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Maximum likelihood estimation problems are, in general, intractable optimization problems. As a result, it is common to approximate the maximum likelihood estimator (MLE) using convex relaxations. In some cases, the relaxation is tight: it recovers the true MLE. Most tightness proofs only apply to situations where the MLE exactly recovers a planted solution (known to the analyst). It is then sufficient to establish that the optimality conditions hold at the planted signal. In this paper, we study an estimation problem (angular synchronization) for which the MLE is not a simple function of the planted solution, yet for which the convex relaxation is tight. To establish tightness in this context, the proof is less direct because the point at which to verify optimality conditions is not known explicitly. Angular synchronization consists in estimating a collection of n phases, given noisy measurements of the pairwise relative phases. The MLE for angular synchronization is the solution of a (hard) non-bipartite Grothendieck problem over the complex numbers. We consider a stochastic model for the data: a planted signal (that is, a ground truth set of phases) is corrupted with non-adversarial random noise. Even though the MLE does not coincide with the planted signal, we show that the classical semidefinite relaxation for it is tight, with high probability. This holds even for high levels of noise. [ABSTRACT FROM AUTHOR]

In this paper, we study the influence of the inertial effect on frequency synchronization in an ensemble of Kuramoto oscillators with finite inertia and symmetric and connected interactions. We present sufficient conditions in terms of coupling strength, algebraic connectivity, natural frequencies, and the inertial term to guarantee the occurrence of frequency synchronization. We also make a comparison with the existing conditions proposed for the first-order Kuramoto model and conclude that the inertial effect, if appropriately small, has little influence on frequency synchronization as long as the initial phase configurations are distributed in a half circle. [ABSTRACT FROM AUTHOR]

This paper investigates the performance of acquisition section of synchronization in direct-sequence spread spectrum (DSSS-CDMA) under jamming attacks. DSSS-CDMA in this study uses chaotic sequences. The synchronization performance is analyzed under Gaussian and repeater jammer. The results of initial investigation show that the synchronization in DSSS-CDMA is vulnerable under these two jammers which may have significant effect on the probability of error rate. The analysis is performed based on the probability of detection and probability of false alarm, and mathematical expressions of these probabilities are derived. The amount of power which is required for each jammer to collapse the synchronization is derived. The theoretical results have been verified through Monte Carlo simulations in MATLAB. [ABSTRACT FROM AUTHOR]

We characterize the phase space for the infinite volume limit of a ferromagnetic mean-field XY model in a random field pointing in one direction with two symmetric values. We determine the stationary solutions and detect possible phase transitions in the interaction strength for fixed random field intensity. We show that at low temperature magnetic ordering appears perpendicularly to the field. The latter situation corresponds to a spin-flop transition. [ABSTRACT FROM AUTHOR]

In dissipationless linear lattices, spatial disorder or quasiperiodic modulations in on-site potentials induce localization of the eigenstates and block the spreading of wave packets. Quasiperiodic inhomogeneities allow for the metal-insulator transition at a finite modulation amplitude already in one dimension. We go beyond the dissipationless limit and consider nonlinear quasi-periodic arrays that are additionally subjected to dissipative losses and energy pumping. We find finite excitation thresholds for oscillatory phases in both metallic and insulating regimes. In contrast to disordered arrays, the transition in the metallic and weakly insulating regimes display features of the second order phase transition accompanied by a large-scale cluster synchronization. In the limit of strong localization, we find the existence of globally stable asymptotic states consisting of several localized modes. These localization attractors and chaotic synchronization effects can be potentially implemented with polariton condensate lattices and cavity-QED arrays. [ABSTRACT FROM AUTHOR]

Time synchronization is a fundamental requirement for many services provided by distributed systems. For this purpose, several time synchronization protocols have been proposed. However, they either achieve high accuracy by adding further network traffic, even more than common protocols such as network time protocol and precision time protocol, or consume a lot of time in additional computations. An online distributed tracing and monitoring system, used to identify functional and performance problems in distributed systems, must offer high precision with minimum time overhead and system resource consumption. The aim of this paper is to propose an efficient algorithm for time synchronization in online mode, applicable for all distributed services. The proposed method in this paper addresses five key requirements for a practical solution in distributed systems. First, it provides microseconds scale accuracy, which is applicable for trace events with nanosecond timestamp granularity. Secondly, it does not require adding new network traffic, using the send and receive time of existing traffic. Thirdly, it synchronizes the distributed traces in average time complexity of O(1) per synchronization update. Fourthly, it updates online synchronization parameters immediately without latency. Finally, it iteratively refines the early estimates without requiring significant buffering of earlier data. Although we used this work for distributed trace synchronization, it is a general, fully incremental, continuous synchronization approach applicable to most synchronization purposes. [ABSTRACT FROM AUTHOR]

In this paper, we consider parallelization of the loop over elements using OpenMP in FEAP (Taylor, ), which is a research FE code, very popular at universities. Even for a serial version of FEAP (a cluster version also exists) such a parallelization is a non-trivial task due to the existing architecture of this code, which complicates efficient parallelization. First, we compare the serial version of FEAP to the parallel code Warp3D (Dodds et al., ), considering the usage of time and memory. As we found, Warp3D is much faster but uses more memory than FEAP. An analysis of Warp3D helps us to devise our method of parallelization of the loop over elements. Next, we describe several changes in FEAP, which were necessary to parallelize the loop over elements using OpenMP. In particular, the subroutine assembling elemental matrices is identified as crucial to good performance, and several directives for the mutual exclusion synchronization of OpenMP are implemented and tested. Finally, we demonstrate the performance of the parallelized FEAP, designated as ompFEAP, on numerical examples involving 3D and shell elements of FEAP as well as user's elements. We conclude that ompFEAP, using the directive ATOMIC for synchronization of the assembling, provides a very good speedup and efficiency. [ABSTRACT FROM AUTHOR]

This paper presents an analytical study of synchronization in an array of output-coupled temporal Boolean networks. A temporal Boolean network (TBN) is a logical dynamic system developed to model Boolean networks with regulatory delays. Both state delay and output delay are considered, and these two delays are assumed to be different. By referring to the algebraic representations of logical dynamics and using the semi-tensor product of matrices, the output-coupled TBNs are firstly converted into a discrete-time algebraic evolution system, and then the relationship between the states of coupled TBNs and the initial state sequence is obtained. Then, some necessary and sufficient conditions are derived for the synchronization of an array of TBNs with an arbitrary given initial state sequence. Two numerical examples including one epigenetic model are finally given to illustrate the obtained results. [ABSTRACT FROM AUTHOR]

This paper proposes a robust nonsingular terminal sliding mode controller for synchronizing two different uncertain chaotic systems with nonlinear inputs. First, a novel nonsingular terminal sliding surface is introduced. Then, based on the finite-time control idea, a robust sliding mode control law is derived to guarantee the existence of the sliding motion in a given finite time. It is mathematically proved that both reaching and sliding phases are stable in finite time. Two illustrative examples are provided to demonstrate the robustness and applicability of the proposed sliding mode technique. It is worth noticing that the introduced nonsingular terminal sliding surface is applicable for a wide variety of nonlinear control problems. [ABSTRACT FROM AUTHOR]

Broad-area semiconductor lasers are unstable light sources even in solitary oscillation owing to the spatial dependence of laser emission along the stripe width. One of the instabilities that occur in the dynamics of broad-area semiconductor lasers is filamentation. Laser oscillations are further affected by optical feedback. In the presence of optical feedback, higher spatial modes related to the filamentations are either excited or suppressed depending on the feedback conditions. As a result, the beam shape of the time-averaged pattern is greatly affected by optical feedback. In this study, we perform the decomposition of spatial-mode components for time-averaged near-field patterns in the presence of optical feedback. A method of simulated annealing (SA) is employed for the decomposition. The beam profiles are well reconstructed by the SA method. A quantitative discussion of the excitation or suppression of higher spatial modes in relation to the optical feedback conditions is given. [ABSTRACT FROM AUTHOR]

We numerically investigate the effects of parameter mismatches on chaos synchronization in vertical-cavity surfaceemitting lasers (VCSELs). We assume injection-locked chaos synchronization in a unidirectionally coupled and openloop optical feedback system. The accuracy of chaos synchronization is greatly affected by the mismatches of the device parameters and operation conditions between the two lasers. In particular, the oscillation frequency of the laser is one of the important parameters in a system of injection-locked chaos synchronization. However, the variations of the device characteristics of VCSELs are very large compared with those of other types of semiconductor lasers. We study the effects of parameter mismatches related to the oscillation frequency of VCSELs on chaos synchronization. We proved that mismatches in terms of the birefringence and the injection current play crucial roles for the quality of chaos synchronization. [ABSTRACT FROM AUTHOR]

The problems of passification and synchronization of nonlinear systems are solved with the aid of the backstepping method for cascade systems of the Lurie type with functional uncertainty. Estimates of the errors caused by bounded disturbances and controller discreteness are given. The stated theorem is extended to the case of net systems. The obtained results are applied to the synchronization problem of movement of two mobile wheeled robots and are illustrated by way of computational modeling. [ABSTRACT FROM AUTHOR]

Methods of synchronizing interaction of the digital devices of distributed systems with the use of a common center relaying the signals from the devices were proposed. They are mostly intended to perform operations like 'all-to-all,' 'all-to-one,' and 'one-to-all.' The center substantially accelerates synchronization and improves efficiency of the communication facilities interconnecting the devices. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new input-to-state stable (ISS) synchronization method for a general class of chaotic systems with disturbances. Based on Lyapunov theory and linear matrix inequality (LMI) approach, for the first time, the ISS synchronization controller is presented not only to guarantee the asymptotic synchronization but also to achieve the bounded synchronization error for any bounded disturbance. The proposed controller can be obtained by solving a convex optimization problem represented by the LMI. Simulation studies are presented to demonstrate the effectiveness of the proposed ISS synchronization scheme. [ABSTRACT FROM AUTHOR]

1/ f β noise has been revealed in both self-paced and synchronized tapping sequences, without being consistently taken into consideration for the modeling of underlying timing mechanisms. In this study we characterize variability, short-range, and long-range correlation properties of asynchronies and inter-tap intervals collected in a synchronization tapping experiment, attesting statistically the presence of 1/ f β noise in asynchronies. We verify that the linear phase correction model of synchronization tapping in its original formulation cannot account for the empirical long-range correlation properties. On the basis of previous accounts of 1/ f β noise in the literature on self-paced tapping, we propose an extension of the original synchronization model by modeling the timekeeping process as a source of 1/ f β fluctuations. Simulations show that this ‘1/ f-AR synchronization model’ accounts for the statistical properties of empirical series, including long-range correlations, and provides an unifying mechanistic account of 1/ f β noise in self-paced and synchronization tapping. This account opens the original synchronization framework to further investigations of timing mechanisms with regard to the serial correlation properties in performed time intervals. [ABSTRACT FROM AUTHOR]

Abstract  The IEEE 802.11 standards support the peer-to-peer mode Independent Basic Service Set (IBSS), which is an ad hoc network with all its stations within each other’s transmission range. In an IBSS, it is important that all stations are synchronized to a common clock. Synchronization is essential for the MAC layer power management. Also, if frequency hopping spread spectrum is used in the physical layer, synchronization is needed to ensure that all stations “hop” at the same time. This paper evaluates the synchronization mechanism as specified in the IEEE 802.11 standards. Through rigorous analysis, it is shown that when the number of stations in an IBSS is not very small, there is a non-negligible probability that stations may get out of synchronization. The more stations, the higher probability of asynchronism. In this sense, the current IEEE 802.11 synchronization algorithm does not scale; it cannot support a large-scale IBSS. To alleviate the asynchronism problem, this paper proposes a simple remedy to the 802.11 algorithm. The resulting algorithm enjoys many nice properties—it is compatible, scalable, effective, mobility-friendly and simple. We are able to exceed the industry expectation of time accuracy (maximum clock offset under 12 μs) without any change of beacon format. [ABSTRACT FROM AUTHOR]

Abstract  A new method of synchronization of atomic timekeepers on the basis of pulsar time that has been synthesized on the basis of observations of the rotation parameters of a pulsar is considered. An analysis of the attainable synchronization precision is presented. [ABSTRACT FROM AUTHOR]

Two types of phase synchronization (accordingly, two scenarios of breaking phase synchronization) between coupled stochastic oscillators are shown to exist depending on the discrepancy between the control parameters of interacting oscillators, as in the case of classical synchronization of periodic oscillators. If interacting stochastic oscillators are weakly detuned, the phase coherency of the attractors persists when phase synchronization breaks. Conversely, if the control parameters differ considerably, the chaotic attractor becomes phase-incoherent under the conditions of phase synchronization break. [ABSTRACT FROM AUTHOR]

A new method is proposed for the investigation of transitions from synchronous dynamics of coupled oscillators to asynchronous regimes attained upon synchronization breakage by a sequence of short phase resetting pulses. The possibility to use the proposed method for determining the coefficient of coupling between interacting systems from an analysis of the signals generated by these systems is considered. [ABSTRACT FROM AUTHOR]

Edwards transformations relating inertial frames with arbitrary clock synchronization are reviewed and put in more general setting. Their group-theoretical context is described. [ABSTRACT FROM AUTHOR]