Differential Models, Numerical Simulations and Applications

This Special Issue includes 12 high-quality articles containing original research findings in the fields of differential and integro-differential models, numerical methods and efficient algorithms for parameter estimation in inverse problems, with applications to biology, biomedicine, land degradation, traffic flows problems, and manufacturing systems

Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008

Sample Path Analysis of Integrate-and-Fire Neurons

Computational neuroscience is concerned with answering two intertwined questions that are based on the assumption that spatio-temporal patterns of spikes form the universal language of the nervous system. First, what function does a specific neural circuitry perform in the elaboration of a behavior? Second, how do neural circuits process behaviorally-relevant information? Non-linear system analysis has proven instrumental in understanding the coding strategies of early neural processing in various sensory modalities. Yet, at higher levels of integration, it fails to help in deciphering the response of assemblies of neurons to complex naturalistic stimuli. If neural activity can be assumed to be primarily driven by the stimulus at early stages of processing, the intrinsic activity of neural circuits interacts with their high-dimensional input to transform it in a stochastic non-linear fashion at the cortical level. As a consequence, any attempt to fully understand the brain through a system analysis approach becomes illusory. However, it is increasingly advocated that neural noise plays a constructive role in neural processing, facilitating information transmission. This prompts to gain insight into the neural code by studying the stochasticity of neuronal activity, which is viewed as biologically relevant. Such an endeavor requires the design of guiding theoretical principles to assess the potential benefits of neural noise. In this context, meeting the requirements of biological relevance and computational tractability, while providing a stochastic description of neural activity, prescribes the adoption of the integrate-and-fire model. In this thesis, founding ourselves on the path-wise description of neuronal activity, we propose to further the stochastic analysis of the integrate-and fire model through a combination of numerical and theoretical techniques. To begin, we expand upon the path-wise construction of linear diffusions, which offers a natural setting to describe leaky integrate-and-fire neurons, as inhomogeneous Markov chains. Based on the theoretical analysis of the first-passage problem, we then explore the interplay between the internal neuronal noise and the statistics of injected perturbations at the single unit level, and examine its implications on the neural coding. At the population level, we also develop an exact event-driven implementation of a Markov network of perfect integrate-and-fire neurons with both time delayed instantaneous interactions and arbitrary topology. We hope our approach will provide new paradigms to understand how sensory inputs perturb neural intrinsic activity and accomplish the goal of developing a new technique for identifying relevant patterns of population activity. From a perturbative perspective, our study shows how injecting frozen noise in different flavors can help characterize internal neuronal noise, which is presumably functionally relevant to information processing. From a simulation perspective, our event-driven framework is amenable to scrutinize the stochastic behavior of simple recurrent motifs as well as temporal dynamics of large scale networks under spike-timing-dependent plasticity

Autonomous Robot Navigation through a Crowded and Dynamic Environment: Using A Novel form of Path Planning to Demonstrate Consideration towards Pedestrians and other Robots

This thesis presents a novel path planning algorithm for robotic crowd navigation through a pedestrian environment. The robot is designed to negotiate its way through the crowd using considerate movements. Unlike many other path planning algorithms, which assume cooperation with other pedestrians, this algorithm is completely independent and requires only observation. A considerate navigation strategy has been developed in this thesis, which utilises consideration as an directs an autonomous mobile robot. Using simple methods of predicting pedestrian movements, as well as simple relative distance and trajectory measurements between the robot and pedestrians, the robot can navigate through a crowd without causing disruption to pedestrian trajectories. Dynamic pedestrian positions are predicted using uncertainty ellipses. A novel Voronoi diagram-visibility graph hybrid roadmap is implemented so that the path planner can exploit any available gaps in between pedestrians, and plan considerate paths. The aim of the considerate path planner is to have the robot behave in specific ways when moving through the crowd. By predicting pedestrian trajectories, the robot can avoid interfering with them. Following preferences to move behind pedestrians, when cutting across their trajectories; to move in the same direction of the crowd when possible; and to slow down in crowded areas, will prevent any interference to individual pedestrians, as well as preventing an increase in congestion to the crowd as a whole. The effectiveness of the considerate navigation strategy is evaluated using simulated pedestrians, multiple mobile robots loaded with the path planning algorithm, as well as a real-life pedestrian dataset. The algorithm will highlight its ability to move with the aforementioned consideration towards each individual dynamic agent

Proceedings of the 9th MIT/ONR workshop on C3 Systems, held at Naval Postgraduate School and Hilton Inn Resort Hotel, Monterey, California June 2 through June 5, 1986

GRSN 627729"December 1986."Includes bibliographical references and index.Sponsored by Massachusetts Institute of Technology, Laboratory for Information and Decision Systems, Cambridge, Mass., with support from the Office of Naval Research. ONR/N00014-77-C-0532(NR041-519) Sponsored in cooperation with IEEE Control Systems Society, Technical Committee on C.edited by Michael Athans, Alexander H. Levis

Autonomous Recovery Of Reconfigurable Logic Devices Using Priority Escalation Of Slack

Field Programmable Gate Array (FPGA) devices offer a suitable platform for survivable hardware architectures in mission-critical systems. In this dissertation, active dynamic redundancy-based fault-handling techniques are proposed which exploit the dynamic partial reconfiguration capability of SRAM-based FPGAs. Self-adaptation is realized by employing reconfiguration in detection, diagnosis, and recovery phases. To extend these concepts to semiconductor aging and process variation in the deep submicron era, resilient adaptable processing systems are sought to maintain quality and throughput requirements despite the vulnerabilities of the underlying computational devices. A new approach to autonomous fault-handling which addresses these goals is developed using only a uniplex hardware arrangement. It operates by observing a health metric to achieve Fault Demotion using Recon- figurable Slack (FaDReS). Here an autonomous fault isolation scheme is employed which neither requires test vectors nor suspends the computational throughput, but instead observes the value of a health metric based on runtime input. The deterministic flow of the fault isolation scheme guarantees success in a bounded number of reconfigurations of the FPGA fabric. FaDReS is then extended to the Priority Using Resource Escalation (PURE) online redundancy scheme which considers fault-isolation latency and throughput trade-offs under a dynamic spare arrangement. While deep-submicron designs introduce new challenges, use of adaptive techniques are seen to provide several promising avenues for improving resilience. The scheme developed is demonstrated by hardware design of various signal processing circuits and their implementation on a Xilinx Virtex-4 FPGA device. These include a Discrete Cosine Transform (DCT) core, Motion Estimation (ME) engine, Finite Impulse Response (FIR) Filter, Support Vector Machine (SVM), and Advanced Encryption Standard (AES) blocks in addition to MCNC benchmark circuits. A iii significant reduction in power consumption is achieved ranging from 83% for low motion-activity scenes to 12.5% for high motion activity video scenes in a novel ME engine configuration. For a typical benchmark video sequence, PURE is shown to maintain a PSNR baseline near 32dB. The diagnosability, reconfiguration latency, and resource overhead of each approach is analyzed. Compared to previous alternatives, PURE maintains a PSNR within a difference of 4.02dB to 6.67dB from the fault-free baseline by escalating healthy resources to higher-priority signal processing functions. The results indicate the benefits of priority-aware resiliency over conventional redundancy approaches in terms of fault-recovery, power consumption, and resource-area requirements. Together, these provide a broad range of strategies to achieve autonomous recovery of reconfigurable logic devices under a variety of constraints, operating conditions, and optimization criteria

Many-agent Reinforcement Learning

Multi-agent reinforcement learning (RL) solves the problem of how each agent should behave optimally in a stochastic environment in which multiple agents are learning simultaneously. It is an interdisciplinary domain with a long history that lies in the joint area of psychology, control theory, game theory, reinforcement learning, and deep learning. Following the remarkable success of the AlphaGO series in single-agent RL, 2019 was a booming year that witnessed significant advances in multi-agent RL techniques; impressive breakthroughs have been made on developing AIs that outperform humans on many challenging tasks, especially multi-player video games. Nonetheless, one of the key challenges of multi-agent RL techniques is the scalability; it is still non-trivial to design efficient learning algorithms that can solve tasks including far more than two agents ($N \gg 2$), which I name by \emph{many-agent reinforcement learning} (MARL\footnote{I use the world of ``MARL" to denote multi-agent reinforcement learning with a particular focus on the cases of many agents; otherwise, it is denoted as ``Multi-Agent RL" by default.}) problems. In this thesis, I contribute to tackling MARL problems from four aspects. Firstly, I offer a self-contained overview of multi-agent RL techniques from a game-theoretical perspective. This overview fills the research gap that most of the existing work either fails to cover the recent advances since 2010 or does not pay adequate attention to game theory, which I believe is the cornerstone to solving many-agent learning problems. Secondly, I develop a tractable policy evaluation algorithm -- $\alpha^\alpha$-Rank -- in many-agent systems. The critical advantage of $\alpha^\alpha$-Rank is that it can compute the solution concept of $\alpha$-Rank tractably in multi-player general-sum games with no need to store the entire pay-off matrix. This is in contrast to classic solution concepts such as Nash equilibrium which is known to be $PPAD$-hard in even two-player cases. $\alpha^\alpha$-Rank allows us, for the first time, to practically conduct large-scale multi-agent evaluations. Thirdly, I introduce a scalable policy learning algorithm -- mean-field MARL -- in many-agent systems. The mean-field MARL method takes advantage of the mean-field approximation from physics, and it is the first provably convergent algorithm that tries to break the curse of dimensionality for MARL tasks. With the proposed algorithm, I report the first result of solving the Ising model and multi-agent battle games through a MARL approach. Fourthly, I investigate the many-agent learning problem in open-ended meta-games (i.e., the game of a game in the policy space). Specifically, I focus on modelling the behavioural diversity in meta-games, and developing algorithms that guarantee to enlarge diversity during training. The proposed metric based on determinantal point processes serves as the first mathematically rigorous definition for diversity. Importantly, the diversity-aware learning algorithms beat the existing state-of-the-art game solvers in terms of exploitability by a large margin. On top of the algorithmic developments, I also contribute two real-world applications of MARL techniques. Specifically, I demonstrate the great potential of applying MARL to study the emergent population dynamics in nature, and model diverse and realistic interactions in autonomous driving. Both applications embody the prospect that MARL techniques could achieve huge impacts in the real physical world, outside of purely video games

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described