on equations of kp type we discuss the local cauchy problem for the generalised kadomtsev petviashvili equation namely in the periodic and nonperiodic settings

global well posedness for the kp i equation on the background of a non localized solution we prove that the cauchy problem for the kp i equation is globally well posed for initial data which are localized perturbations of arbitrary size of a non localized i e not decaying in all directions traveling wave solution e g the kdv line solitary wave or the zaitsev solitary waves which are localized in x and y periodic or conversely

duration of transient oscillations in ring networks of unidirectionally coupled neurons abstract properties of the duration of long lasting transient oscillations in ring networks of unidirectionally coupled sigmoidal neurons are derived with a kinematical model of traveling waves in the network the duration of the transient oscillations occurring from random initial conditions increases exponentially as the number of neurons the distribution of the duration is approximated by a power law function when the number of neurons is large further transient oscillations which oscillate about one thousand cycles before ceasing are observed in a network of forty neurons in circuit experiments though the duration decreases owing to random biases

phase locked patterns and amplitude death in a ring of delay coupled limit cycle oscillators we study the existence and stability of phase locked patterns and amplitude death states in a closed chain of delay coupled identical limit cycle oscillators that are near a supercritical hopf bifurcation the coupling is limited to nearest neighbors and is linear we analyze a model set of discrete dynamical equations using the method of plane waves the resultant dispersion relation which is valid for any arbitrary number of oscillators displays important differences from similar relations obtained from continuum models we discuss the general characteristics of the equilibrium states including their dependencies on various system parameters we next carry out a detailed linear stability investigation of these states in order to delineate their actual existence regions and to determine their parametric dependence on time delay time delay is found to expand the range of possible phase locked patterns and to contribute favorably toward their stability the amplitude death state is studied in the parameter space of time delay and coupling strength it is shown that death island regions can exist for any number of oscillators n in the presence of finite time delay a particularly interesting result is that the size of an island is independent of n when n is even but is a decreasing function of n when n is odd

strichartz inequalities and the nonlinear schrodinger equation on compact manifolds kklwe prove strichartz estimates with fractional loss of derivatives for the schrodinger equation on any riemannian compact manifold as a consequence we infer low regularity local well posedness results in any dimension as well as global existence results for the cauchy problem of nonlinear schrodinger equations on surfaces in the case of defocusing polynomial nonlinearities and on three manifolds in the case of cubic defocusing nonlinearities we also discuss the optimality of these strichartz estimates on spheres

periodic patterns in a ring of delay coupled oscillators we describe the appearance and stability of spatiotemporal periodic patterns rotating waves in unidirectional rings of coupled oscillators with delayed couplings we show how delays in the coupling lead to the splitting of each rotating wave into several new ones the appearance of rotating waves is mediated by the hopf bifurcations of the symmetric equilibrium we also conclude that the coupling delays can be effectively replaced by increasing the number of oscillators in the chain the phenomena are shown for the stuart landau oscillators as well as for the coupled fitzhugh nagumo systems modeling an ensemble of spiking neurons interacting via excitatory chemical synapses

generalized union bound for space time codes gallager s second bounding technique also known as the generalized union bound is employed to derive a new upper bound on the error probability of space time codes stcs with maximum likelihood ml decoding on quasi static rayleigh fading channels the new bound is distinguished by two characteristics unlike the classical union bound the new bound is rapidly convergent and is only a few decibels away from simulation results and compared with gallager s first bound it has better computational efficiency and numerical stability hence the new bound is a useful tool for performance analysis and computer search of good stcs moreover the correlation between fading coefficients is easily accommodated by the new bound the application of the new bound to convolutional coding on block fading channels is also demonstrated and an improved version is derived for the bit error probability of maximum a posteriori probability decoding

the cauchy problem for the rotation modified kadomtsev petviashvili type equation abstract this paper is devoted to studying the cauchy problem for the rotation modified kadomtsev petviashvili rmkp type equation x u t x 3 u x u 2 y 2 u u 0 in the anisotropic sobolev spaces h s 1 s 2 r 2 when 0 and 0 0 we show that the cauchy problem is locally well posed in h s 1 s 2 r 2 with s 1 1 2 and s 2 0 the main difficulty in establishing bilinear estimates related to nonlinear term of rmkp type equation is that the resonant function 3 1 2 1 2 1 2 2 2 1 2 1 2 1 1 2 2 2 may tend to zero since 0 0 and 0 when 0 and 0 and 0 we also prove that the cauchy problem for rmkp equation is ill posed in h s 1 0 r 2 with s 1 1 2 in the sense that the flow map associated to the rotation modified kadomtsev petviashvili is not c 3

stability of the line soliton of the kp ii equation under periodic transverse perturbations we prove the nonlinear stability of the kdv solitary waves considered as solutions of the kp ii equation with respect to periodic transverse perturbations our proof uses a miura transform which sends the solutions of an mkp ii equation to solutions of the kp ii equation

periodic solutions of kadomtsev petviashvili on etablit l existence de solutions globales pour l equation non lineaire de kadomtsev petviashvili u t uu x u xxx d 1 u yy periodiques en x et en y et d 1 denote la primitive en x

multistability in spiking neuron models of delayed recurrent inhibitory loops we consider the effect of the effective timing of a delayed feedback on the excitatory neuron in a recurrent inhibitory loop when biological realities of firing and absolute refractory period are incorporated into a phenomenological spiking linear or quadratic integrate and fire neuron model we show that such models are capable of generating a large number of asymptotically stable periodic solutions with predictable patterns of oscillations we observe that the number of fixed points of the so called phase resetting map coincides with the number of distinct periods of all stable periodic solutions rather than the number of stable patterns we demonstrate how configurational information corresponding to these distinct periods can be explored to calculate and predict the number of stable patterns

stochastic switching in delay coupled oscillators a delay is known to induce multistability in periodic systems under influence of noise coupled oscillators can switch between coexistent orbits with different frequencies and different oscillation patterns for coupled phase oscillators we reduce the delay system to a nondelayed langevin equation which allows us to analytically compute the distribution of frequencies and their corresponding residence times the number of stable periodic orbits scales with the roundtrip delay time and coupling strength but the noisy system visits only a fraction of the orbits which scales with the square root of the delay time and is independent of the coupling strength in contrast the residence time in the different orbits is mainly determined by the coupling strength and the number of oscillators and only weakly dependent on the coupling delay finally we investigate the effect of a detuning between the oscillators we demonstrate the generality of our results with delay coupled fitzhugh nagumo oscillators

error probability for digital transmission over nonlinear channels with application to tcm the computation of upper and lower bounds to error probability in digital transmission over nonlinear channels with a finite memory is considered by using orthogonal volterra series the authors derive a canonical representation for discrete nonlinear systems based on a linear convolutional code and a memoryless mapper this representation shows that finite memory discrete nonlinear systems can be analyzed in much the same way as tcm trellis coded modulation schemes in particular tcm over nonlinear channels can be analyzed a technique is derived that expresses an upper bound to error probability based on the computation of the transfer of a state diagram with n branches and whose branch labels are matrices rather than scalars some examples of its application are given in particular error bounds are derived for nonlinear tcm schemes and for tcm schemes operating on nonlinear channels

on joint source and channel coding using trellis coded cpm analytical bounds on the channel distortion joint source and channel coding jscc using trellis coded quantization tcq in conjunction with trellis coded continuous phase modulation cpm is studied the channel is assumed to be the additive white gaussian noise awgn channel analytical bounds on the channel distortion for the investigated systems with maximum likelihood sequence detection mlsd are developed the bounds are based on the transfer function technique which was modified and generalized to include continuous amplitude discrete time signals for a memoryless uniform source the constructed bounds for the investigated systems are shown to be asymptotically tight for increasing channel signal to noise ratio snr values for a memoryless nonuniform source the constructed bounds are not as tight as the one for the uniform source however it still can be used as an indication to how the system performs it is concluded that the minimum euclidean distance of the system alone is not enough to evaluate the performance of the considered systems the number of error events having minimum euclidean distance and the total distortion caused by those error events also affect the asymptotic performance this work provides an analysis tool for the investigated systems the analysis method is very general it may be applied to any trellis based jscc schemes

waves and patterns in ring lattices with delays abstract we investigate the existence and the stability of waves and phase locked states in rings of coupled oscillators with delayed interactions using center manifold reduction and the normal form method we reduce the equation governing the dynamics of the whole network to an amplitude phase model i e a set of coupled ordinary differential equations describing the evolution of both the amplitudes and the phases of the oscillators then we prove the existence of traveling waves in phase and anti phase locked oscillations in both one dimensional and two dimensional lattices the influence of the interaction strength and the number of oscillators is investigated and the possible coexistence of waves and phase locked oscillations is shown

global well posedness for the kp i equation we prove the global well posedness of the kp i equation in bbb r 2 for data of arbitrary size in a suitable sobolev class we use a compactness method to get local solutions we extend the solutions thanks to some conservation laws an almost conserved quantity and strichartz estimates

stability and instability of the kdv solitary wave under the kp i flow we consider the kp i and gkp i equations in mathbb r times mathbb r 2 pi mathbb z we prove that the kdv soliton with subcritical speed 0 c in the spirit of the work by duyckaerts and merle gafa 18 1787 1840 2009 we sharpen our previous instability result and construct a global solution which is different from the solitary wave and its translates and which converges to the solitary wave as time goes to infinity this last result also holds for the gkp i equation

low regularity for the fifth order kadomtsev petviashvili i type equation abstract the cauchy problem of the fifth order kadomtsev petviashvili i equation fifth kp i 0 1 t u x 5 u x 3 u x 1 y y u x u 2 0 x y t r 3 is considered it follows that the fifth order kadomtsev petviashvili i equation 0 1 is locally well posed in h s 0 with s 3 4 where the norm h s r is defined by f h x y s r s r f l 2

performance of space time codes gallager bounds and weight enumeration since the standard union bound for space time codes may diverge in quasi static fading channels the limit before average lba technique has been exploited to derive tight performance bounds however it suffers from the computational burden arising from a multidimensional integral in this paper efficient bounding techniques for space time codes are developed in the framework of gallager bounds two closed form upper bounds the ellipsoidal bound and the spherical bound are proposed that come close to simulation results within a few tenths of a decibel in addition two novel methods of weight enumeration operating on a further reduced state diagram are presented which in conjunction with the bounding techniques give a thorough treatment of performance bounds for space time codes

delay and periodicity systems with time delay play an important role in modeling of many physical and biological processes in this paper we describe generic properties of systems with time delay which are related to the appearance and stability of periodic solutions in particular we show that delay systems generically have families of periodic solutions which are reappearing for infinitely many delay times as delay increases the solution families overlap leading to increasing coexistence of multiple stable as well as unstable solutions we also consider stability issue of periodic solutions with large delay by explaining asymptotic properties of the spectrum of characteristic multipliers we show that the spectrum of multipliers can be split into two parts pseudocontinuous and strongly unstable the pseudocontinuous part of the spectrum mediates destabilization of periodic solutions

on the asymptotic behavior of solutions to the generalized kadomtsev petviashvili burgers equations we show global existence and sharp results on the asymptotic decay of solutions to the generalized kp equations with a power nonlinearityupuxand with a burgers type dissipation in the main direction of propagation appended furthermore we prove that forp n the decay rate of thel2 norm of the solution of these equations is that exhibited by the solution of these same equations linearized around the zero solution and that forp 2 this also holds for thel norm this limitation seems due to the presence of a dispersive effect in the transverse direction

synchronized states in a ring of mutually coupled self sustained electrical oscillators we investigate in this paper different states of synchronization in a ring of mutually coupled self sustained electrical oscillators the good coupling parameters leading to complete and partial synchronization or disordered states are calculated using the properties of the variational equations of stability a stability map showing domains of synchronization to an external excitation locally injected in the ring is also obtained in both cases the numerical simulation validates and complements the results of the analytical investigation

efficient computation of trellis code generating functions for trellis codes generating function techniques provide the distance spectrum and a union bound on bit error rate the computation of the generating function of a trellis code may be separated into two stages the first stage reduces the number of states as much as possible using low complexity approaches the second stage produces the generating function from the reduced state diagram through some form of matrix inversion which has a relatively high complexity in this paper we improve on the amount of state reduction possible during the low complexity first stage we also show that for a trellis code that is a linear convolutional code followed by a signal mapper the number of states may always be reduced from n sup 2 to n sup 2 n 2 1 using low complexity techniques finally we analytically compare the complexity of various matrix inversion techniques and verify through simulation that the two stage approach we propose has the lowest complexity in an example the new technique produced the union bound in about half the time required by the best algorithm already in the literature

reduced state representations for trellis codes using constellation symmetry this paper presents a symmetry based technique for trellis code state diagram reduction that has more general applicability than the quasi regularity technique of rouanne et al and zehavi et al for trellis codes using standard constellations and labelings for a 2 sup spl nu x state trellis code the new technique reduces the 2 sup 2 spl nu x state diagram to 2 sup spl nu x spl nu q state diagram where 0 spl les spl nu sub q spl les spl nu sub x the particular value of spl nu sub q depends on the constellation labeling and the convolutional encoder for standard rate k k 1 set partitioned trellis codes spl nu sub q 0 and the overall number of states is the same with the new technique as with quasi regularity for codes that are not quasi regular and thus not amenable to the quasi regularity technique the new technique often provides some improvement when spl nu sub q spl nu sub x for 8 phase shift keying trellis codes the new technique always yields spl nu sub q 0

multiple scale analysis of delayed dynamical systems abstract the model equations of a semiconductor laser with delayed feeback are studied as a prototype of general delayed systems in the case of long delay thermodynamic limit it is shown that its behaviour in the vicinity of the hopf bifurcation can be described by suitable amplitude equations the derivation of the final model follows naturally from the space time representation of the evolution and by the corresponding re formulation of the linear stability problem regions characterized by both direct and inverse hopf bifurcations are found and in particular parameter values are identified for which a chaotic evolution is expected

how can we speed up matrix multiplication due to the new algebraic methods of algorithm design recently it became possible to perform multiplication and inversion of n times n matrices using o n 2 496 rather than o n 3 arithmetical operations consequently algorithms for several other computational problems of linear algebra and combinatorics have been accelerated the major ideas and techniques that have led to that progress are surveyed

on the computation of weight enumerators for convolutional codes performance bounds for maximum likelihood decoding of convolutional codes over memoryless channels are commonly measured using the distance weight enumerator t x y also referred to as the transfer function of the code this paper presents an efficient iterative method to obtain t x y called the state reduction algorithm the algorithm is a systematic technique to simplify signal flow graphs that algebraically manipulate the symbolic adjacency matrix associated with the convolutional code next the algorithm is modified to compute the first few terms of the series expansion of t 1 y and spl part t x y spl part x sub x 1 the distance spectra without first computing the complete t x y

information storage loop motifs and clustered structure in complex networks we use a standard discrete time linear gaussian model to analyze the information storage capability of individual nodes in complex networks given the network structure and link weights in particular we investigate the role of two and three node motifs in contributing to local information storage we show analytically that directed feedback and feedforward loop motifs are the dominant contributors to information storage capability with their weighted motif counts locally positively correlated to storage capability we also reveal the direct local relationship between clustering coefficient s and information storage these results explain the dynamical importance of clustered structure and offer an explanation for the prevalence of these motifs in biological and artificial networks

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

destabilization patterns in chains of coupled oscillators we describe the mechanism of destabilization in a chain of identical coupled oscillators along with the transition from stationary to oscillatory behavior of the single oscillator the network undergoes a complicated bifurcation scenario including the coexistence of multiple periodic orbits with different frequencies spatial patterns and modulation instabilities this scenario which is similar to the well known eckhaus scenario in spatially extended systems occurs here also in the case of purely convective unidirectional coupling and hence it cannot be explained as a simple discretization of its spatially continuous counterpart although the number of coexisting periodic orbits grows with the number of oscillators we are able to treat this problem independently of the actual size of the network by investigating the limiting equations for the related spectral problems

uniform distance and error probability properties of tcm schemes the class of uniform trellis coded modulation tcm techniques is defined and simple explicit conditions for uniformity are derived uniformity is shown to depend on the metric properties of the two subconstellations resulting from the first step in set partitioning as well as on the assignment of binary labels to channel symbols the uniform distance property and uniform error property which are both derived from uniformity but are not equivalent are discussed the derived concepts are extended to encompass transmission over a not necessarily gaussian memoryless channel in which the metric used for detection may not be maximum likelihood an appropriate distance measure is defined that generalizes the euclidean distance it is proved that uniformity of a tcm scheme can also be defined under this new distance the results obtained are shown to hold for channels with phase offset or independent amplitude only fading examples are included to illustrate the applicability of the results

geometrically uniform codes a signal space code c is defined as geometrically uniform if for any two code sequences in c there exists an isometry that maps one sequence into the other while leaving the code c invariant geometrical uniformity a strong kind of symmetry implies such properties as a the distance profiles from code sequences in c to all other code sequences are all the same and b all voronoi regions of code sequences in c have the same shape it is stronger than ungerboeck zehavi wolf symmetry or calderbank sloane regularity nonetheless most known good classes of signal space codes are shown to be generalized coset codes and therefore geometrically uniform including a lattice type trellis codes based on lattice partitions lambda lambda such that z sup n lambda lambda 4z sup n is a lattice partition chain and b phase shift keying psk type trellis codes based on up to four way partitions of a 2 sup n psk signal set

embedding the dynamics of a single delay system into a feed forward ring we investigate the relation between the dynamics of a single oscillator with delayed self feedback and a feed forward ring of such oscillators where each unit is coupled to its next neighbor in the same way as in the self feedback case we show that periodic solutions of the delayed oscillator give rise to families of rotating waves with different wave numbers in the corresponding ring in particular if for the single oscillator the periodic solution is resonant to the delay it can be embedded into a ring with instantaneous couplings we discover several cases where the stability of a periodic solution for the single unit can be related to the stability of the corresponding rotating wave in the ring as a specific example we demonstrate how the complex bifurcation scenario of simultaneously emerging multijittering solutions can be transferred from a single oscillator with delayed pulse feedback to multijittering rotating waves in a sufficiently large ring of oscillators with instantaneous pulse coupling finally we present an experimental realization of this dynamical phenomenon in a system of coupled electronic circuits of fitzhugh nagumo type

nondegeneracy morse index and orbital stability of the kp i lump solution using backlund transformation we analyze the spectral property of the kp i lump solution it is proved that the lump is nondegenerate and its morse index equals one as a consequence we show that it is orbitally stable

emergence and combinatorial accumulation of jittering regimes in spiking oscillators with delayed feedback interaction via pulses is common in many natural systems especially neuronal in this article we study one of the simplest possible systems with pulse interaction a phase oscillator with delayed pulsatile feedback when the oscillator reaches a specific state it emits a pulse which returns after propagating through a delay line the impact of an incoming pulse is described by the oscillator s phase reset curve prc in such a system we discover an unexpected phenomenon for a sufficiently steep slope of the prc a periodic regular spiking solution bifurcates with several multipliers crossing the unit circle at the same parameter value the number of such critical multipliers increases linearly with the delay and thus may be arbitrary large this bifurcation is accompanied by the emergence of numerous jittering regimes with nonequal interspike intervals isis each of these regimes corresponds to a periodic solution of the system with a period roughly proportional to the delay the number of different jittering solutions emerging at the bifurcation point increases exponentially with the delay we describe the combinatorial mechanism that underlies the emergence of such a variety of solutions in particular we show how a periodic solution exhibiting several distinct isis can imply the existence of multiple other solutions obtained by rearranging of these isis we show that the theoretical results for phase oscillators accurately predict the behavior of an experimentally implemented electronic oscillator with pulsatile feedback

interaction of chaotic rotating waves in coupled rings of chaotic cells abstract the interaction of two chaotic rotating waves of the type recently reported by matias et al europhys lett 37 1997 379 is studied experimentally with arrays of non linear electronic circuits arranged in ring geometries unidirectional coupling is assumed for the cell to cell coupling within the same ring but between rings cells are coupled diffusively depending on the relative sense of driving competition between a rotating chaotic wave and a global synchronized state has been observed the results are rationalized by means of a linear stability analysis around the uniform synchronized behavior where the circulant symmetry of the system allows to express the problem as a superposition of a series of fourier modes

gain of regularity for the kp i equation abstract in this paper we study the smoothness properties of solutions to the kp i equation we show that the equation s dispersive nature leads to a gain in regularity for the solution in particular if the initial data possesses certain regularity and sufficient decay as x then the solution u t will be smoother than for 0 t t where t is the existence time of the solution