McKean-Vlasov limits, propagation of chaos and long-time behavior of some mean field interacting particle systems

In this thesis we study mean field interacting particle systems and their McKean-Vlasov limiting processes, in particular we focus on three different interaction mechanisms, mainly emerging from biological modelling. The first type of interaction is given by the so called simultaneous jumps. We consider a system of interacting jump-diffusion processes that interact by means of the discontinuous component: each particle performs a main jump and it simultaneously induces in all the other particles a simultaneous jump whose amplitude is rescaled with the size of the system. This peculiar interaction is motivated by recent neuroscience models and here we depict a general framework for this type of processes. We focus on the well-posedness of the McKean-Vlasov limits of these particle systems under different assumptions on the coefficients and we prove a pathwise propagation of chaos result. The second interaction we consider is an asymmetric one. We describe a system of biased random walks on the positive integers, reflected at zero, where each particle may perform a leftward jump with a rate proportional to the fraction of particles which are strictly at its left. We study the critical interaction strength able to ensure ergodicity to this system, that would be transient in absence of interaction. We compare this model with existing models of diffusions interacting through their CDF and we highlight their differences, mainly caused by the presence of clusters of particles in the discrete model. The third interaction we account for is based on a dynamical version of the generalized Curie-Weiss model. We modify a Langevin dynamics for this model with a dissipative evolution of the interaction component, breaking the reversibility of the system. We prove that, in the mean field limit, this gives rise to stable limit cycles, explaining self-sustained periodic behaviors. In particular, we build a flexible model in which a suitable change in the interaction function can result in a system which, in certain regimes of parameters, displays coexistence of stable periodic orbits

Neuromorphic nanophotonic systems for artificial intelligence

Over the last decade, we have witnessed an astonishing pace of development in the field of artificial intelligence (AI), followed by proliferation of AI algorithms into virtually every domain of our society. While modern AI models boast impressive performance, they also require massive amounts of energy and resources for operation. This is further fuelling the research into AI-specific, optimised computing hardware. At the same time, the remarkable energy efficiency of the brain brings an interesting question: Can we further borrow from the working principles of biological intelligence to realise a more efficient artificial intelligence? This can be considered as the main research question in the field of neuromorphic engineering. Thanks to the developments in AI and recent advancements in the field of photonics and photonic integration, research into light-powered implementations of neuromorphic hardware has recently experienced a significant uptick of interest. In such hardware, the aim is to seize some of the highly desirable properties of photonics not just for communication, but also to perform computation. Neurons in the brain frequently process information (compute) and communicate using action potentials, which are brief voltage spikes that encode information in the temporal domain. Similar dynamical behaviour can be elicited in some photonic devices, at speeds multiple orders of magnitude higher. Such devices with the capability of neuron-like spiking are of significant research interest for the field of neuromorphic photonics. Two distinct types of such excitable, spiking systems operating with optical signals are studied and investigated in this thesis. First, a vertical cavity surface emitting laser (VCSEL) can be operated under a specific set of conditions to realise a high-speed, all-optical excitable photonic neuron that operates at standard telecom wavelengths. The photonic VCSEL-neuron was dynamically characterised and various information encoding mechanisms were studied in this device. In particular, a spiking rate-coding regime of operation was experimentally demonstrated, and its viability for performing spiking domain conversion of digital images was explored. Furthermore, for the first time, a joint architecture utilising a VCSEL-neuron coupled to a photonic integrated circuit (PIC) silicon microring weight bank was experimentally demonstrated in two different functional layouts. Second, an optoelectronic (O/E/O) circuit based upon a resonant tunnelling diode (RTD) was introduced. Two different types of RTD devices were studied experimentally: a higher output power, µ-scale RTD that was RF coupled to an active photodetector and a VCSEL (this layout is referred to as a PRL node); and a simplified, photosensitive RTD with nanoscale injector that was RF coupled to a VCSEL (referred to as a nanopRL node). Hallmark excitable behaviours were studied in both devices, including excitability thresholding and refractory periods. Furthermore, a more exotic resonate and-fire dynamical behaviour was also reported in the nano-pRL device. Finally, a modular numerical model of the RTD was introduced, and various information processing methods were demonstrated using both a single RTD spiking node, as well as a perceptron-type spiking neural network with physical models of optoelectronic RTD nodes serving as artificial spiking neurons.Over the last decade, we have witnessed an astonishing pace of development in the field of artificial intelligence (AI), followed by proliferation of AI algorithms into virtually every domain of our society. While modern AI models boast impressive performance, they also require massive amounts of energy and resources for operation. This is further fuelling the research into AI-specific, optimised computing hardware. At the same time, the remarkable energy efficiency of the brain brings an interesting question: Can we further borrow from the working principles of biological intelligence to realise a more efficient artificial intelligence? This can be considered as the main research question in the field of neuromorphic engineering. Thanks to the developments in AI and recent advancements in the field of photonics and photonic integration, research into light-powered implementations of neuromorphic hardware has recently experienced a significant uptick of interest. In such hardware, the aim is to seize some of the highly desirable properties of photonics not just for communication, but also to perform computation. Neurons in the brain frequently process information (compute) and communicate using action potentials, which are brief voltage spikes that encode information in the temporal domain. Similar dynamical behaviour can be elicited in some photonic devices, at speeds multiple orders of magnitude higher. Such devices with the capability of neuron-like spiking are of significant research interest for the field of neuromorphic photonics. Two distinct types of such excitable, spiking systems operating with optical signals are studied and investigated in this thesis. First, a vertical cavity surface emitting laser (VCSEL) can be operated under a specific set of conditions to realise a high-speed, all-optical excitable photonic neuron that operates at standard telecom wavelengths. The photonic VCSEL-neuron was dynamically characterised and various information encoding mechanisms were studied in this device. In particular, a spiking rate-coding regime of operation was experimentally demonstrated, and its viability for performing spiking domain conversion of digital images was explored. Furthermore, for the first time, a joint architecture utilising a VCSEL-neuron coupled to a photonic integrated circuit (PIC) silicon microring weight bank was experimentally demonstrated in two different functional layouts. Second, an optoelectronic (O/E/O) circuit based upon a resonant tunnelling diode (RTD) was introduced. Two different types of RTD devices were studied experimentally: a higher output power, µ-scale RTD that was RF coupled to an active photodetector and a VCSEL (this layout is referred to as a PRL node); and a simplified, photosensitive RTD with nanoscale injector that was RF coupled to a VCSEL (referred to as a nanopRL node). Hallmark excitable behaviours were studied in both devices, including excitability thresholding and refractory periods. Furthermore, a more exotic resonate and-fire dynamical behaviour was also reported in the nano-pRL device. Finally, a modular numerical model of the RTD was introduced, and various information processing methods were demonstrated using both a single RTD spiking node, as well as a perceptron-type spiking neural network with physical models of optoelectronic RTD nodes serving as artificial spiking neurons

Notes in Pure Mathematics & Mathematical Structures in Physics

These Notes deal with various areas of mathematics, and seek reciprocal combinations, explore mutual relations, ranging from abstract objects to problems in physics.Comment: Small improvements and addition

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018

This open access book features a selection of high-quality papers from the presentations at the International Conference on Spectral and High-Order Methods 2018, offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions

References, Appendices & All Parts Merged

Includes: Appendix MA: Selected Mathematical Formulas; Appendix CA: Selected Physical Constants; References; EGP merged file (all parts, appendices, and references)https://commons.library.stonybrook.edu/egp/1007/thumbnail.jp

Designing Embodied Interactive Software Agents for E-Learning: Principles, Components, and Roles

Embodied interactive software agents are complex autonomous, adaptive, and social software systems with a digital embodiment that enables them to act on and react to other entities (users, objects, and other agents) in their environment through bodily actions, which include the use of verbal and non-verbal communicative behaviors in face-to-face interactions with the user. These agents have been developed for various roles in different application domains, in which they perform tasks that have been assigned to them by their developers or delegated to them by their users or by other agents. In computer-assisted learning, embodied interactive pedagogical software agents have the general task to promote human learning by working with students (and other agents) in computer-based learning environments, among them e-learning platforms based on Internet technologies, such as the Virtual Linguistics Campus (www.linguistics-online.com). In these environments, pedagogical agents provide contextualized, qualified, personalized, and timely assistance, cooperation, instruction, motivation, and services for both individual learners and groups of learners. This thesis develops a comprehensive, multidisciplinary, and user-oriented view of the design of embodied interactive pedagogical software agents, which integrates theoretical and practical insights from various academic and other fields. The research intends to contribute to the scientific understanding of issues, methods, theories, and technologies that are involved in the design, implementation, and evaluation of embodied interactive software agents for different roles in e-learning and other areas. For developers, the thesis provides sixteen basic principles (Added Value, Perceptible Qualities, Balanced Design, Coherence, Consistency, Completeness, Comprehensibility, Individuality, Variability, Communicative Ability, Modularity, Teamwork, Participatory Design, Role Awareness, Cultural Awareness, and Relationship Building) plus a large number of specific guidelines for the design of embodied interactive software agents and their components. Furthermore, it offers critical reviews of theories, concepts, approaches, and technologies from different areas and disciplines that are relevant to agent design. Finally, it discusses three pedagogical agent roles (virtual native speaker, coach, and peer) in the scenario of the linguistic fieldwork classes on the Virtual Linguistics Campus and presents detailed considerations for the design of an agent for one of these roles (the virtual native speaker)

A complex systems approach to education in Switzerland

The insights gained from the study of complex systems in biological, social, and engineered systems enables us not only to observe and understand, but also to actively design systems which will be capable of successfully coping with complex and dynamically changing situations. The methods and mindset required for this approach have been applied to educational systems with their diverse levels of scale and complexity. Based on the general case made by Yaneer Bar-Yam, this paper applies the complex systems approach to the educational system in Switzerland. It confirms that the complex systems approach is valid. Indeed, many recommendations made for the general case have already been implemented in the Swiss education system. To address existing problems and difficulties, further steps are recommended. This paper contributes to the further establishment complex systems approach by shedding light on an area which concerns us all, which is a frequent topic of discussion and dispute among politicians and the public, where billions of dollars have been spent without achieving the desired results, and where it is difficult to directly derive consequences from actions taken. The analysis of the education system's different levels, their complexity and scale will clarify how such a dynamic system should be approached, and how it can be guided towards the desired performance

Collected Papers (on various scientific topics), Volume XIII

This thirteenth volume of Collected Papers is an eclectic tome of 88 papers in various fields of sciences, such as astronomy, biology, calculus, economics, education and administration, game theory, geometry, graph theory, information fusion, decision making, instantaneous physics, quantum physics, neutrosophic logic and set, non-Euclidean geometry, number theory, paradoxes, philosophy of science, scientific research methods, statistics, and others, structured in 17 chapters (Neutrosophic Theory and Applications; Neutrosophic Algebra; Fuzzy Soft Sets; Neutrosophic Sets; Hypersoft Sets; Neutrosophic Semigroups; Neutrosophic Graphs; Superhypergraphs; Plithogeny; Information Fusion; Statistics; Decision Making; Extenics; Instantaneous Physics; Paradoxism; Mathematica; Miscellanea), comprising 965 pages, published between 2005-2022 in different scientific journals, by the author alone or in collaboration with the following 110 co-authors (alphabetically ordered) from 26 countries: Abduallah Gamal, Sania Afzal, Firoz Ahmad, Muhammad Akram, Sheriful Alam, Ali Hamza, Ali H. M. Al-Obaidi, Madeleine Al-Tahan, Assia Bakali, Atiqe Ur Rahman, Sukanto Bhattacharya, Bilal Hadjadji, Robert N. Boyd, Willem K.M. Brauers, Umit Cali, Youcef Chibani, Victor Christianto, Chunxin Bo, Shyamal Dalapati, Mario Dalcín, Arup Kumar Das, Elham Davneshvar, Bijan Davvaz, Irfan Deli, Muhammet Deveci, Mamouni Dhar, R. Dhavaseelan, Balasubramanian Elavarasan, Sara Farooq, Haipeng Wang, Ugur Halden, Le Hoang Son, Hongnian Yu, Qays Hatem Imran, Mayas Ismail, Saeid Jafari, Jun Ye, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Darjan Karabašević, Abdullah Kargın, Vasilios N. Katsikis, Nour Eldeen M. Khalifa, Madad Khan, M. Khoshnevisan, Tapan Kumar Roy, Pinaki Majumdar, Sreepurna Malakar, Masoud Ghods, Minghao Hu, Mingming Chen, Mohamed Abdel-Basset, Mohamed Talea, Mohammad Hamidi, Mohamed Loey, Mihnea Alexandru Moisescu, Muhammad Ihsan, Muhammad Saeed, Muhammad Shabir, Mumtaz Ali, Muzzamal Sitara, Nassim Abbas, Munazza Naz, Giorgio Nordo, Mani Parimala, Ion Pătrașcu, Gabrijela Popović, K. Porselvi, Surapati Pramanik, D. Preethi, Qiang Guo, Riad K. Al-Hamido, Zahra Rostami, Said Broumi, Saima Anis, Muzafer Saračević, Ganeshsree Selvachandran, Selvaraj Ganesan, Shammya Shananda Saha, Marayanagaraj Shanmugapriya, Songtao Shao, Sori Tjandrah Simbolon, Florentin Smarandache, Predrag S. Stanimirović, Dragiša Stanujkić, Raman Sundareswaran, Mehmet Șahin, Ovidiu-Ilie Șandru, Abdulkadir Șengür, Mohamed Talea, Ferhat Taș, Selçuk Topal, Alptekin Ulutaș, Ramalingam Udhayakumar, Yunita Umniyati, J. Vimala, Luige Vlădăreanu, Ştefan Vlăduţescu, Yaman Akbulut, Yanhui Guo, Yong Deng, You He, Young Bae Jun, Wangtao Yuan, Rong Xia, Xiaohong Zhang, Edmundas Kazimieras Zavadskas, Zayen Azzouz Omar, Xiaohong Zhang, Zhirou Ma.‬‬‬‬‬‬‬