The Experts below are selected from a list of 5232 Experts worldwide ranked by ideXlab platform
C. Spitoni - One of the best experts on this subject based on the ideXlab platform.
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Sharp Asymptotics for Stochastic Dynamics with Parallel Updating Rule
Journal of Statistical Physics, 2012Co-Authors: F. R. Nardi, C. SpitoniAbstract:In this paper we study the metastability problem for a stochastic dynamics with a parallel updating rule; in particular we consider a finite volume Probabilistic Cellular Automaton (PCA) in a small external field at low temperature regime. We are interested in the nucleation of the system, i.e., the typical excursion from the metastable phase (the configuration with all minuses) to the stable phase (the configuration with all pluses), triggered by the formation of a critical droplet. The main result of the paper is the sharp estimate of the nucleation time: we show that the nucleation time divided by its average converges to an Exponential Random Variable and that the rate of the Exponential Random Variable is an Exponential function of the inverse temperature β times a prefactor that does not scale with β . Our approach combines geometric and potential theoretic arguments.
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Sharp asymptotics for stochastic dynamics with parallel updating rule
2012Co-Authors: F. R. Nardi, C. SpitoniAbstract:In this paper we study the metastability problem for a stochastic dynamics with a parallel updating rule; in particular we consider a finite volume Probabilistic Cellular Automaton (PCA) in a small external field at low temperature regime. We are interested in the nucleation of the system, i.e., the typical excursion from the metastable phase (the configuration with all minuses) to the stable phase (the configuration with all pluses), triggered by the formation of a critical droplet. The main result of the paper is the sharp estimate of the nucleation time: we show that the nucleation time divided by its average converges to an Exponential Random Variable and that the rate of the Exponential Random Variable is an Exponential function of the inverse temperature \beta times a prefactor that does not scale with \beta. Our approach combines geometric and potential theoretic arguments.
F. R. Nardi - One of the best experts on this subject based on the ideXlab platform.
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Long Paths in First Passage Percolation on the Complete Graph II. Global Branching Dynamics
Journal of Statistical Physics, 2020Co-Authors: Maren Eckhoff, Jesse Goodman, Remco Hofstad, F. R. NardiAbstract:We study the Random geometry of first passage percolation on the complete graph equipped with independent and identically distributed positive edge weights. We consider the case where the lower extreme values of the edge weights are highly separated. This model exhibits strong disorder and a crossover between local and global scales. Local neighborhoods are related to invasion percolation that display self-organised criticality. Globally, the edges with relevant edge weights form a barely supercritical Erdős–Rényi Random graph that can be described by branching processes. This near-critical behaviour gives rise to optimal paths that are considerably longer than logarithmic in the number of vertices, interpolating between Random graph and minimal spanning tree path lengths. Crucial to our approach is the quantification of the extreme-value behavior of small edge weights in terms of a sequence of parameters $$(s_n)_{n\ge 1}$$ ( s n ) n ≥ 1 that characterises the different universality classes for first passage percolation on the complete graph. We investigate the case where $$s_n\rightarrow \infty $$ s n → ∞ with $$s_n=o(n^{1/3})$$ s n = o ( n 1 / 3 ) , which corresponds to the barely supercritical setting. We identify the scaling limit of the weight of the optimal path between two vertices, and we prove that the number of edges in this path obeys a central limit theorem with mean approximately $$s_n\log {(n/s_n^3)}$$ s n log ( n / s n 3 ) and variance $$s_n^2\log {(n/s_n^3)}$$ s n 2 log ( n / s n 3 ) . Remarkably, our proof also applies to n -dependent edge weights of the form $$E^{s_n}$$ E s n , where E is an Exponential Random Variable with mean 1, thus settling a conjecture of Bhamidi et al. (Weak disorder asymptotics in the stochastic meanfield model of distance. Ann Appl Probab 22(1):29–69, 2012). The proof relies on a decomposition of the smallest-weight tree into an initial part following invasion percolation dynamics, and a main part following branching process dynamics. The initial part has been studied in Eckhoff et al. (Long paths in first passage percolation on the complete graph I. Local PWIT dynamics. Electron. J. Probab. 25:1–45, 2020 . https://doi.org/10.1214/20-EJP484 ); the current paper focuses on the global branching dynamics.
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Sharp Asymptotics for Stochastic Dynamics with Parallel Updating Rule
Journal of Statistical Physics, 2012Co-Authors: F. R. Nardi, C. SpitoniAbstract:In this paper we study the metastability problem for a stochastic dynamics with a parallel updating rule; in particular we consider a finite volume Probabilistic Cellular Automaton (PCA) in a small external field at low temperature regime. We are interested in the nucleation of the system, i.e., the typical excursion from the metastable phase (the configuration with all minuses) to the stable phase (the configuration with all pluses), triggered by the formation of a critical droplet. The main result of the paper is the sharp estimate of the nucleation time: we show that the nucleation time divided by its average converges to an Exponential Random Variable and that the rate of the Exponential Random Variable is an Exponential function of the inverse temperature β times a prefactor that does not scale with β . Our approach combines geometric and potential theoretic arguments.
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Sharp asymptotics for stochastic dynamics with parallel updating rule
2012Co-Authors: F. R. Nardi, C. SpitoniAbstract:In this paper we study the metastability problem for a stochastic dynamics with a parallel updating rule; in particular we consider a finite volume Probabilistic Cellular Automaton (PCA) in a small external field at low temperature regime. We are interested in the nucleation of the system, i.e., the typical excursion from the metastable phase (the configuration with all minuses) to the stable phase (the configuration with all pluses), triggered by the formation of a critical droplet. The main result of the paper is the sharp estimate of the nucleation time: we show that the nucleation time divided by its average converges to an Exponential Random Variable and that the rate of the Exponential Random Variable is an Exponential function of the inverse temperature \beta times a prefactor that does not scale with \beta. Our approach combines geometric and potential theoretic arguments.
Yeh Lam - One of the best experts on this subject based on the ideXlab platform.
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A general model for consecutive-k-out-of-n: F repairable system with Exponential distribution and (k−1)-step Markov dependence
European Journal of Operational Research, 2001Co-Authors: Yeh LamAbstract:Abstract In this paper, a general model for consecutive-k-out-of-n: F repairable system with Exponential distribution and (k−1)-step Markov dependence is introduced. The lifetime of a component is an Exponential Random Variable, its parameter depends on the number of consecutive failed components that precede the component. The repair time is also an Exponential Random Variable. A priority repair rule on the basis of the system failure risk is adopted. Then the transition density matrix of the system is determined. Some reliability indices, including the system availability, rate of occurrence of failures and reliability are evaluated accordingly. For the demonstration of the model and methodology, a linear system example and a circular system example are investigated.
Denise L. Haynie - One of the best experts on this subject based on the ideXlab platform.
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Fundamental misunderstanding of the relation between energy density (kcal/g) and energy cost ($/kcal)
The American Journal of Clinical Nutrition, 2011Co-Authors: Leah M. Lipsky, Tonja R. Nansel, David R. Just, Denise L. HaynieAbstract:Dear Sir: We are writing to comment on the recent article by Drewnowski (1) regarding the relative prices of food groups. First, we commend the thorough data collection methods, which ensured a comprehensive investigation of the research question. However, we have significant concerns regarding certain elements of the data analysis, interpretation, and conclusions put forth in the article. Most important, we state as fact that there is always an association between any number (X) and its reciprocal (1/X), and that this association is necessarily negative. This is relevant to the relation between energy density (kcal/g) and energy cost ($/kcal), because the relation is influenced by the presence of kcal in both Variables and on opposite sides of the divisor (2). For example, 3 statistically independent and unrelated Exponentially distributed Random Variables x, y, and z (representing energy, cost, and mass, respectively) could be used to create ratios r = x/z and q = y/x. It can be shown that, where 1/λi is the mean of the Exponential Random Variable i, the conditional expectation of r given a value of q is the expectation of (r|q) = (λxq + λy)/λzq, which has a negative first derivative ( 0) and appears as the familiar hyperbolic shape reported in numerous studies of the relation between energy density and energy cost (proof available on request). However, the unconditional medians of r and q will vary independently depending on the distributional parameters of x and y. We select the Exponential distribution because of the relative ease of analytic computations, but this same principle is true for more general distributions. In Drewnowski's recent article, “x”, “y” and “z”, used to create “x/y” and “y/z”, were each Randomly generated Variables specified with a uniform distribution and identical range. Given the distributions of each Variable, individual realizations of x/y are systematically related to y/z. However, the analysis merely illustrated that, as expected, the unconditional means and medians of x/y and y/z have no particular implied relation. Rather, his analysis served more to show that, empirically, the distribution of kcal/g is associated with food category: fruit and vegetables have lower mean and median energy density than do other food groups and thus also have high $/kcal due to the tautological inverse relation between kcal and 1/kcal and the relatively smaller variance of $ and g (2). We also wish to highlight the article's empirical finding that the relative price of foods depended on the specific outcome price measure used (1). For example, fruit and vegetables had the highest $/kcal but had among the lowest $/100g and a relatively moderate to high $/serving. These differences raise the unanswered question as to the relevance of these metrics for how consumers perceive food cost and evaluate food choices. The hypothesis that $/kcal is a key influence on consumer behavior is inconsistent with much in the literature about food preferences (3) and leads to many improbable outcomes. For example, in Drewnowski's article, legumes had among the lowest $/kcal, whereas meat had the highest $/100g and $/serving and among the highest $/kcal. However, Americans’ intake of legumes is extremely low, whereas meat intake is far more adequate (4). Furthermore, if consumers perceived food cost in terms of $/kcal, marketers would avoid labeling foods as “reduced calorie” or similar, because it would indicate more expensive calories. Likewise, providing menu calorie information would actually promote energy-dense options because this would clearly show the “value” of these foods; yet, evidence suggests such information instead discourages intake of high-calorie foods and promotes low-calorie menu items (5), which cost more per kcal. When evaluating food groups by any price measure, it is imperative to acknowledge the dangers of comparing “apples to oranges” or, in this case, “apples to potato chips,” as there are many differences between food groups that influence food choice besides nutritive value and price (6). Thus, to assume consumers choose potato chips over apples due to their cheap calories requires a huge leap in logic and cannot be tested by a simple correlation analysis of food attributes (energy density and energy cost). An unintended consequence of focusing primarily on $/kcal is the creation of a belief among consumers and health professionals that a healthy diet is unaffordable to persons with low socioeconomic status, which does a disservice to this population. Indeed, there exists a wide range of cost among fruit and vegetables (7, 8), and longitudinal research indicates that food expenditure does not necessarily increase as individuals increase diet quality (9), which suggests that people are able to select healthful options within their budget. Of greater concern may be the Variable availability of produce in some areas (10), which further speaks to the need to address the complexity of these issues. We fully appreciate the importance to public health of policies aimed at reallocating subsidies away from nutrient-poor foods toward nutrient-rich fruit and vegetables. However, we believe that the argument for such policies should not be based on the correlation between Variables with untested effect on consumer behavior but rather on the urgent need to promote intake patterns to reduce morbidity, mortality, and related health expenditures.
Paul S. P. Cowpertwait - One of the best experts on this subject based on the ideXlab platform.
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A Generalized Spatial-Temporal Model of Rainfall Based on a Clustered Point Process
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 1995Co-Authors: Paul S. P. CowpertwaitAbstract:The objective in this paper is to present and fit a relatively simple stochastic spatial-temporal model of rainfall in which the arrival times of rain cells occur in a clustered point process. In the x - y plane, rain cells are represented as discs; each disc having a Random radius; the locations of the disc centres being given by a two-dimensional Poisson process. The intensity of each cell is a Random Variable that remains constant over the area of the disc and throughout the lifetime of the cell, the lifetime being an Exponential Random Variable. The cells are Randomly classified from 1 to n with different parameters for the different cell types, so that the Random Variables of an arbitrary cell, e. g. radius and intensity, are correlated. Multi-site second-order properties are derived and used to fit the model to hourly rainfall data taken from six sites in the Thames basin, UK.
