Unidirectional Rings Research Articles

Unidirectional and hierarchical on-chip interconnected architecture for large-scale hardware spiking neural networks

Spiking Neural Networks (SNNs) exhibit the strong capability to address spatiotemporal dynamic problems. Recent research has explored the hardware SNN systems to solve the spatiotemporal problems in real-time. The Network-on-Chip (NoC) is an effective scheme for building large-scale hardware SNNs. However, for the existing NoC-based hardware SNNs, large area overhead and hardware power are consumed by their interconnections, because of complex topologies and router structures. Therefore, in this work a novel Unidirectional and Hierarchical on-Chip Interconnected Architecture (UHCIA) is proposed to address this problem. The proposed UHCIA mainly combines the novel hybrid topology of unidirectional multiple loops and rings, and uses a deflection router technique. Experimental results show that compared to other works, the UHCIA achieves ∼23.6X of area reduction and ∼6.4X of power reduction, with high system throughput and biological real-time computations.

Dynamics of coexisting rotating waves in unidirectional rings of bistable Duffing oscillators

We study the dynamics of multistable coexisting rotating waves that propagate along a unidirectional ring consisting of coupled double-well Duffing oscillators with different numbers of oscillators. By employing time series analysis, phase portraits, bifurcation diagrams, and basins of attraction, we provide evidence of multistability on the route from coexisting stable equilibria to hyperchaos via a sequence of bifurcations, including the Hopf bifurcation, torus bifurcations, and crisis bifurcations, as the coupling strength is increased. The specific bifurcation route depends on whether the ring comprises an even or odd number of oscillators. In the case of an even number of oscillators, we observe the existence of up to 32 coexisting stable fixed points at relatively weak coupling strengths, while a ring with an odd number of oscillators exhibits 20 coexisting stable equilibria. As the coupling strength increases, a hidden amplitude death attractor is born in an inverse supercritical pitchfork bifurcation in the ring with an even number of oscillators, coexisting with various homoclinic and heteroclinic orbits. Additionally, for stronger coupling, amplitude death coexists with chaos. Notably, the rotating wave speed of all coexisting limit cycles remains approximately constant and undergoes an exponential decrease as the coupling strength is increased. At the same time, the wave frequency varies among different coexisting orbits, exhibiting an almost linear growth with the coupling strength. It is worth mentioning that orbits originating from stronger coupling strengths possess higher frequencies.

Election in unidirectional rings with homonyms

We study leader election in unidirectional rings of homonyms that have no a priori knowledge of the number of processes. In this context, we show that there exists no algorithm that solves the process-terminating leader election problem for the class of asymmetrically labeled unidirectional rings. More precisely, we prove that there is no process-terminating leader election algorithm even for the subclass of unidirectional rings where at least one label is unique. Message-terminating leader election is also impossible for the class of unidirectional rings where only a bound on multiplicity is known. However, we show that the process-terminating leader election is possible for two particular subclasses of asymmetrically labeled unidirectional rings where the multiplicity is bounded. We propose three efficient algorithms and analyze their complexities. We also give some non-trivial lower bounds.

Space-efficient uniform deployment of mobile agents in asynchronous unidirectional rings

In this paper, we consider the uniform deployment problem of mobile agents in asynchronous unidirectional ring networks. This problem requires agents to spread uniformly in the network. In this paper, we focus on the memory space per agent required to solve the problem. We consider two problem settings. The first setting assumes that agents have no multiplicity detection, that is, agents cannot detect whether another agent is staying at the same node or not. In this case, we show that each agent requires Ω(log⁡n) memory space to solve the problem, where n is the number of nodes. In addition, we propose an algorithm to solve the problem with O(k+log⁡n) memory space per agent, where k is the number of agents. The second setting assumes that each agent is equipped with the weak multiplicity detection, that is, agents can detect whether another agent is staying at the same node or not, but cannot get any other information about the number of the agents. Then, we show that the memory space per agent can be reduced to O(log⁡k+log⁡log⁡n). To the best of our knowledge, this is the first research considering the effect of the multiplicity detection on memory space required to solve problems.

Topology-Specific Synthesis of Self-Stabilizing Parameterized Systems with Constant-Space Processes

This paper investigates the synthesis of parameterized systems that are self-stabilizing by construction. To this end, we present several significant results. First, we show a counterintuitive result that despite the undecidability of verifying self-stabilization for parameterized unidirectional rings, synthesizing self-stabilizing unidirectional rings is decidable! This is surprising because it is known that, in general, the synthesis of distributed systems is harder than their verification. Second, we present a topology-specific synthesis method (derived from our proof of decidability) that generates the state transition system of template processes of parameterized self-stabilizing systems with elementary unidirectional topologies (e.g., rings, chains, trees). We also provide a software tool that implements our synthesis algorithms and generates interesting self-stabilizing parameterized unidirectional rings in less than 50 microseconds on a regular laptop. We validate the proposed synthesis algorithms for decidable cases in the context of several interesting distributed protocols. Third, we show that synthesis of self-stabilizing bidirectional rings remains undecidable.

On the Verification of Livelock-Freedom and Self-Stabilization on Parameterized Rings

This article investigates the verification of livelock-freedom and self-stabilization on parameterized rings consisting of symmetric, constant space, deterministic, and self-disabling processes. The results of this article have a significant impact on several fields, including scalable distributed systems, resilient and self- * systems, and verification of parameterized systems. First, we identify necessary and sufficient local conditions for the existence of global livelocks in parameterized unidirectional rings with unbounded (but finite) number of processes under the interleaving semantics. Using a reduction from the periodic domino problem, we show that, in general, verifying livelock-freedom of parameterized unidirectional rings is undecidable (specifically, Π 1 0 -complete) even for constant space, deterministic, and self-disabling processes. This result implies that verifying self-stabilization for parameterized rings of self-disabling processes is also undecidable. We also show that verifying livelock-freedom and self-stabilization remain undecidable under (1) synchronous execution semantics, (2) the FIFO consistency model, and (3) any scheduling policy. We then present a new scope-based method for detecting and constructing livelocks in parameterized rings. The proposed semi-algorithm behind our scope-based verification is based on a novel paradigm for the detection of livelocks that totally circumvents state space exploration. Our experimental results on an implementation of the proposed semi-algorithm are very promising as we have found livelocks in parameterized rings in a few microseconds on a regular laptop. The results of this article have significant implications for scalable distributed systems with cyclic topologies.

Research on Complex Structures in Space Fault Network for Fault Data Mining in System Fault Evolution Process

To study the system fault evolution process, and mine the relationships among the fault data, fault factors and fault events, we propose the theory of space fault network. The paper is composed of three parts. In the first part, the shortcomings of the existing studies on unidirectional ring in space fault network are discussed, and three new network description forms of typical unidirectional rings are formulated and the corresponding space fault tree transformation mechanism. The concepts of ring structure, ordered relation, equivalence event and equivalence connection are defined according to the need. Three methods for calculating the target event probability are given. The second part studies the all event induction fault evolution process. All of its edge events and process events lead to the target event. The meaning of all event induction fault evolution process is discussed. Two methods, general fault evolution process and all event induction fault evolution process, are used to calculate the target event probability in the evolution process of a single route and network structure. In the third part, the impact of some event repeatability on the fault and the time characteristics of the evolution process are studied, and the definitions of event repeatability and timeliness are proposed. The occurrence time and duration of events and connections are given to characterize the time characteristics. Finally, according to repeatability and timeliness, the measures to prevent the target event are given. The paper provides a new theory and method for mining system fault evolution process from fault data, fault factors and fault events.

Uniform deployment of mobile agents in asynchronous rings

In this paper, we consider the uniform deployment problem of mobile agents in asynchronous unidirectional rings, which requires the agents to uniformly spread in the ring. The uniform deployment problem is in striking contrast to the rendezvous problem which requires the agents to meet at the same node. While rendezvous aims to break the symmetry, uniform deployment aims to attain the symmetry. It is well known that the symmetry breaking is difficult in distributed systems and the rendezvous problem cannot be solved from some initial configurations. Hence, we are interested in clarifying what difference the uniform deployment problem has on the solvability and the number of agent moves compared to the rendezvous problem. We consider two problem settings, with knowledge of k (or n) and without knowledge of k or n where k is the number of agents and n is the number of nodes. First, we consider agents with knowledge of k (or n since k andn can be easily obtained if one of them is given). In this case, we propose two algorithms. The first algorithm solves the uniform deployment problem with termination detection. This algorithm requires O(klogn) memory space per agent, O(n) time, and O(kn) total moves. The second algorithm also solves the uniform deployment problem with termination detection. This algorithm reduces the memory space per agent to O(logn), but uses O(nlogk) time, and requires O(kn) total moves. Both algorithms are asymptotically optimal in terms of total moves since there are some initial configurations such that agents require Ω(kn) total moves to solve the problem. Next, we consider agents with no knowledge of k or n. In this case, we show that, when termination detection is required, there exists no algorithm to solve the uniform deployment problem. For this reason, we consider the relaxed uniform deployment problem that does not require termination detection, and we propose an algorithm to solve the relaxed uniform deployment problem. This algorithm requires O((k∕l)log(n∕l)) memory space per agent, O(n∕l) time, and O(kn∕l) total moves when the initial configuration has symmetry degree l. This means that the algorithm can solve the problem more efficiently when the initial configuration has higher symmetric degree (i.e., is closer to uniform deployment). Note that all the proposed algorithms achieve uniform deployment from any initial configuration, which is a striking difference from the rendezvous problem because the rendezvous problem is not solvable from some initial configurations.

Influence of the binder filtration on residual stresses at the composite constructions manufacturing

Stress changes generated during the composite winding on the mandrel surface is investigated. A model of liquid binder filtration through the fibrous filler in the form of disc-shaped gap in the structure of the coil-processing material is proposed. An equation, considering the stress decrease occurring in consequence of the coils winding due to binder filtration is suggested. Experimental results of unidirectional rings winding on mandrels studied using strain gages are demonstrated.

Shadow/Puppet Synthesis: A Stepwise Method for the Design of Self-Stabilization

This paper presents a novel two-step method for automated design of self-stabilization. The first step enables the specification of legitimate states and an intuitive (but imprecise) specification of the desired functional behaviors in the set of legitimate states (hence the term “shadow”). After creating the shadow specifications, we systematically introduce the main variables and the topology of the desired self-stabilizing system. Subsequently, we devise a parallel and complete backtracking search towards finding a self-stabilizing solution that implements a precise version of the shadow behaviors, and guarantees recovery to legitimate states from any state. To the best of our knowledge, the shadow/puppet synthesis is the first sound and complete method that exploits parallelism and randomization along with the expansion of the state space towards generating self-stabilizing systems that cannot be synthesized with existing methods. We have validated the proposed method by creating both a sequential and a parallel implementation in the context of a software tool, called Protocon. Moreover, we have used Protocon to automatically design three new self-stabilizing protocols that we conjecture to require the minimal number of states per process to achieve stabilization (when processes are deterministic): 2-state maximal matching on bidirectional rings, 5-state token passing on unidirectional rings, and 3-state token passing on bidirectional chains.

Interactions between unidirectional quantized vortex rings

We have used the vortex filament method to numerically investigate the interactions between pairs of quantized vortex rings that are initially traveling in the same direction but with their axes offset by a variable impact parameter. The interaction of two circular rings of comparable radii produce outcomes that can be categorized into four regimes, dependent only on the impact parameter; the two rings can either miss each other on the inside or outside, or they can reconnect leading to final states consisting of either one or two deformed rings. The fraction of of energy went into ring deformations and the transverse component of velocity of the rings are analyzed for each regime. We find that rings of very similar radius only reconnect for a very narrow range of the impact parameter, much smaller than would be expected from geometrical cross-section alone. In contrast, when the radii of the rings are very different, the range of impact parameters producing a reconnection is close to the geometrical value. A second type of interaction considered is the collision of circular rings with a highly deformed ring. This type of interaction appears to be a productive mechanism for creating small vortex rings. The simulations are discussed in the context of experiments on colliding vortex rings and quantum turbulence in superfluid helium in the zero temperature limit.

Studying residual strains in ring-shaped specimens made of polymer composite materials with unidirectional structure

Residual strains in unidirectional fiberglass rings have been studied. The results of an experiment on the determination of the certain properties of the rings and the values of the residual strains in them are presented. Ways to change residual strains in structures incorporating anisotropic rings made of polymer composite materials have been considered.

Partial gathering of mobile agents in asynchronous unidirectional rings

In this paper, we consider the partial gathering problem of mobile agents in asynchronous unidirectional rings equipped with whiteboards on nodes. The partial gathering problem is a new generalization of the total gathering problem. The partial gathering problem requires, for a given integer g, that each agent should move to a node and terminate so that at least g agents should meet at the same node. The requirement for the partial gathering problem is weaker than that for the (well-investigated) total gathering problem, and thus, we have interests in clarifying the difference on the move complexity between them. We propose three algorithms to solve the partial gathering problem. The first algorithm is deterministic but requires unique ID of each agent. This algorithm achieves the partial gathering in O(gn) total moves, where n is the number of nodes. The second algorithm is randomized and requires no unique ID of each agent (i.e., anonymous). This algorithm achieves the partial gathering in expected O(gn) total moves. The third algorithm is deterministic and requires no unique ID of each agent. For this case, we show that there exist initial configurations in which no algorithm can solve the problem and agents can achieve the partial gathering in O(kn) total moves for solvable initial configurations, where k is the number of agents. Note that the total gathering problem requires Ω(kn) total moves, while the partial gathering problem requires Ω(gn) total moves in each model. Hence, we show that the move complexity of the first and second algorithms is asymptotically optimal.

Determining the True Strength of the Material of Fiberglass Thick Rings when Stretched with Half-Disks

The article presents the results of a study of elastic-strength properties of unidirectional rings of fiberglass in tension them with half-disks at a variation in a wide range of diameter and thickness of the rings. The analysis of the results clarified the mechanisms of destruction fibreglasses and the possibility of expanding the application of the method.

Strange Dynamics in a Fractional Derivative of Complex-Order Network of Chaotic Oscillators

We study the peculiar dynamical features of a fractional derivative of complex-order network. The network is composed of two unidirectional rings of cells, coupled through a "buffer" cell. The network has a Z3 × Z5 cyclic symmetry group. The complex derivative Dα±jβ, with α, β ∈ R+ is a generalization of the concept of integer order derivative, where α = 1, β = 0. Each cell is modeled by the Chen oscillator. Numerical simulations of the coupled cell system associated with the network expose patterns such as equilibria, periodic orbits, relaxation oscillations, quasiperiodic motion, and chaos, in one or in two rings of cells. In addition, fixing β = 0.8, we perceive differences in the qualitative behavior of the system, as the parameter c ∈ [13, 24] of the Chen oscillator and/or the real part of the fractional derivative, α ∈ {0.5, 0.6, 0.7, 0.8, 0.9, 1.0}, are varied. Some patterns produced by the coupled system are constrained by the network architecture, but other features are only understood in the light of the internal dynamics of each cell, in this case, the Chen oscillator. What is more important, architecture and/or internal dynamics?

Reconnections of quantized vortex rings in superfluid 4He at very low temperatures.

Collisions in a beam of unidirectional quantized vortex rings of nearly identical radii R in superfluid 4He in the limit of zero temperature (0.05 K) were studied using time-of-flight spectroscopy. Reconnections between two primary rings result in secondary vortex loops of both smaller and larger radii. Discrete steps in the distribution of flight times, due to the limits on the earliest possible arrival times of secondary loops created after either one or two consecutive reconnections, are observed. The density of primary rings was found to be capped at the value 500 cm-2R-1 independent of the injected density. This is due to collisions between rings causing the piling up of many other vortex rings. Both observations are in quantitative agreement with our theory.

Evaluation of asynchronous multi‐swarm particle optimization on several topologies

SUMMARYParticle swarm optimization is a population‐based stochastic optimization technique that is easy to implement and has been successfully applied in many areas. However, its performance often deteriorates as the dimensionality of the problem increases. Recently, parallel strategies based on multiple swarms (multi‐swarm) have been investigated as an alternative to overcome this problem. In this paper, we evaluate the impact of the topology on multi‐swarm systems, considering that swarms are independent, and interact by means of particle migration. We focus on asynchronous communication, that is, only when an improvement occurs on the best particle that the solution migrates among swarms. The goal is to check how different communication strategies affect the parallel execution of the optimization tasks. Several different topologies and communication strategies have been evaluated, including broadcast and gossip on fully connected networks, unidirectional and bidirectional rings, hypercubes, and a dynamic topology. Extensive experimental results were obtained and are reported using several traditional benchmark functions. We evaluated the impact of the topologies in terms of the number of iterations and the communication overhead. With the results, a ranking of the different topologies is presented. The impact of the number of swarms on the optimization process is also evaluated. Copyright © 2012 John Wiley & Sons, Ltd.

Optimal dimensioning of the WDM unidirectional ECOFRAME optical packet ring

To efficiently support the high rate and the high dynamicity of the traffic in metro networks, an optical packet-switched WDM ring, named ECOFRAME, is proposed. The key features of the proposed ring are optical transparency and statistical multiplexing of optical packets on parallel WDM channels. Such features can be exploited by properly allocating wavelengths and receivers. This paper aims to optimally dimension the unidirectional ECOFRAME rings. The dimensioning at minimum cost (i.e., for wavelengths and receivers) is modeled with an mixed-integer linear programming formulation. An heuristic algorithm is also proposed, and its performance is compared against the optimal solutions and bounds. When considering the receiver and wavelength cost, results indicate that trading the wavelengths for receivers allows cost saving of up to 75% with respect to WDM optical packet rings with a single dedicated wavelength per node (i.e., single receiver at each node).

Fast leader election in anonymous rings with bounded expected delay

We propose a probabilistic network model, called asynchronous bounded expected delay (ABE), which requires a known bound on the expected message delay. In ABE networks all asynchronous executions are possible, but executions with extremely long delays are less probable. Thus, the ABE model captures asynchrony that occurs in sensor networks and ad-hoc networks. At the example of an election algorithm, we show that the minimal assumptions of ABE networks are sufficient for the development of efficient algorithms. For anonymous, unidirectional ABE rings of known size n we devise a probabilistic election algorithm having average message and time complexity O ( n ) .

Edge-Partitioning Regular Graphs for Ring Traffic Grooming with a Priori Placement of the ADMs

We study the following graph partitioning problem: Given two positive integers C and $\Delta$, find the least integer $M(C,\Delta)$ such that the edges of any graph with maximum degree at most $\Delta$ can be partitioned into subgraphs with at most C edges and each vertex appears in at most $M(C,\Delta)$ subgraphs. This problem is naturally motivated by traffic grooming, which is a major issue in optical networks. Namely, we introduce a new pseudodynamic model of traffic grooming in unidirectional rings, in which the aim is to design a network able to support any request graph with a given bounded degree. We show that optimizing the equipment cost under this model is essentially equivalent to determining the parameter $M(C,\Delta)$. We establish the value of $M(C,\Delta)$ for almost all values of C and $\Delta$, leaving open only the case where $\Delta \geq 5$ is odd, $\Delta \pmod{2C}$ is between 3 and $C-1$, $C\geq 4$, and the request graph does not contain a perfect matching. For these open cases, we provide upper bounds that differ from the optimal value by at most one.