Pairwise Synchronization Research Articles

Product-Forms in Multi-Way Synchronizations

A new algorithm is given to find product-form solutions for the joint equilibrium probabilities in a class of synchronized Markov processes.This is based on, and proved by, multiple applications of the Reversed CompoundAgent Theorem (RCAT) and can describe multi-way synchronizations (seen as chains of pairwise synchronizations) that occur in a prescribed order. The length of the sequence is unbounded but finite with probability 1. Several applications are given to illustrate the methodology, which include various modes of resets in queueing networks with negative customers. In particular, it is shown that there is a type of reset that can propagate further transitions in a chain actively. Furthermore, a number of completely new product-form models, for example, where the transitions in a chain are non-homogeneous, are given.

무선 센서 네트워크에서 시각 동기 정확도 분석

센서 네트워크의 여러 핵심 기술 요소 중에서 시각 동기 기술은 센서 네트워크 응용에 필수 요소이다. 여러 노드들로부터 같은 이벤트의 중복 감지 인식, 기록된 이벤트의 발생순서 구분, 이동체의 이동 속도 계산 등에 시각 정보는 기저 데이터가 된다. 본 논문에서는 다양한 무선 센서 네트워크 시각 동기 기법 중 대표적인 시각 동기 모델인 pair-wise 시각 동기 알고리즘을 대상으로 시각 동기 오류 요소를 추출하고 이러한 오류 요소가 시각 동기 정확도에 끼치는 영향을 이론적으로 분석하였다. 또한 시뮬레이션을 통해 이론적 분석 결과를 검증하였다. 이러한 결과는 향후 센서 네트워크 시각 동기 알고리즘의 성능 개선이나 개발에 활용될 것으로 기대된다. Time synchronization is a prerequisite in wireless sensor network applications such as object tracking, consistent state update, duplication detection, and temporal order delivery. This paper analyze time synchronization accuracy of pair-wise time synchronization algorithm which is a typical time synchronization model of time synchronization method in wireless sensor networks. In addition, the analyzed results are verified by simulations. These results can be utilized for performance improvement or development of time synchronization in wireless sensor networks.

Joint Estimation of Clock Skew and Offset in Pairwise Broadcast Synchronization Mechanism

The problem of jointly estimating clock skew and offset for wireless sensor networks (WSNs) in a pairwise broadcast synchronization (PBS) protocol is considered. The random part of the delay is supposed to be an exponential random variable. We consider two estimators, i.e., joint maximum-likelihood estimator (JMLE) and generalized ML-like estimator (GMLLE) proposed by Leng and Wu . For both estimators, the corresponding algorithms are explicitly derived and presented. For the GMLLE, the corresponding performance bound based on the reduced set of observations is derived and the optimal value of a user-defined parameter is identified accordingly. At last, analytical results are corroborated by numerical experiments. We observe that: (i) JMLE usually outperforms GMLLE at the cost of larger computational complexity; (ii) JMLE, while achieving the same estimation accuracy as that of the LP method presented in , enjoys significantly lower computational complexity than that of the latter.

Stable pairwise time synchronization in the application layer for capillary machine-to-machine networks

This paper presents the design and performance evaluation of a stable pairwise time synchronization protocol (abbreviated SPS) for capillary machine-to-machine (M2M) networks that provides underlying platform independence and operational stability, even under harsh conditions. SPS achieves the first criterion using a novel technique whereby the M2M device captures incoming or outgoing moments of timing messages. The second criterion is achieved by adaptively adjusting the resynchronization interval. Extensive simulations are conducted to demonstrate the validity and effectiveness of SPS.

Stability of Coupled Local Minimizers Within the Lagrange Programming Network Framework

Coupled local minimizers (CLMs) turn out to be a potential global optimization strategy to explore a search space, avoid overfitting and produce good generalization. In this paper, convergence properties of CLMs based on an augmented Lagrangian function in the context of equality constrained minimization, are studied. We first consider the augmented Lagrangian by taking the objective of minimizing the average cost of an ensemble of local minimizers subject to pairwise synchronization constraints. Then we study an array of CLMs within the Lagrange programming network framework and analyze the local stability of CLMs using a linearization strategy. We further show that, under some mild conditions, global asymptotical stability of the unique equilibrium point of the network can be guaranteed. Afterwards, some sufficient conditions are presented to ensure the stability of synchronization between any two minimizers via a directed graph method. The results show that the CLMs usually can be synchronized if the penalty factors in the array of CLMs are chosen large enough. It is worth pointing out that CLMs possess the capability of global exploration in the search space and the advantage of faster running time on convex problems in comparison with most of the neural network approaches, which is also illustrated through two test functions and their numerical simulations.

Effect of phase response curve skew on synchronization with and without conduction delays

A central problem in cortical processing including sensory binding and attentional gating is how neurons can synchronize their responses with zero or near-zero time lag. For a spontaneously firing neuron, an input from another neuron can delay or advance the next spike by different amounts depending upon the timing of the input relative to the previous spike. This information constitutes the phase response curve (PRC). We present a simple graphical method for determining the effect of PRC shape on synchronization tendencies and illustrate it using type 1 PRCs, which consist entirely of advances (delays) in response to excitation (inhibition). We obtained the following generic solutions for type 1 PRCs, which include the pulse-coupled leaky integrate and fire model. For pairs with mutual excitation, exact synchrony can be stable for strong coupling because of the stabilizing effect of the causal limit region of the PRC in which an input triggers a spike immediately upon arrival. However, synchrony is unstable for short delays, because delayed inputs arrive during a refractory period and cannot trigger an immediate spike. Right skew destabilizes antiphase and enables modes with time lags that grow as the conduction delay is increased. Therefore, right skew favors near synchrony at short conduction delays and a gradual transition between synchrony and antiphase for pairs coupled by mutual excitation. For pairs with mutual inhibition, zero time lag synchrony is stable for conduction delays ranging from zero to a substantial fraction of the period for pairs. However, for right skew there is a preferred antiphase mode at short delays. In contrast to mutual excitation, left skew destabilizes antiphase for mutual inhibition so that synchrony dominates at short delays as well. These pairwise synchronization tendencies constrain the synchronization properties of neurons embedded in larger networks.

A dataflow-like programming model for future hybrid clusters

It is expected that the first exascale supercomputer will be deployed within the next 10 years, however both its CPU architecture and programming model are not known yet. Multicore CPUs are not expected to scale to the required number of cores per node, but hybrid multicore CPUs consisting of different kinds of processing elements are expected to solve this issue. They come at the cost of increased software development complexity with \eg, missing cache coherency and on-chip NUMA effects. It is unclear whether MPI and OpenMP will scale to exascale systems and support easy development and scalable and efficient programs. One of the programming models considered as an alternative is the the so-called partitioned global address space~(PGAS) model, which is targeted at easy development by providing one common memory address space across all cluster nodes. In this paper we first outline current and possible future hardware and introduce a new abstract hardware model able to describe hybrid clusters. We discuss how current shared memory, GPU and PGAS programming models can deal with the upcoming hardware challenges and describe how synchronization can generate unneeded inter- and intra-node transfers in case the memory consistency model is not optimal. As a major contribution, we introduce our variation of the PGAS model allowing implicit fine-grained pair-wise synchronization among the nodes and the different kinds of processors. We furthermore offer easy deployment of RDMA transfers and provide communication algorithms commonly used in MPI collective operations, but lift the requirement of the operations to be collective. Our model is based on single assignment variables and uses a data-flow like synchronization mechanism. Reading uninitialized variables results in the reading thread to be blocked until data are made available by another thread. That way synchronization is done implicitly when data are read. Explicit tiling is used to reduce synchronization overhead and to increase cache and network utilization. Broadcast, scatter and gather are modeled based on data distribution among the nodes, whereas reduction and scan follow a combining PRAM approach of having multiple threads write to the same memory location. We discuss the GauAŸ-Seidel stencil, bitonic sort, FFT and a manual scan implementation in our model. We implemented a proof-of-concept library showing the usability and scalability of the model. With this library the GauAŸ-Seidel stencil scaled well in initial experiments on an 8-node machine and we show that it is easy to keep two GPUs and multiple cores busy when computing a scan.

Soft-TDMAC: A Software-Based 802.11 Overlay TDMA MAC with Microsecond Synchronization

We implement a new software-based multihop TDMA MAC protocol (Soft-TDMAC) with microsecond synchronization using a novel system interface for development of 802.11 overlay TDMA MAC protocols (SySI-MAC). SySI-MAC provides a kernel independent message-based interface for scheduling transmissions and sending and receiving 802.11 packets. The key feature of SySI-MAC is that it provides near deterministic timers and transmission times, which allows for implementation of highly synchronized TDMA MAC protocols. Building on SySI-MAC's predictable transmission times, we implement Soft-TDMAC, a software-based 802.11 overlay multihop TDMA MAC protocol. Soft-TDMAC has a synchronization mechanism, which synchronizes all pairs of network clocks to within microseconds of each other. Building on pairwise synchronization, Soft-TDMAC achieves tight network-wide synchronization. With network-wide synchronization independent of data transmissions, Soft-TDMAC can schedule arbitrary TDMA transmission patterns. For example, Soft-TDMAC allows schedules that decrease end-to-end delay and take end-to-end rate demands into account. We summarize hundreds of hours of testing Soft-TDMAC on a multihop testbed, showing the synchronization capabilities of the protocol and the benefits of flexible scheduling.

Nonlinear integration of multispectral information: Human colour vision analogues to sensory integration in rattlesnake

Information integration occurs at every sensory scale and although distinctions are made for integration between and within senses, integration at intermediate scales may exploit familiar mechanisms. Here, we explore this idea by applying a sensory integration mechanism to some poorly understood multispectral integration problems in human colour vision. Billock and Tsou (IMRF, 2011) used a binding-like neural synchronization mechanism to model intensity-dependent (inverse) enhancement of visual responses by auditory stimulation in cat. The same model also applies to mutual enhancement of visual and infrared responses in rattlesnake, suggesting that a similar mechanism could model integration of spectral information in human colour vision. For example, chromatic brightness is thought to be a vector-like nonlinear combination of luminance and chromatic channels; its neural correlate is unknown. We model its spectral sensitivity by pairwise excitatory synchronization between luminance (broadband) neurons and cortically rectified L+M- and S+M-L- LGN neurons. Similarly, the yellow lobe of the yellow-blue opponent channel is known to be a nonlinearly enhanced combination of long- and medium-wavelength-sensitive inputs, but no sensible neural model for this interaction has been advanced. We model the spectral sensitivity of ‘yellowness’ using excitatory synchronization between cortically rectified L+M+S- and M+L- LGN units. The inputs for both simulations were macaque neural firing rate data (DeValois et al., 1966). Fascinatingly, in both cases, multispectral integration in human colour vision was well modeled using the rattlesnake/cat neural synchronization equations without any use of fitting parameters. This is the first application of sensory integration concepts to human colour vision transformations.

Special issue on "Towards the connected body: advances in body communications"

Body area networks (BANs) are quickly becoming a key technology for wireless communications. They consist of body-worn or implanted sensors that wirelessly communicate, leading either to inor on-body communications between sensors, or to off-body communications with devices located in the close vicinity. BAN’s potential applications include, among others, m-health information systems collecting vital parameters in real-time, high-speed connections over the body surface for multimedia transfers or human body interactions with its environment for augmented reality devices. Several technologies are currently under development in order to enable these communications, either narrowband (including RFID technologies), or ultra-wideband (IR-UWB). The latter could be advantageously coupled with positioning algorithms for simultaneous body motion capture. However, in practice, numerous challenges still need to be tackled in order to make BANs viable. The sensor’s autonomy, size, and cost are critical parameters which can only be optimized by adopting an interdisciplinary approach, where the propagation phenomena, the coding or relaying strategies, the MAC protocols, and the network topology are strongly interrelated. The coexistence issue with other networks also seems to be crucial, especially in the hospital environment. This special issue goes through all the layers of telecommunication systems dedicated to body communications, from channel models for onor off-body communications, to global telecare systems based on Bluetooth, smartphones, and GPS. The article “Experimental characterization of an UWB channel for body area networks” by P. Chiang et al. presents UWB channel measurement campaigns, for both onand off-body communications. The measured path loss and multipath analysis suggest that a LOS UWB channel is excellent for low-power, high-data-rate transmission, while NLOS and on-body channels need to be reconfigured to operate at a lower data rate due to high path loss. The article “An analytical modeling of polarized timevariant on-body propagation channels with dynamic body scattering” by L. Liu et al. presents an analytical model of the on-body scattering and propagation on the trunk of a walking person. The results act as an example of how analytical models can provide efficient yet precise predictions of time-variant, on-body propagation to understand the mechanisms underlying the propagation characteristics. The article “In-body Path Loss Models for Implants in Heterogeneous Human Tissues using Implantable Slot Dipole Conformal Flexible Antennas” by F. Axisa et al. discusses the path loss of implant communication channel for a 6-year male child with slot dipole conformal antennas at 2.45 GHz via 3D electromagnetic simulations. The article proves that exponential attenuation model is well applicable to the heterogeneous model as well, but homogeneous phantom may underestimate the pathloss compared with more realistic heterogeneous phantom. The article “Secure Precise Clock Synchronization for Interconnected Body Area Networks” by D. Sanchez et al. tackles secure time synchronization in BANs. A combination of secure pairwise synchronization, rate adaptive time synchronization, and μTESLA is used to achieve energy efficient, accurate, and secure synchronization between BAN nodes. In “Emergency Handling for MAC protocol in Human Body Communication (HBC-MAC)” by O. Buyanjargal et al., a specific emergency handling operation is proposed for BAN’s MAC protocol in order to meet the emergency requirements for BAN without wasteful dedicated slots for emergency in each superframe. The article “Impact of the Environment and the Topology on the Performance of Hierarchical Body Area Networks” by J.-M. Dricot et al. addresses the throughput and energy consumption of various BAN topologies * Correspondence: pdedonck@ulb.ac.be Universite libre de Bruxelles, Bruxelles, Belgium Full list of author information is available at the end of the article De Doncker et al. EURASIP Journal on Wireless Communications and Networking 2011, 2011:203 http://jwcn.eurasipjournals.com/content/2011/1/203

Gibbs distribution analysis of temporal correlations structure in retina ganglion cells

We present a method to estimate Gibbs distributions with spatio-temporal constraints on spike trains statistics. We apply this method to spike trains recorded from ganglion cells of the salamander retina, in response to natural movies. Our analysis, restricted to a few neurons, performs more accurately than pairwise synchronization models (Ising) or the 1-time step Markov models (Marre et al., 2009) to describe the statistics of spatio-temporal spike patterns and emphasizes the role of higher order spatio-temporal interactions.

Loss of ‘Small-World’ Networks in Alzheimer's Disease: Graph Analysis of fMRI Resting-State Functional Connectivity

BackgroundLocal network connectivity disruptions in Alzheimer's disease patients have been found using graph analysis in BOLD fMRI. Other studies using MEG and cortical thickness measures, however, show more global long distance connectivity changes, both in functional and structural imaging data. The form and role of functional connectivity changes thus remains ambiguous. The current study shows more conclusive data on connectivity changes in early AD using graph analysis on resting-state condition fMRI data.Methodology/Principal Findings18 mild AD patients and 21 healthy age-matched control subjects without memory complaints were investigated in resting-state condition with MRI at 1.5 Tesla. Functional coupling between brain regions was calculated on the basis of pair-wise synchronizations between regional time-series. Local (cluster coefficient) and global (path length) network measures were quantitatively defined. Compared to controls, the characteristic path length of AD functional networks is closer to the theoretical values of random networks, while no significant differences were found in cluster coefficient. The whole-brain average synchronization does not differ between Alzheimer and healthy control groups. Post-hoc analysis of the regional synchronization reveals increased AD synchronization involving the frontal cortices and generalized decreases located at the parietal and occipital regions. This effectively translates in a global reduction of functional long-distance links between frontal and caudal brain regions.Conclusions/SignificanceWe present evidence of AD-induced changes in global brain functional connectivity specifically affecting long-distance connectivity. This finding is highly relevant for it supports the anterior-posterior disconnection theory and its role in AD. Our results can be interpreted as reflecting the randomization of the brain functional networks in AD, further suggesting a loss of global information integration in disease.

Inferring the physical connectivity of complex networks from their functional dynamics

BackgroundBiological networks, such as protein-protein interactions, metabolic, signalling, transcription-regulatory networks and neural synapses, are representations of large-scale dynamic systems. The relationship between the network structure and functions remains one of the central problems in current multidisciplinary research. Significant progress has been made toward understanding the implication of topological features for the network dynamics and functions, especially in biological networks. Given observations of a network system's behaviours or measurements of its functional dynamics, what can we conclude of the details of physical connectivity of the underlying structure?ResultsWe modelled the network system by employing a scale-free network of coupled phase oscillators. Pairwise phase coherence (PPC) was calculated for all the pairs of oscillators to present functional dynamics induced by the system. At the regime of global incoherence, we observed a Significant pairwise synchronization only between two nodes that are physically connected. Right after the onset of global synchronization, disconnected nodes begin to oscillate in a correlated fashion and the PPC of two nodes, either connected or disconnected, depends on their degrees.Based on the observation of PPCs, we built a weighted network of synchronization (WNS), an all-to-all functionally connected network where each link is weighted by the PPC of two oscillators at the ends of the link. In the regime of strong coupling, we observed a Significant similarity in the organization of WNSs induced by systems sharing the same substrate network but different configurations of initial phases and intrinsic frequencies of oscillators.We reconstruct physical network from the WNS by choosing the links whose weights are higher than a given threshold. We observed an optimal reconstruction just before the onset of global synchronization.Finally, we correlated the topology of the background network to the observed change of the functional activities in the system.ConclusionsThe results presented in this study indicate a strong relationship between the structure and dynamics of complex network systems. As coupling strength increases, synchronization emerges among hub nodes and recruits small-degree nodes. The results show that the onset of global synchronization in the system hinders the reconstruction of an underlying complex structure. Our analysis helps to clarify how the synchronization is achieved in systems of different network topologies.

Network synchronization landscape reveals compensatory structures, quantization, and the positive effect of negative interactions

Synchronization, in which individual dynamical units keep in pace with each other in a decentralized fashion, depends both on the dynamical units and on the properties of the interaction network. Yet, the role played by the network has resisted comprehensive characterization within the prevailing paradigm that interactions facilitating pairwise synchronization also facilitate collective synchronization. Here we challenge this paradigm and show that networks with best complete synchronization, least coupling cost, and maximum dynamical robustness, have arbitrary complexity but quantized total interaction strength, which constrains the allowed number of connections. It stems from this characterization that negative interactions as well as link removals can be used to systematically improve and optimize synchronization properties in both directed and undirected networks. These results extend the recently discovered compensatory perturbations in metabolic networks to the realm of oscillator networks and demonstrate why "less can be more" in network synchronization.

A distributed multihop time synchronization protocol for wireless sensor networks using Pairwise Broadcast Synchronization

Recently, a time synchronization algorithm called pairwise broadcast synchronization (PBS) is proposed. With PBS, a sensor can be synchronized by overhearing synchronization packet exchange among its neighbouring sensors without sending out any packet itself. In an one-hop sensor network where every node is a neighbour of each other, a single PBS message exchange between two nodes would facilitate all nodes to synchronize. However, in a multi-hop sensor network, PBS message exchanges in several node pairs are needed in order to achieve network-wide synchronization. To reduce the number of message exchanges, these node pairs should be carefully chosen. In this paper, we investigate how to choose these ldquoappropriaterdquo sensors aiming at reducing the number of PBS message exchanges while allowing every node to synchronize. This selection problem is shown to be NP-complete, for which the greedy heuristic is a good polynomial-time approximation algorithm. Nevertheless, a centralized algorithm is not suitable for wireless sensor networks. Therefore, we develop a distributed heuristic algorithm allowing a sensor to determine how to synchronize itself based on its neighbourhood information only. The protocol is tested through extensive simulations. The simulation results reveal that the proposed protocol gives consistent performance under different conditions with its performance comparable to that of the centralized algorithm.

Broadband Criticality of Human Brain Network Synchronization

Self-organized criticality is an attractive model for human brain dynamics, but there has been little direct evidence for its existence in large-scale systems measured by neuroimaging. In general, critical systems are associated with fractal or power law scaling, long-range correlations in space and time, and rapid reconfiguration in response to external inputs. Here, we consider two measures of phase synchronization: the phase-lock interval, or duration of coupling between a pair of (neurophysiological) processes, and the lability of global synchronization of a (brain functional) network. Using computational simulations of two mechanistically distinct systems displaying complex dynamics, the Ising model and the Kuramoto model, we show that both synchronization metrics have power law probability distributions specifically when these systems are in a critical state. We then demonstrate power law scaling of both pairwise and global synchronization metrics in functional MRI and magnetoencephalographic data recorded from normal volunteers under resting conditions. These results strongly suggest that human brain functional systems exist in an endogenous state of dynamical criticality, characterized by a greater than random probability of both prolonged periods of phase-locking and occurrence of large rapid changes in the state of global synchronization, analogous to the neuronal “avalanches” previously described in cellular systems. Moreover, evidence for critical dynamics was identified consistently in neurophysiological systems operating at frequency intervals ranging from 0.05–0.11 to 62.5–125 Hz, confirming that criticality is a property of human brain functional network organization at all frequency intervals in the brain's physiological bandwidth.

Constraining Minimum-Norm Inverse by Phase Synchronization and Signal Power of the Scalp EEG Channels

In this paper, the goal is to further improve the output of the scalp EEG source localization by the Euclidean minimum-norm (MN) inverse during single trials. Trials have been selected based on signal power at specific time intervals in specific locations. Then the source localization has been performed by MN. It has been observed that close to a dominant cortical source of EEG, as determined by the MN, both pairwise phase synchronization of a channel with its nearest neighbors and the cumulative signal power of the channels within that neighborhood become high (normalized values remain above certain thresholds). This has also been verified through simulations on the subject's real head model. The conclusion of our study is that only those sources are to be chosen for which MN inverse, and signal power and phase synchronization profile converge. A novel fast Fourier transform (FFT) based phase synchronization measuring algorithm between a pair of signals has been developed whose time complexity is no more than that of the FFT.

Combined vehicle routing and scheduling with temporal precedence and synchronization constraints

We present a mathematical programming model for the combined vehicle routing and scheduling problem with time windows and additional temporal constraints. The temporal constraints allow for imposing pairwise synchronization and pairwise temporal precedence between customer visits, independently of the vehicles. We describe some real world problems where in the literature the temporal constraints are usually remarkably simplified in the solution process, even though these constraints may significantly improve the solution quality and/or usefulness. We also propose an optimization based heuristic to solve real size instances. The results of numerical experiments substantiate the importance of the temporal constraints in the solution approach. We also make a computational study by comparing a direct use of a commercial solver against the proposed heuristic, where the latter approach can find high quality solutions within specific time limits.

Neuronal Activity of the Human Subthalamic Nucleus in the Parkinsonian and Nonparkinsonian State

We recorded resting-state neuronal activity from the human subthalamic nucleus (STN) during functional stereotactic surgeries. By inserting up to five parallel microelectrodes for single- or multiunit recordings and applying statistical spike-sorting methods, we were able to isolate a total of 351 single units in 65 patients with Parkinson's disease (PD) and 33 single units in 9 patients suffering from essential tremor (ET). Among these were 93 pairs of simultaneously recorded neurons in PD and 17 in ET, which were detected either by the same (n = 30) or neighboring microelectrodes (n = 80). Essential tremor is a movement disorder without any known basal ganglia pathology and with normal dopaminergic brain function. By comparing the neuronal activity of the STN in patients suffering from PD and ET we intended to characterize, for the first time, changes of basal ganglia activity in the human disease state that had previously been described in animal models of Parkinson's disease. We found a significant increase in the mean firing rate of STN neurons in PD and a relatively larger fraction of neurons exhibiting burstlike activity compared with ET. The overall proportion of neurons exhibiting intrinsic oscillations or interneuronal synchronization as defined by significant spectral peaks in the auto- or cross-correlations functions did not differ between PD and ET when considering the entire frequency range of 1-100 Hz. The distribution of significant oscillations across the theta (1-8 Hz), alpha (8-12 Hz), beta (12-35 Hz), and gamma band (>35 Hz), however, was uneven in ET and PD, as indicated by a trend in Fisher's exact test (P = 0.05). Oscillations and pairwise synchronizations within the 12- to 35-Hz band were a unique feature of PD. Our results confirm the predictions of the rate model of Parkinson's disease. In addition, they emphasize abnormalities in the patterning and dynamics of neuronal discharges in the parkinsonian STN, which support current concepts of abnormal motor loop oscillations in Parkinson's disease.

Secure Time Synchronization in Sensor Networks

Time synchronization is critical in sensor networks at many layers of their design. It enables better duty-cycling of the radio, accurate and secure localization, beamforming, and other collaborative signal processing tasks. These benefits make time-synchronization protocols a prime target of malicious adversaries who want to disrupt the normal operation of a sensor network. In this article, we analyze attacks on existing time synchronization protocols for wireless sensor networks and we propose a secure time synchronization toolbox to counter these attacks. This toolbox includes protocols for secure pairwise and group synchronization of nodes that either lie in the neighborhood of each other or are separated by multiple hops. We provide an in-depth analysis of the security and the energy overhead of the proposed protocols. The efficiency of these protocols has been tested through an experimental study on Mica2 motes.