semilinear parabolic equation of the following type tu u a0 x uq 0 where a0 x d0exp x x 2 d0 0 1 q 0 and is a positive continuous radial function we give a dini like condition on the function by two different methods which implies that any solution of the above equation vanishes in a finite time the first one is a variant of a local energy method and the second one is derived from semi classical limits of some schrodinger operators

extinction and asymptotic behavior of solutions for the ω heat equation on graphs with source and interior absorption abstract in this paper we consider the extinction and asymptotic behavior of the solutions for the following heat equation on graphs with source and interior absorption u t x t u x t u q x t u p x t where is called the discrete weighted laplacian operator and p q 0 we first prove the local existence of the solutions and show that all solutions exist globally when q max p 1 then we obtain the following extinction and asymptotic properties of the solutions when q 1 and the initial datum are small enough the solution vanishes in infinite time when q 1 p 1 and is appropriately small the solution becomes extinct in finite time when q 1 p 1 and is appropriately small the solution vanishes in infinite time when q 1 and is appropriately large the solution is non extinction when q 1 q p is the critical extinction exponent moreover for the case that p q 1 and is appropriately large we show that the non extinction solution is asymptotically stable and lim t u x t u x where u x is the unique positive equilibrium solution finally we demonstrate our results through some numerical examples

multiple access capability of frequency hopped spread spectrum revisited an analysis of the effect of unequal power levels a method for the evaluation of the probability of error of uncoded asynchronous frequency hopped spread spectrum multiple access communications is presented for systems with binary fsk modulation this method provides an accurate approximation and a tight upper bound to the bit error probability for systems with m ary fsk modulation it provides tight upper bounds to the symbol error probability the method enables the computationally efficient averaging of the error probability with respect to the delays phase angles and data streams of the different users it relies on the integration of the product of the characteristic function of the envelope of the branch of the bfsk demodulator which carries the desired signal and of the derivative of the characteristic function of the envelope of the other branch for sufficient frequency separation between the bfsk tones the method can achieve any desirable accuracy moreover the computational effort required for its evaluation grows linearly with the number of interfering users in the m ary case tight upper bounds based on the union bound and the results of the binary case are derived the method allows the effect of unequal power levels on other user interference in fh ssma systems to be quantified accurately for the first time the results indicate that the fh ssma systems suffer from the near far problem although less seriously than direct sequence ssma systems

optimally near far resistant multiuser detection in differentially coherent synchronous channels the noncoherent demodulation of differentially phase shift keyed signals transmitted simultaneously via a synchronous code division multiple access cdma channel is studied under the assumption of white gaussian background noise a class of noncoherent linear detectors is defined with the objective of obtaining the optimal one the performance criterion considered is near far resistance that denotes worst case multiuser asymptotic efficiency over near far environments it is shown that the optimal linear detector is a noncoherent decorrelating detector the commonality between the properties of the decorrelating detectors for coherent and noncoherent channels is established in particular it is shown that no other differential phase shift keying dpsk multiuser detector achieves a higher near far resistance than does the noncoherent decorrelator

extinction and positivity for the evolution p laplacian equations with absorption on networks in this paper we discuss the extinction and positivity of solutions to evolution p laplacian equations u t p u u q 1 u 0 with absorption on finite networks with p 1 q 0 and 0 we present necessary and sufficient conditions for parameters p q and in order that solutions to the equation are extinctive or positive respectively in addition when a solution is positive we provide its decay rate and when a solution becomes extinctive in finite time we give estimate for the extinction time

vanishing solutions of anisotropic parabolic equations with variable nonlinearity abstract we study the property of finite time vanishing of solutions of the homogeneous dirichlet problem for the anisotropic parabolic equations u t i 1 n d i a i x t u d i u p i x t 2 d i u c x t u x t 2 u f x t with variable exponents of nonlinearity p i x t x t 1 we show that the solutions of this problem may vanish in a finite time even if the equation combines the directions of slow and fast diffusion and estimate the extinction moment in terms of the data if the solution does not identically vanish in a finite time we estimate the rate of vanishing of the solution as t we establish conditions on the nonlinearity exponents which guarantee vanishing of the solution at a finite instant even if the equation eventually transforms into the linear one

coevolutionary games on networks we study agents on a network playing an iterated prisoner s dilemma against their neighbors the resulting spatially extended coevolutionary game exhibits stationary states which are nash equilibria after perturbation of these equilibria avalanches of mutations reestablish a stationary state scale free avalanche distributions are observed that are in accordance with calculations from the nash equilibria and a confined branching process the transition from subcritical to critical avalanche dynamics can be traced to a change in the degeneracy of the cooperative macrostate and is observed for many variants of this game

nd convolutional codes ii structural analysis for pt i see ibid vol 43 no 2 p 558 75 1997 the structural properties of a noncoherent coded system which incorporates convolutional codes in conjunction with multiple symbol noncoherent detection is presented in this second part of a two part paper where the performance analysis was provided in part i these convolutional codes are referred to as nd convolutional codes and they provide a general framework for various noncoherent coding systems including differential systems for several practical models of the carrier phase the exponential rate in which the error probability decays to zero derived in part i of the paper is used here to obtain the free equivalent distance of nd codes which is the single parameter dominating the error performance at large signal to noise ratios the free equivalent distance is upper bounded by the free nd distance which constitutes a more convenient and practical parameter to work with and it is the basis for a computer search for optimal nd codes the resultant codes of the computer search are compared to codes which are optimal for coherent detection and it is verified that the latter codes are not necessarily optimal for noncoherent detection since they exhibit in many cases a relatively small nd distance the ambiguity problem inherent to noncoherent systems is also treated in this paper in the general framework of nd catastrophic codes and necessary and sufficient conditions for catastrophic error propagation are identified

error performance of binary ncfsk in the presence of multiple tone interference and system noise this paper presents a general solution to the problem of calculating the error performance of binary ncfsk systems in the presence of multiple tone interference and system noise the development uses the concepts of circularly symmetric signals and expresses the results in terms of a bessel integral this integral is then evaluated using a rapidly converging fourier bessel series the error in this approximation to the integral is controlled by two parameters which may be adjusted so that the desired accuracy is attained it is determined that in the useful probability of error range and when the total tone power is constrained the error rate increases for an increase in the number of interfering tones in addition for equal amplitude tones the performance is independent of the distribution of the tones within the channel the technique used is also applicable to other detection problems where the threshold is a random variable

graph fission in an evolving voter model we consider a simplified model of a social network in which individuals have one of two opinions called 0 and 1 and their opinions and the network connections coevolve edges are picked at random if the two connected individuals hold different opinions then with probability 1 one imitates the opinion of the other otherwise i e with probability the link between them is broken and one of them makes a new connection to an individual chosen at random i from those with the same opinion or ii from the network as a whole the evolution of the system stops when there are no longer any discordant edges connecting individuals with different opinions letting be the fraction of voters holding the minority opinion after the evolution stops we are interested in how depends on and the initial fraction u of voters with opinion 1 in case i there is a critical value c which does not depend on u with u for c and 0 for c u u but for c u we have u 1 2 using simulations and approximate calculations we explain why these two nearly identical models have such dramatically different phase transitions

maximum likelihood differential detection of uncoded and trellis coded amplitude phase modulation over awgn and fading channels spl minus metrics and performance this paper derives metrics for maximum likelihood differential detection of uncoded and trellis coded mpsk and qam transmitted over rayleigh and rician fading channels receiver structures based on these metrics are proposed and their error probability performance analyzed and or simulated the results represent a generalization of the notion of multiple symbol differential detection previously introduced by the authors for mpsk over an awgn to the fading channel and other modulations for the coded cases ideal interleaving deinterleaving is assumed and furthermore the presence or absence of channel state information an interesting side result is that for a constant envelope modulation transmitted over a fading channel with unknown but rapidly varying phase error the other extreme to the slowly varying phase error case normally assumed for differential detection under certain practical assumptions it is shown that the optimum receiver is of the limiter discriminator type

throughput performance of an fhma system with variable rate coding we compare throughput bounds for a frequency hopped multiple access fhma system employing variable rate as well as fixed rate coding frc nonfading as well as rayleigh fading channels are explored the throughput bounds for the variable rate coding vrc schemes are based on the assumption that the number of active users in the system m is known at any time while the bounds for the frc scheme assumes that the fixed code rate is optimized for the user population mean spl lambda where the population is assumed to be poisson distributed we present bounds for theoretical perfect codes which achieve the capacity as well as bounds for reed solomon rs codes of practical block lengths finally we show the dependence of a vrc scheme upon the accuracy of the estimates of m and present a general comparison of the gains of using vrc versus a realistic frc scheme