Asynchronous Multi-Context Systems

In this work, we present asynchronous multi-context systems (aMCSs), which provide a framework for loosely coupling different knowledge representation formalisms that allows for online reasoning in a dynamic environment. Systems of this kind may interact with the outside world via input and output streams and may therefore react to a continuous flow of external information. In contrast to recent proposals, contexts in an aMCS communicate with each other in an asynchronous way which fits the needs of many application domains and is beneficial for scalability. The federal semantics of aMCSs renders our framework an integration approach rather than a knowledge representation formalism itself. We illustrate the introduced concepts by means of an example scenario dealing with rescue services. In addition, we compare aMCSs to reactive multi-context systems and describe how to simulate the latter with our novel approach.Comment: International Workshop on Reactive Concepts in Knowledge Representation (ReactKnow 2014), co-located with the 21st European Conference on Artificial Intelligence (ECAI 2014). Proceedings of the International Workshop on Reactive Concepts in Knowledge Representation (ReactKnow 2014), pages 31-37, technical report, ISSN 1430-3701, Leipzig University, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-15056

Probability currents as principal characteristics in the statistical mechanics of non-equilibrium steady states

One of the key features of non-equilibrium steady states (NESS) is the presence of nontrivial probability currents. We propose a general classification of NESS in which these currents play a central distinguishing role. As a corollary, we specify the transformations of the dynamic transition rates which leave a given NESS invariant. The formalism is most transparent within a continuous time master equation framework since it allows for a general graph-theoretical representation of the NESS. We discuss the consequences of these transformations for entropy production, present several simple examples, and explore some generalizations, to discrete time and continuous variables.Comment: 39 pages, 5 figures. Invited article for JSTAT Special Issue on 'Principles of Dynamics of Nonequilibrium Systems', held at the Newton Institute, Cambridge, UK, in 200

The scaling attractor and ultimate dynamics for Smoluchowski's coagulation equations

We describe a basic framework for studying dynamic scaling that has roots in dynamical systems and probability theory. Within this framework, we study Smoluchowski's coagulation equation for the three simplest rate kernels $K(x,y)=2$, $x+y$ and $xy$. In another work, we classified all self-similar solutions and all universality classes (domains of attraction) for scaling limits under weak convergence (Comm. Pure Appl. Math 57 (2004)1197-1232). Here we add to this a complete description of the set of all limit points of solutions modulo scaling (the scaling attractor) and the dynamics on this limit set (the ultimate dynamics). The main tool is Bertoin's L\'{e}vy-Khintchine representation formula for eternal solutions of Smoluchowski's equation (Adv. Appl. Prob. 12 (2002) 547--64). This representation linearizes the dynamics on the scaling attractor, revealing these dynamics to be conjugate to a continuous dilation, and chaotic in a classical sense. Furthermore, our study of scaling limits explains how Smoluchowski dynamics ``compactifies'' in a natural way that accounts for clusters of zero and infinite size (dust and gel)

GNNFlow: A Distributed Framework for Continuous Temporal GNN Learning on Dynamic Graphs

Graph Neural Networks (GNNs) play a crucial role in various fields. However, most existing deep graph learning frameworks assume pre-stored static graphs and do not support training on graph streams. In contrast, many real-world graphs are dynamic and contain time domain information. We introduce GNNFlow, a distributed framework that enables efficient continuous temporal graph representation learning on dynamic graphs on multi-GPU machines. GNNFlow introduces an adaptive time-indexed block-based data structure that effectively balances memory usage with graph update and sampling operation efficiency. It features a hybrid GPU-CPU graph data placement for rapid GPU-based temporal neighborhood sampling and kernel optimizations for enhanced sampling processes. A dynamic GPU cache for node and edge features is developed to maximize cache hit rates through reuse and restoration strategies. GNNFlow supports distributed training across multiple machines with static scheduling to ensure load balance. We implement GNNFlow based on DGL and PyTorch. Our experimental results show that GNNFlow provides up to 21.1x faster continuous learning than existing systems

A framework of nonequilibrium statistical mechanics. I. Role and type of fluctuations

Understanding the fluctuations by which phenomenological evolution equations with thermodynamic structure can be enhanced is the key to a general framework of nonequilibrium statistical mechanics. These fluctuations provide an idealized representation of microscopic details. We consider fluctuation-enhanced equations associated with Markov processes and elaborate the general recipes for evaluating dynamic material properties, which characterize force-flux constitutive laws, by statistical mechanics. Markov processes with continuous trajectories are conveniently characterized by stochastic differential equations and lead to Green-Kubo-type formulas for dynamic material properties. Markov processes with discontinuous jumps include transitions over energy barriers with the rates calculated by Kramers. We describe a unified approach to Markovian fluctuations and demonstrate how the appropriate type of fluctuations (continuous versus discontinuous) is reflected in the mathematical structure of the phenomenological equations.Comment: This paper and its continuation (II) replace the previous paper arXiv:1809.07253. Now the content and the presentation style are more targeted to physicists, with particular emphasis on the applications to specific physical systems. The theoretical and the practical aspects have been separated from each other in the two paper

Stability results for constrained dynamical systems

Differential-Algebraic Equations (DAE) provide an appropriate framework to model and analyse dynamic systems with constraints. This framework facilitates modelling of the system behaviour through natural physical variables of the system, while preserving the topological constraints of the system. The main purpose of this dissertation is to investigate stability properties of two important classes of DAEs. We consider some special cases of Linear Time Invariant (LTI) DAEs with control inputs and outputs, and also a special class of Linear switched DAEs. In the first part of the thesis, we consider LTI systems, where we focus on two properties: passivity and a generalization of passivity and small gain theorems called mixed property. These properties play an important role in the control design of large-scale interconnected systems. An important bottleneck for a design based on the aforementioned properties is their verification. Hence we intend to develop easily verifiable conditions to check passivity and mixedness of Single Input Single Output (SISO) and Multiple Input Multiple Output (MIMO) DAEs. For linear switched DAEs, we focus on the Lyapunov stability and this problem forms the basis for the second part of the thesis. In this part, we try to find conditions under which there exists a common Lyapunov function for all modes of the switched system, thus guaranteeing exponential stability of the switched system. These results are primarily developed for continuous-time systems. However, simulation and control design of a dynamic system requires a discrete-time representation of the system that we are interested in. Thus, it is critical to establish whether discrete-time systems, inherit fundamental properties of the continuous-time systems from which they are derived. Hence, the third part of our thesis is dedicated to the problems of preserving passivity, mixedness and Lyapunov stability under discretization. In this part, we examine several existing discretization methods and find conditions under which they preserve the stability properties discussed in the thesis

Stability results for constrained dynamical systems

Differential-Algebraic Equations (DAE) provide an appropriate framework to model and analyse dynamic systems with constraints. This framework facilitates modelling of the system behaviour through natural physical variables of the system, while preserving the topological constraints of the system. The main purpose of this dissertation is to investigate stability properties of two important classes of DAEs. We consider some special cases of Linear Time Invariant (LTI) DAEs with control inputs and outputs, and also a special class of Linear switched DAEs. In the first part of the thesis, we consider LTI systems, where we focus on two properties: passivity and a generalization of passivity and small gain theorems called mixed property. These properties play an important role in the control design of large-scale interconnected systems. An important bottleneck for a design based on the aforementioned properties is their verification. Hence we intend to develop easily verifiable conditions to check passivity and mixedness of Single Input Single Output (SISO) and Multiple Input Multiple Output (MIMO) DAEs. For linear switched DAEs, we focus on the Lyapunov stability and this problem forms the basis for the second part of the thesis. In this part, we try to find conditions under which there exists a common Lyapunov function for all modes of the switched system, thus guaranteeing exponential stability of the switched system. These results are primarily developed for continuous-time systems. However, simulation and control design of a dynamic system requires a discrete-time representation of the system that we are interested in. Thus, it is critical to establish whether discrete-time systems, inherit fundamental properties of the continuous-time systems from which they are derived. Hence, the third part of our thesis is dedicated to the problems of preserving passivity, mixedness and Lyapunov stability under discretization. In this part, we examine several existing discretization methods and find conditions under which they preserve the stability properties discussed in the thesis

Decentralized adaptive neural network control of interconnected nonlinear dynamical systems with application to power system

Traditional nonlinear techniques cannot be directly applicable to control large scale interconnected nonlinear dynamic systems due their sheer size and unavailability of system dynamics. Therefore, in this dissertation, the decentralized adaptive neural network (NN) control of a class of nonlinear interconnected dynamic systems is introduced and its application to power systems is presented in the form of six papers. In the first paper, a new nonlinear dynamical representation in the form of a large scale interconnected system for a power network free of algebraic equations with multiple UPFCs as nonlinear controllers is presented. Then, oscillation damping for UPFCs using adaptive NN control is discussed by assuming that the system dynamics are known. Subsequently, the dynamic surface control (DSC) framework is proposed in continuous-time not only to overcome the need for the subsystem dynamics and interconnection terms, but also to relax the explosion of complexity problem normally observed in traditional backstepping. The application of DSC-based decentralized control of power system with excitation control is shown in the third paper. On the other hand, a novel adaptive NN-based decentralized controller for a class of interconnected discrete-time systems with unknown subsystem and interconnection dynamics is introduced since discrete-time is preferred for implementation. The application of the decentralized controller is shown on a power network. Next, a near optimal decentralized discrete-time controller is introduced in the fifth paper for such systems in affine form whereas the sixth paper proposes a method for obtaining the L2-gain near optimal control while keeping a tradeoff between accuracy and computational complexity. Lyapunov theory is employed to assess the stability of the controllers --Abstract, page iv

Lyapunov function search method for analysis of nonlinear systems stability using genetic algorithm

This paper considers a wide class of smooth continuous dynamic nonlinear systems (control objects) with a measurable vector of state. The problem is to find a special function (Lyapunov function), which in the framework of the second Lyapunov method guarantees asymptotic stability for the above described class of nonlinear systems. It is well known that the search for a Lyapunov function is the "cornerstone" of mathematical stability theory. Methods for selecting or finding the Lyapunov function to analyze the stability of closed linear stationary systems, as well as for nonlinear objects with explicit linear dynamic and nonlinear static parts, have been well studied (see works by Lurie, Yakubovich, Popov, and many others). However, universal approaches to the search for the Lyapunov function for a more general class of nonlinear systems have not yet been identified. There is a large variety of methods for finding the Lyapunov function for nonlinear systems, but they all operate within the constraints imposed on the structure of the control object. In this paper we propose another approach, which allows to give specialists in the field of automatic control theory a new tool/mechanism of Lyapunov function search for stability analysis of smooth continuous dynamic nonlinear systems with measurable state vector. The essence of proposed approach consists in representation of some function through sum of nonlinear terms, which are elements of object's state vector, multiplied by unknown coefficients, raised to positive degrees. Then the unknown coefficients are selected using genetic algorithm, which should provide the function with all necessary conditions for Lyapunov function (in the framework of the second Lyapunov method).Comment: in Russian languag

Patient-Centric Ethical Frameworks for Privacy, Transparency, and Bias Awareness in Deep Learning-Based Medical Systems

The rapid advancement and deployment of deep learning-enabled medical systems have necessitated the development of robust ethical frameworks to address potential challenges and pitfalls. Based on the foundational principles of medical ethics—non-maleficence, beneficence, respect for patient autonomy, and justice—three ethical frameworks are proposed in this study for the deployment and oversight of deep learning systems in healthcare. This study presents these three distinct yet interconnected ethical frameworks focusing on patient privacy, transparency, and bias mitigation. The patient privacy framework argues for the importance of patient autonomy. It advocates for informed consent, emphasizing the need for patients to be apprised of the system's workings, benefits, potential risks, and alternatives. Consent should be voluntary, devoid of implicit coercion, and patients must retain the right to revoke it without repercussions. The framework also included the principles of transparency, beneficence, privacy, continual consent, accessibility, and accountability. It champions the idea that consent is dynamic, necessitating regular updates, especially when significant system changes occur. Our ethical framework for transparency accentuates the need for full disclosure. Stakeholders should be provided with a general overview of the system's operations, its inputs, and decision-making processes. Performance metrics, including accuracy, sensitivity, and specificity, should be transparently communicated. Openness, through open-source initiatives and third-party audits, is promoted. The principles of accountability, data transparency, continuous improvement, inclusivity, and external validation are also made integral to this framework, ensuring that stakeholders are consistently informed and engaged. The bias minimization framework highlights the imperative of awareness. Stakeholders should be educated about potential biases and their ramifications. The system should be regularly evaluated for inherent biases, both overt and subtle. Representation is crucial; training data must reflect diverse populations, considering various demographic factors. This framework also promotes fairness, ensuring equitable system performance across different patient groups. Transparency in bias reporting, accountability in bias correction, continuous monitoring, inclusivity in stakeholder engagement, and collaboration with interdisciplinary teams are also included and discussed