Komparativ analyse av heterogene og homogene nevrale feltmodeller

The present thesis is devoted to the comparative analysis of heterogeneous and homogeneous neural field models. The motivation for this work stems from the fact that there is considerable interest in processes in neural tissue, which can underlie both natural and pathological neurobiological phenomena (e.g., orientation tuning in primary visual cortex, short term working memory, control of head direction, motion perception, visual hallucinations and EEG rhythms). The main aim of this thesis is to investigate the outcome of the analysis of a heterogeneous neural field model and its homogeneous counterpart. Another goal is to get more realistic dynamical models for the brain function which takes into account microscopic effects. Mathematically, this approach is formulated in terms of (a system of) nonlinear integro-differential equations. These models describe nonlinear interactions between neuron populations. They are used as a starting point to study traveling wave fronts, localized stationary solutions (bumps) and pattern formation. The first part of the thesis consists of the introduction. Here we first give a short review of the neurophysical background. Secondly, we introduce the key mathematical objects of the present thesis, namely a neural field model of the Amari type and a 2-population homogenized neural field model. We also review the basic ideas of homogenization theory and the two-scale convergence method. Then we summarize the results and give ideas for future works. The second part of the thesis consists of three papers. Paper I deals with the existence and linear stability of stationary periodic bump solutions to a neural field model of the Amari type. In Paper II and III we focus on 2-population homogenized neural field models where the cortical microstructure is taken into account in the connectivity strength. We study the existence and stability of localized stationary single bump solutions (Paper II). In Paper III we investigate pattern forming processes in the same neural field model. The key methods in the present study are a pinning function technique for the existence of bumps, spectral methods and properties, block diagonalization and the Fourier decomposition method in the stability assessment and numerical simulations. We believe that the present thesis contributes to the understanding of the brain functions, both in normal and pathological cases.I denne avhandlingen utføres en komparativ analyse av heterogene og homogene nevrale nettverksmodeller. Motivasjonen for dette arbeidet er interessen for prosesser i hjernebarken, som kan være grunnlag for både naturlige og patologiske nevrobiologiske fenomener (for eksempel i orienteringsinnstilling i den primære visuelle hjernebarken, korttidsminne, kontroll av hoderetning, bevegelsesoppfattelse, visuelle hallusinasjoner og EEG-rytmer). Hovedformålet med denne avhandlingen er å analysere en heterogen nevral nettverksmodell og dens homogene motstykke. Et annet mål er å få mer realistiske dynamiske modeller for hjernefunksjonen, som tar hensyn til mikroskopiske effekter. Disse modellene er gitt som (et system av) ikke-lineære integro-differensiallikninger. Disse modellene beskriver ikke-lineære interaksjoner mellom nevronpopulasjoner. De brukes som utgangspunkt for å studere bølgeforplantning, lokaliserte stasjonære løsninger (bumps) og mønsterdannelse. I introduksjonen presenterer vi en oversikt over den nevrofysiologiske bakgrunnen. Videre introduserer vi de matematiske modellene som er sentrale i denne avhandlingen, det vil si en nevral nettverksmodell av Amari- typen og en homogenisert 2-populasjon nevral nettverksmodell. Vi gjennomgår også grunnbegrepene i homogeniseringsteori og toskala konvergensmetoden. Deretter oppsummerer vi resultatene og fremlegger ideer for videre arbeid. Den andre delen av denne avhandlingen består av tre artikler. Artikkel I omhandler eksistensen og den lineære stabiliteten til stasjonære periodiske bump-løsninger i en nettverksmodell av Amari-typen. I artikkel II og III fokuserer vi på en homogenisert 2-populasjons nevral nettverksmodell, hvor mikrostrukturen i hjernebarken tas med i beregningen av konnektivitetsstyrken. Vi undersøker eksistensen og stabiliteten til lokaliserte stasjonære bump-løsninger (artikkel II). I artikkel III studerer vi mønsterdannende prosesser i den samme nevrale nettverksmodellen. De sentrale metodene i denne studien er en pinning-funksjonsteknikk for eksistens av bumps. Stabilitetsanalysen er gjennomført ved hjelp av spektral metoder , blokk diagonalisering og Fouriertransformasjon og numeriske simuleringer. Vi mener at denne avhandlingen bidrar til forståelsen av hjernens funksjoner, både under normale og patologiske omstendigheter

The Locked-in Syndrome of Panpsychism: Integrated Information Theory, Orch-OR, TGD and the Search for the Right Experimental Model

N/

Deep Learning based data-fusion methods for remote sensing applications

In the last years, an increasing number of remote sensing sensors have been launched to orbit around the Earth, with a continuously growing production of massive data, that are useful for a large number of monitoring applications, especially for the monitoring task. Despite modern optical sensors provide rich spectral information about Earth's surface, at very high resolution, they are weather-sensitive. On the other hand, SAR images are always available also in presence of clouds and are almost weather-insensitive, as well as daynight available, but they do not provide a rich spectral information and are severely affected by speckle "noise" that make difficult the information extraction. For the above reasons it is worth and challenging to fuse data provided by different sources and/or acquired at different times, in order to leverage on their diversity and complementarity to retrieve the target information. Motivated by the success of the employment of Deep Learning methods in many image processing tasks, in this thesis it has been faced different typical remote sensing data-fusion problems by means of suitably designed Convolutional Neural Networks

Complex extreme nonlinear waves: classical and quantum theory for new computing models

The historical role of nonlinear waves in developing the science of complexity, and also their physical feature of being a widespread paradigm in optics, establishes a bridge between two diverse and fundamental fields that can open an immeasurable number of new routes. In what follows, we present our most important results on nonlinear waves in classical and quantum nonlinear optics. About classical phenomenology, we lay the groundwork for establishing one uniform theory of dispersive shock waves, and for controlling complex nonlinear regimes through simple integer topological invariants. The second quantized field theory of optical propagation in nonlinear dispersive media allows us to perform numerical simulations of quantum solitons and the quantum nonlinear box problem. The complexity of light propagation in nonlinear media is here examined from all the main points of view: extreme phenomena, recurrence, control, modulation instability, and so forth. Such an analysis has a major, significant goal: answering the question can nonlinear waves do computation? For this purpose, our study towards the realization of an all-optical computer, able to do computation by implementing machine learning algorithms, is illustrated. The first all-optical realization of the Ising machine and the theoretical foundations of the random optical machine are here reported. We believe that this treatise is a fundamental study for the application of nonlinear waves to new computational techniques, disclosing new procedures to the control of extreme waves, and to the design of new quantum sources and non-classical state generators for future quantum technologies, also giving incredible insights about all-optical reservoir computing. Can nonlinear waves do computation? Our random optical machine draws the route for a positive answer to this question, substituting the randomness either with the uncertainty of quantum noise effects on light propagation or with the arbitrariness of classical, extremely nonlinear regimes, as similarly done by random projection methods and extreme learning machines

A comparative review of peridynamics and phase-field models for engineering fracture mechanics

Computational modeling of the initiation and propagation of complex fracture is central to the discipline of engineering fracture mechanics. This review focuses on two promising approaches: phase-field (PF) and peridynamic (PD) models applied to this class of problems. The basic concepts consisting of constitutive models, failure criteria, discretization schemes, and numerical analysis are briefly summarized for both models. Validation against experimental data is essential for all computational methods to demonstrate predictive accuracy. To that end, the Sandia Fracture Challenge and similar experimental data sets where both models could be benchmarked against are showcased. Emphasis is made to converge on common metrics for the evaluation of these two fracture modeling approaches. Both PD and PF models are assessed in terms of their computational effort and predictive capabilities, with their relative advantages and challenges are summarized

A comparative review of peridynamics and phase-field models for engineering fracture mechanics

Computational modeling of the initiation and propagation of complex fracture is central to the discipline of engineering fracture mechanics. This review focuses on two promising approaches: phase-field (PF) and peridynamic (PD) models applied to this class of problems. The basic concepts consisting of constitutive models, failure criteria, discretization schemes, and numerical analysis are briefly summarized for both models. Validation against experimental data is essential for all computational methods to demonstrate predictive accuracy. To that end, the Sandia Fracture Challenge and similar experimental data sets where both models could be benchmarked against are showcased. Emphasis is made to converge on common metrics for the evaluation of these two fracture modeling approaches. Both PD and PF models are assessed in terms of their computational effort and predictive capabilities, with their relative advantages and challenges are summarized. © 2022, The Author(s)

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

An Algorithm for Integrated Subsystem Embodiment and System Synthesis

Consider the statement,'A system has two coupled subsystems, one of which dominates the design process. Each subsystem consists of discrete and continuous variables, and is solved using sequential analysis and solution.' To address this type of statement in the design of complex systems, three steps are required, namely, the embodiment of the statement in terms of entities on a computer, the mathematical formulation of subsystem models, and the resulting solution and system synthesis. In complex system decomposition, the subsystems are not isolated, self-supporting entities. Information such as constraints, goals, and design variables may be shared between entities. But many times in engineering problems, full communication and cooperation does not exist, information is incomplete, or one subsystem may dominate the design. Additionally, these engineering problems give rise to mathematical models involving nonlinear functions of both discrete and continuous design variables. In this dissertation an algorithm is developed to handle these types of scenarios for the domain-independent integration of subsystem embodiment, coordination, and system synthesis using constructs from Decision-Based Design, Game Theory, and Multidisciplinary Design Optimization. Implementation of the concept in this dissertation involves testing of the hypotheses using example problems and a motivating case study involving the design of a subsonic passenger aircraft

Dynamics of Patterns

Patterns and nonlinear waves arise in many applications. Mathematical descriptions and analyses draw from a variety of fields such as partial differential equations of various types, differential and difference equations on networks and lattices, multi-particle systems, time-delayed systems, and numerical analysis. This workshop brought together researchers from these diverse areas to bridge existing gaps and to facilitate interaction