General Topology Research Articles

Learning structured communication for multi-agent reinforcement learning

This work explores the large-scale multi-agent communication mechanism for multi-agent reinforcement learning (MARL). We summarize the general topology categories for communication structures, which are often manually specified in MARL literature. A novel framework termed Learning Structured Communication (LSC) is proposed by learning a flexible and efficient communication topology (hierarchical structure). It contains two modules: structured communication module and communication-based policy module. The structured communication module learns to form a hierarchical structure by maximizing the cumulative reward of the agents under the current communication-based policy. The communication-based policy module adopts hierarchical graph neural networks to generate messages, propagate information based on the learned communication structure, and select actions. In contrast to existing communication mechanisms, our method has a learnable and hierarchical communication structure. Experiments on large-scale battle scenarios show that the proposed LSC has high communication efficiency and global cooperation capability.

Computability Theory

Over the last decade computability theory has seen many new and fascinating developments that have linked the subject much closer to other mathematical disciplines inside and outside of logic. This includes, for instance, work on enumeration degrees that has revealed deep and surprising relations to general topology, the work on algorithmic randomness that is closely tied to symbolic dynamics and geometric measure theory. Inside logic there are connections to model theory, set theory, effective descriptive set theory, computable analysis and reverse mathematics. In some of these cases the bridges to seemingly distant mathematical fields have yielded completely new proofs or even solutions of open problems in the respective fields. Thus, over the last decade, computability theory has formed vibrant and beneficial interactions with other mathematical fields. The goal of this workshop was to bring together researchers representing different aspects of computability theory to discuss recent advances, and to stimulate future work.

Connected and automated vehicle platoon formation control via differential games

In this study, the connected and automated vehicles (CAVs) platooning problem is resolved under a differential game framework. Three information topologies are considered here. Firstly, Predecessor-following (PF) topology is utilized where the vehicles control the distance with respect to the merely nearest predecessor via a sensor link-based information flow. Secondly, Two-predecessor-following topology (TPF) is exploited where each vehicle controls the distance with respect to the two nearest predecessors. In this topology, the second predecessor is communicated via a Vehicle-to-vehicle (V2V) link. The individual trajectories of CAVs under the Nash equilibrium are derived in closed-form for these two information topologies. Finally, general information topology is examined and the differential game is formulated in this context. In all these options, Pontryagin's principle is employed to investigate the existence and uniqueness of the Nash equilibrium and obtain its corresponding trajectories. In the general topology, we suppose numerical computation of eigenvalues and eigenvectors. All these approaches represent promising and powerful analytical representations of the CAV platoons under the differential games. Simulation experiments have verified the efficiency of the proposed models and their solutions.

More properties of generalized open sets in generalized topological spaces

Abstract Sarsak [M. S. Sarsak, On some properties of generalized open sets in generalized topological spaces, Demonstr. Math. 46 (2013), no. 2, 415–427] studied some properties of generalized open sets in generalized topological spaces (GTSs); the primary purpose of this article is to investigate more properties of generalized open sets in GTSs. We mainly study the behaviours of regular closed sets, semi-open sets, regular semi-open sets, preopen sets, and β \beta -open sets in GTSs analogous to their behaviours in topological spaces.

Engineering and design of a novel high-current source for testing low-voltage electrical equipment

This article presents the specification and design of a low-voltage high-current source with a capacity of up to 65 kA and 1 kV for testing electrical equipment such as low-voltage power circuit breaker switchgear, metal-enclosed switchgear, transformers, and cables, among others. Tests that can be performed with the proposed source include the short-circuit withstand on the low-voltage side of transformers, verification in temperature rise limits on electrical power connectors and transformers, and other compliance tests on power circuit breaker switchgear and controlgear assemblies. The design results from the comparison of general topologies of high-current sources according to the literature and test requirements established in current IEEE and IEC standards. In addition, the low-voltage high-current source emerged as a need for the Colombian electricity sector and will help comply with the test guidelines for switchgear and other low-voltage equipment, according to the national standard, also contributing to reducing costs of conducting tests abroad. The specification of the source resulted in the definition of three operating ranges for different types of tests, equipment, voltage, and current levels. Moreover, the general scheme of the low-voltage high-current source is provided with a description of the major components, namely, the novel medium- and low-voltage power modules based on the parallel and series arrangements of toroidal transformers to obtain levels of current and voltage of up to 65 kA and 1 kV, and the switching and protection, control, and measurement systems. Finally, a discussion of the results is presented, and the conclusions are highlighted. © 2017 Elsevier Inc. All rights reserved.

A Generalized Topology from the Edge Set of Maximal Paths of Directed Graphs

This study intends to provide a fundamental step towards studying the properties of directed graphs with their corresponding generalized topological spaces. A generalized topology (GT) \(\mu\) on a nonempty set X is defined as a family of subsets of X such that \(\Theta\) and an arbitrary union of sets in \(\mu\) is in \(\mu\) . In this study, we introduce a new generalized topology generated by the set of edges of maximal paths of the directed graph D called the maximal path edge generalized topology (MPE\(\Gamma\)), denoted by \(\Gamma\)MP (D). The basic topological properties and connectedness in the context of this new structure are explored and illustrated. In particular, this paper established that (E(D); \(\Gamma\)MP (D)) is a strong generalized topological space and characterized the open and closed sets in this space. Moreover, it was seen that the MPE\(\Gamma\) space of every disconnected digraph is \(\Gamma\)MPMP -disconnected and the MPE\(\Gamma\) space of every connected digraph is also characterized.

Optimal power flow under stochastic N-1 disruptions in electric transmission grids

We consider a multi-period optimal power flow (OPF) problem in transmission systems with a generic network topology subject to stochastic N−1 contingencies (disruptions). We propose a multi-stage stochastic convex programming formulation for such a disruption problem and solve it using an efficient decomposition algorithm. We compare the disruption optimization formulation with the conventional N−1 security-constrained OPF formulation and show that our proposed model can utilize the generation resource more efficiently in a realistic contingency setting. We also present computational results comparing multiple convex relaxation schemes of the non-convex alternating current OPF (ACOPF) problem in transmission networks under stochastic disruptions. Through this, we provide insights on the performance of the policy trained by convex relaxations of an ACOPF problem.

End-to-end capacities of imperfect-repeater quantum networks

The optimal performance of a communication network is limited not only by the quality of point-to-point channels, but by the efficacy of its constituent technologies. Understanding the limits of quantum networks requires an understanding of both the ultimate capacities of quantum channels and the efficiency of imperfect quantum repeaters. In this work, using a recently developed node-splitting technique which introduces internal losses and noise into repeater devices, we present achievable end-to-end rates for noisy-repeater quantum networks. These are obtained by extending the coherent and reverse coherent information (single channel capacity lower bounds) into end-to-end capacity lower bounds, both in the context of single-path and multi-path routing. These achievable rates are completely general, and apply to networks composed of arbitrary channels arranged in general topologies. Through this general formalism, we show how tight upper-bounds can also be derived by supplementing appropriate single-edge capacity bounds. As a result, we develop tools which provide tight performance bounds for quantum networks constituent of channels whose capacities are not exactly known, and reveal critical network properties which are necessary for high-rate quantum communications. This permits the investigation of pertinent classes of quantum networks with realistic technologies; qubit amplitude damping networks and bosonic thermal-loss networks.

Recollections of logicians, mathematicians and philosophers

For John Crossley John Crossley played a major role in my becoming a mathematical logician. But before meeting him I had other aspirations. In my youth, I dreamt of becoming a theoretical physicist, and Einstein, George Gamow and Fred Hoyle headed my list of scientific heroes. I was initially accepted at Oxford to study physics, but by the time I got there my interest had shifted to mathematics. This was in no small part due to the influence of my earliest mentor, the Cambridge mathematician and astronomer E. H. Linfoot, about whom I have written elsewhere ([1]). Linfoot had an extensive mathematical library. It included a copy of John Kelley’s pedagogic masterpiece General Topology, which he was kind enough to lend me. Kelley’s book was my introduction to the elegant abstractions of 20th century mathematics, which supplanted the tortuous intricacies of the traditional mathematical analysis I had wrestled with up to then. From Kelley’s book I learned, not just about general topology, but about set theory and the concept—which I found bewitching—of a Boolean algebra. Many years later I had the good fortune to meet Kelley, who proved to be as engaging in person as he was as an author.

Optimization of Magnetic Gear Patterns Based on Taguchi Method Combined with Genetic Algorithm

Magnetic gears (MGs) have gained increasing attention due to their sound performance in high torque density and low friction loss. Aiming to maximize the torque density, topology design has been a popular issue in recent years. However, studies on the optimization comparisons of a general MG topology pattern are very limited. This paper proposes a Taguchi-method-based optimization method for a general MG topology pattern, which can cover most of the common types of radially magnetized concentric-surface-mounted MGs (RMCSM-MGs). The Taguchi method is introduced to evaluate the influence of each parameter in MGs. Moreover, the parameter value range is re-examined based on the sensitivity analysis results. The genetic algorithm (GA) method is adopted to optimize the topology pattern in the study.

On dimensions of finite approximation and functors preserving ε-nets

The dimension of finite approximation dim F ξ is defined for any point ξ of the space F(X), where F is a metrizable seminormal functor and X is a metric compactum. Such points can represent closed subsets, probability measures, maximal linked systems of closed sets, etc. The analysis shows that for many functorial constructions of general topology (exponential functor, probability measures functor, superextension functor, etc.) the dimension of finite approximation dimF ξ does not exceed the box dimension dim B of the support supp(ξ) of this point. In this connection, the problem naturally arises of how to describe the class of functors for which the indicated restriction on the dimensionality of the finite approximation holds. This paper introduces the notion of a metrizable functor that preserves ε-nets. The condition that ε-nets be preserved by the functor F proved to be sufficient for the inequality dim F ξ B(supp(ξ)) for any point ξ ∈ F(X). It is proved that a number of well-known metrizable functors preserve ε-nets.

On axiomatic characterization of Alexander-Spanier normal homology theory of general topological spaces

The Alexandroff-Čech normal cohomology theory [27], [3], [1], [2] is the unique continuous extension [36] of the additive cohomology theory [26], [4] from the category of polyhedral pairs KPol2 to the category of closed normally embedded, the so called, P-pairs of general topological spaces KTop2. In this paper we define the Alexander-Spanier normal cohomology theory based on all normal coverings and show that it is isomorphic to the Alexandroff-Čech normal cohomology. Using this fact and methods developed in [6] we construct an exact, the so called, Alexander-Spanier normal homology theory on the category KTop2, which is isomorphic to the Steenrod homology theory on the subcategory of compact pairs KC2. Moreover, we give an axiomatic characterization of the constructed homology theory.

Partial event coincidence analysis for distinguishing direct and indirect coupling in functional network construction

Correctly identifying interaction patterns from multivariate time series presents an important step in functional network construction. In this context, the widespread use of bivariate statistical association measures often results in a false identification of links because strong similarity between two time series can also emerge without the presence of a direct interaction due to intermediate mediators or common drivers. In order to properly distinguish such direct and indirect links for the special case of event-like data, we present here a new generalization of event coincidence analysis to a partial version thereof, which is aimed at excluding possible transitive effects of indirect couplings. Using coupled chaotic systems and stochastic processes on two generic coupling topologies (star and chain configuration), we demonstrate that the proposed methodology allows for the correct identification of indirect interactions. Subsequently, we apply our partial event coincidence analysis to multi-channel EEG recordings to investigate possible differences in coordinated alpha band activity among macroscopic brain regions in resting states with eyes open (EO) and closed (EC) conditions. Specifically, we find that direct connections typically correspond to close spatial neighbors while indirect ones often reflect longer-distance connections mediated via other brain regions. In the EC state, connections in the frontal parts of the brain are enhanced as compared to the EO state, while the opposite applies to the posterior regions. In general, our approach leads to a significant reduction in the number of indirect connections and thereby contributes to a better understanding of the alpha band desynchronization phenomenon in the EO state.

Fixed-Point Theorem-Based Voltage Stability Margin Estimation Techniques for Distribution Systems With Renewables

The future distribution systems expose to an unprecedented level of uncertainties due to renewable resources, nontraditional loads, aging infrastructure, etc., posing potential risks to secure operation of the system.This article proposes a new technique to estimate the voltage stability margin of the distribution systems with high penetration of renewables.Its convergence and robustness under complex and stressed working conditions are guaranteed in theory. This technique is handy for the operation as it features self-adaptive step size and is applicable to general system topology. It leverages a newly derived analytical solvability certificate based on the Kantorovich fixed-point theorem. A fast version of the proposed technique is duly proposed to speed up the computation up to 8 times while maintaining high accuracy, which lends itself to online and time-sensitive emergency tasks. Numerical simulations with various IEEE test feeders verify the performance of the techniques.

Distributed Differential Games for Control of Multi-Agent Systems

Motivated by the challenges arising in the field of multi-agent system (MAS) control, we consider linear heterogeneous MAS subject to local communication and investigate the problem of designing distributed controllers for such systems. We provide a game theoretic framework for systematically designing distributed controllers, taking into account individual objectives of the agents and their possibly incomplete knowledge of the MAS. Linear state-feedback control laws are obtained via the introduction of a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">distributed differential game</i> , namely, the combination of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">local non-cooperative differential games</i> , which are solved in a decentralized fashion. Conditions for stability of the MAS are provided for the special cases of acyclic and strongly connected communication graph topologies. These results are then exploited to provide stability conditions for general graph topologies. The proposed framework is demonstrated on a tracking synchronization problem associated with the design of a distributed secondary voltage controller for microgrids and on a numerical example.

Prescribed sets of continuity: Baire–Kuratowski theorem, derivatives, and lineability

The existence of large convex cones inside the family of real functions whose continuity set is a prescribed subset of a rather general topological space is established in this paper. This complements a number of recent assertions concerning lineability that have been obtained by several authors about functions defined on an interval of R. When the prescribed subset is a dense Gδ-set of a topological space satisfying appropriate conditions, an almost reciprocal of the Baire–Kuratowski theorem on 1-Baire functions is obtained, and again the family of functions satisfying the conclusion contains a large convex cone. For a dense Gδ-subset G of R, it is proved the existence of a dense vector subspace with maximal dimension in the space of continuous real functions all of whose nonzero members are derivable and the derivatives are continuous exactly at the points of G. Again, this complements a number of recent results made in the case that G is an open set of R, and yields as a consequence the existence of large vector spaces of 1-Baire functions with prescribed continuity set.

Stability, Scalability, Speedability, and String Stability of Connected Vehicle Systems

This article considers the third-order connected vehicle systems (CVSs) to implement cooperative formation control for autonomous vehicles. The error dynamics is modeled based on the proposed distributed control protocols for two large classes of general network topologies. The performance indices, such as stability, scalability, speedability, and string stability (4S) indices, are investigated. The necessary and sufficient conditions of stability for CVSs are derived and properties of characteristic roots are discussed. These roots are dependent on information of the given network topology. The sufficient conditions of stability, which are independent of network topology, are given by analyzing the range of eigenvalues of the Laplacian matrix of the corresponding network topology, so scalability is guaranteed. To guarantee fast convergence speed, the upper boundary of stability margin is derived, which is also independent of the size of the network topology and can be conveniently tuned by the controller gains and model parameter. The necessary and sufficient conditions of stability are also achieved for the bidirectional-leader following (BLF) network topology. The conditions of string stability are further derived to ensure that spacing errors (caused by disturbances) decay along the vehicle platoon. Furthermore, combining the conditions of stability, speedability, and string stability, the CVSs are proven to be not only stable but also string stable and quickly convergent. Thus, the 4S indices can be guaranteed. Numerical simulations are provided to validate the theoretical results.

X-ray source design optimization using differential evolution algorithms-A case study.

Traditional x-ray sources used today for multiple applications, such as medical imaging (computed tomography, radiography, mammography, and interventional radiology) or industrial inspection, are vacuum based electron beam devices that include several key components, such as electron emitters, electron guns/cathodes, and anodes/targets. The associated electronics for electron beam generation, focusing and control, and beam acceleration are located outside the vacuum chamber. The general topology of these tubes has been directionally unchanged for more than 100 years; however, tube design remains a long, inefficient, tedious, and complex process; blind design of experiments do not necessarily make the process more efficient. As a case study, in this paper, we introduce the differential evolution (DE), an artificial intelligence-based optimization algorithm, for the design optimization of x-ray source beam optics. Using a small-scale design problem, we demonstrate that DE can be an effective optimization method for x-ray source beam optics design.

On the robustness of networked cooperative tracking systems

This paper provides an analytical framework for the robustness of networked multi-agent systems (MAS). It is well-known that a single-agent linear quadratic regulator (LQR) system can guarantee 60° phase margin and infinite gain margin. However, for networked MAS, there exist no theoretical results on guaranteed stability margins, due to the complexity caused by the interplay of communication structure and agents’ dynamics. In this paper, we analyze the effect of communication graph topology on the robustness properties of networked cooperative tracking systems with local LQR designs. For such systems, we provide closed-form expressions of phase and gain margins modulated by their graph topology, following a Lyapunov type of analysis. We further derive upper bounds of stability margins for MAS with general graph topology, through a structural analysis based on the algebraic graph theory. We prove that the directed tree communication topology is among the most robust graph topology that promises the best stability margins, which are as good as the ones in a single-agent LQR system

Synthesis and Numerical Analysis of Compliant Devices: A Topology Optimization Approach for Mechanisms and Robotic Systems

The topology optimization design invariably shall be used in various applications such as four bar mechanisms, robotics designs, aircraft engineering designs, and many other mechanical innovative systems for improving the efficiency in the system. This research paper emphasizes more on general topology optimization design for a rectangular domain in which numerically analyzed with defined boundary conditions. Furthermore, the same setting geometry has been taken for sensitivity analysis to find the objective stress and nonstress zones. Then, the geometry is topology optimized to analyze stress, safety factor, output deflection, and mass reduction. Also this research work focuses more on topology optimization, design synthesis, and objective function comparison in different materials. Hence, the results are suitable volume and mass reduction in various robotic devices. Validation and comparison of compliance base materials will further support the paper to extend the work for experimental analysis. This final topology optimized and validated device can be manufactured and forced to experimental fatigue endurance test cycle test condition in static and dynamic state. The results outshoot the final destination of this optimization design.