minimum probability of error for asynchronous gaussian multiple access channels consider a gaussian multiple access channel shared by k users who transmit asynchronously independent data streams by modulating a set of assigned signal waveforms the uncoded probability of error achievable by optimum multiuser detectors is investigated it is shown that the k user maximum likelihood sequence detector consists of a bank of single user matched filters followed by a viterbi algorithm whose complexity per binary decision is o 2 k the upper bound analysis of this detector follows an approach based on the decomposition of error sequences the issues of convergence and tightness of the bounds are examined and it is shown that the minimum multiuser error probability is equivalent in the iow noise region to that of a single user system with reduced power these results show that the proposed multiuser detectors afford important performance gains over conventional single user systems in which the signal constellation carries the entire burden of complexity required to achieve a given performance level

optimum asymptotic multiuser efficiency of randomly spread cdma this correspondence analyzes the high signal to noise ratio snr performance of optimum multiuser detectors for synchronous direct sequence spread spectrum with random spreading in an additive white gaussian noise channel under very general conditions on the received powers we show that the optimum asymptotic efficiency of a k user system with spreading gain n converges to 1 almost surely as k spl rarr spl infin and k n is kept equal to an arbitrary nonzero constant therefore the asymptotic behavior of the minimum bit error rate is equivalent to that of a single user system

some exact results for the trapping of subdiffusive particles in one dimension we study a generalization of the standard trapping problem of random walk theory in which particles move subdiffusively on a one dimensional lattice we consider the cases in which the lattice is filled with a one sided and a two sided random distribution of static absorbing traps with concentration c the survival probability t that the random walker is not trapped by time t is obtained exactly in both versions of the problem through a fractional diffusion approach comparison with simulation results is made

molecular evolution modeled as a fractal statistical process abstract modeling the rate of nucleotide substitutions in dna as a dichotomous stochastic process with an inverse power law correlation function describes evolution by a fractal stochastic process fsp this fsp model agrees with recent findings on the relationship between the variance and mean number of synonymous and nonsynonymous substitutions in 49 different genes in mammals that being a power law increase in the ratio of the variance to the mean the index of dispersion with the number of substitutions in a protein the probability of a given number of substitutions occuring in a time t is determined by a fractional diffusion equation whose solution is a truncated levy distribution implying that evolution is a levy process in time and yields the same functional behavior for the variance in the number of substitutions as does the fsp model in addition to obtaining these relationships the fsp model implies lognormal statistics for the index of dispersion as a function of the mean number of substitutions in a protein which is confirmed in the regression of the fsp model to data lognormal statistics suggest that molecular evolution can be viewed as a multiplicative stochastic process rather than the linear additive processes of darwinian selection and drift

random walk in chemical space of cantor dust as a paradigm of superdiffusion we point out that the chemical space of a totally disconnected cantor dust k n ensuremath subset e n is a compact metric space c n with the spectral dimension d s d ensuremath ell ngd where d and d ensuremath ell n are the fractal and chemical dimensions of k n respectively hence we can define a random walk in the chemical space as a markovian gaussian process the mapping of a random walk in c n into k n ensuremath subset e n defines the quenched l evy flight on the cantor dust with a single step duration independent of the step length the equations describing the superdiffusion and diffusion reaction front propagation ruled by the local quenched l evy flight on k n ensuremath subset e n are derived the use of these equations to model superdiffusive phenomena observed in some physical systems in which propagators decay faster than algebraically is discussed

performance of blind and group blind multiuser detectors in blind or group blind linear multiuser detection the detector is estimated from the received signals with the prior knowledge of only the signature waveform of the desired user or the signature waveforms of some but not all users the performance of a number of such estimated linear detectors including the direct matrix inversion dmi blind linear minimum mean square error mmse detector the subspace blind linear mmse detector and the form i and form ii group blind linear hybrid detectors are analyzed asymptotic limit theorems for each of the estimates of these detectors when the signal sample size is large are established based on which approximate expressions for the average output signal to interference plus noise ratios sinrs and bit error rates bers are given to gain insights on these analytical results the performance of these detectors in an equicorrelated code division multiple acces cdma system is compared examples are provided to demonstrate the excellent match between the theory developed here and the simulation results

fractional diffusion probability distributions and random walk models abstract we present a variety of models of random walk discrete in space and time suitable for simulating random variables whose probability density obeys a space time fractional diffusion equation

multidimensional solutions of space fractional diffusion equations green s functions and propagators for the multidimensional anisotropic spacetime fractional diffusion equation are obtained in integral form uniqueness of the solutions is studied in the framework

boundary problems for diffusion in a fluctuating potential abstract using a newly developed formalism adapted for diffusion in the presence of partially absorbing boundaries we treat the overdamped motion of a particle in a fluctuating potential and in a restricted space the potential is assumed to be linear with a slope switching between two possible values the switching process is taken as the standard markov alternating process we first construct the free dynamics propagator no boundaries which controls the evolution of the joint probability for both the particle s position and the state of the potential secondly at a given spatial point we affix a two channel boundary a given channel absorbs the trajectories arriving at the boundary with the potential in a given state we demonstrate the asymmetry of the filling process for the individual channels and we discuss their asymptotic occupation depending on the mean switching frequency finally we study the motion in a domain restricted by two boundaries of the above two channel type and the corresponding first passage time the simple problem setting allows for an explicit analysis of the correlation between the particle s motion and the potential switching process

analytically pricing double barrier options based on a time fractional black scholes equation this paper investigates the pricing of double barrier options when the price change of the underlying is considered as a fractal transmission system in this scenario the option price is governed by a modified black scholes equation with a time fractional derivative in comparison with standard derivatives of integer order the fractional order derivatives are characterized by their globalness i e the rate of change of a function near a point is affected by the property of the function defined in the entire domain of definition rather than just near the point itself the existence of the time fractional derivative in conjunction with the presence of two barriers of the double barrier options has added an additional degree of difficulty not only when a purely numerical solution is sought but also when an analytical method is attempted albeit difficult we have managed to find an explicit closed form analytical solution for double barrier options which has been taken to price the single barrier options and european path independent options under the same framework as a special case of the current solution in addition not only have we provided a theoretical proof for the convergence of the newly found analytic solution in series form which is a vital step to show the closeness of our solution we have also proposed an efficient numerical evaluation technique to facilitate the implementation of our formula so that it can be easily used in trading practice

fractional fokker planck equation on heterogeneous fractal structures in external force fields and its solutions abstract we introduce a heterogeneous fractional fokker planck equation hffpe involving external force fields describing systems on heterogeneous fractal structure medium the hffpe is shown to obey generalized einstein relation and its stationary solution is the generalized boltzmann distribution it is proved that the asymptotic shape of its solution is a stretched gaussian and that its solution can be expressed in the form of a function of a dimensionless similarity variable for generic potentials furthermore it is shown that the solution of ffpe with parameter has the same properties as that ones of hffpe

a family of likelihood ascent search multiuser detectors approaching optimum performance via random multicodes with linear complexity tse and verdu proved that the global maximum likelihood gml detector achieves unit asymptotic multiuser efficiency ame in the limit of large random spreading cdma in this paper we show that the wide sense sequential likelihood ascent search wslas detectors achieve unit ame with channel load 1 2 1 4 ln 2 bits s hz in simulations for random multicode equal power systems the wslas with a linear per bit complexity approaches the gml ber in all snr with channel load as high as 1 05 bits s hz

hierarchical spatio temporal coupling in fractional wanderings i continuous time weierstrass flights abstract the one dimensional continuous time weierstrass flights ctwf model is considered in the framework of the nonseparable continuous time random walks formalism ctrw a novel spatio temporal coupling is introduced by assuming that in each scale the probability density for the flight and for waiting are joined hence we treat the spatio temporal relations in terms of the self similar structure of the weierstrass process this stochastic structure is characterized by the spatial fractional dimension 1 representing the flights and the temporal one 1 representing the waiting time was assumed here as the only independent truncation range in this work we study the asymptotic properties of the ctwf model for example by applying the method of steepest descents we obtained the particle propagator in the approximate scaling form p x t t pt 2 f where the scalingfunction f pt exp const pt while the scaling variable x t pt 2 is large the principal result of our analysis is that the exponents and depend on more fundamental ones and what leads to a novel scaling as a result of competition between exponents and an enhanced dispersive or normal diffusion was recognized in distinction from the prediction of the separable ctrw model where the enhanced diffusion is lost and the dispersive one is strongly limited it should be noted that we compare here partially thermalized versions of both approaches where some initial fluctuations were also included in agreement with the spirit of the theory of the renewal processes having the propogator we calculated for example the particle mean square displacement and found its novel asymptotic scaling with time for enhanced diffusion given by t1 2 1 in distinction from its diverging for

limit of the smallest eigenvalue of a large dimensional sample covariance matrix in this paper the authors show that the smallest if p leq n or the p n 1 th smallest if p n eigenvalue of a sample covariance matrix of the form 1 n xx tends almost surely to the limit 1 sqrt y 2 as n rightarrow infty and p n rightarrow y in 0 infty where x is a p times n matrix with iid entries with mean zero variance 1 and fourth moment finite also as a by product it is shown that the almost sure limit of the largest eigenvalue is 1 sqrt y 2 a known result obtained by yin bai and krishnaiah the present approach gives a unified treatment for both the extreme eigenvalues of large sample covariance matrices

tight bounds on the capacity of binary input random cdma systems in this paper we consider code division multiple access cdma communication over a binary input additive white gaussian noise awgn channel using random spreading for a general class of symmetric distributions for spreading sequences in the limit of a large number of users we prove an upper bound to the capacity the bound matches the formula obtained by tanaka using the replica method we also show concentration of various relevant quantities including mutual information and free energy the mathematical methods are quite general and allow us to discuss extensions to other multiuser scenarios

generalized space time fractional diffusion equation with composite fractional time derivative abstract we investigate the solution of space time fractional diffusion equations with a generalized riemann liouville time fractional derivative and riesz feller space fractional derivative the laplace and fourier transform methods are applied to solve the proposed fractional diffusion equation the results are represented by using the mittag leffler functions and the fox h function special cases of the initial and boundary conditions are considered numerical scheme and grunwald letnikov approximation are also used to solve the space time fractional diffusion equation the fractional moments of the fundamental solution of the considered space time fractional diffusion equation are obtained many known results are special cases of those obtained in this paper we investigate also the solution of a space time fractional diffusion equations with a singular term of the form x t 1 0

on a 145 32 binary cyclic code we discovered that a 145 32 binary cyclic code generated by the product of an irreducible polynomial of degree 28 with exponent 145 and the polynomial x sup 4 x sup 3 x sup 2 x 1 has a minimum distance of 44

hierarchical spatio temporal coupling in fractional wanderings ii diffusion phase diagram for weierstrass walks abstract the one dimensional weierstrass walks ww model is developed in the framework of the extended nonseparable continuous time random walk ctrw formalism 1 2 3 4 5 6 7 8 9 10 11 12 the ww model is a lacunary foundation of levy walks 6 7 8 9 10 11 12 generalized to a nonconstant velocity this nonconstant velocity is introduced by hierarchical coherent spatio temporal coupling adopted from the continuous time weierstrass flights ctwf model developed in the previous paper 13 hence for the probability density to pass by a walker in a single step a random displacement with finite velocity is constructed as a geometric series of the corresponding probability densities defined within a sequence of spatio temporal scales we calculated analytically and by monte carlo simulations the asymptotic in time mean square displacement msd of the walker obtaining very good agreement between both approaches also comparison with corresponding results of the ctwf model is made considering different types of the diffusion exponents we constructed a diffusion phase diagram on the plane defined by the spatial and temporal fractional dimensions which characterize our coupling we obtained a diffusion exponent as a function of these fractional dimensions covering all types of nonbiased diffusion known up to now from the dispersive one over the normal enhanced ballistic and hyperdiffusion up to the richardson law of diffusion which defines here a part of the borderline of the region where the msd diverges we observed that all kinds of anomalous diffusion are characterized by three types of diffusion exponents only for example we found an asymptotic scaling of msd to occur with time for enhanced diffusion which was discovered by us within the ctwf model but is valid for a much more extended range of spatio and temporal fractional dimensions

on optimum asymptotic multiuser efficiency of randomly spread cdma we extend the result by tse and verdu on the optimum asymptotic multiuser efficiency of randomly spread code division multiple access cdma with binary phase shift keying input random gaussian and random binary antipodal spreading are considered we obtain the optimum asymptotic multiuser efficiency of a k user system with spreading gain n when k and n rightarrow infty and the loading factor k n grows logarithmically with k under some conditions it is shown that the optimum detector in a gaussian randomly spread cdma system has a performance close to the single user system at high signal to noise ratio when k and n rightarrow infty and the loading factor k n is kept less than log 3 k 2 random binary antipodal matrices are also studied and a lower bound for the optimum asymptotic multiuser efficiency is obtained furthermore we investigate the connection between detecting matrices in the coin weighing problem and optimum asymptotic multiuser efficiency we obtain a condition such that for any binary input an n times k random matrix whose entries are chosen randomly from a finite set is a detecting matrix as k and n rightarrow infty

green function of the double fractional fokker planck equation path integral and stochastic differential equations the statistics of rare events the so called black swan events is governed by non gaussian distributions with heavy power like tails we calculate the green functions of the associated fokker planck equations and solve the related stochastic differential equations we also discuss the subject in the framework of path integration

a family of likelihood ascent search multiuser detectors an upper bound of bit error rate and a lower bound of asymptotic multiuser efficiency in this paper the bit error performance of a family of likelihood ascent search las multiuser detectors is analyzed an upper bound on the ber of any las detector is obtained by bounding the fixed point region with the worst initial detector the concept of indecomposable errors developed by verdu is applied to tighten the upper bound in a special instance the upper bound is reduced to that for all the local maximum likelihood detectors the upper bound is comparable with that of the optimum detector obtained by verdu a lower bound on the asymptotic multiuser efficiency ame is then obtained it is shown that there are nontrivial cdma channels such that a las detector can achieve unit ame regardless of user number the ame lower bound provides a means for further seeking a good set of spreading sequences and power distribution for spectral and power efficient cdma

measuring complexity nonextensivity and chaos in the dna sequence of the major histocompatibility complex abstract we analyze 4 mb sequences of the major histocompatibility complex mhc which is a dna segment on chromosome 6 with high gene density controlling many immunological functions and associated with many diseases the analysis is based on modern theoretical and mathematical tools of complexity theory such as nonlinear time series analysis and tsallis non extensive statistics the results revealed that the dna complexity and self organization can be related to fractional dynamical nonlinear processes with low dimensional deterministic chaotic and non extensive statistical character which generate the dna sequences under the extremization of tsallis q entropy principle while it still remains an open question as to whether the dna walk is a fractional brownian motion fbm a static anomalous diffusion process or a non gaussian dynamical fractional anomalous diffusion process the results of this study testify for the latter providing also a possible explanation for the previously observed long range power law correlations of nucleotides as well as the long range correlation properties of coding and non coding sequences present in dna sequences

on the capacity loss due to separation of detection and decoding the performance loss due to separation of detection and decoding on the binary input additive white gaussian noise awgn channel is quantified in terms of mutual information results are reported for both the code division multiple access cdma channel in the large system limit and the intersymbol interference isi channel the results for cdma rely on the replica method developed in statistical mechanics it is shown that a previous result of shamai and verdu found for gaussian input alphabet holds also for binary input alphabets for the isi channel the performance loss is calculated via the bahl cocke jelinek raviv bcjr algorithm comparisons are made to the capacity of separate detection and decoding using suboptimum detectors such as a decision feedback equalizer

answer to an open problem proposed by r metzler and j klafter in a positive answer to the open problem proposed by r metzler and j klafter it is proved that the asymptotic shape of the solution for a wide class of fractional fokker planck equations is a stretched gaussian for the initial condition being a pulse function in the homogeneous and heterogeneous fractal structures whose mean square displacement behaves like x 2 t t and x 2 t x t 0 1 respectively

fractional diffusion exact representations of spectral functions for all the relevant transformed spaces i e fourier laplace and fourier laplace we present exact solutions of a fractional diffusion equation describing random transport on fractals the potential importance of such spectral representations lies in their applications to interpreting experimental measurements of anomalous diffusion processes in contrast to the well known asymptotic results the exact representations provide a much broader basis for comparison with data

fractional diffusion equation on fractals one dimensional case and asymptotic behaviour a fractional differential equation is studied and its application for describing diffusion on random fractal structures is considered it represents the simplest generalization of the fractional diffusion equation valid in euclidean systems the solution of the fractional equation in one dimension is discussed and compared with exact results for the fractional brownian motion and the one dimensional version of the standard diffusion equation on fractals in higher dimensions it correctly describes the asymptotic scaling behaviour of the probability density function on random fractals as obtained recently by using scaling arguments and exact enumeration calculations for the infinite percolation cluster at criticality

bounds on the sum capacity of synchronous binary cdma channels in this paper we obtain a family of lower bounds for the sum capacity of code division multiple access cdma channels assuming binary inputs and binary signature codes in the presence of additive noise with an arbitrary distribution the envelope of this family gives a relatively tight lower bound in terms of the number of users spreading gain and the noise distribution the derivation methods for the noiseless and the noisy channels are different but when the noise variance goes to zero the noisy channel bound approaches the noiseless case the behavior of the lower bound shows that for small noise power the number of users can be much more than the spreading gain without any significant loss of information overloaded cdma a conjectured upper bound is also derived under the usual assumption that the users send out equally likely binary bits in the presence of additive noise with an arbitrary distribution as the noise level increases and or the ratio of the number of users and the spreading gain increases the conjectured upper bound approaches the lower bound we have also derived asymptotic limits of our bounds that can be compared to a formula that tanaka obtained using techniques from statistical physics his bound is close to that of our conjectured upper bound for large scale systems

fast numerical simulation of a new time space fractional option pricing model governing european call option abstract when the fluctuation of option price is regarded as a fractal transmission system and the stock price follows a levy distribution a time space fractional option pricing model tsfopm is obtained then we discuss the numerical simulation of the tsfopm a discrete implicit numerical scheme with a second order accuracy in space and a 2 order accuracy in time is constructed where is a transmission exponent the stability and convergence of the obtained numerical scheme are analyzed moreover a fast bi conjugate gradient stabilized method is proposed to solve the numerical scheme in order to reduce the storage space and computational cost then a numerical example with exact solution is presented to demonstrate the accuracy and effectiveness of the proposed numerical method finally the tsfopm and the above numerical technique are applied to price european call option the characteristics of the fractional option pricing model are analyzed in comparison with the classical black scholes b s model

optimum multiuser asymptotic efficiency the degradation in bit error rate due to the presence of multiple access interference in a white gaussian channel can be measured by the multiuser asymptotic efficiency defined as the ratio between the snr required to achieve the same uncoded bit error rate in the absence of interfering users and the actual snr in this paper the asymptotic efficiency of the optimum multiuser demodulator a bank of matched filters followed by a viterbi algorithm is investigated and compared to that of the conventional single user matched filter receiver the computation of the optimum asymptotic efficiency of any given user is equivalent to the minimization of the euclidean distance between any pair of multiuser signals which differ in at least one of the symbols of that user it is shown that the optimum multiuser efficiency of asynchronous systems is nonzero with probability 1 and therefore the optimum demodulator does not become multiple access limited in contrast to the single user receiver a class of signal constellations with moderate cross correlation requirements is shown to achieve unit optimum multiuser efficiencies and hence to be equivalent to orthogonal signal sets from the viewpoint of performance of the optimum multiuser detector

universality of stretched gaussian asymptotic behaviour for the fractional fokker planck equation in external force fields we introduce a heterogeneous fractional fokker planck equation hffpe on heterogeneous fractal structure media describing systems involving external force fields the hffpe is shown to obey the generalized einstein relation and its stationary solution is the boltzmann distribution it is proven that the asymptotic shape of its solution is a stretched gaussian and that its solution can be expressed in the form of a function of a dimensionless similarity variable for constant and generic potentials with polar singularity at origin

diffusion on complex cellular automata patterns we studied random walks on two dimensional patterns formed by the sequence of configurations of complex elementary cellular automata ca with random initial configurations the walkers are allowed to jump between nearest neighbours or next nearest neighbours 1 sites on patterns of rules 22 54 90 122 126 150 and 182 the diffusion is normal 1 2 on patterns 18 and 146 the diffusion is anomalous with 0 415 0 005 and the spectral dimension is ds 1 25 0 1 from the analysis of the diffusion in the horizontal and vertical directions space and time directions of the ca problem respectively of patterns 18 and 146 we obtained x 0 22 and y 0 42 because they have branches of 1 sites which are long in the vertical direction but narrow in the horizontal direction due to the anisotropic diffusion the results do not satisfy the relation ds 2df dw with dw 1 and fractal dimension df 2 considering that the fractal dimension of the region visited by the walker is equal to the dimension of the substrate df we suggest the new scaling relation ds 2 x y this relation is supported by our numerical results and may be generalized to other structures with anisotropic diffusion

randomly spread cdma asymptotics via statistical physics this paper studies randomly spread code division multiple access cdma and multiuser detection in the large system limit using the replica method developed in statistical physics arbitrary input distributions and flat fading are considered a generic multiuser detector in the form of the posterior mean estimator is applied before single user decoding the generic detector can be particularized to the matched filter decorrelator linear minimum mean square error mmse detector the jointly or the individually optimal detector and others it is found that the detection output for each user although in general asymptotically non gaussian conditioned on the transmitted symbol converges as the number of users go to infinity to a deterministic function of a hidden gaussian statistic independent of the interferers thus the multiuser channel can be decoupled each user experiences an equivalent single user gaussian channel whose signal to noise ratio snr suffers a degradation due to the multiple access interference mai the uncoded error performance e g symbol error rate and the mutual information can then be fully characterized using the degradation factor also known as the multiuser efficiency which can be obtained by solving a pair of coupled fixed point equations identified in this paper based on a general linear vector channel model the results are also applicable to multiple input multiple output mimo channels such as in multiantenna systems

spectral efficiency of cdma with random spreading the cdma channel with randomly and independently chosen spreading sequences accurately models the situation where pseudonoise sequences span many symbol periods furthermore its analysis provides a comparison baseline for cdma channels with deterministic signature waveforms spanning one symbol period we analyze the spectral efficiency total capacity per chip as a function of the number of users spreading gain and signal to noise ratio and we quantify the loss in efficiency relative to an optimally chosen set of signature sequences and relative to multiaccess with no spreading white gaussian background noise and equal power synchronous users are assumed the following receivers are analyzed a optimal joint processing b single user matched filtering c decorrelation and d mmse linear processing

time and space fractional partial differential equations the fundamental solution for time and space fractional partial differential operator dt a2 2 0 is given in terms of the fox s h function here the time fractional derivative in the sense of generalized functions distributions dt is defined by the convolution dt f t t f t where t t 1 and f t 0 as t 0 and the fractional n dimensional laplace operator 2 is defined by its fourier transform with respect to spatial variable f 2g x f g x the solutions for initial value problems for time and space fractional partial differential equation in the sense of caputo and riemann liouville time fractional derivatives respectively are obtained by the fundamental solution

the generalized cattaneo equation for the description of anomalous transport processes the cattaneo equation which describes a diffusion process with a finite velocity of propagation is generalized to describe anomalous transport three possible generalizations are proposed each one supported by a different scheme continuous time random walks non local transport theory and delayed flux force relation the properties of these generalizations are studied in both the long time and the short time regimes in the long time limit we recover the mean square displacement which is characteristic for these anomalous processes as expected the short time behaviour is modified in comparison to generalized diffusion equations

large system analysis of multiuser detection with an unknown number of users a high snr approach we analyze multiuser detection under the assumption that the number of users accessing the channel is unknown by the receiver in this environment users activity must be estimated along with any other parameters such as data power and location our main goal is to determine the performance loss caused by the need for estimating the identities of active users which are not known a priori to prevent a loss of optimality we assume that identities and data are estimated jointly rather than in two separate steps we examine the performance of multiuser detectors when the number of potential users is large statistical physics methodologies are used to determine the macroscopic performance of the detector in terms of its multiuser efficiency special attention is paid to the fixed point equation whose solution yields the multiuser efficiency of the optimal maximum a posteriori detector in the large signal to noise ratio regime our analysis yields closed form approximate bounds to the minimum mean squared error in this regime these illustrate the set of solutions of the fixed point equation and their relationship with the maximum system load next we study the maximum load that the detector can support for a given quality of service specified by error probability

fractional diffusion and levy stable processes anomalous diffusion in which the mean square distance between diffusing quantities increases faster than linearly in time has been observed in all manner of physical and biological systems from macroscopic surface growth to dna sequences herein we relate the cause of this nondiffusive behavior to the statistical properties of an underlying process using an exact statistical model this model is a simple two state process with long time correlations and is shown to produce a random walk described by an exact fractional diffusion equation fractional diffusion equations describe anomalous transport and are shown to have exact solutions in terms of fox functions including l evy ensuremath alpha stable processes in the superdiffusive domain 1 21

iterative multiuser joint decoding optimal power allocation and low complexity implementation we consider a canonical model for coded code division multiple access cdma with random spreading where the receiver makes use of iterative belief propagation bp joint decoding we provide simple density evolution analysis in the large system limit large number of users of the performance of the bp decoder and of some suboptimal approximations based on interference cancellation ic based on this analysis we optimize the received user signal to noise ratio snr distribution in order to maximize the system spectral efficiency for given user channel codes channel load users per chip and target user bit error rate ber the optimization of the received snr distribution is obtained by solving a simple linear program and can be easily incorporated into practical power control algorithms remarkably under the optimized snr assignment the suboptimal minimum mean square error mmse ic based decoder performs almost as well as the more complex bp decoder moreover for a large class of commonly used convolutional codes we observe that the optimized snr distribution consists of a finite number of discrete snr levels based on this observation we provide a low complexity approximation of the mmse ic decoder that suffers from very small performance degradation while attaining considerable savings in complexity as by products of this work we obtain a closed form expression of the multiuser efficiency me of power mismatched mmse filters in the large system limit and we extend the analysis of the symbol by symbol maximum a posteriori probability map multiuser detector in the large system limit to the case of nonconstant user powers and nonuniform symbol prior probabilities

off lattice anomalous diffusion in a thin sticks system abstract an off lattice monte carlo simulation of a diffusion process through a random sticks network in two dimensions is presented in this paper the statistical properties of the hindered motion are analysed according to the geometric characteristics and concentration of obstacles here represented by randomly disperse segments parallel to one another in particular short and long time behaviour of the mean square displacements are considered with respect to the type of interactions between the tracer and the sticks the diffusion coefficient is estimated and a power law dependence on the obstacle length is determined finally an application of the present results to experimental data of diffusion processes in inhomogeneous media is discussed

on the average near far resistance for mmse detection of direct sequence cdma signals with random spreading the performance of a near far resistant finite complexity minimum mean squared error mmse linear detector for demodulating direct sequence ds code division multiple access cdma signals is studied assuming that the users are assigned random signature sequences we obtain tight upper and lower bounds on the expected near far resistance of the mmse detector averaged over signature sequences and delays as a function of the processing gain and the number of users since the mmse detector is optimally near far resistant these bounds apply to any multiuser detector that uses the same observation interval and sampling rate the lower bound on near far resistance implies that even without power control linear multiuser detection provides near far resistant performance for a number of users that grows linearly with the processing gain

topology of finite graphs this paper derives from a course in group theory which i gave at berkeley in 1982 i wanted to prove the standard theorems on free groups and discovered that after a few preliminaries the notion of locally injective map or immersion of graphs was very useful this enables one to see in an effective easy algorithmic way just what happens with finitely generated free groups one can understand in this way 1 howson s theorem that if a and b are finitely generated subgroups of a free group then a b is finitely generated and 2 m hall s theorem that finitely generated subgroups of free groups are closed in the profinite topology during this course s m gersten came up with a simple proof of h neumann s inequality on the ranks in howson s theorem one of the ideas in gersten s proof was to use core graphs graphs with no trees hanging on subsequently i found that some consequences of a paper of greenberg s could be proved using core graphs and covering translations of immersions the most striking such result is that if a and b are finitely generated subgroups of a free group and if a c b is of finite index in both a and b then a b is of finite index in a v b the subgroup generated by a ub

a statistical mechanics approach to large system analysis of cdma multiuser detectors we present a theory based on statistical mechanics to evaluate analytically the performance of uncoded fully synchronous randomly spread code division multiple access cdma multiuser detectors with additive white gaussian noise awgn channel under perfect power control and in the large system limit application of the replica method a tool developed in the literature of statistical mechanics allows us to derive analytical expressions for the bit error rate as well as the multiuser efficiency of the individually optimum io and jointly optimum jo multiuser detectors over the whole range of noise levels the information theoretic capacity of the randomly spread cdma channel and the performance of decorrelating and linear minimum mean square error mmse detectors are also derived in the same replica formulation thereby demonstrating validity of the statistical mechanical approach

quasi isometrically embedded subgroups of braid and diffeomorphism groups we show that a large class of right angled artin groups in particular those with planar complementary defining graph can be embedded quasi isometrically in pure braid groups and in the group of area preserving diffeomorphisms of the disk fixing the boundary with respect to the norm metric this extends results of benaim and gambaudo who gave quasi isometric embeddings of and for all as a consequence we are also able to embed a variety of gromov hyperbolic groups quasi isometrically in pure braid groups and in the group examples include hyperbolic surface groups some hnn extensions of these along cyclic subgroups and the fundamental group of a certain closed hyperbolic 3 manifold

existence and regularity of a linear nonlocal fokker planck equation with growing drift abstract the nonlocal fokker planck equations for a class of stochastic differential equations with non gaussian stable levy motion in euclidean space are studied the existence and uniqueness of weak solution are obtained with rough drift the solution is shown to be smooth on spatial variable if all derivatives of the drift are bounded moreover the solution is jointly smooth on spatial and time variable if we assume further that the drift grows like a power of logarithm function at infinity

second order accuracy finite difference methods for space fractional partial differential equations abstract space fractional partial differential equations are used for simulations of for example diffusion of radioactive materials and financial and other models which are characterized by heavy tailed distributions a number of first order accuracy finite difference methods have been proposed in the present paper we introduce second order accuracy finite difference methods with dirichlet boundary conditions these methods have a parameter in these schemes and the parameter stabilizes the schemes this means that there exist various schemes with second order accuracy but the stability of each scheme is different in the present paper we introduce the most stable scheme for any fractional calculus order by choosing the optimal parameter in addition we describe a phenomenon whereby the expected accuracy cannot be obtained if the analytical solution can be expanded to a series having less than second order around boundaries this also happens in both existing methods and the proposed methods in the present paper we develop the stability conditions for the proposed schemes and numerical examples of second order accuracy and accuracy decay are shown

solutions for a fractional nonlinear diffusion equation spatial time dependent diffusion coefficient and external forces we analyze a generalized diffusion equation which extends some known equations such as the fractional diffusion equation and the porous medium equation we start our investigation by considering the linear case and the nonlinear case afterward the linear case is discussed taking fractional time and spatial derivatives into account in a unified approach we also discuss the modifications that emerge by employing simple drifts and the diffusion coefficient given by d x t d t x for the nonlinear case we study scaling behavior of the time in connection with the asymptotic behavior for the solution of the nonlinear fractional diffusion equation

embedddings between partially commutative groups two counterexamples abstract in this note we give two examples of partially commutative subgroups of partially commutative groups our examples are counterexamples to the extension graph conjecture and to the weakly chordal conjecture of kim and koberda 2013 12 on the other hand we extend the class of partially commutative groups for which it is known that the extension graph conjecture holds to include those with commutation graph containing no induced c 4 or p 3 in the process some new embeddings of surface groups into partially commutative groups emerge

transfer processes in fractal media an irreversible process in fractal media involves coupling relation between the space and the time the present note displays how the fractional derivation has to be introduced to describe this effect as a result the law of the chemical diffusion to a fractal is given

path lifting properties and embedding between raags abstract for a finite simplicial graph let g denote the right angled artin group on the complement graph of in this article we introduce the notions of induced path lifting property and semi induced path lifting property for immersions between graphs and obtain graph theoretical criteria for the embeddability between right angled artin groups we recover the result of s h kim and t koberda that an arbitrary g admits a quasi isometric group embedding into g t for some finite tree t the upper bound on the number of vertices of t is improved from 2 2 m 1 2 to m 2 m 1 where m is the number of vertices of we also show that the upper bound on the number of vertices of t is at least 2 m 4 lastly we show that g c m embeds in g p n for n 2 m 2 where c m and p n denote the cycle and path graphs on m and n vertices respectively

persistent random walk of cells involving anomalous effects and random death the purpose of this paper is to implement a random death process into a persistent random walk model which produces sub ballistic superdiffusion levy walk we develop a stochastic two velocity jump model of cell motility for which the switching rate depends upon the time which the cell has spent moving in one direction it is assumed that the switching rate is a decreasing function of residence running time this assumption leads to the power law for the velocity switching time distribution this describes the anomalous persistence of cell motility the longer the cell moves in one direction the smaller the switching probability to another direction becomes we derive master equations for the cell densities with the generalized switching terms involving the tempered fractional material derivatives we show that the random death of cells has an important implication for the transport process through tempering of the superdiffusive process in the long time limit we write stationary master equations in terms of exponentially truncated fractional derivatives in which the rate of death plays the role of tempering of a levy jump distribution we find the upper and lower bounds for the stationary profiles corresponding to the ballistic transport and diffusion with the death rate dependent diffusion coefficient monte carlo simulations confirm these bounds