coded continuous phase modulation with low complexity noncoherent reception coded continuous phase modulation based on a feedback free modulator with noncoherent detection is discussed low complexity receiver processing is achieved by using only two or three linear filters for demodulation and applying noncoherent sequence estimation with reduced state viterbi decoding and simple branch metric calculation overall the proposed noncoherent receiver provides significant advantages over previously presented approaches

asymptotic expansion of solutions to the drift diffusion equation with large initial data abstract we consider the large time behavior of the solution to the initial value problem for the nernst planck type drift diffusion equation in whole spaces in the l p framework the global existence and the decay of the solution were shown moreover the second order asymptotic expansion of the solution as t was derived we also deduce the higher order asymptotic expansion of the solution especially we discuss the contrast between the odd dimensional case and the even dimensional case

maximum principles extension problem and inversion for nonlocal one sided equations abstract we study one sided nonlocal equations of the form x 0 u x u x 0 x x 0 1 d x f x 0 on the real line notice that to compute this nonlocal operator of order 0 1 at a point x 0 we need to know the values of u x to the right of x 0 that is for x x 0 we show that the operator above corresponds to a fractional power of a one sided first order derivative maximum principles and a characterization with an extension problem in the spirit of caffarelli silvestre and stinga torrea are proved it is also shown that these fractional equations can be solved in the general setting of weighted one sided spaces in this regard we present suitable inversion results along the way we are able to unify and clarify several notions of fractional derivatives found in the literature

on the existence of local strong solutions to chemotaxis shallow water system with large data and vacuum abstract in this paper motivated by the chemotaxis navier stokes system arising from mathematical biology 43 a modified shallow water type chemotactic model is derived for large initial data allowing vacuum the local existence of strong solutions together with the blow up criterion is established

chemotaxis with logistic source very weak global solutions and their boundedness properties abstract we consider the chemotaxis system u t u u v g u x t 0 0 v v u x t 0 in a smooth bounded domain r n where 0 and g generalizes the logistic function g u a u b u with 1 a 0 and b 0 a concept of very weak solutions is introduced and global existence of such solutions for any nonnegative initial data u 0 l 1 is proved under the assumption that 2 1 n moreover boundedness properties of the constructed solutions are studied inter alia it is shown that if b is sufficiently large and u 0 l has small norm in l for some n 2 then the solution is globally bounded finally in the case that additionally n 2 holds a bounded set in l can be found which eventually attracts very weak solutions emanating from arbitrary l 1 initial data the paper closes with numerical experiments that illustrate some of the theoretically established results

aggregation blowup and collapse the abc s of taxis in reinforced random walks in many biological systems movement of an organism occurs in response to a diffusible or otherwise transported signal and in its simplest form this can be modeled by diffusion equations with advection terms of the form first derived by patlak bull of math biophys 15 1953 pp 311 338 however other systems are more accurately modeled by random walkers that deposit a nondiffusible signal that modifies the local environment for succeeding passages in these systems one example of which is the myxobacteria the question arises as to whether aggregation is possible under suitable hypotheses on the transition rules and the production of a control species that modulates the transition rates davis probab theory related fields 84 1990 pp 203 229 has studied this question for a certain class of random walks and here we extend this analysis to the continuum limit of such walks we first derive several general classes of partial differential equations that depend on how the movement rules are

minimum euclidean distance for combinations of short rate 1 2 convolutional codes and cpfsk modulation continuous phase frequency shift keying cpfsk is a constant amplitude modulation method with good spectral sidelobe properties good error probability properties can be obtained with coherent maximum likelihood detection in this paper we study the euclidean distance properties of signals formed by a conventional rate 1 2 convolutional encoder followed by a binary or 4 level cpfsk modulator the minimum euclidean distance is calculated for these signal sets as a function of the modulation index and the observation interval length the optimum detector is discussed for rational modulation index values the best obtainable codes are found for the case of short rate 1 2 codes with binary or 4 level cpfsk modulation lists of the best codes are given among the results are that the noncatastrophic rate 1 2 convolutional codes with optimum free hamming distance do not in general give the best euclidean distance with cpfsk

reinforced random walk leta i i 1 be a sequence of nonnegative numbers difine a nearest neighbor random motion overrightarrow x x 0 x 1 on the integers as follows initially the weight of each interval i i 1 i an integer equals 1 if at timen an interval i i 1 has been crossed exactlyk times by the motion its weight is 1 sum limits j 1 k a j given x 0 x 1 x n i0 i1 in the probability thatx n 1 isi n 1 ori n 1 is proportional to the weights at timen of the intervals i n 1 i n and i n iin 1 we prove that overrightarrow x either visits all integers infinitely often a s or visits a finite number of integers eventually oscillating between two adjacent integers a s and that mathop lim limits n to infty x n n 0 a s for much more general reinforcement schemes we provep overrightarrow x visits all integers infinitely often p overrightarrow x has finite range 1

nonlinear aggregation diffusion equations radial symmetry and long time asymptotics we analyze under which conditions equilibration between two competing effects repulsion modeled by nonlinear diffusion and attraction modeled by nonlocal interaction occurs this balance leads to continuous compactly supported radially decreasing equilibrium configurations for all masses all stationary states with suitable regularity are shown to be radially symmetric by means of continuous steiner symmetrization techniques calculus of variations tools allow us to show the existence of global minimizers among these equilibria finally in the particular case of newtonian interaction in two dimensions they lead to uniqueness of equilibria for any given mass up to translation and to the convergence of solutions of the associated nonlinear aggregation diffusion equations towards this unique equilibrium profile up to translations as t rightarrow infty

convergence of vertex reinforced jump processes to an extension of the supersymmetric hyperbolic nonlinear sigma model in this paper we define an extension of the supersymmetric hyperbolic nonlinear sigma model introduced by zirnbauer we show that it arises as a weak joint limit of a time changed version introduced by sabot and tarres of the vertex reinforced jump process it describes the asymptotics of rescaled crossing numbers rescaled fluctuations of local times asymptotic local times on a logarithmic scale endpoints of paths and last exit trees

how edge reinforced random walk arises naturally we give a characterization of a modified edge reinforced random walk in terms of certain partially exchangeable sequences in particular we obtain a characterization of an edge reinforced random walk introduced by coppersmith and diaconis on a 2 edge connected graph modifying the notion of partial exchangeability introduced by diaconis and freedman in 3 we characterize unique mixtures of reversible markov chains under a recurrence assumption

vertex reinforced random walk on arbitrary graphs vertex reinforced random walk vrrw defined by pemantle is a random process in a continuously changing environment which is more likely to visit states it has visited before we consider vrrw on arbitrary graphs and show that on almost all of them vrrw visits only finitely many vertices with a positive probability we conjecture that on all graphs of bounded degree this happens with probability 1 and provide a proof only for trees of this type we distinguish between several different patterns of localization and explicitly describe the long run structure of vrrw which depends on whether a graph contains triangles or not while the results of this paper generalize those obtained by pemantle and volkov for z 1 ideas of proofs are different and typically based on a large deviation principle rather than a martingale approach

global boundedness in a fully parabolic quasilinear chemotaxis system with singular sensitivity abstract in this paper we study the global boundedness of solutions to the quasilinear fully parabolic chemotaxis system u t d u u s u v v t v v u where bounded domain r n n 2 subject to the non flux boundary conditions the diffusivity fulfills d u a 0 u 1 with a 0 0 and 0 while the density signal governed sensitivity satisfies 0 s u b 0 u 1 and 0 v v k for b 0 0 and k r it is shown that the solution is globally bounded provided 1 and k 1 this result demonstrates the effect of signal dependent sensitivity on the blow up prevention

coded continuous phase modulation using ring convolutional codes rate 1 2 convolutional codes over the ring of integers modulo m are combined with m ary continuous phase modulation cpm schemes whose modulation indices are of the form h 1 m an m ary cpm scheme with h 1 m can be modeled by a continuous phase encoder cpe followed by a memoryless modulator mm where the cpe is linear over the ring of integers modulo m the fact that the convolutional code and the cpe are over the same algebra allows the state of the cpe to be fed back and used by the convolutional encoder a modified euclidean distance function that substantially simplifies the search for good codes has been derived and used to find new codes numerical results show that this approach consistently improves the performance as compared to coded schemes using binary convolutional codes with the same decoding complexity

the branching random walk and contact process on galton watson and nonhomogeneous trees we show that the branching random walk on a galton watson tree may have one or two phase transitions depending on the relative sizes of the mean degree and the maximum degree we show that there are some galton watson trees on which the branching random walk has one phase transition while the contact process has two this contradicts a conjecture of madras and schinazi we show that the contact process has only one phase transition on some trees of uniformly exponential growth and bounded degree contradicting a conjecture of pemantle

vertex reinforced random walk this paper considers a class of non markovian discrete time random processes on a finite state space 1 d the transition probabilities at each time are influenced by the number of times each state has been visited and by a fixed a priori likelihood matrix r which is real symmetric and nonnegative lets i n keep track of the number of visits to statei up to timen and form the fractional occupation vector v n where v i n s i n mathord left vphantom s i n left sum limits j 1 d s j n right right kern nulldelimiterspace left sum limits j 1 d s j n right it is shown thatv n converges to to a set of critical points for the quadratic formh with matrixr and that under nondegeneracy conditions onr there is a finite set of points such that with probability one v n p for somep in the set there may be more than onep in this set for whichp v n p 0 on the other handp v n p 0 wheneverp fails in a strong enough sense to be maximum forh

singularity formation in chemotaxis a conjecture of nagai consider the initial boundary value problem for the system s ut uxx uvx x vt u av on an interval 0 1 for t 0 where a 0 with ux 0 t ux 1 t 0 suppose mu v0 are positive constants the corresponding spatially homogeneous global solution u t mu v t mu a v0 mu a exp at is stable in the sense that if mu v0 are positive constants the corresponding spatially homogeneous solution will be uniformly close to u cdot v cdot we consider in sequence space an approximate system s which is related to s in the following sense the chemotactic term uvx x is replaced by the inverse fourier transform of the finite part of the convolution integral for the fourier transform of uvx x here the finite part of the convolution on the line at a point x of two functions f g is defined as int 0 x f y g y x dy we prove the following if mu a then in every neighborhood of mu v0 there are spatially nonconstant initial data for which the solution of proble

convolutional coding combined with continuous phase modulation background theory and specific coding designs for combined coding modulation schemes utilizing convolutional codes and continuous phase modulation cpm are presented in this paper the case of r 1 2 coding onto a 4 ary cpm is emphasized with short constraint length codes presented for continuous phase fsk double raised cosine and triple raised cosine modulation coding buys several decibels of coding gain over the gaussian channel with an attendant increase of bandwidth performance comparisons in the power bandwidth tradeoff with other approaches are made

structure optimization and realization of ffsk trellis codes the structure of combinations of l k binary trellis encoders and fast frequency shift keying ffsk modulation is studied a novel method for the optimization of these combinations is proposed it is concluded that regardless of the particular realization the best combinations can always be obtained by using a so called matched convolutional code optimum ffsk codes of rates 1 2 and 2 3 for up to 64 and 32 states respectively are reported it is shown that the best matched encoders for ffsk modulation are also matched and best for any ffsk type scheme where the pulse shape is required to satisfy nyquist s third criterion

vertex reinforced random walk on z has finite range a stochastic process called vertex reinforced random walk vrrw is defined in pemantle ann probab 16 1229 1241 we consider this process in the case where the underlying graph is an infinite chain i e process in the case where the underlying graph is an infinite chain i e the one dimensional integer lattice we show that the range is almost surely finite that at least five points are visited infinitely often almost surely and that with positive probability the range contains exactly five points there are always points visited infinitely often but at a set of times of zero density and we show that the number of visits to such a point to time n may be asymptotically n for a dense set of values 0 1 the power law analysis relies on analysis of a related urn model

coding cpfsk for differential demodulation a model is developed for finding codes for differentially demodulated continuous phase frequency shift keying with modulation index h 1 m where m is the size of the symbol alphabet the results of codes searches show that there is very little loss in squared euclidean distance when comparing differential codes with coherent codes

cauchy problems for keller segel type time space fractional diffusion equation abstract this paper investigates cauchy problems for nonlinear fractional time space generalized keller segel equation d t 0 c 2 b 0 where caputo derivative d t 0 c models memory effects in time fractional laplacian 2 represents levy diffusion and b s n r n x y x y n 2 y d y is the riesz potential with a singular kernel which takes into account the long rang interaction we first establish l r l q estimates and weighted estimates of the fundamental solutions p x t y x t or equivalently the solution operators s t t t then we prove the existence and uniqueness of the mild solutions when initial data are in l p spaces or the weighted spaces similar to keller segel equations if the initial data are small in critical space l p c r n p c n 2 we construct the global existence furthermore we prove the l 1 integrability and integral preservation when the initial data are in l 1 r n l p r n or l 1 r n l p c r n finally some important properties of the mild solutions including the nonnegativity preservation mass conservation and blowup behaviors are established

a decomposition approach to cpm it is shown that any continuous phase modulation cpm system can be decomposed into a continuous phase encoder and a memoryless modulator in such a way that the former is a linear modulo some integer p time invariant sequential circuit and the latter is also time invariant this decomposition is exploited to obtain alternative realizations of the continuous phase encoder and hence of cpm and also to obtain alternative forms of the optimum decoding algorithm when p is a prime p so that the encoder is linear over the finite field gf p it is shown that cascading it with an outside convolutional encoder is equivalent to a single convolutional encoder it is pointed out that the cascade of the modulator the waveform channel which it is assumed is characterized by additive white gaussian noise and the demodulator that operates over one symbol interval yield a discrete memoryless channel that can be studied without the distractions introduced by continuous phase encoding

analysis for a system of coupled reaction diffusion parabolic equations arising in biology we study a system where the equations are coupled by transport and reaction terms in the general case we prove local existence and uniqueness of the solution and in a particular case for a priori fixed time t global existence on 0 t

on the recurrence of edge reinforced random walk on z x g let g be a finite tree it is shown that edge reinforced random walk on g with large initial weights is recurrent this includes recurrence on multi level ladders of arbitrary width for edge reinforced random walk on 0 1 n g it is proved that asymptotically with high probability the normalized edge local times decay exponentially in the distance from the starting level the estimates are uniform in n they are used in the recurrence proof

global existence versus blow up in a high dimensional keller segel equation with degenerate diffusion and nonlocal aggregation abstract in this paper we study the degenerate keller segel equation with nonlocal aggregation u t u m u b u in r d r where m 1 d 3 and b u 2 u with 2 d by analyzing the interaction between the degenerate diffusion and the nonlocal aggregation we determine the conditions for initial data under which weak solutions globally exist or blow up in finite time with m 1 d d d furthermore a sharper criterion is given for global existence and finite time blow up of weak solutions with m in the subrange 2 d 2 d d d 1 d d

dynamics in a parabolic elliptic two species population competition model with cross diffusion for one species abstract this work deals with a simplified parabolic elliptic population competition model with cross diffusion for one species we first claim that this model has at least a non trivial global smooth solution and then we detect explicit parameter ranges under which the coexistence steady state and the two semi trivial steady states are globally and asymptotically stable

limit theorems for reinforced random walks on certain trees consider a linearly edge reinforced random walk defined on the b ary tree b 70 we prove the strong law of large numbers for the distance of this process from the root we give a sufficient condition for this strong law to hold for general edge reinforced random walks and random walks in a random environment we also provide a central limit theorem

joint source and channel coding using punctured ring convolutional coded cpm in this paper a novel trellis source encoding scheme based on punctured ring convolutional codes is presented joint source and channel coding jscc using trellis coded continuous phase modulation cpm with punctured convolutional codes over rings is investigated the channels considered are the additive white gaussian noise awgn channel and the rayleigh fading channel optimal soft decoding for the proposed jscc scheme is studied the soft decoder is based on the a posteriori probability app algorithm for trellis coded cpm with punctured ring convolutional codes it is shown that these systems with soft decoding outperform the same systems with hard decoding especially when the systems operate at low to medium signal to noise ratio snr furthermore adaptive jscc approaches based on the proposed source coding scheme are investigated compared with jscc schemes with fixed source coding rates the proposed adaptive approaches can achieve much better performance in the high snr region the novelties of this work are the development of a trellis source encoding method based on punctured ring convolutional codes the use of a soft decoder the app algorithm for the combined systems and the adaptive approaches to the jscc problem

application of an adams type inequality to a two chemical substances chemotaxis system abstract this paper deals with positive solutions of the fully parabolic system u t u u v in 0 1 v t v v w in 0 2 w t w w u in 0 under homogeneous neumann boundary conditions or mixed boundary conditions no flux and dirichlet conditions in a smooth bounded domain r n n 4 with positive parameters 1 2 0 and nonnegative smooth initial data u 0 v 0 w 0 in the lower dimensional case n 3 it is proved that for all reasonable initial data solutions of the system exist globally in time and remain bounded in the case n 4 it is shown that in the radially symmetric setting solutions to the neumann boundary value problem of the system exist globally in time and remain bounded if u 0 l 1 8 2 as to the mixed boundary value problem we will establish global existence and boundedness of solutions if u 0 l 1 8 2 without radial symmetry the key ingredients are a lyapunov functional and an adams type inequality a lyapunov functional of the above problems will be constructed and the constant 8 2 is deduced from the critical constant in the adams type inequality this result is regarded as a generalization of the well known 8 problem in the keller segel system to higher dimensions

on explosions of solutions to a system of partial differential equations modelling chemotaxis a system of partial differential equations modelling chemotactic aggregation is analysed keller segel model conditions on the system of paramaters are given implying global existence of smooth solutions in two space dimensions and radially symmetric situations explosion of the bacteria concentration in finite time is shown for a class of initial values

blow up and decay criteria for a model of chemotaxis for a system of equations introduced by jager and luckhaus 1992 6 as a model of chemotaxis the questions of blow up and global existence criteria are investigated specifically for a convex region a lower bound for the blow up time is derived if the solution blows up and explicit criteria to ensure non blow up are determined

representation of solutions and large time behavior for fully nonlocal diffusion equations abstract we study the cauchy problem for a nonlocal heat equation which is of fractional order both in space and time we prove four main theorems i a representation formula for classical solutions ii a quantitative decay rate at which the solution tends to the fundamental solution iii optimal l 2 decay of mild solutions in all dimensions iv l 2 decay of weak solutions via energy methods the first result relies on a delicate analysis of the definition of classical solutions after proving the representation formula we carefully analyze the integral representation to obtain the quantitative decay rates of ii next we use fourier analysis techniques to obtain the optimal decay rate for mild solutions here we encounter the critical dimension phenomenon where the decay rate attains the decay rate of that in a bounded domain for large enough dimensions consequently the decay rate does not anymore improve when the dimension increases the theory is markedly different from that of the standard caloric functions and this substantially complicates the analysis finally we use energy estimates and a comparison principle to prove a quantitative decay rate for weak solutions defined via a variational formulation our main idea is to show that the l 2 norm is actually a subsolution to a purely time fractional problem which allows us to use the known theory to obtain the result

random walks and percolation on trees there is a way to define an average number of branches per vertex for an arbitrary infinite locally finite tree it equals the exponential of the hausdorff dimension of the boundary in an appropriate metric its importance for probabilistic processes on a tree is shown in several ways including random walk and percolation where it provides points of phase transition

repulsion effects on boundedness in the higher dimensional fully parabolic attraction repulsion chemotaxis system abstract this paper deals with an attraction repulsion chemotaxis system u t d u u u v u w x t 0 1 v t v u v x t 0 2 w t w u w x t 0 under homogeneous neumann boundary conditions in a smooth bounded domain r n n 2 where parameters i i 1 2 and are positive and diffusion coefficient d u c 2 0 satisfies d u 0 for u 0 d u d u m 1 with d 0 and m 1 for all u 0 it is proved that the corresponding initial boundary value problem possesses a unique global bounded classical solution for m 2 2 n in particular in the case 1 2 and the solution is globally bounded if m 2 2 n n 2 n 2 n 2 therefore due to the inhibition of repulsion to the attraction the range of m 2 2 n of boundedness is enlarged and the results of 21 is thus extended to the higher dimensional attraction repulsion chemotaxis system with nonlinear diffusion

cauchy problem for fractional diffusion equations abstract we consider an evolution equation with the regularized fractional derivative of an order 0 1 with respect to the time variable and a uniformly elliptic operator with variable coefficients acting in the spatial variables such equations describe diffusion on inhomogeneous fractals a fundamental solution of the cauchy problem is constructed and investigated

biased random walks on galton watson trees we consider random walks with a bias toward the root on the family tree t of a supercritical galton watson branching process and show that the speed is positive whenever the walk is transient the corresponding harmonic measures are carried by subsets of the boundary of dimension smaller than that of the whole boundary when the bias is directed away from the root and the extinction probability is positive the speed may be zero even though the walk is transient the critical bias for positive speed is determined

global asymptotic stability of constant equilibria in a fully parabolic chemotaxis system with strong logistic dampening abstract this paper deals with nonnegative solutions of the neumann initial boundary value problem for the parabolic chemotaxis system u t u u v u u 2 x t 0 v t v v u x t 0 in bounded convex domains r n n 1 with smooth boundary it is shown that if the ratio is sufficiently large then the unique nontrivial spatially homogeneous equilibrium given by u v 1 is globally asymptotically stable in the sense that for any choice of suitably regular nonnegative initial data u 0 v 0 such that u 0 0 the above problem possesses a uniquely determined global classical solution u v with u v t 0 u 0 v 0 which satisfies u t 1 l 0 and v t 1 l 0 as t

continuous time vertex reinforced jump processes we study the continuous time integer valued process which jumps to each of its two nearest neighbors at the rate of one plus the total time the process has previously spent at that neighbor we show that the proportion of the time before t which this process spends at integers j converges to positive random variables v j which sum to one and whose joint distribution is explicitly described we also show

space time coded systems using continuous phase modulation we develop space time trellis coded stc schemes using continuous phase modulation cpm we employ the rimoldi model of cpm to create a decomposed model of stc cpm the decomposition separates the coding from the modulation the space time encoding and the inherent cpm encoding is combined into a single trellis encoder on the ring of integers modulo this is followed by a bank of memoryless modulators the model allows the search for good space time codes to take into account the inherent encoding of the modulation

bayesian analysis for reversible markov chains we introduce a natural conjugate prior for the transition matrix of a reversible markov chain this allows estimation and testing the prior arises from random walk with reinforcement in the same way the dirichlet prior arises from polya s urn we give closed form normalizing constants a simple method of simulation from the posterior and a characterization along the lines of w e johnson s characterization of the dirichlet prior

the basin of attraction of the steady states for a chemotaxis model in mathbb r 2 with critical mass we consider the cauchy problem for a parabolic elliptic system in mathbb r 2 which is amathematical model of chemotaxis and also amodel of self attracting particles in the critical mass case we determine the basin of attraction of the steady states for the cauchy problem through a lyapunov functional

inverting ray knight identity we provide a short proof of the ray knight second generalized theorem using a martingale which can be seen on the positive quadrant as the radon nikodym derivative of the reversed vertex reinforced jump process measure with respect to the markov jump process with the same conductances next we show that a variant of this process provides an inversion of that ray knight identity we give a similar result for the ray knight first generalized theorem

unboundedness for solutions to a degenerate drift diffusion equation with the l1 supercritical and the energy subcritical exponent abstract we consider large time behavior of weak solutions to a degenerate drift diffusion system related to keller segel system with the l 1 supercritical and the energy subcritical cases under relaxed weight condition it is known that the large time behavior of solutions is classified by the invariant norms of initial data for the l 1 critical case ogawa wakui proved that the negative entropy condition induces the unboundedness of corresponding solutions with the initial data decaying slowly at spacial infinity here the result is a continuous analogy of the l 1 critical case analogous results have been obtained in the theory of nonlinear schrodinger equations

the diffusion limit of transport equations ii chemotaxis equations in this paper we use the diffusion limit expansion of transport equations developed earlier t hillen and h g othmer siam j appl math 61 2000 pp 751 775 to study the limiting equation under a variety of external biases imposed on the motion when applied to chemotaxis or chemokinesis these biases produce modification of the turning rate the movement speed or the preferred direction of movement depending on the strength of the bias it leads to anisotropic diffusion to a drift term in the flux or to both in the parabolic limit we show that the classical chemotaxis equation which we call the patlak keller segel alt pksa equation arises only when the bias is sufficiently small using this general framework we derive phenomenological models for chemotaxis of flagellated bacteria of slime molds and of myxobacteria we also show that certain results derived earlier for one dimensional motion can easily be generalized to two or three dimensional motion as well

global existence and blow up of solutions of the cauchy problem for a time fractional diffusion system abstract we prove sharp blow up and global existence results for the cauchy problem of a time fractional diffusion system when initial values u 0 0 and v 0 0 the critical exponent of this problem is determined

a de giorgi nash type theorem for time fractional diffusion equations we study the regularity of weak solutions to linear time fractional diffusion equations in divergence form of arbitrary time order alpha in 0 1 the coefficients are merely assumed to be bounded and measurable and they satisfy a uniform parabolicity condition our main result is a de giorgi nash type theorem which gives an interior holder estimate for bounded weak solutions in terms of the data and the l infty bound of the solution the proof relies on new a priori estimates for time fractional problems and uses de giorgi s technique and the method of non local growth lemmas which has been introduced recently in the context of nonlocal elliptic equations involving operators like the fractional laplacian

phase transition for the once reinforced random walk on mathbb z d like trees in this short paper we consider the once reinforced random walk with reinforcement parameter a on trees with bounded degree which are transient for the simple random walk on each of these trees we prove that there exists an explicit critical parameter a 0 such that the once reinforced random walk is almost surely recurrent if a a 0 and almost surely transient if a a 0 this provides the first examples of phase transition for the once reinforced random walk

spectrum distance and receiver complexity of encoded continuous phase modulation a comparison of different classes of encoded continuous phase modulation cpm schemes is presented in terms of joint power bandwidth performance it is found that coded eight level systems are better than coded four level systems and that partial response signalling is better than full response signalling in general the price paid for better performance is increased receiver complexity heuristic design rules have been used to find good codes for cpm in most cases the coding gains found are identical to published results that were generated by exhaustive search indicating that the choice of design rules is quite appropriate in the present study bandwidth efficiency is considered from both the 99 and 99 9 power bandwidth points of view it is found that partial response signalling is even more jointly power and bandwidth efficient for the latter than for the former bandwidth criterion

global existence of solutions for a strongly coupled quasilinear parabolic system we are interested in existence uniqueness and a priori estimates of non negative solutions to the following problem begin gathered u t delta left left 1 alpha v right u right uf u v hfill v t delta v vg u v quad in 0 infty times omega hfill u v 0 quad in 0 infty times partial omega hfill u 0 u 0 v 0 v 0 quad in omega hfill end gathered 1 0

formes de dirichlet generales et densite des variables aleatoires reelles sur l espace de wiener abstract it is shown that the main properties of dirichlet spaces can be proved without the classical local compacity hypothesis to this purely measurable framework we extend the functional calculus and the energy image density property these results are then applied to the ornstein uhlenbeck semi group on wiener space where it is obtained that the real random variables which are solutions of lipschitzian stochastic differential equations always have probability densities after perhaps an initial deterministic phase

local null controllability for a chemotaxis system of parabolic elliptic type abstract we consider the controllability of a chemotaxis system of parabolic elliptic type by linearizing the nonlinear system into two separate linear equations we can bypass the obstacle caused by the nonlinear drift term and establish local null controllability of the original nonlinear system this approach is different from the usual method for dealing with coupled parabolic systems

design of ring convolutional trellis codes for map decoding of mpeg 4 images we propose a trellis coded modulation system using continuous phase frequency shift keying cpfsk and ring convolutional codes for transmitting the bits generated by an embedded zerotree wavelet encoder improved performance is achieved by using maximum a posteriori decoding of the zerotree symbols and ring convolutional trellis codes are determined for this decoding method the cpfsk transmitter is decomposed into a memoryless modulator and a continuous phase encoder over the ring of integers modulo 4 the latter is combined with a polynomial convolutional encoder over the same ring in the code design process a search is made of the combined trellis where the branch metrics are modified to include the source transition matrix simulation results of image transmission are provided using the optimized system including mismatched channel cases

stability of constant steady states and existence of unbounded solutions in time to a reaction diffusion equation modelling chemotaxis abstract we consider the initial boundary value problem to a reaction diffusion equation modelling chemotaxis in one space dimension under neumann boundary conditions we study the stability of constant steady states and show that there exists an unbounded solution in time induced by the instability of constant steady states

a parabolic problem with a fractional time derivative we study regularity for a parabolic problem with fractional diffusion in space and a fractional time derivative our main result is a de giorgi nash moser holder regularity theorem for solutions in a divergence form equation we also prove results regarding existence uniqueness and higher regularity in time

rate 1 2 component codes for nonbinary turbo codes the iterative decoding structure and component maximum a posteriori decoders used for decoding binary concatenated codes can be extended to the nonbinary domain this paper considers turbo codes over nonbinary rings specifically ternary quaternary penternary hexernary and octernary codes the best rate 1 2 component codes are determined using a practical search algorithm the performance of the resulting rate 1 3 turbo codes on an additive white gaussian noise channel using q ary phase shift keying modulation is given

global solutions in a fully parabolic chemotaxis system with singular sensitivity and nonlinear signal production a fully parabolic chemotaxis system with singular sensitivity and nonlinear signal production is considered under suitable assumption on the sensitivity value and the signal production term it is shown that this system admits a global classical solution the proof is based on a series of a priori estimate techniques a fully parabolic chemotaxis system with singular sensitivity and nonlinear signal production is considered under suitable assumption on the sensitivity value and the signal production term it is shown that this system admits a global classical solution the proof is based on a series of a priori estimate techniques

on the transience of processes defined on galton watson trees we introduce a simple technique for proving the transience of certain processes defined on the random tree mathcal g generated by a supercritical branching process we prove the transience for once reinforced random walks on mathcal g that is a generalization of a result of durrett kesten and limic probab theory related fields 122 2002 567 592 moreover we give a new proof for the transience of a family of biased random walks defined on mathcal g other proofs of this fact can be found in ann probab 16 1988 1229 1241 and ann probab 18 1990 931 958 as part of more general results a similar technique is applied to a vertex reinforced jump process a by product of our result is that this process is transient on the 3 ary tree davis and volkov probab theory related fields 128 2004 42 62 proved that a vertex reinforced jump process defined on the b ary tree is transient if b 4 and recurrent if b 1 the case b 2 is still open

fractional stochastic differential equations satisfying fluctuation dissipation theorem we propose in this work a fractional stochastic differential equation fsde model consistent with the over damped limit of the generalized langevin equation model as a result of the fluctuation dissipation theorem the differential equations driven by fractional brownian noise to model memory effects should be paired with caputo derivatives and this fsde model should be understood in an integral form we establish the existence of strong solutions for such equations and discuss the ergodicity and convergence to gibbs measure in the linear forcing regime we show rigorously the algebraic convergence to gibbs measure when the fluctuation dissipation theorem is satisfied and this verifies that satisfying fluctuation dissipation theorem indeed leads to the correct physical behavior we further discuss possible approaches to analyze the ergodicity and convergence to gibbs measure in the nonlinear forcing regime while leave the rigorous analysis for future works the fsde model proposed is suitable for systems in contact with heat bath with power law kernel and subdiffusion behaviors

serially concatenated continuous phase modulation with convolutional codes over rings in this paper we investigate serially concatenated continuous phase modulation sccpm with convolutional codes cc over rings the transmitted signals are disturbed by additive white gaussian noise the properties for systems with both infinite and finite block lengths are investigated for an infinite length system we check the convergence threshold using the extrinsic information transfer chart for a finite length system we use union bound techniques to estimate the error floors in the union bound analysis we consider both the order and the position of nonzero permuted symbols a simple method for determining a cpm error event through the sum of the input symbol sequence is shown thus we can determine if the output symbol sequence of an error event in the ring cc can form an error event in cpm two properties concerning the interleaver gain ig are investigated a recursive search algorithm for the maximal ig is shown compared with previous sccpm with a binary cc the proposed system shows an improvement concerning the convergence threshold or error floors

once edge reinforced random walk on a tree we consider a nearest neighbor walk on a regular tree with transition probabilities proportional to weights or conductances of the edges initially all edges have weight 1 and the weight of an edge is increased to c 1 when the edge is traversed for the first time after such a change the weight of an edge stays at c forever we show that such a walk is transient for all values of c ge 1 and that the walk moves off to infinity at a linear rate we also prove an invariance principle for the height of the walk

trellis coded continuous phase frequency shift keying with ring convolutional codes trellis coding techniques are applied to continuous phase frequency shift keying cpfsk a new coding scheme based on convolutional codes on the ring of integers modulo p is shown to be a natural way to apply trellis coding to cpfsk previous work has decomposed cpfsk into two parts a linear encoder with memory called the continuous phase encoder cpe and a memoryless modulator mm where the cpe often has a code structure defined over the ring of integers modulo p the combination of a modulo p convolutional channel encoder ce and the cpe is a linear modulo p encoder design examples are given for rate 1 2 coded quaternary cpfsk with modulation indexes 1 2 and 1 4 and rate 2 3 coded octal cpfsk with modulation index 1 8 combinations are optimized in the normalized minimum euclidean distance sense for a given total number of states in the overall mlse receiver numerical results show that this new coding scheme consistently obtains better performance than previous schemes

better rate 1 2 coded continuous phase modulation schemes and the m algorithm continuous phase modulation cpm signals may be precoded by a convolutional code followed by a mapping rule better codes may however be obtained by a more general code formed by a finite state machine we provide improved codes for one such finite state machine a new description of codes and design rules are presented better results are demonstrated for the partial response cpm schemes and previous optimum results are matched for the full response case tests of an m algorithm decoder achieve near maximum likelihood performance with only a fraction of the complexity of the viterbi algorithm

serially concatenated continuous phase modulation with iterative decoding serially concatenated and interleaved continuous phase modulation cpm with iterative decoding is investigated an a posteriori probability app algorithm for cpm is developed based on the classic app algorithm for channel codes the system is analyzed through upper bounds on the average bit error probability for coded and interleaved minimum shift keying the weight spectrum is computed resulting in a transfer function bound this is cumbersome for a general cpm system instead only the most significant error events contributing to the weight spectrum are identified simulations show that firstly these events give a satisfactory view of system performance when equal outer codes are used and secondly that remarkably good performance can be obtained for some simple systems finally power spectral densities and bandwidths are computed allowing for a bandwidth performanee comparison of different combinations

energy type estimates and global solvability in a two dimensional chemotaxis haptotaxis model with remodeling of non diffusible attractant this paper deals with the coupled chemotaxis haptotaxis model ut u u v u w u 1 u w x t 0 0 v u v x t 0 wt vw w 1 w u x t 0 which was initially proposed by chaplain and lolas 2006 10 to describe the interactions between cancer cells the matrix degrading enzyme and the host tissue in a process of cancer cell invasion of tissue extracellular matrix here r2 is a bounded domain with smooth boundary and and are positive parameters as compared to previous mathematical studies the novelty here consists of allowing for positive values of reflecting processes of self remodeling of the extracellular matrix under zero flux boundary conditions it is shown that for any sufficiently smooth initial data u0 w0 satisfying first order compatibility conditions the model admits a unique global smooth solution a crucial ingredient in the proof is an energy like inequality which given t 0 yields boundedness of u t in llogl this serves as a starting point for a bootstrap argument used to derive higher regularity estimates sufficient for global extensibility of solutions

phase transition in reinforced random walk and rwre on trees a random walk on an infinite tree is given a particular kind of positive feedback so edges already traversed are more likely to be traversed in the future using exchangeability theory the process is shown to be equivalent to a random walk in a random environment rwre that is to say a mixture of markov chains criteria are given to determine whether a rwre is transient or recurrent these criteria apply to show that the reinforced random walk can vary from transient to recurrent depending on the value of an adjustable parameter measuring the strength of the feedback the value of the parameter at the phase transition is calculated

design of coded cpfsk modulation systems for bandwidth and energy efficiency consideration is given to the problems related to the design of m ary continuous phase frequency shift keying cpfsk systems with modulation index h j m combined with eternal rate r binary convolution encoders the following questions are raised and answered 1 how should different encoder modulator systems be compared and how can comparable systems be recognized from the system parameters i e m h and r 2 what are the limits on the information rate per unit bandwidth versus signal to noise ratio when reliable transmission is required 3 how does one choose the system parameters m h and r when the overall system has to achieve a specified performance and 4 how does one design the external rate r binary convolutional encoder to put in front of the m ary cpfsk modulation system with h j m a simple approximation for the bandwidth of a cpfsk signal is given and shown to be sufficiently accurate for system design purposes the design of the external convolutional encoder is carried out in a novel way that leads to fewer states in the combined encoder modulator system and thus yields improved performance for a given demodulation decoding complexity compared to previous approaches for the design of coded cpfsk systems