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## Simulações atomísticas de eventos raros através de Transition Path Sampling; Atomistic simulation of rare events using Transition Path Sampling

Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Dissertação de Mestrado Formato: application/pdf
Relevância na Pesquisa
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Nesta dissertação abordamos o estudo de uma das limitações da simulação atomística denominada o evento raro, quem é responsável pela limitação temporal, exemplos de problemas que envolvem os eventos raros são, o enovelamento de proteínas, mudanças conformacionais de moléculas, reações químicas (em solução), difusão de sólidos e os processos de nucleação numa transição de fase de 1a ordem, entre outros. Métodos convencionais como Dinâmica Molecular (MD) ou Monte Carlo (MC) são úteis para explorar a paisagem de energia potencial de sistemas muito complexos, mas em presença de eventos raros se tornam muito ineficientes, devido à falta de estatística na amostragem do evento. Estes métodos gastam muito tempo computacional amostrando as configurações irrelevantes e não as transições de interesse. Neste sentido o método Transition Path Sampling (TPS), desenvolvido por D. Chandler e seus colaboradores, consegue explorar a paisagem de energia potencial e obter um conjunto de verdadeiras trajetórias dinâmicas que conectam os estados metaestáveis em presença de evento raros. A partir do ensemble de caminhos a constante de reação e o mecanismo de reação podem ser extraídos com muito sucesso. Neste trabalho de mestrado implementamos com muito sucesso o método TPS e realizamos uma comparação quantitativa em relação ao método MC configuracional num problema padrão da isomerização de uma molécula diatômica imersa num líquido repulsivo tipo Weeks-Chandler-Andersen (WCA). A aplicação destes métodos mostrou como o ambiente...

## Simulações atomísticas de eventos raros através do método super-simétrico; Atomistic simulation of rare events via the super-symmetric method

Edgar Josué Landinez Borda
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Dissertação de Mestrado Formato: application/pdf
Relevância na Pesquisa
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Nesta dissertação abordamos o problema da escala temporal nas simulações atomísticas, focando no problema de eventos raros. A solução deste problema so e possível com o desenvolvimento de técnicas especiais. Especificamente, estudamos o método super-simétrico para encontrar caminhos de reação. Este metodo não apresenta as limitições comuns de outros metodos para eventos raros. Aplicamos o método a três problemas padrão e encontramos que o método permite estudar as transições raras sem precisar de um conhecimento detalhado do sistema. Além disso permite observar qualitativamente os mecanismos de transição; This thesis deals with the problem of time scale in atomistic simulations, focusing on the problem of rare events. The solution to this problem is only possible with the development of special techniques. Specifically, we studied the super-symmetric method to find reaction pathways. This method does not have the usual limitations of other methods for rare events. We apply the method to three standard problems and find that the method allows to study the rare transitions without a detailed knowledge of the system. In addition, it allows us to observe qualitatively the transition mechanisms

## Loss Due to Missing Data in Efficiency of a Locally Optimal Test for Homogeneity with Respect to Very Rare Events*

Puri, Prem S.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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With reference to observations of supernovae in galaxies, a locally optimal test for the hypothesis of homogeneity of the observational units with respect to occurrence of supernovae (treated as a very rare event) is obtained for the case where the data are available only for those galaxies where at least one supernova is observed. It is shown that the loss in the asymptotic efficiency of the test due to lack of reporting of galaxies with no supernovae is very heavy and in fact is infinite for the case of very rare events.

## Of Black Swans and Tossed Coins: Is the Description-Experience Gap in Risky Choice Limited to Rare Events?

Ludvig, Elliot A.; Spetch, Marcia L.
Fonte: Public Library of Science Publicador: Public Library of Science
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.95883%
When faced with risky decisions, people tend to be risk averse for gains and risk seeking for losses (the reflection effect). Studies examining this risk-sensitive decision making, however, typically ask people directly what they would do in hypothetical choice scenarios. A recent flurry of studies has shown that when these risky decisions include rare outcomes, people make different choices for explicitly described probabilities than for experienced probabilistic outcomes. Specifically, rare outcomes are overweighted when described and underweighted when experienced. In two experiments, we examined risk-sensitive decision making when the risky option had two equally probable (50%) outcomes. For experience-based decisions, there was a reversal of the reflection effect with greater risk seeking for gains than for losses, as compared to description-based decisions. This fundamental difference in experienced and described choices cannot be explained by the weighting of rare events and suggests a separate subjective utility curve for experience.

## Gauging the flexibility of the active site in soybean lipoxygenase-1 (SLO-1) through an atom-centered density matrix propagation (ADMP) treatment that facilitates the sampling of rare events

Phatak, Prasad; Sumner, Isaiah; Iyengar, Srinivasan S.
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
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We present a computational methodology to sample rare events in large biological enzymes that may involve electronically polarizing, reactive processes. The approach includes simultaneous dynamical treatment of electronic and nuclear degrees of freedom, where contributions from the electronic portion are computed using hybrid density functional theory and the computational costs are reduced through a hybrid quantum mechanics/molecular mechanics (QM/MM) treatment. Thus, the paper involves a QM/MM dynamical treatment of rare events. The method is applied to probe the effect of the active site elements on the critical hydrogen transfer step in the soybean lipoxygenase-1 (SLO-1) catalyzed oxidation of linoleic acid. It is found that the dynamical fluctuations and associated flexibility of the active site are critical towards maintaining the electrostatics in the regime where the reactive process can occur smoothly. Physical constraints enforced to limit the active site flexibility are akin to mutations and, in the cases studied, have a detrimental effect on the electrostatic fluctuations, thus adversely affecting the hydrogen transfer process.

## Adaptively biased sequential importance sampling for rare events in reaction networks with comparison to exact solutions from finite buffer dCME method

Cao, Youfang; Liang, Jie
Fonte: AIP Publishing LLC Publicador: AIP Publishing LLC
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
47.255728%
Critical events that occur rarely in biological processes are of great importance, but are challenging to study using Monte Carlo simulation. By introducing biases to reaction selection and reaction rates, weighted stochastic simulation algorithms based on importance sampling allow rare events to be sampled more effectively. However, existing methods do not address the important issue of barrier crossing, which often arises from multistable networks and systems with complex probability landscape. In addition, the proliferation of parameters and the associated computing cost pose significant problems. Here we introduce a general theoretical framework for obtaining optimized biases in sampling individual reactions for estimating probabilities of rare events. We further describe a practical algorithm called adaptively biased sequential importance sampling (ABSIS) method for efficient probability estimation. By adopting a look-ahead strategy and by enumerating short paths from the current state, we estimate the reaction-specific and state-specific forward and backward moving probabilities of the system, which are then used to bias reaction selections. The ABSIS algorithm can automatically detect barrier-crossing regions, and can adjust bias adaptively at different steps of the sampling process...

## High-resolution X-ray spectroscopy of rare events: a different look at local structure and chemistry

Bergmann, Uwe; Glatzel, Pieter; Robblee, John H.; Messinger, Johannes; Fernandez, Carmen; Cinco, Roehl; Visser, Henk; McFarlane, Karen; Bellacchio, Emanuele; Pizarro, Shelly; Sauer, Kenneth; Yachandra, Vittal K.; Klein, Melvin P.; Cox, Billie L.; Nealson,
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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The combination of large-acceptance high-resolution X-ray optics with bright synchrotron sources permits quantitative analysis of rare events such as X-ray fluorescence from very dilute systems, weak fluorescence transitions or X-ray Raman scattering. Transition-metal Kβ fluorescence contains information about spin and oxidation state; examples of the characterization of the Mn oxidation states in the oxygen-evolving complex of photosystem II and Mn-consuming spores from the marine bacillus SG-1 are presented. Weaker features of the Kβ spectrum resulting from valence-level and ‘interatomic’ ligand to metal transitions contain detailed information on the ligand-atom type, distance and orientation. Applications of this spectral region to characterize the local structure of model compounds are presented. X-ray Raman scattering (XRS) is an extremely rare event, but also represents a unique technique to obtain bulk-sensitive low-energy (<600 eV) X-ray absorption fine structure (XAFS) spectra using hard (~10 keV) X-rays. A photon is inelastically scattered, losing part of its energy to promote an electron into an unoccupied level. In many cases, the cross section is proportional to that of the corresponding absorption process yielding the same X-ray absorption near-edge structure (XANES) and extended X-ray absorption fine structure (EXAFS) features. XRS finds application for systems that defy XAFS analysis at low energies...

## Logistic Regression in Rare Events Data

King, Gary; Zeng, Langche
Fonte: Oxford University Press Publicador: Oxford University Press
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
47.26447%
We study rare events data, binary dependent variables with dozens to thousands of times fewer ones (events, such as wars, vetoes, cases of political activism, or epidemiological infections) than zeros (“nonevents”). In many literatures, these variables have proven difficult to explain and predict, a problem that seems to have at least two sources. First, popular statistical procedures, such as logistic regression, can sharply underestimate the probability of rare events. We recommend corrections that outperform existing methods and change the estimates of absolute and relative risks by as much as some estimated effects reported in the literature. Second, commonly used data collection strategies are grossly inefficient for rare events data. The fear of collecting data with too few events has led to data collections with huge numbers of observations but relatively few, and poorly measured, explanatory variables, such as in international conflict data with more than a quarter-million dyads, only a few of which are at war. As it turns out, more efficient sampling designs exist for making valid inferences, such as sampling all available events (e.g., wars) and a tiny fraction of nonevents (peace). This enables scholars to save as much as 99% of their (nonfixed) data collection costs or to collect much more meaningful explanatory variables.We provide methods that link these two results...

## Essays on Asset Pricing and Econometrics

Jin, Tao
Fonte: Harvard University Publicador: Harvard University
Tipo: Thesis or Dissertation
Português
Relevância na Pesquisa
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This dissertation presents three essays on asset pricing and econometrics. The first chapter identifies rare events and long-run risks simultaneously from a rich data set (the Barro-Ursua macroeconomic data set) and evaluates their contributions to asset pricing in a unified framework. The proposed model of rare events and long-run risks is estimated using a Bayesian Markov-chain Monte-Carlo method, and the estimates for the disaster process are closer to the data than those in the previous studies. Major evaluation results in asset pricing include: (1) for the unleveraged annual equity premium, the predicted values are 4.8%, 4.2%, and 1.0%, respectively; (2) for the Sharpe ratio, the values are 0.72, 0.66, and 0.15, respectively.; Economics

## Coarse-Grained Analysis of Microscopic Neuronal Simulators on Networks: Bifurcation and Rare-events computations

Spiliotis, Konstantinos G.; Siettos, Constantinos I.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.99793%
We show how the Equation-Free approach for mutliscale computations can be exploited to extract, in a computational strict and systematic way the emergent dynamical attributes, from detailed large-scale microscopic stochastic models, of neurons that interact on complex networks. In particular we show how the Equation-Free approach can be exploited to perform system-level tasks such as bifurcation, stability analysis and estimation of mean appearance times of rare events, bypassing the need for obtaining analytical approximations, providing an "on-demand" model reduction. Using the detailed simulator as a black-box timestepper, we compute the coarse-grained equilibrium bifurcation diagrams, examine the stability of the solution branches and perform a rare-events analysis with respect to certain characteristics of the underlying network topology such as the connectivity degree

## Laws of rare events for deterministic and random dynamical systems

Aytaç, Hale; Freitas, Jorge Milhazes; Vaienti, Sandro
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
46.99793%
The object of this paper is twofold. From one side we study the dichotomy, in terms of the Extremal Index of the possible Extreme Value Laws, when the rare events are centred around periodic or non periodic points. Then we build a general theory of Extreme Value Laws for randomly perturbed dynamical systems. We also address, in both situations, the convergence of Rare Events Point Processes. Decay of correlations against $L^1$ observables will play a central role in our investigations.

## An Efficient Self-optimized Sampling Method for Rare Events in Nonequilibrium Systems

Jiang, Huijun; Pu, Mingfeng; Hou, Zhonghuai
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.99793%
Rare events such as nucleation processes are of ubiquitous importance in real systems. The most popular method for nonequilibrium systems, forward flux sampling (FFS), samples rare events by using interfaces to partition the whole transition process into sequence of steps along an order parameter connecting the initial and final states. FFS usually suffers from two main difficulties: low computational efficiency due to bad interface locations and even being not applicable when trapping into unknown intermediate metastable states. In the present work, we propose an approach to overcome these difficulties, by self-adaptively locating the interfaces on the fly in an optimized manner. Contrary to the conventional FFS which set the interfaces with euqal distance of the order parameter, our approach determines the interfaces with equal transition probability which is shown to satisfy the optimization condition. This is done by firstly running long local trajectories starting from the current interface $\l_i$ to get the conditional probability distribution $P_c$, and then determining $\l_{i+1}$ by equalling $P_c$ to a give value $p_0$. With these optimized interfaces, FFS can be run in a much efficient way. In addition, our approach can conveniently find the intermediate metastable states by monitoring some special long trajectories that nither end at the initial state nor reach the next interface...

## Rare events statistics of random walks on networks: localization and other dynamical phase transitions

De Bacco, Caterina; Guggiola, Alberto; Kühn, Reimer; Paga, Pierre
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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Rare event statistics for random walks on complex networks are investigated using the large deviations formalism. Within this formalism, rare events are realized as typical events in a suitably deformed path-ensemble, and their statistics can be studied in terms of spectral properties of a deformed Markov transition matrix. We observe two different types of phase transition in such systems: (i) rare events which are singled out for sufficiently large values of the deformation parameter may correspond to {\em localized\/} modes of the deformed transition matrix, (ii) "mode-switching transitions" may occur as the deformation parameter is varied. Details depend on the nature of the observable for which the rare event statistics is studied, as well as on the underlying graph ensemble. In the present letter we report on the statistics of the average degree of the nodes visited along a random walk trajectory in Erd\H{o}s-R\'enyi networks. Large deviations rate functions and localization properties are studied numerically. For observables of the type considered here, we also derive an analytical approximation for the Legendre transform of the large-deviations rate function, which is valid in the large connectivity limit. It is found to agree well with simulations.; Comment: 5 pages...

## Quick Search for Rare Events

Tajer, Ali; Poor, H. Vincent
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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Rare events can potentially occur in many applications. When manifested as opportunities to be exploited, risks to be ameliorated, or certain features to be extracted, such events become of paramount significance. Due to their sporadic nature, the information-bearing signals associated with rare events often lie in a large set of irrelevant signals and are not easily accessible. This paper provides a statistical framework for detecting such events so that an optimal balance between detection reliability and agility, as two opposing performance measures, is established. The core component of this framework is a sampling procedure that adaptively and quickly focuses the information-gathering resources on the segments of the dataset that bear the information pertinent to the rare events. Particular focus is placed on Gaussian signals with the aim of detecting signals with rare mean and variance values.

## A probabilistic decomposition-synthesis method for the quantification of rare events due to internal instabilities

Mohamad, Mustafa A.; Cousins, Will; Sapsis, Themistoklis P.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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We consider the problem of probabilistic quantification of dynamical systems that have heavy-tailed characteristics. These heavy-tailed features are associated with rare transient responses due to the occurrence of internal instabilities. Here we develop a computational method, a probabilistic decomposition-synthesis technique, that takes into account the nature of internal instabilities to inexpensively determine the non-Gaussian probability density function for any arbitrary quantity of interest. Our approach relies on the decomposition of the statistics into a non-extreme core', typically Gaussian, and a heavy-tailed component. This decomposition is in full correspondence with a partition of the phase space into a stable' region where we have no internal instabilities, and a region where non-linear instabilities lead to rare transitions with high probability. We quantify the statistics in the stable region using a Gaussian approximation approach, while the non-Gaussian distributions associated with the intermittently unstable regions of the phase space are inexpensively computed through order-reduction methods that take into account the strongly nonlinear character of the dynamics. The probabilistic information in the two domains is analytically synthesized through a total probability argument. The proposed approach allows for the accurate quantification of non-Gaussian tails at more than 10 standard deviations...

## Reduced order prediction of rare events in unidirectional nonlinear water waves

Cousins, Will; Sapsis, Themistoklis P.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
47.151616%
We consider the problem of short-term prediction of rare, extreme water waves in unidirectional fields, a critical topic for ocean structures and naval operations. One possible mechanism for the occurrence of such rare, unusually-intense waves is nonlinear wave focusing. Recent results have demonstrated that random localizations of energy, induced by the dispersive mixing of different harmonics, can grow significantly due to localized nonlinear focusing. Here we show how the interplay between i) statistical properties captured through linear information such as the waves power spectrum and ii) nonlinear dynamical properties of focusing localized wave groups defines a critical length scale associated with the formation of extreme events. The energy that is locally concentrated over this length scale acts as the "trigger" of nonlinear focusing for wave groups and the formation of subsequent rare events. We use this property to develop inexpensive, short-term predictors of large water waves. Specifically, we show that by merely tracking the energy of the wave field over the critical length scale allows for the robust, inexpensive prediction of the location of intense waves with a prediction window of 25 wave periods. We demonstrate our results in numerical experiments of unidirectional water wave fields described by the Modified Nonlinear Schrodinger equation. The presented approach introduces a new paradigm for understanding and predicting intermittent and localized events in dynamical systems characterized by uncertainty and potentially strong nonlinear mechanisms.

## Dynamics of the Wang-Landau algorithm and complexity of rare events for the three-dimensional bimodal Ising spin glass

Alder, S.; Trebst, S.; Hartmann, A. K.; Troyer, M.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.99793%
We investigate the performance of flat-histogram methods based on a multicanonical ensemble and the Wang-Landau algorithm for the three-dimensional +/- J spin glass by measuring round-trip times in the energy range between the zero-temperature ground state and the state of highest energy. Strong sample-to-sample variations are found for fixed system size and the distribution of round-trip times follows a fat-tailed Frechet extremal value distribution. Rare events in the fat tails of these distributions corresponding to extremely slowly equilibrating spin glass realizations dominate the calculations of statistical averages. While the typical round-trip time scales exponential as expected for this NP-hard problem, we find that the average round-trip time is no longer well-defined for systems with N >= 8^3 spins. We relate the round-trip times for multicanonical sampling to intrinsic properties of the energy landscape and compare with the numerical effort needed by the genetic Cluster-Exact Approximation to calculate the exact ground state energies. For systems with N >= 8^3 spins the simulation of these rare events becomes increasingly hard. For N >= 14^3 there are samples where the Wang-Landau algorithm fails to find the true ground state within reasonable simulation times. We expect similar behavior for other algorithms based on multicanonical sampling.; Comment: 9 pages...

## Control of rare events in reaction and population systems by deterministic processes and the speedup of disease extinction

Khasin, M.; Dykman, M. I.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
47.151616%
We consider control of reaction and population systems by deterministically imposed transitions between the states with different numbers of particles or individuals. Even where the imposed transitions are significantly less frequent than spontaneous transitions, they can exponentially strongly modify the rates of rare events, including switching between metastable states or population extinction. We also study optimal control of rare events, and specifically, optimal control of disease extinction for a limited vaccine supply. A comparison is made with control of rare events by modulating the rates of elementary transitions rather than imposing transitions. It is found that, unexpectedly, for the same mean control parameters, controlling the transitions rates can be more efficient.

## Distribution of Return Periods of Rare Events in Correlated Time Series

Pennetta, Cecilia; Alfinito, Eleonora
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
46.99793%
We study the effect on the distribution of return periods of rare events of the presence in a time series of finite-term correlations with non-exponential decay. Precisely, we analyze the auto-correlation function and the statistics of the return intervals of extreme values of the resistance fluctuations displayed by a resistor with granular structure in a nonequilibrium stationary state. The resistance fluctuations, $\delta R$, are calculated by Monte Carlo simulations using the SBRN model introduced some years ago by Pennetta, Tref\'an and Reggiani and based on a resistor network approach. A rare event occurs when $\delta R$ overcomes a threshold value $q$ significantly higher than the average value of the resistance. We have found that for highly disordered networks, when the auto-correlation function displays a non-exponential decay but yet the resistance fluctuations are characterized by a finite correlation time, the distribution of return intervals of the extreme values is well described by a stretched exponential, with exponent largely independent of the threshold $q$. We discuss this result and some of the main open questions related to it, also in connection with very recent findings by other authors concerning the observation of stretched exponential distributions of return intervals of extreme events in long-term correlated time series.; Comment: 10 pages...

## Can rare events explain the equity premium puzzle?

Julliard, Christian; Ghosh, Anisha
Fonte: Financial Markets Group, London School of Economics and Political Science Publicador: Financial Markets Group, London School of Economics and Political Science
Tipo: Monograph; NonPeerReviewed Formato: application/pdf