solution and analysis of tdoa localization of a near or distant source in closed form point positioning and direction of arrival doa localization require separate estimators depending on whether the source is near or distant from the sensors the use of modified polar representation mpr for the source location enables the integration of the two estimators together and eliminates the knowledge needed if the source is in the near field or far field the previous work on mpr only provides an iterative implementation of the maximum likelihood estimator mle initialized by a coarse semidefinite relaxation sdr solution this paper proposes a formulation for time difference of arrival tdoa localization of a 2 d or 3 d source in mpr that would lead to a closed form solution through the minimization of a quadratic function with a quadratic constraint two techniques the successive unconstrained minimization sum and the generalized trust region subproblem gtrs are applied to solve the optimization detailed analysis in the first order for mean square and in the second order for estimation bias is performed for both methods the theoretical results illustrate that the closed form solution from each of the methods provides the cramer rao lower bound performance for gaussian noise the gtrs solution has better accuracy than the sum solution when the source signal is arriving at an azimuth or elevation angle close to zero 90 circ or 180 circ or when the measurement noise level is large they yield comparable performance with the mle albeit having less complexity and avoiding possible divergence behavior they outperform the closed form solutions from the literature in angle estimation and have smaller bias

compactness and the fixed point property in l1 abstract in this paper we prove that compactness can be characterized by means of the existence of a fixed point for some classes of mappings defined on convex closed subsets of the space l 1 nominally our result involves nonexpansive mappings uniformly lipschitzian mappings and cascading nonexpansive mappings we also extend the results to some more general classes of banach spaces

general framework for phase synchronization through localized sets we present an approach which enables one to identify phase synchronization in coupled chaotic oscillators without having to explicitly measure the phase we show that if one defines a typical event in one oscillator and then observes another one whenever this event occurs these observations give rise to a localized set our result provides a general and easy way to identify ps which can also be used to oscillators that possess multiple time scales we illustrate our approach in networks of chemically coupled neurons we show that clusters of phase synchronous neurons may emerge before the onset of phase synchronization in the whole network producing a suitable environment for information exchanging furthermore we show the relation between the localized sets and the amount of information that coupled chaotic oscillator can exchange

transmission of information in active networks shannon s capacity theorem is the main concept behind the theory of communication it says that if the amount of information contained in a signal is smaller than the channel capacity of a physical media of communication it can be transmitted with arbitrarily small probability of error this theorem is usually applicable to ideal channels of communication in which the information to be transmitted does not alter the passive characteristics of the channel that basically tries to reproduce the source of information for an active channel a network formed by elements that are dynamical systems such as neurons chaotic or periodic oscillators it is unclear if such theorem is applicable once an active channel can adapt to the input of a signal altering its capacity to shed light into this matter we show among other results how to calculate the information capacity of an active channel of communication then we show that the channel capacity depends on whether the active channel is self excitable or not and that contrary to a current belief desynchronization can provide an environment in which large amounts of information can be transmitted in a channel that is self excitable an interesting case of a self excitable active channel is a network of electrically connected hindmarsh rose chaotic neurons

robust convex approximation methods for tdoa based localization under nlos conditions in this paper we develop a novel robust optimization approach to source localization using time difference of arrival tdoa measurements that are collected under non line of sight nlos conditions a key feature of our approach is that it does not require knowledge of the distribution or statistics of the nlos errors which are often difficult to obtain in practice instead it only assumes that the nlos errors have bounded supports based on this assumption we formulate the tdoa based source localization problem as a robust least squares rls problem in which a location estimate that is robust against the nlos errors is sought since the rls problem is non convex we propose two efficiently implementable convex relaxation based approximation methods to tackle it we then conduct a thorough theoretical analysis of the approximation quality and computational complexity of these two methods in particular we establish conditions under which they will yield a unique localization of the source simulation results on both synthetic and real data show that the performance of our approach under various nlos settings is very stable and is significantly better than that of several existing non robust approaches

remote synchronization in star networks we study phase synchronization in a network motif with a starlike structure in which the central node s the hub s frequency is strongly detuned against the other peripheral nodes we find numerically and experimentally a regime of remote synchronization rs where the peripheral nodes form a phase synchronized cluster while the hub remains free with its own dynamics and serves just as a transmitter for the other nodes we explain the mechanism for this rs by the existence of a free amplitude and also show that systems with a fixed or constant amplitude such as the classic kuramoto phase oscillator are not able to generate this phenomenon further we derive an analytic expression which supports our explanation of the mechanism

global phase synchronization in an array of time delay systems we report the identification of global phase synchronization gps in a linear array of unidirectionally coupled mackey glass time delay systems exhibiting highly non phase coherent chaotic attractors with complex topological structure in particular we show that the dynamical organization of all the coupled time delay systems in the array to form gps is achieved by sequential synchronization as a function of the coupling strength further the asynchronous ones in the array with respect to the main sequentially synchronized cluster organize themselves to form clusters before they achieve synchronization with the main cluster we have confirmed these results by estimating instantaneous phases including phase difference average phase average frequency frequency ratio and their differences from suitably transformed phase coherent attractors after using a nonlinear transformation of the original non phase coherent attractors the results are further corroborated using two other independent approaches based on recurrence analysis and the concept of localized sets from the original non phase coherent attractors directly without explicitly introducing the measure of phase

semidefinite programming approach for range difference based source localization a common technique for passive source localization is to utilize the range difference rd measurements between the source and several spatially separated sensors the rd information defines a set of hyperbolic equations from which the source position can be calculated with the knowledge of the sensor positions under the standard assumption of gaussian distributed rd measurement errors it is well known that the maximum likelihood ml position estimation is achieved by minimizing a multimodal cost function which corresponds to a difficult task in this correspondence we propose to approximate the nonconvex ml optimization by relaxing it to a convex optimization problem using semidefinite programming a semidefinite relaxation rd based positioning algorithm which makes use of the admissible source position information is proposed and its estimation performance is contrasted with the two step weighted least squares method and nonlinear least squares estimator as well as cramer rao lower bound

fixed points of uniformly lipschitzian mappings in spaces with uniformly normal structure dans un espace de banach x on etudie quand reflexivite et structure normale sont suffisantes pour assurer pour de bon 1 la propriete de point fixe pour des auto applications uniformement lipschitziennes

exact and approximate solutions of source localization problems we consider least squares ls approaches for locating a radiating source from range measurements which we call r ls or from range difference measurements rd ls collected using an array of passive sensors we also consider ls approaches based on squared range observations sr ls and based on squared range difference measurements srd ls despite the fact that the resulting optimization problems are nonconvex we provide exact solution procedures for efficiently computing the sr ls and srd ls estimates numerical simulations suggest that the exact sr ls and srd ls estimates outperform existing approximations of the sr ls and srd ls solutions as well as approximations of the r ls and rd ls solutions which are based on a semidefinite relaxation

outage constrained robust transmit optimization for multiuser miso downlinks tractable approximations by conic optimization in this paper we study a probabilistically robust transmit optimization problem under imperfect channel state information csi at the transmitter and under the multiuser multiple input single output miso downlink scenario the main issue is to keep the probability of each user s achievable rate outage as caused by csi uncertainties below a given threshold as is well known such rate outage constraints present a significant analytical and computational challenge indeed they do not admit simple closed form expressions and are unlikely to be efficiently computable in general assuming gaussian csi uncertainties we first review a traditional robust optimization based method for approximating the rate outage constraints and then develop two novel approximation methods using probabilistic techniques interestingly these three methods can be viewed as implementing different tractable analytic upper bounds on the tail probability of a complex gaussian quadratic form and they provide convex restrictions or safe tractable approximations of the original rate outage constraints in particular a feasible solution from any one of these methods will automatically satisfy the rate outage constraints and all three methods involve convex conic programs that can be solved efficiently using off the shelf solvers we then proceed to study the performance complexity tradeoffs of these methods through computational complexity and comparative approximation performance analyses finally simulation results are provided to benchmark the three convex restriction methods against the state of the art in the literature the results show that all three methods offer significantly improved solution quality and much lower complexity

normal structure coefficients of l p ω let x be a uniformly convex banach space and n x the normal structure coefficient of x in this paper it is proved that n x can be calculated by considering only sets whose points are equidistant from their chebyshev centre this result is applied to prove that n l p min 2 1 1 p 2 1 p being a finite measure space the computation of n l p lets us also calculate some other coefficients related to the normal structure

fixed point theorems for uniformly lipschitzian semigroups in uniformly convex spaces for all x y in c and each n 1 2 goebel and kirk 2 first studied these mappings and they proved that such t has a fixed point if c is a closed bounded convex subset of a uniformly convex banach space x and k k k is the unique solution of the equation 1 a l k k 1 with 6 being the modulus of convexity of x lifschitz s showed that in a hilbert space i a uniformly k lipschitzian mapping t with k c 21j2 has a fixed point lim 6 7 and lim et al 8 extended goebel kirk s theorem in lp spaces recently downing and ray l and ishihara and takahashi 3 verified that lifschitz s theorem is valid for uniformly lipschitzian semigroups in hifbert spaces the purpose of this paper is to prove fixed point theorems for a uniformly k lipschitzian semigroup in uniformly convex banach spaces which is left reversible or for which the space of right uniformly continuous functions on the semigroup has a left invariant mean the results generalize those of downing and ray l lau 4 lim 6 7 and ishihara and takahashi 3

detecting phase synchronization in noisy data from coupled chaotic oscillators two schemes are proposed to detect phase synchronization from chaotic data contaminated by noise the first is a neighborhood based method which links time delay embedding with instantaneous phase estimation the second adopts the local projection method as a preprocessing filter to noisy data both schemes utilize the state recurrence an important feature of chaotic data the proposed schemes are applied to data measured from two typical chaotic systems i e the coupled rossler systems and the coupled lorenz systems respectively the results show that phase synchronization which may be buried by noise is detected even when the noise level is high moreover the overestimation of the degree of phase synchronization which may be introduced by the hilbert transform combined with a traditional linear bandpass filter can be avoided when the data are contaminated by only measurement noise

chaotic phase synchronization in bursting neuron models driven by a weak periodic force we investigate the entrainment of a neuron model exhibiting a chaotic spiking bursting behavior in response to a weak periodic force this model exhibits two types of oscillations with different characteristic time scales namely long and short time scales several types of phase synchronization are observed such as 1 1 phase locking between a single spike and one period of the force and 1 l phase locking between the period of slow oscillation underlying bursts and l periods of the force moreover spiking bursting oscillations with chaotic firing patterns can be synchronized with the periodic force such a type of phase synchronization is detected from the position of a set of points on a unit circle which is determined by the phase of the periodic force at each spiking time we show that this detection method is effective for a system with multiple time scales owing to the existence of both the short and the long time scales two characteristic phenomena are found around the transition point to chaotic phase synchronization one phenomenon shows that the average time interval between successive phase slips exhibits a power law scaling against the driving force strength and that the scaling exponent has an unsmooth dependence on the changes in the driving force strength the other phenomenon shows that kuramoto s order parameter before the transition exhibits stepwise behavior as a function of the driving force strength contrary to the smooth transition in a model with a single time scale

competition of synchronization domains in arrays of chaotic homoclinic systems we investigate the response of an open chain of bidirectionally coupled chaotic homoclinic systems to external periodic stimuli when one end of the chain is driven by a periodic signal the system propagates a phase synchronization state in a certain range of coupling strengths and external frequencies when two simultaneous forcings are applied at different points of the array a rich phenomenology of stable competitive states is observed including temporal alternation and spatial coexistence of synchronization domains

on the existence of fixed points and ergodic retractions for lipschitzian semigroups in hilbert spaces and especially nonexpansive in the case of k 1 let s be a semitopological semigroup and let s c s e s be a continuous representation of s as lipschitzian mappings of c into itself which is said to be a lipschitzian semigroup on c a lipschitzian semigroup s t s e s with lipschitz constants k s e s is called a uniformly k lipschitzian semigroup and a nonexpansive semigroup when k k and k 1 for all s e s respectively goebel and kirk 7 first called a mapping t of c into itself a uniformly k lipschitzian mapping on c in the case when s t n e n is a lipschitzian semigroup with k k for all n e n lifschitz 12 obtained a fixed point theorem for uniformly k lipschitzian mappings on c with k 5 and this result was extended to uniformly k lipschitzian semigroups which are left reversible by downing and ray 6 lau l l showed that a nonexpansive semigroup has a common fixed point if there exists a left invariant mean on the space rug s of bounded right uniformly continuous functions on the semigroup furthermore ishihara and takahashi 9 extended lau s result to uniformly k lipschitzian semigroups and also gave a simpler proof of downing and ray s theorem on the other hand the first nonlinear ergodic theorem for nonexpansive mappings was established by baillon 11 let t be a nonexpansive mapping of c into itself and suppose that the set f t of fixed points of t is nonempty the the cesaro means

uniformly normal structure and uniformly lipschitzian semigroups abstract assume that x is a real banach space with uniformly normal structure and c is a nonempty closed convex subset of x we show that a uniformly lipschitzian semigroup of nonlinear self mappings of c admits a common fixed point if the semigroup has a bounded orbit and if is appropriately greater than one this result applies in particular to the framework of uniformly convex banach spaces

estimating the support of a high dimensional distribution suppose you are given some data set drawn from an underlying probability distribution p and you want to estimate a simple subset s of input space such that the probability that a test point drawn from p lies outside of s equals some a priori specified value between 0 and 1 we propose a method to approach this problem by trying to estimate a function f that is positive on s and negative on the complement the functional form of f is given by a kernel expansion in terms of a potentially small subset of the training data it is regularized by controlling the length of the weight vector in an associated feature space the expansion coefficients are found by solving a quadratic programming problem which we do by carrying out sequential optimization over pairs of input patterns we also provide a theoretical analysis of the statistical performance of our algorithm the algorithm is a natural extension of the support vector algorithm to the case of unlabeled data

efficient convex relaxation methods for robust target localization by a sensor network using time differences of arrivals we consider the problem of target localization by a network of passive sensors when an unknown target emits an acoustic or a radio signal its position can be localized with multiple sensors using the time difference of arrival tdoa information in this paper we consider the maximum likelihood formulation of this target localization problem and provide efficient convex relaxations for this nonconvex optimization problem we also propose a formulation for robust target localization in the presence of sensor location errors two cramer rao bounds are derived corresponding to situations with and without sensor node location errors simulation results confirm the efficiency and superior performance of the convex relaxation approach as compared to the existing least squares based approach when large sensor node location errors are present

non transitive maps in phase synchronization abstract concepts from ergodic theory are used to describe the existence of special non transitive maps in attractors of phase synchronous chaotic oscillators in particular it is shown that for a class of phase coherent oscillators these special maps imply phase synchronization we illustrate these ideas in the sinusoidally forced chua s circuit and two coupled rossler oscillators furthermore these results are extended to other coupled chaotic systems in addition a phase for a chaotic attractor is defined from the tangent vector of the flow finally it is discussed how these maps can be used for the real time detection of phase synchronization in experimental systems

phase synchronization in the perturbed chua circuit we show experimental and numerical results of phase synchronization between the chaotic chua circuit and a small sinusoidal perturbation experimental real time phase synchronized states can be detected with oscilloscope visualization of the attractor using specific sampling rates arnold tongues demonstrate robust phase synchronized states for perturbation frequencies close to the characteristic frequency of the unperturbed chua

existence and approximation of fixed points of nonlinear mappings in spaces with weak uniform normal structure it is shown that in a banach space x with weak uniform normal structure every demicontinuous asymptotically regular nearly lipschitzian self mapping t with lim sup n h t n

a class of p convex spaces lacking normal structure abstract we prove that for any 1 the space e l 2 where max 2 is p convex it is known that for 2 e lacks normal structure

random fixed points of uniformly lipschitzian mappings abstract let be a measurable space x a banach space c a weakly convex subset of x and t c c a random operator we prove the random version of a deterministic fixed point theorem when t is an asymptotically nonexpansive mapping and the characteristic of convexity e0 x is less than 1 let n x be the normal structure coefficient of x and 0 x its lifschitz constant if t is k uniformly lipschitzian and there exists a constant c such that k c 1 1 4n x 0 x 1 2 we prove that t has a random fixed point

inequalities in banach spaces with applications well known that many problems in a hilbert space h are solved by applying the following identity ilax 1 a yi12 a412 1 llyl12 a 1 mx yl12 1 1 for all x y in h and 0 5 i 5 1 therefore one natural method to solve problems in a banach space xis to establish equalities and usually inequalities in xanalogous to 1 1 this is in fact shown by some authors recent work see for example reich l poffald and reich 2 lim 3 lim et af 4 prus and smarzewski 5 smarzewski 6 and reich 21 the purpose of this paper is to continue carrying out investigations in this line more precisely in section 3 we establish some inequalities analogous to 1 l in either uniformly convex or uniformly smooth banach spaces as corollaries we obtain new characteristics of p uniform convexity and q uniform smoothness of a banach space x via the functionals i lip and ii llq respectively we give in section 4 applications of the inequalities obtained in section 3 to fixed points of uniformly lipschitzian mappings and to best approximation theory

second order cone programming relaxation of sensor network localization the sensor network localization problem has been much studied recently biswas and ye proposed a semidefinite programming sdp relaxation of this problem which has various nice properties and for which a number of solution methods have been proposed here we study a second order cone programming socp relaxation of this problem motivated by its simpler structure and its potential to be solved faster than sdp we show that the socp relaxation though weaker than the sdp relaxation has nice properties that make it useful as a problem preprocessor in particular sensors that are uniquely positioned among interior solutions of the socp relaxation are accurate up to the square root of the distance error thus these sensors which are easily identified are accurately positioned in our numerical simulation the interior solution found can accurately position up to 80 90p of the sensors we also propose a smoothing coordinate gradient descent method for finding an interior solution that is faster than an interior point method

a simple and efficient estimator for hyperbolic location an effective technique in locating a source based on intersections of hyperbolic curves defined by the time differences of arrival of a signal received at a number of sensors is proposed the approach is noniterative and gives an explicit solution it is an approximate realization of the maximum likelihood estimator and is shown to attain the cramer rao lower bound near the small error region comparisons of performance with existing techniques of beamformer spherical interpolation divide and conquer and iterative taylor series methods are made the proposed technique performs significantly better than spherical interpolation and has a higher noise threshold than divide and conquer before performance breaks away from the cramer rao lower bound it provides an explicit solution form that is not available in the beamforming and taylor series methods computational complexity is comparable to spherical interpolation but substantially less than the taylor series method