14,766 research outputs found
Range separation: The divide between local structures and field theories
This work presents parallel histories of the development of two modern
theories of condensed matter: the theory of electron structure in quantum
mechanics, and the theory of liquid structure in statistical mechanics.
Comparison shows that key revelations in both are not only remarkably similar,
but even follow along a common thread of controversy that marks progress from
antiquity through to the present. This theme appears as a creative tension
between two competing philosophies, that of short range structure (atomistic
models) on the one hand, and long range structure (continuum or density
functional models) on the other. The timeline and technical content are
designed to build up a set of key relations as guideposts for using density
functional theories together with atomistic simulation.Comment: Expanded version of a 30 minute talk delivered at the 2018 TSRC
workshop on Ions in Solution, to appear in the March, 2019 issue of
Substantia (https://riviste.fupress.net/index.php/subs/index
Platonic model of mind as an approximation to neurodynamics
Hierarchy of approximations involved in simplification of microscopic theories, from sub-cellural to the whole brain level, is presented. A new approximation to neural dynamics is described, leading to a Platonic-like model of mind based on psychological spaces. Objects and events in these spaces correspond to quasi-stable states of brain dynamics and may be interpreted from psychological point of view. Platonic model bridges the gap between neurosciences and psychological sciences. Static and dynamic versions of this model are outlined and Feature Space Mapping, a neurofuzzy realization of the static version of Platonic model, described. Categorization experiments with human subjects are analyzed from the neurodynamical and Platonic model points of view
Machine Learning for Fluid Mechanics
The field of fluid mechanics is rapidly advancing, driven by unprecedented
volumes of data from field measurements, experiments and large-scale
simulations at multiple spatiotemporal scales. Machine learning offers a wealth
of techniques to extract information from data that could be translated into
knowledge about the underlying fluid mechanics. Moreover, machine learning
algorithms can augment domain knowledge and automate tasks related to flow
control and optimization. This article presents an overview of past history,
current developments, and emerging opportunities of machine learning for fluid
mechanics. It outlines fundamental machine learning methodologies and discusses
their uses for understanding, modeling, optimizing, and controlling fluid
flows. The strengths and limitations of these methods are addressed from the
perspective of scientific inquiry that considers data as an inherent part of
modeling, experimentation, and simulation. Machine learning provides a powerful
information processing framework that can enrich, and possibly even transform,
current lines of fluid mechanics research and industrial applications.Comment: To appear in the Annual Reviews of Fluid Mechanics, 202
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PATTERN FORMATION AND PHASE TRANSITION OF CONNECTIVITY IN TWO DIMENSIONS
This dissertation is devoted to the study and analysis of different types of emergent behavior in physical systems. Emergence is a phenomenon that has fascinated researchers from various fields of science and engineering. From the emergence of global pandemics to the formation of reaction-diffusion patterns, the main feature that connects all these diverse systems is the appearance of a complex global structure as a result of collective interactions of simple underlying components. This dissertation will focus on two types of emergence in physical systems: emergence of long-range connectivity in networks and emergence and analysis of complex patterns.
The most prominent theory which deals with the emergence of long-range connectivity is the percolation theory. This dissertation employs many concepts from the percolation theory to study connectivity transitions in various systems. Ordinary percolation theory is founded upon two main assumptions, namely locality and independence of the underlying components. In Chapters 2 and 3, we relax these assumptions in different manners and show that relaxing these assumptions leads to irregular behaviors such as appearance of different universality classes and, in some instances, violation of universality. Chapter 2 deals with relaxing the assumption of locality of interactions. In this Chapter, we define a hierarchy of various measures of robust connectivity. We study the phase transition of these robustness metrics as a function of site/bond occupation/removal probability on the square lattice. Furthermore, we perform extensive numerical analysis and extract these robustness metrics\u27 critical thresholds and critical behaviors. We show that some of these robustness metrics do not fall under the regular percolation universality class. The extensive numerical results in this work can serve as a foundation for any researcher who aims to design/study various degrees of connectivity in networks.
In Chapter 3, we study the non-equilibrium phase transition of long-range connectivity in a multi-particle interacting system on the square lattice. The interactions between different particles translate to relaxing the assumption of independence in the percolation theory. Using extensive numerical simulations, we show that the phase transition observed in this system violates the regular concept of universality. However, it conforms well with the concept of weak-universality recently introduced in the literature. We observe that by varying inter-particle interaction strength in our model, one can control the critical behavior of this phase transition. These observations could be pivotal in studying phase transitions and universality classes.
Chapter 4 focuses on the analysis of reaction-diffusion patterns. We utilize a multitude of machine learning algorithms to analyze reaction-diffusion patterns. In particular, we address two main problems using these techniques, namely, pattern regression and pattern classification. Given an observed instance of a pattern with a known generative function, in the pattern regression task, we aim to predict the specific set of reaction-diffusion parameters (i.e. diffusion constant) which can reproduce the observed pattern. We employ supervised learning techniques to successfully solve this problem and show the performance of our model in some real-world instances. We also address the task of pattern classification. In this task, we are interested in grouping different instances of similar patterns together. This task is usually performed visually by the researcher studying certain natural phenomena. However, this method is tedious and can be inconsistent among different researchers. We utilize supervised and unsupervised machine learning algorithms to classify patterns of the Gray-Scott model. We show that our methods show outstanding performance both in supervised and unsupervised settings. The methods introduced in this Chapter could bridge the gaps between researchers studying patterns in different fields of science and engineering
The EM Algorithm and the Rise of Computational Biology
In the past decade computational biology has grown from a cottage industry
with a handful of researchers to an attractive interdisciplinary field,
catching the attention and imagination of many quantitatively-minded
scientists. Of interest to us is the key role played by the EM algorithm during
this transformation. We survey the use of the EM algorithm in a few important
computational biology problems surrounding the "central dogma"; of molecular
biology: from DNA to RNA and then to proteins. Topics of this article include
sequence motif discovery, protein sequence alignment, population genetics,
evolutionary models and mRNA expression microarray data analysis.Comment: Published in at http://dx.doi.org/10.1214/09-STS312 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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