Academic literature on the topic 'Continuous random energy model'

Cette thèse explore les perspectives algorithmiques de la marche aléatoire branchante et du modèle continu d'énergie aléatoire (CREM). Nous nous intéressons notamment à la construction d'algorithmes en temps polynomial capables d'échan¬tillonner la mesure de Gibbs du modèle avec une grande probabilité, et à identifier le régime de dureté, qui consiste en toute température inverse bêta telle que de tels algorithmes en temps polynomial n'existent pas. Dans le Chapitre 1, nous fournissons un aperçu historique des modèles et moti¬vons les problèmes algorithmiques étudiés. Nous donnons également un aperçu des verres de spin à champ moyen qui motive la ligne de notre recherche. Dans le Chapitre 2, nous abordons le problème de l'échantillonnage de la mesure de Gibbs dans le contexte de la marche aléatoire branchante. Nous identifions une température inverse critique bêta_c, identique au point critique statique, où une tran¬sition de dureté se produit. Dans le régime sous-critique bêta &lt; bêta_c, nous établissons qu'un algorithme d'échantillonnage récursif est capable d'échantillonner efficace¬ment la mesure de Gibbs. Dans le régime supercritique bêta &gt; bêta_c, nous montrons que nous ne pouvons pas trouver d'algorithme en temps polynomial qui appartienne à une certaine classe d'algorithmes. Dans le Chapitre 3, nous portons notre attention sur le même problème d'échan¬tillonnage pour le modèle continu d'énergie aléatoire (CREM). Dans le cas où la fonction de covariance de ce modèle est concave, nous montrons que pour toute température inverse bêta &lt; à l'infini, l'algorithme d'échantillonnage récursif considéré au Chapitre 2 est capable d'échantillonner efficacement la mesure de Gibbs. Pour le cas non concave, nous identifions un point critique bêta_G où une transition de dureté similaire à celle du Chapitre 2 se produit. Nous fournissons également une borne inférieure de l'énergie libre du CREM qui pourrait être d'un intérêt indépendant. Dans le Chapitre 4, nous étudions le moment négatif de la fonction de partition du CREM. Bien que cela ne soit pas directement lié au thème principal de la thèse, cela découle du cours de la recherche. Dans le Chapitre 5, nous donnons un aperçu de certaines orientations futures qui pourraient être intéressantes à étudier<br>This thesis explores the algorithmic perspectives of the branching random walk and the continuous random energy model (CREM). Namely, we are interested in constructing polynomial-time algorithms that can sample the model's Gibbs measure with high probability, and to indentify the hardness regime, which consists of any inverse temperature bêta such that such polynomial-time algorithms do not exist. In Chapter 1, we provide a historical overview of the models and motivate the algorithmic problems under investigation. We also provide an overview on the mean-field spin glasses that motivates the line of our research. In Chapter 2, we address the sampling problem of the Gibbs measure in the context of branching random walk. We identify a critical inverse temperature bêta_c, identical to the static critical point, that the a hardness transition occurs. In the subcritical regime bêta &lt; bêta_c, we establish a recursive sampling algorithm is able to sample the Gibbs measure efficiently. In the supercritical regime bêta &gt; bêta_c,we show that we cannot find polynomial-time algorithm that belongs to a certain class of algorithms. In Chapter 3, we turn our attention to the same sampling problem for the con¬tinuous random energy model (CREM). For the case where the covariance function of this model is concave, we show that for any inverse temperature bêta &lt; to infinity, the recursive sampling algorithm considered in Chapter 2 is able to sample the Gibbs measure efficiently. For the non-concave case, we identify a critical point bêta_G that similar hardness transition as the one in Chapter 2 occurs. We also provide a lower bound of the CREM free energy that might be of independent interest. In Chapter 4, we study the negative moment of the CREM partition function. While this is not connected directly to the main theme of the thesis, it spins off during the course of research. In Chapter 5, we provide an outlook of some further directions that might be interesting to investigate

<p> In this dissertation, we are mainly concerned with the sum of random exponentials. Here, the random variables are independent and identically distributed. Another distinctive assumption is the number of variables in this sum is a function of the constant on the exponent. Our first goal is to find the limiting distributions of the random exponential sums for new class of the random variables. For some classes, such results are known; normal distribution, Weibull distribution etc. </p><p> Secondly, we apply these limit theorems to some insurance models and the random energy model in statistical physics. Specifically for the first case, we give the estimate of the ruin probability in terms of the empirical data. For the random energy model, we present the analysis of the free energy for new class of distribution. In some particular cases, we prove the existence of several critical points for the free energy. In some other cases, we prove the absence of phase transitions. </p><p> Our results give a new approach to compute the ruin probabilities of insurance portfolios empirically when there is a sequence of insurance portfolios with a custom growth rate of the claim amounts. The second application introduces a simple method to drive the free energy in the case the random variables in the statistical sum can be represented as a function of standard exponential random variables. The technical tool of this study includes the classical limit theory for the sum of independent and identically distributed random variables and different asymptotic methods like the Euler-Maclaurin formula and Laplace method.</p>

The study of supercooled liquids and glasses remains one of the most divisive and divided fields in modern physics. Despite a vast amount of effort and research time invested in this topic, the answers to many central questions remain disputed and incomplete. However, the link between the behaviour of supercooled liquids and their energy landscapes is well established and widely accepted. Understanding this link would be a key step towards resolving many of the mysteries and controversies surrounding the glass transition. Therefore the study of glassy energy landscapes is an important area of research. In this thesis, I report some of the most detailed computational studies of glassy potential energy landscapes ever performed. Using geometry optimisation techniques, I have sampled the local minima and saddle points of the landscapes for several supercooled liquids to analyse their dynamics and thermodynamics. Some of my analysis follows previous work on the binary Lennard-Jones fluid (BLJ), a model atomic liquid. BLJ is a fragile glass former, meaning that its transport coefficients have super-Arrhenius temperature dependence, rather than the more usual Arrhenius behaviour exhibited by strong liquids. The difference in behaviour between these two classes of liquid has previously been attributed to differing degrees of structure in the relevant energy landscapes. I have studied models for both fragile and strong glass formers: the molecular liquid ortho-terphenyl (OTP) and viscous silica (SiO$_{2}$) respectively. My results for OTP agree closely with trends observed for BLJ, suggesting that the same diffusion mechanism is applicable to fragile molecular liquids as well as to atomic. However, the dynamics and energy landscape of OTP are made complicated by the molecular orientational degrees of freedom, making the analysis more challenging for this system. Dynamics of BLJ, OTP and silica are all dominated by cage-breaking events: structural rearrangements in which atoms change their nearest neighbours. I propose a robust and general method to identify cage breaks for small rigid molecules, and compare some properties of cage breaks between strong and fragile systems. The energy landscapes of BLJ and OTP both display hierarchical ordering of potential energy minima into metabasins. These metabasins can be detected by the cage-breaking method. It has previously been suggested that metabasins are responsible for super-Arrhenius behaviour, and are absent from the landscapes of strong liquids such as SiO2. My results indicate that metabasins are present on the silica landscape, but that they each contain fewer minima than metabasins in BLJ or OTP. Metabasins are associated with anticorrelated particle motion, mediated by reversed transitions between minima of the potential energy landscape. I show that accounting for time-correlation of particle displacement vectors is essential to describe super-Arrhenius behaviour in BLJ and OTP, but also required to reproduce strong behaviour in silica. I hypothesise that the difference between strong and fragile liquids arises from a longer correlation timescale in the latter case, and I suggest a number of ways in which this proposition could be tested. I have investigated the effect on the landscape of freezing the positions of some particles in a BLJ fluid. This “pinning” procedure induces a dynamical crossover that has been described as an equilibrium “pinning transition”, related to the hypothetical ideal glass transition. I show that the pinning transition is related to (and probably caused by) a dramatic change in the potential energy landscape. Pinning a large fraction of the particles in a supercooled liquid causes its energy landscape to acquire global structure and hence structure-seeking behaviour, very different from the landscape of a typical supercooled liquid. I provide a detailed description of this change in structure, and investigate the mechanism underlying it. I introduce a new algorithm for identifying hierarchical organisation of a landsape, which uses concepts related to the pinning transition but is applicable to unpinned liquids as well. This definition is complementary to metabasins, but the two methods often identify the same higher-order structures. The new “packings” algorithm offers a route to test thermodynamic theories of the glass transition in the context of the potential energy landscape. Over the course of this thesis, I discuss several different terms and methods to identify higher-order structures in the landscapes of model glass formers, and investigate how this organisation varies between different systems. Although little variation is immediately apparent between most glassy landscapes, deeper analysis reveals a surprising diversity, which has important implications for dynamical behaviour in the vicinity of the glass transition.

<p>In this work, an existing RAM generator is analysed and evaluated. Some of the aspects that were considered in the evaluation are the optimization of the basic SRAM cell, how the RAM generator can be ported to newer technologys, automating the simulation process and the creation of the workflow for the energy model.</p><p>One of the main focus of this thesis work is to optimize the basic SRAM cell. The SRAM cell which is used in the RAM generator is not optimized for area nor power. A compact layout is suggested which saves a lot of area and power. The technology that is used to create the RAM generator is old and a suitable way to port it to newer technology has also been found.</p><p>To create an energy model one has to simulate a lot of memories with a lot of data. This cannot be done in the traditional way of simulating circuits using the GUI. Hence an automation procedure has been suggested which can be made to work to create energy models by simulating the memories comprehensively.</p><p>Finally, basic ground work has been initiated by creating a workflow for the creation of the energy model.</p>

Among the latest achievements in gasification technology, one may list the development of a method to preheat gasification agents using switched ceramic honey combs. The best output from this technology is achieved with use of water steam as a gasification agent, which is heated up to 1600 °C. The application of these temperatures with steam as a gasification agent provides a cleaner syngas (no nitrogen from air, cracked tars) and the ash melts into easily utilised glass-like sludge. High hydrogen content in output gas is also favourable for end-user applications.Among the other advantages of this technology is the presumable application of fixed-bed-type reactors fed by separately produced and preheated steam. This construction assumes relatively high steam flow rates to deliver the heat needed for endothermic reactions involving biomass. The biomass is to be heated uniformly and evenly in the volume of the whole reactor, providing easier and simpler control and operation in comparison to other types of reactors. To provide potential constructors and exploiters of these reactors with the kinetic data needed for the calculations of vital parameters for both reactor construction and exploitation, basic experimental research of high-temperature steam gasification of four types of industrially produced biomass has been conducted.Kinetic data have been obtained for straw and wood pellets, wood-chip charcoal and compressed charcoal of mixed origin. Experiments were conducted using two experimental facilities at the Energy and Furnace Division of the Department of Material Science and Engineering (MSE) at the School of Industrial Engineering and Management (ITM) of the Royal Institute of Technology (KTH) and at the Combustion Laboratory of the Mechanical Engineering Department of the University of Maryland (UMD), USA. The experimental facility at the Energy and Furnace Division has been improved with the addition of several constructive elements, providing better possibilities for thermo-gravimetric measurements.The obtained thermo-gravimetric data were analysed and approximated using several models described in the literature. In addition, appropriate software based on the Scilab package was developed. The implementation of the isothermal method based on optimisation algorithms has been developed and tested on the data obtained under the conditions of a slow decrease of temperature in experiments with the char gasification in small-scale experimental facilities in the Energy and Furnace Division.The composition of the gases generated during the gasification of straw and wood pellets by high-temperature steam has been recorded and analysed for different experimental conditions.<br><p>QC 20101124</p><br>Study of ignition and kinetics of biomass/solid waste thermal conversion with high-temperature air/steam

Machine learning models increase their representational power by increasing the number of parameters in the model. The number of parameters in the model can be increased by introducing hidden nodes, higher-order interaction effects or by introducing new features into the model. In this thesis we study different approaches to increase the representational power in unsupervised machine learning models. We investigate the use of incidence algebra and information geometry to develop novel machine learning models to include higher-order interactions effects into the model. Incidence algebra provides a natural formulation for combinatorics by expressing it as a generative function and information geometry provides many theoretical guarantees in the model by projecting the problem onto a dually flat Riemannian structure for optimization. Combining the two techniques together formulates the information geometric formulation of the binary log-linear model. We first use the information geometric formulation of the binary log-linear model to formulate the higher-order Boltzmann machine (HBM) to compare the different behaviours when using hidden nodes and higher-order feature interactions to increase the representational power of the model. We then apply the concepts learnt from this study to include higher-order interaction terms in Blind Source Separation (BSS) and to create an efficient approach to estimate higher order functions in Poisson process. Lastly, we explore the possibility to use Bayesian non-parametrics to automatically reduce the number of higher-order interactions effects included in the model.

In this thesis, we would like to present a new way to enhance the “depth map” image which is called as the fusion of depth images. The goal of our thesis is to try to enhance the “depth images” through a fusion of different classification methods. For that, we will use three similar but different methodologies, the Graph-Cut, Super-Pixel and Principal Component Analysis algorithms to solve the enhancement and output of our result. After that, we will compare the effect of the enhancement of our result with the original depth images. This result indicates the effectiveness of our methodology.<br>Room 401, No.56, Lane 21, Yin Gao Road, Shanghai, China

The thesis presents results of a numerical study on the performance of 3D discrete meso–scale lattice–particle model of concrete. The existing model was extended by introducing the spatial variability of chosen material parameter in form of random field. An experimental data from bending tests on notched and unnotched beams was exploited for the identification of model parameters as well as for the subsequent validation of its performance. With the basic and the extended randomized version of the model, numerical simulations were calculated so that the influence of the rate of fluctuation of the random field (governed by the correlation length) could be observed. The final part of the thesis describes the region in the beam active during the test in which the most of the fracture energy is released in terms of its size and shape. This region defines the strength of the whole member and as shown in the thesis, it does not have a constant size but it is influenced by the geometrical setup and the correlation length of the random field.