convergence of vector quantizers with applications to optimal quantization suppose that a sequence of probability distribution functions f n converges weakly to a distribution function f does the sequence of optimal quantizers for the f n s converge to an optimal quantizer for f if so do the respective distortions converge to the optimal distortion for f sufficient conditions are given to guarantee the convergence for both scalar and vector quantizers with a general class of distortion measures these results are used to prove the existence of minimum rth power distortion vector quantizers and the convergence of a proposed algorithm for constructing optimal quantizers

control of unstable steady states by extended time delayed feedback time delayed feedback methods can be used to control unstable periodic orbits as well as unstable steady states we present an application of extended time delay autosynchronization introduced by socolar et al phys rev e 50 3245 1994 to an unstable focus this system represents a generic model of an unstable steady state which can be found for instance in hopf bifurcation in addition to the original controller design we investigate effects of control loop latency and a bandpass filter on the domain of control furthermore we consider coupling of the control force to the system via a rotational coupling matrix parametrized by a variable phase we present an analysis of the domain of control and support our results by numerical calculations

oscillator death in populations of all to all coupled nonlinear oscillators abstract the behavior of finitely many and infinitely many coupled weakly nonlinear oscillators is studied and it is shown that the uniform rest state can become stable if the coupling is sufficiently strong and the frequencies are sufficiently disparate numerical results show that the phenomenon is robust and occurs when many of the hypotheses are relaxed

state difference feedback for stabilizing uncertain steady states of non linear systems supposing a non linear system is subjected to parametric uncertainties the present paper aims at stabilizing its unstable steady states a distinctive feature of the problem is that exact information about the steady state is unavailable to cope with the difficulty we have examined the applicability of the state difference feedback which uses the difference between the present state x t and the past state x t t a rigorous stability analysis has been executed for the case where state deviations are controllable by a single input variable the stability analysis has led to a favourable conclusion that if the number of unstable modes is just two and if they are not associated with the origin in the complex plane we are always able to find a controller which stabilizes the deviations from the unknown steady state design process is illustrated by using two kinds of pendulum systems

nature of the phase flip transition in the synchronized approach to amplitude death we study the dynamics of time delay coupled limit cycle oscillators in the amplitude death regime through a detailed analysis of the jacobian at the fixed point we show that the phase flip transition namely the abrupt change from in phase synchronized dynamics to antiphase synchronized dynamics is associated with an interchange of the imaginary parts of complex pairs of eigenvalues at an avoided crossing of lyapunov exponents as a parameter is varied an order parameter for the transition is constructed through the eigenvectors of the jacobian

oscillator death on small world networks we have investigated the oscillator death behavior on small world networks on one hand we find that small world connectivity can eliminate the oscillator death present in the regular lattice on the other hand the small world connectivity can also lead to global oscillator death which is absent in the regular lattice or the completely random network

jointly optimal lqg quantization and control policies for multi dimensional systems for controlled bbr n valued linear systems driven by gaussian noise under quadratic cost criteria we investigate the existence and the structure of optimal quantization and control policies for fully observed and partially observed systems we establish the global optimality of a class of predictive encoders and show that an optimal quantization policy exists provided that the quantizers allowed are ones which have convex codecells furthermore optimal control policies are linear in the conditional estimate of the state and a form of separation of estimation and control holds

time delay effects on coupled limit cycle oscillators at hopf bifurcation abstract we present a detailed study of the effect of time delay on the collective dynamics of coupled limit cycle oscillators at hopf bifurcation for a simple model consisting of just two oscillators with a time delayed coupling the bifurcation diagram obtained by numerical and analytical solutions shows significant changes in the stability boundaries of the amplitude death phase locked and incoherent regions a novel result is the occurrence of amplitude death even in the absence of a frequency mismatch between the two oscillators similar results are obtained for an array of n oscillators with a delayed mean field coupling and the regions of such amplitude death in the parameter space of the coupling strength and time delay are quantified some general analytic results for the n thermodynamic limit are also obtained and the implications of the time delay effects for physical applications are discussed

lyapunov exponents in disordered chaotic systems avoided crossing and level statistics the behavior of the lyapunov exponents les of a disordered system consisting of mutually coupled chaotic maps with different parameters is studied the les are demonstrated to exhibit avoided crossing and level repulsion qualitatively similar to the behavior of energy levels in quantum chaos recent results for the coupling dependence of the les of two coupled chaotic systems are used to explain the phenomenon and to derive an approximate expression for the distribution functions of le spacings the depletion of the level spacing distribution is shown to be exponentially strong at small values the results are interpreted in terms of the random matrix theory

triple products and yang baxter equation i octonionic and quaternionic triple systems the yang baxter equation can be recast as a triple product equation assuming the triple product to satisfy some algebraic relations new solutions of the yang baxter equation can be found this program has been completed here for the simplest triple systems which are called octonionic and quaternionic the solutions are of rational type

chaotic maps coupled with random delays connectivity topology and network propensity for synchronization abstract we study the influence of network topology and connectivity on the synchronization properties of chaotic logistic maps interacting with random delay times four different types of topologies are investigated two regular a ring type and a ring type with a central node and two random free scale barabasi albert and small world newman watts the influence of the network connectivity is studied by varying the average number of links per node while keeping constant the total input that each map receives from its neighbors for weak coupling the array does not synchronize regardless the topology or connectivity of the network however for certain connectivity values there is enhanced coherence for strong coupling the array synchronizes in the homogeneous steady state where the chaotic dynamics of the individual maps is suppressed for both weak and strong coupling the array propensity for synchronization is largely independent of the network topology and depends mainly on the average number of links per node

oscillator death in coupled functional differential equations near hopf bifurcation abstract the stability of the equilibrium solution is analyzed for coupled systems of retarded functional differential equations near a supercritical hopf bifurcation necessary and sufficient conditions are derived for asymptotic stability under general coupling conditions it is shown that the largest eigenvalue of the graph laplacian completely characterizes the effect of the connection topology on the stability of diffusively and symmetrically coupled identical systems in particular all bipartite graphs have identical stability characteristics regardless of their size furthermore bipartite graphs and large complete graphs provide respectively lower and upper bounds for the parametric stability regions for arbitrary connection topologies generalizations are given for networks with asymmetric coupling the results characterize the connection topology as a mechanism for the death of coupled oscillators near hopf bifurcation

can distributed delays perfectly stabilize dynamical networks department of physics kyoto university sakyo ku kyoto 606 8502 japan dated february 2 2008 signal transmission delays tend to destabilize dynamical networks leading to oscillation but theirdispersion contributes oppositely toward stabilization we analyze an integro di erential equationthat describes the collective dynamics of a neural network with distributed signal delays with thegamma distributed delays less dispersed than exponential distribution the system exhibits reentrantphenomena in which the stability is once lost but then recovered as the mean delay is increased with delays dispersed more highly than exponential the system never destabilizes

dynamical effects of integrative time delay coupling we study coupled dynamical systems wherein the influence of one system on the other is cumulative coupling signals are integrated over a time interval t a major consequence of integrative coupling is that amplitude death occurs over a wider range and in a single region in parameter space for coupled limit cycle oscillators the landau stuart model we obtain an analytic estimate for the boundary of this region while for coupled chaotic lorenz oscillators numerical results are presented for given t we find that there is a critical coupling strength at which the frequency of oscillations changes discontinuously

epidemics and percolation in small world networks we study some simple models of disease transmission on small world networks in which either the probability of infection by a disease or the probability of its transmission is varied or both the resulting models display epidemic behavior when the infection or transmission probability rises above the threshold for site or bond percolation on the network and we give exact solutions for the position of this threshold in a variety of cases we confirm our analytic results by numerical simulation

phase flip bifurcation induced by time delay we present a general bifurcation in the synchronized dynamics of time delay coupled nonlinear oscillators the relative phase between the oscillators jumps from zero to ensuremath pi as a function of the coupling this phase flip bifurcation is accompanied by a discontinuous change in the frequency of the synchronized oscillators this phenomenon is of broad relevance being observed in regimes of oscillator death as well as in periodic quasiperiodic and chaotic dynamics time delay coupling is necessary for the phase flip bifurcation we illustrate the phenomenon and present analytical results for paradigmatic nonlinear systems possible applications are discussed

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

amplitude death in the absence of time delays in identical coupled oscillators we study the dynamics of oscillators that are mutually coupled via dissimilar or conjugate variables and find that this form of coupling leads to a regime of amplitude death analytic estimates are obtained for coupled landau stuart oscillators and this is supplemented by numerics for this system as well as for coupled lorenz oscillators time delay does not appear to be necessary to cause amplitude death when conjugate variables are employed in coupling identical systems coupled chaotic oscillators also show multistability prior to amplitude death and the basins of the coexisting attractors appear to be riddled this behavior is quantified an appropriately defined uncertainty exponent in the coupled lorenz system is shown to be zero

control of unstable steady states by long delay feedback we present an asymptotic analysis of time delayed feedback control of steady states for large delay time by scaling arguments and a detailed comparison with exact solutions we establish the parameter ranges for successful stabilization of an unstable fixed point of focus type insight into the control mechanism is gained by analyzing the eigenvalue spectrum which consists of a pseudocontinuous spectrum and up to two strongly unstable eigenvalues although the standard control scheme generally fails for large delay we find that if the uncontrolled system is sufficiently close to its instability threshold control does work even for relatively large delay times

conversion of stability in systems close to a hopf bifurcation by time delayed coupling we propose a control method with time delayed coupling which makes it possible to convert the stability features of systems close to a hopf bifurcation we consider two delay coupled normal forms for hopf bifurcation and demonstrate the conversion of stability i e an interchange between the sub and supercritical hopf bifurcation the control system provides us with an unified method for stabilizing both the unstable periodic orbit and the unstable steady state and reveals typical effects like amplitude death and phase locking the main method and the results are applicable to a wide class of systems showing hopf bifurcations for example the van der pol oscillator the analytical theory is supported by numerical simulations of two delay coupled van der pol oscillators which show good agreement with the theory

discrete time controlled markov processes with average cost criterion a survey this work is a survey of the average cost control problem for discrete time markov processes the authors have attempted to put together a comprehensive account of the considerable research on this problem over the past three decades the exposition ranges from finite to borel state and action spaces and includes a variety of methodologies to find and characterize optimal policies the authors have included a brief historical perspective of the research efforts in this area and have compiled a substantial yet not exhaustive bibliography the authors have also identified several important questions that are still open to investigation

amplitude death in oscillators coupled by a one way ring time delay connection the coupling induced stabilization of a steady state which is called amplitude death cannot be observed in identical nonlinear oscillators coupled by diffusive connections however it has been analytically confirmed that amplitude death can be induced by using a diffusive time delay coupling in this paper a one way ring time delay coupled system consisting of n identical oscillators is proposed this system is equivalent to a delayed feedback control system when n 1 and to a time delay coupled oscillator system when n 2 in the proposed system amplitude death never occurs at a steady state when the jacobi matrix evaluated at a fixed point has an odd number of real positive eigenvalues furthermore a simple systematic graphical procedure to test the stability of the system is presented this procedure is illustrated in two numerical examples coupled r ossler oscillators and coupled lorenz oscillators

optimal causal coding decoding problems the symbols produced by a finite markov source are causally encoded so as to be transmitted through a noisy memoryless channel the encoder is assumed to have channel feedback information and the decoder to be causal the feedback information is shown to be useful in general separation results are derived and used to prove that encoding is useless for a class of symmetric channels

amplitude death induced by dynamic coupling the present paper shows that dynamic coupling induces amplitude death in coupled identical oscillators for a simple limit cycle oscillator our theoretical analysis provides the necessary and sufficient condition for amplitude death furthermore we guarantee that amplitude death never occurs if each oscillator satisfies the odd number property that is known in the field of delayed feedback control of chaos

a structure theory of freudenthal kantor triple systems abstract the notion of the radical of a freudenthal kantor triple system is introduced using this it is shown that a semisimple freudenthal kantor triple system is decomposed into a direct sum of simple ideals also this paper defines and characterizes the structure groups for freudenthal kantor triple systems

synchronized states in chaotic systems coupled indirectly through a dynamic environment we consider synchronization of chaotic systems coupled indirectly through common environment where the environment has an intrinsic dynamics of its own modulated via feedback from the systems we find that a rich variety of synchronization behavior such as in phase antiphase complete and antisynchronization is possible we present an approximate stability analysis for the different synchronization behaviors the transitions to different states of synchronous behavior are analyzed in the parameter plane of coupling strengths by numerical studies for specific cases such as rossler and lorenz systems and are characterized using various indices such as correlation average phase difference and lyapunov exponents the threshold condition obtained from numerical analysis is found to agree with that from the stability analysis

beyond the odd number limitation a bifurcation analysis of time delayed feedback control we investigate the normal form of a subcritical hopf bifurcation subjected to time delayed feedback control bifurcation diagrams which cover time dependent states as well are obtained by analytical means the computations show that unstable limit cycles with an odd number of positive floquet exponents can be stabilized by time delayed feedback control contrary to incorrect claims in the literature the model system constitutes one of the few examples where a nonlinear time delay system can be treated entirely by analytical means

amplitude death in complex networks induced by environment we present a mechanism for amplitude death in coupled nonlinear dynamical systems on a complex network having interactions with a common environment like external system we develop a general stability analysis that is valid for any network topology and obtain the threshold values of coupling constants for the onset of amplitude death an important outcome of our study is a universal relation between the critical coupling strength and the largest nonzero eigenvalue of the coupling matrix our results are fully supported by the detailed numerical analysis for different network topologies

on codecell convexity of optimal multiresolution scalar quantizers for continuous sources it has been shown by earlier results that for fixed rate multiresolution scalar quantizers and for mean squared error distortion measure codecell convexity precludes optimality for certain discrete sources however it was unknown whether the same phenomenon can occur for any continuous source in this paper examples of continuous sources even with bounded continuous densities are presented for which optimal fixed rate multiresolution scalar quantizers cannot have only convex codecells proving that codecell convexity precludes optimality also for such regular sources

steady state stabilization due to random delays in maps with self feedback loops and in globally delayed coupled maps we study the stability of the fixed point solution of an array of mutually coupled logistic maps focusing on the influence of the delay times ij of the interaction between the ith and jth maps two of us recently reported phys rev lett 94 134102 2005 that if ij are random enough the array synchronizes in a spatially homogeneous steady state here we study this behavior by comparing the dynamics of a map of an array of n delayed coupled maps with the dynamics of a map with n self feedback delayed loops if n is sufficiently large the dynamics of a map of the array is similar to the dynamics of a map with self feedback loops with the same delay times several delayed loops stabilize the fixed point when the delays are not the same however the distribution of delays plays a key role if the delays are all odd a periodic orbit and not the fixed point is stabilized we present a linear stability analysis and apply some mathematical theorems that explain the numerical results

on properties of locally optimal multiple description scalar quantizers with convex cells it is known that the generalized lloyd method is applicable to locally optimal multiple description scalar quantizer mdsq design however it remains unsettled when the resulting mdsq is also globally optimal we partially answer the above question by proving that for a fixed index assignment there is a unique locally optimal fixed rate mdsq of convex cells under trushkin s sufficient conditions for the uniqueness of locally optimal fixed rate single description scalar quantizer this result holds for fixed rate multiresolution scalar quantizer mrsq of convex cells as well thus the well known log concave probability density function pdf condition can be extended to the multiple description and multiresolution cases

quantization as histogram segmentation optimal scalar quantizer design in network systems an algorithm for scalar quantizer design on discrete alphabet sources is proposed the proposed algorithm can be used to design fixed rate and entropy constrained conventional scalar quantizers multiresolution scalar quantizers multiple description scalar quantizers and wyner ziv scalar quantizers the algorithm guarantees globally optimal solutions for conventional fixed rate scalar quantizers and entropy constrained scalar quantizers for the other coding scenarios the algorithm yields the best code among all codes that meet a given convexity constraint in all cases the algorithm run time is polynomial in the size of the source alphabet the algorithm derivation arises from a demonstration of the connection between scalar quantization histogram segmentation and the shortest path problem in a certain directed acyclic graph

conservative algebras of 2 dimensional algebras abstract in 1990 kantor introduced the conservative algebra w n of all algebras i e bilinear maps on the n dimensional vector space in case n 1 the algebra w n does not belong to well known classes of algebras such as associative lie jordan leibniz algebras we describe the algebra of all derivations of w 2 and subalgebras of w 2 of codimension one we also study similar problems for the algebra w 2 of all commutative algebras on the two dimensional vector space and the algebra s 2 of all commutative algebras with trace zero multiplication on the two dimensional space

stabilizing unstable periodic orbits in the lorenz equations using time delayed feedback control for many years it was believed that an unstable periodic orbit with an odd number of real floquet multipliers greater than unity cannot be stabilized by the time delayed feedback control mechanism of pyragas a recent paper by fiedler et al phys rev lett 98 114101 2007 uses the normal form of a subcritical hopf bifurcation to give a counterexample to this theorem using the lorenz equations as an example we demonstrate that the stabilization mechanism identified by fiedler et al for the hopf normal form can also apply to unstable periodic orbits created by subcritical hopf bifurcations in higher dimensional dynamical systems our analysis focuses on a particular codimension two bifurcation that captures the stabilization mechanism in the hopf normal form example and we show that the same codimension two bifurcation is present in the lorenz equations with appropriately chosen pyragas type time delayed feedback this example suggests a possible strategy for choosing the feedback gain matrix in pyragas control of unstable periodic orbits that arise from a subcritical hopf bifurcation of a stable equilibrium in particular our choice of feedback gain matrix is informed by the fiedler et al example and it works over a broad range of parameters despite the fact that a center manifold reduction of the higher dimensional problem does not lead to their model problem

real time coding with limited lookahead a real time coding system with lookahead consists of a memoryless source a memoryless channel an encoder which encodes the source symbols sequentially with knowledge of future source symbols up to a fixed finite lookahead d with or without feedback of the past channel output symbols and a decoder which sequentially constructs the source symbols using the channel output the objective is to minimize the expected per symbol distortion for a fixed finite lookahead d 1 we invoke the theory of controlled markov chains to obtain an average cost optimality equation acoe the solution of which denoted by d d is the minimum expected per symbol distortion with increasing d d d bridges the gap between causal encoding d 0 where symbol by symbol encoding decoding is optimal and the infinite lookahead case d where shannon theoretic arguments show that separation is optimal we extend the analysis to a system with finite state decoders with or without noise free feedback for a bernoulli source and binary symmetric channel under hamming loss we compute the optimal distortion for various source and channel parameters and thus obtain computable bounds on d d we also identify regions of source and channel parameters where symbol by symbol encoding decoding is suboptimal finally we demonstrate the wide applicability of our approach by applying it in additional coding scenarios such as the case where the sequential decoder can take cost constrained actions affecting the quality or availability of side information about the source

conformal and quasiconformal realizations of exceptional lie groups we present a nonlinear realization of e8 8 on a space of 57 dimensions which is quasiconformal in the sense that it leaves invariant a suitably defined light cone in 57 this realization which is related to the freudenthal triple system associated with the unique exceptional jordan algebra over the split octonions contains previous conformal realizations of the lower rank exceptional lie groups on generalized space times and in particular a conformal realization of e7 7 on 27 which we exhibit explicitly possible applications of our results to supergravity and m theory are briefly mentioned

stability analysis of amplitude death in delay coupled high dimensional map networks and their design procedure abstract the present paper studies amplitude death in high dimensional maps coupled by time delay connections a linear stability analysis provides several sufficient conditions for an amplitude death state to be unstable i e an odd number property and its extended properties furthermore necessary conditions for stability are provided these conditions which reduce trial and error tasks for design and the convex direction which is a popular concept in the field of robust control allow us to propose a design procedure for system parameters such as coupling strength connection delay and input output matrices for a given network topology these analytical results are confirmed numerically using delayed logistic maps generalized henon maps and piecewise linear maps

transitions to amplitude death in a regular array of nonlinear oscillators we investigate amplitude death in a regular array of nonlinear oscillators we find that the system undergoes three transitions during the road to complete amplitude death the first two are related to partial amplitude death one induces partial amplitude death and the other enhances it the last transition establishes complete amplitude death we also find that the first two belong to a second order transition and are universal while the last one is strongly dependent on the system parameters

difference feedback can stabilize uncertain steady states the paper is concerned with the stabilization of uncertain steady states by the state difference feedback the feedback method has a peculiar feature that it uses only the difference between the present state x t and the past state x t t considering exact information on the steady state is unavailable hitherto a condition is known under which such stabilization can not be realized the article conversely shows that the state difference feedback can stabilize only if the exclusion condition is not true furthermore a dynamic output difference feedback is shown to be able to stabilize under quite a mild condition that the steady state is not associated with zero eigenvalues the ability of the method is illustrated by using a cart pendulum system which moves along a one dimensional varying slope

on optimal causal coding of partially observed markov sources in single and multiterminal settings the optimal causal zero delay coding of a partially observed markov process is studied where the cost to be minimized is a bounded nonnegative additive measurable single letter function of the source and the receiver output a structural result is obtained extending witsenhausen s and walrand varaiya s structural results on optimal causal coders to more general state spaces and to a partially observed setting the decentralized multiterminal setup is also considered for the case where the source is an i i d process it is shown that an optimal solution to the decentralized causal coding of correlated observations problem is memoryless for markov sources a counterexample to a natural separation conjecture is presented

amplitude death through a hopf bifurcation in coupled electrochemical oscillators experiments and simulations amplitude death was observed in experiments with two coupled periodic electrochemical oscillators without time delay simulation results confirmed that the observed amplitude death was obtained via a hopf bifurcation the two oscillators must have a minimum discrepancy and both be near their individual hopf bifurcations for amplitude death to occur phase drift coexisting with unstable asymmetric phase locked solutions amplitude death and in phase synchronization were observed in both the experiments and simulations as coupling strength was increased in addition the simulations showed that a stable asymmetric phase locked solution exists between the phase drift and amplitude death regions

central extensions of lie algebras graded by finite root systems lie algebras graded by finite irreducible reduced root systems have been classified up to central extensions by berman and moody benkart and zelmanov and neher in this paper we determine the central extensions of these lie algebras and hence describe them completely up to isomorphism

randomized quantization and source coding with constrained output distribution this paper studies fixed rate randomized vector quantization under the constraint that the quantizer s output has a given fixed probability distribution a general representation of randomized quantizers that includes the common models in the literature is introduced via appropriate mixtures of joint probability measures on the product of the source and reproduction alphabets using this representation and results from optimal transport theory the existence of an optimal minimum distortion randomized quantizer having a given output distribution is shown under various conditions for sources with densities and the mean square distortion measure it is shown that this optimum can be attained by randomizing quantizers having convex codecells for stationary and memoryless source and output distributions a rate distortion theorem is proved providing a single letter expression for the optimum distortion in the limit of large blocklengths

quantization and the method of k means asymptotic results from the statistical theory of k means clustering are applied to problems of vector quantization the behavior of quantizers constructed from long training sequences of data is analyzed by relating it to the consistency problem for k means

amplitude response of coupled oscillators abstract we investigate the interaction of a pair of weakly nonlinear oscillators eg each near a hopf bifurcation when the coupling strength is comparable to the attraction of the limit cycles changes in amplitude cannot then be ignored and there are new phenomena we show that even for simple forms of these equations there are parameter regimes in which the interaction causes the system to stop oscillating and the rest state at zero stabilized by the interaction is the only stable solution when the uncoupled oscillators have a local frequency that is independent of amplitude zero shear and the coupling is scalar we give a complete description of the behavior we then analyze more complicated equations to show the effects of amplitude dependent frequency in the uncoupled equations nonzero shear and nonscalar coupling for example when there is shear there can be bistability between a phase locked solution and an unlocked drift solution in which the oscillators go at different average frequencies there can also be bistability between a phase locked solution and an equilibrium nonoscillatory solution the equations for the zero shear case have a pair of degenerate bifurcation points and the new phenomena in the nonzero shear case arise from a partial unfolding of these singularities when the coupling is nonscalar there are a variety of new behaviors including bistability of an in phase and an anti phase solution for two identical oscillators parameters for which only the anti phase solution is stable and phase trapping i e nonlocked solutions in which the oscillators still have the same average frequency it is shown that whether the coupling is diffusive or direct has many effects on the behavior of the system

optimal zero delay coding of markov sources stationary and finite memory codes the optimal zero delay coding of a finite state markov source is considered the existence and structure of optimal codes are studied using a stochastic control formulation prior results in the literature established the optimality of deterministic markov walrand varaiya type coding policies for the finite time horizon problem and the optimality of both deterministic nonstationary and randomized stationary policies for the infinite time horizon problem our main result here shows that for any irreducible and aperiodic markov source with a finite alphabet deterministic and stationary markov coding policies are optimal for the infinite horizon problem in addition the finite block length time horizon performance of an optimal stationary and markov coding policy is shown to approach the infinite time horizon optimum at a rate o 1 t the results are extended to systems where zero delay communication takes place across a noisy channel with noiseless feedback

control of unstable steady states by time delayed feedback methods we show that time delayed feedback methods which have successfully been used to control unstable periodic orbits provide a tool to stabilize unstable steady states we present an analytical investigation of the feedback scheme using the lambert function and discuss effects of both a low pass filter included in the control loop and nonzero latency times associated with the generation and injection of the feedback signal

amplitude death in an array of limit cycle oscillators we analyze a large system of limit cycle oscillators with mean field coupling and randomly distributed natural frequencies we prove that when the coupling is sufficiently strong and the distribution of frequencies has sufficiently large variance the system undergoes amplitude death the oscillators pull each other off their limit cycles and into the origin which in this case is astable equilibrium point for the coupled system we determine the region in couplingvariance space for which amplitude death is stable and present the first proof that the infinite system provides an accurate picture of amplitude death in the large but finite system

on causal source codes with side information we study the effect of the introduction of side information into the causal source coding setting of neuhoff and gilbert we find that the spirit of their result namely the sufficiency of time sharing scalar quantizers followed by appropriate lossless coding for attaining optimum performance within the family of causal source codes extends to many scenarios involving availability of side information at both encoder and decoder or only on one side for example in the case where side information is available at both encoder and decoder we find that time sharing side information dependent scalar quantizers at most two for each side information symbol attains optimum performance this remains true even when the reproduction sequence is allowed noncausal dependence on the side information and even for the case where the source and the side information rather than consisting of independent and identically distributed i i d pairs form respectively the output of a memoryless channel and its stationary ergodic input

analytical criterion for amplitude death in nonautonomous systems with piecewise nonlinear coupling we investigate the amplitude death phenomenon in a nonautonomous chained network with complicated piecewise nonlinear coupling functions an analytical criterion for the boundary of the amplitude death region is derived by using the average method the mechanism of the amplitude death in the nonautonomous networks is very different from that of autonomous systems and rapid dynamic transitions could halt the amplitude death numerical verifications are carried out to check jump transitions among different solution branches and further confirm the correctness of the theoretical results

structurable superalgebras of cartan type abstract we describe the simple lie superalgebras arising from the unital structurable superalgebras of characteristic 0 and construct four series of the unital simple structurable superalgebras of cartan type we give a classification of simple structurable superalgebras of cartan type over an algebraically closed field f of characteristic 0 together with the faulkner theorem on the classification of classical such superalgebras it gives a classification of the simple structurable superalgebras over f

coupled chaotic chemical oscillators we present a model study of two mass coupled reactors containing the belousov zhabotinsky reaction under chaotic conditions the critical coupling strength is estimated for symmetry breaking when two identical low flow rate chaotic modes are coupled our results confirm that the critical coupling strength is directly proportional to the maximum lyapunov exponent of the uncoupled system the constant of proportionality is found to be somewhat larger than the theoretical value direct integration reveals a rich structure of dynamical behavior when the coupling strength and the flow rate in one cell are varied our simulations reveal domains of oscillator death in which a stable steady state coexists with limit cycle oscillations we introduce a simple model for predicting the dynamics of the coupled system from the dynamical behavior of the uncoupled subsystems and the dependence on the coupling strength of the hopf bifurcation of the coupled system the model gives good estimates of the dynamical behavior of two coupled oscillators with a small difference in one parameter at intermediate and high coupling strengths textcopyright 1996 the american physical society

on optimal zero delay coding of vector markov sources optimal zero delay coding quantization of a vector valued markov source driven by a noise process is consid ered using a stochastic control problem formulation the exis tence and structure of optimal quantization policies are studied for a finite horizon problem with bounded per stage distortion measure the existence of an optimal zero delay quantization policy is shown provided that the quantizers allowed are ones with convex codecells the bounded distortion assumption is relaxed to cover cases that include the linear quadratic gaussian problem for the infinite horizon problem and a stationary markov source the optimality of deterministic markov coding policies is shown the existence of optimal stationary markov quantization policies is also shown provided randomization that is shared by the encoder and the decoder is allowed

total and partial amplitude death in networks of diffusively coupled oscillators networks of weakly nonlinear oscillators are considered with diffusive and time delayed coupling averaging theory is used to determine parameter ranges for which the network experiences amplitude death whereby oscillations are quenched and the equilibrium solution has a large domain of attraction the amplitude death is shown to be a common phenomenon which can be observed regardless of the precise nature of the nonlinearities and under very general coupling conditions in addition when the network consists of dissimilar oscillators there exist parameter values for which only parts of the network are suppressed sufficient conditions are derived for total and partial amplitude death in arbitrary network topologies with general nonlinearities coupling coefficients and connection delays

disorder can eliminate oscillator death we use an array of diffusively coupled limit cycle oscillators with a regular monotonic trend of natural frequencies to demonstrate that the disorder introduced in the form of random deviations from a linear trend of frequencies can weaken considerably desynchronization induced oscillator death and as a result increase oscillation intensity substantially there exist definite optimal levels of magnitude of spatial disorder at which maximal oscillatory energy is attained in the array

stabilization of a steady state in network oscillators by using diffusive connections with two long time delays the present study shows that diffusive connections with two long time delays can induce the stabilization of a steady state in network oscillators a linear stability analysis shows that if the two delay times retain a proportional relation with a certain bias the stabilization can be achieved independent of the delay times furthermore a simple systematic procedure for designing the coupling strength and the delay times in the connections is proposed the procedure has the following two advantages one can employ time delays as long as one wants and the stabilization can be achieved independently of its network topology our analytical results are applied to the well known double scroll circuit model on a small world network

adaptive control of unknown unstable steady states of dynamical systems a simple adaptive controller based on a low pass filter to stabilize unstable steady states of dynamical systems is considered the controller is reference free it does not require knowledge of the location of the fixed point in the phase space a topological limitation similar to that of the delayed feedback controller is discussed we show that the saddle type steady states cannot be stabilized by using the conventional low pass filter the limitation can be overcome by using an unstable low pass filter the use of the controller is demonstrated for several physical models including the pendulum driven by a constant torque the lorenz system and an electrochemical oscillator linear and nonlinear analyses of the models are performed and the problem of the basins of attraction of the stabilized steady states is discussed the robustness of the controller is demonstrated in experiments and numerical simulations with an electrochemical oscillator the dissolution of nickel in sulfuric acid a comparison of the effect of using direct and indirect variables in the control is made with the use of the controller all unstable phase space objects are successfully reconstructed experimentally

theory of self synchronization in the presence of native frequency distribution and external noises abstract a general scheme is presented for the theoretical treatment of self synchronization of many body oscillators with variable amplitudes close to harmonic ones with small nonlinearity and dissipative interactions in the presence of external noises and a native frequency distribution applications of the theory are given to interacting van der pol oscillators with various frequency distributions the critical condition which leads to a nonvanishing order parameter is studied in detail it turns out that the synchronization is described in terms of two kinds of bifurcation mechanism mechanical and thermal ones new strong slaving emerges in the case of the mechanical bifurcation multifarious dependences of the order parameter on the width of native frequency distribution appears in some cases because of the presence of these two bifurcation mechanisms however only one bifurcation of landau type is observable since hybridization occurs when the two mechanisms coexist

frequency discontinuity and amplitude death with time delay asymmetry we consider oscillators coupled with asymmetric time delays namely when the speed of information transfer is direction dependent as the coupling parameter is varied there is a regime of amplitude death within which there is a phase flip transition at this transition the frequency changes discontinuously but unlike the equal delay case when the relative phase difference changes by ensuremath pi here the phase difference changes by an arbitrary value that depends on the difference in delays we consider asymmetric delays in coupled landau stuart oscillators and r ossler oscillators analytical estimates of phase synchronization frequencies and phase differences are obtained by separating the evolution equations into phase and amplitude components eigenvalues and eigenvectors of the jacobian matrix in the neighborhood of the transition also show an avoided crossing as has been observed in previous studies with symmetric delays

lie algebras with s4 action and structurable algebras abstract the normal symmetric triality algebras sta s and the normal lie related triple algebras lrta s have been recently introduced by the second author in connection with the principle of triality it turns out that the unital normal lrta s are precisely the structurable algebras extensively studied by allison it will be shown that the normal sta s respectively lrta s are the algebras that coordinatize those lie algebras whose automorphism group contains a copy of the alternating respectively symmetric group of degree 4

optimization and convergence of observation channels in stochastic control this paper studies the optimization of observation channels stochastic kernels in partially observed stochastic control problems in particular existence and continuity properties are investigated mostly but not exclusively concentrating on the single stage case continuity properties of the optimal cost in channels are explored under total variation setwise convergence and weak convergence sufficient conditions for compactness of a class of channels under total variation and setwise convergence are presented and applications to quantization are explored

the capacity of channels with feedback in this paper we introduce a general framework for treating channels with memory and feedback first we prove a general feedback channel coding theorem based on massey s concept of directed information second we present coding results for markov channels this requires determining appropriate sufficient statistics at the encoder and decoder we give a recursive characterization of these sufficient statistics third a dynamic programming framework for computing the capacity of markov channels is presented fourth it is shown that the average cost optimality equation acoe can be viewed as an implicit single letter characterization of the capacity fifth scenarios with simple sufficient statistics are described sixth error exponents for channels with feedback are presented

on the eigenvalue spectrum for time delayed floquet problems abstract a linear homogeneous scalar differential difference equation with harmonic time dependence is investigated the associated eigenvalue problem is solved in terms of a continued fraction expansion for the characteristic equation the dependence of the largest eigenvalue on the system parameters being relevant for stability of periodic states in delay systems is discussed in detail the competition between the two timescales the delay and the external period cause intricate structures the result suggests features to improve control of chaos by time delayed feedback schemes with time dependent control amplitudes

on the structure of optimal real time encoders and decoders in noisy communication the output of a discrete time markov source must be encoded into a sequence of discrete variables the encoded sequence is transmitted through a noisy channel to a receiver that must attempt to reproduce reliably the source sequence encoding and decoding must be done in real time and the distortion measure does not tolerate delays the structure of real time encoding and decoding strategies that jointly minimize an average distortion measure over a finite horizon is determined the results are extended to the real time broadcast problem and a real time variation of the wyner ziv problem

structurable algebras and groups of type e6 and e7 abstract it is well known that every group of type f 4 is the automorphism group of an exceptional jordan algebra and that up to isogeny all groups of type 1 e 6 with trivial tits algebras arise as the isometry groups of norm forms of such jordan algebras we describe a similar relationship between groups of type e 6 and groups of type e 7 and use it to give explicit descriptions of the homogeneous projective varieties associated to groups of type e 7 with trivial tits algebras

amplitude death in coupled chaotic oscillators amplitude death can occur in chaotic dynamical systems with time delay coupling similar to the case of coupled limit cycles the coupling leads to stabilization of fixed points of the subsystems this phenomenon is quite general and occurs for identical as well as nonidentical coupled chaotic systems using the lorenz and rossler chaotic oscillators to construct representative systems various possible transitions from chaotic dynamics to fixed points are discussed

trace forms for structurable algebras structurable algebras were defined in 2 as a generalization of jordan algebras and finite dimensional simple structurable algebras of characteristic 0 were classified in that paper as a generalization of the tits koecher construction for jordan algebras a lie algebra xx has been associated in 3 with each structurable algebra ccp by transferring properties of x to a structure theory for linite dimensional structurable algebras of characteristic 0 was obtained in 9 111 in this paper we consider two trace forms on structurable algebras the symmetric bilinear form

optimal design of sequential real time communication systems optimal design of sequential real time communication of a markov source over a noisy channel is investigated in such a system the delay between the source output and its reconstruction at the receiver should equal a fixed prespecified amount an optimal communication strategy must minimize the total expected symbol by symbol distortion between the source output and its reconstruction design techniques or performance bounds for such real time communication systems are unknown in this paper a systematic methodology based on the concepts of information structures and information states to search for an optimal real time communication strategy is presented this methodology trades off complexity in communication length linear in contrast to doubly exponential with complexity in alphabet sizes doubly exponential in contrast to exponential as the communication length is usually order of magnitudes bigger than the alphabet sizes the proposed methodology simplifies the search for an optimal communication strategy in spite of this simplification the resultant optimality equations cannot be solved efficiently using existing algorithmic techniques the main idea is to formulate a zero delay communication problem as a dynamic team with nonclassical information structure then an appropriate choice of information states converts the dynamic team problem into a centralized stochastic control problem in function space thereafter markov decision theory is used to derive nested optimality equations for choosing an optimal design for infinite horizon problems these optimality equations give rise to a fixed point functional equation communication systems with fixed finite delay constraint a higher order markov source and channels with memory are treated in the same manner after an appropriate expansion of the state space thus this paper presents a comprehensive methodology to study different variations of real time communication

on algebras satisfying x 2x 2 n x x the commutative algebras satisfying the adjoint identity x 2x 2 n x x where n is a cubic form are shown to be related to a class of generically algebraic jordan algebras of degree at most 4 and to the pseudo composition algebras they are classified under a nondegeneracy condition

structure theorems for real time variable rate coding with and without side information the output of a discrete markov source is to be encoded instantaneously by a variable rate encoder and decoded by a finite state decoder our performance measure is a linear combination of the distortion and the instantaneous rate structure theorems pertaining to the encoder and next state functions are derived for every given finite state decoder which can have access to side information