This article identifies the maximum entropy distribution among those in the polytope of probability distributions cohering with quantum theoretic prescriptions pertinent to Bell’s inequality in the optical context. P...This article identifies the maximum entropy distribution among those in the polytope of probability distributions cohering with quantum theoretic prescriptions pertinent to Bell’s inequality in the optical context. Perhaps surprisingly, the maxent distribution is not a uniform mixture of the extreme vertices of the convex hull of distributions agreeing with the theory. The expectation E(s) it supports equals 1.1296, within the permitted coherent interval of (1.1213,2]. The maxent mixture of the extreme agreeable vertices is compared herein with two other mixture distributions over the convex hull of those supported by quantum theory. One of these is a simple uniform mixture over the solution vectors to the appropriate linear programming problems that specify the polytope. The other is the mixture underlying simulated results of Aspect’s experiments that have been shown to estimate E(s) as 1.7678. Further computations provide examples of the types of claims that would be entailed in a unique distribution within the cohering convex hull such as maxent. These defy quantum theoretic adherence to the general uncertainty principle which proclaims an agnostic position with respect to imagined joint observation operators that do not commute. They also display questionable implications of the “many worlds” proposal which the author does not favour. The article raises questions that deserve to be discussed concerning the general proposal that the maximum entropy principle should be employed to make precise probabilistic assertions about equilibrium phenomena when specific physical theory prescribes only an interval.展开更多
Distributions of invasive species are commonly predicted with species distribution models that build upon the statistical relationships between observed species presence data and climate data. We used field observatio...Distributions of invasive species are commonly predicted with species distribution models that build upon the statistical relationships between observed species presence data and climate data. We used field observations, climate station data, and Maximum Entropy species distribution models for 13 invasive plant species in the United States, and then compared the models with inputs from a General Circulation Model （hereafter GCM-based models） and a downscaled Regional Climate Model （hereafter, RCM-based models）. We also compared species distributions based on either GCM-based or RCM-based models for the present （1990-1999） to the future （2046- 2055）. RCM-based species distribution models replicated observed distributions remarkably better than GCM- based models for all invasive species under the current climate. This was shown for the presence locations of the species, and by using four common statistical metrics to compare modeled distributions. For two widespread invasive taxa （Bromus tectorum or cheatgrass, and Tamarix spp. or tamarisk）, GCM-based models failed miserably to reproduce observed species distributions. In contrast, RCM-based species distribution models closely matched observations. Future species distributions may be significantly affected by using GCM-based inputs. Because invasive plants species often show high resilience and low rates of local extinction, RCM-based species distribution models may perform better than GCM-based species distribution models for planning containment programs for invasive species.展开更多
文摘This article identifies the maximum entropy distribution among those in the polytope of probability distributions cohering with quantum theoretic prescriptions pertinent to Bell’s inequality in the optical context. Perhaps surprisingly, the maxent distribution is not a uniform mixture of the extreme vertices of the convex hull of distributions agreeing with the theory. The expectation E(s) it supports equals 1.1296, within the permitted coherent interval of (1.1213,2]. The maxent mixture of the extreme agreeable vertices is compared herein with two other mixture distributions over the convex hull of those supported by quantum theory. One of these is a simple uniform mixture over the solution vectors to the appropriate linear programming problems that specify the polytope. The other is the mixture underlying simulated results of Aspect’s experiments that have been shown to estimate E(s) as 1.7678. Further computations provide examples of the types of claims that would be entailed in a unique distribution within the cohering convex hull such as maxent. These defy quantum theoretic adherence to the general uncertainty principle which proclaims an agnostic position with respect to imagined joint observation operators that do not commute. They also display questionable implications of the “many worlds” proposal which the author does not favour. The article raises questions that deserve to be discussed concerning the general proposal that the maximum entropy principle should be employed to make precise probabilistic assertions about equilibrium phenomena when specific physical theory prescribes only an interval.
文摘Distributions of invasive species are commonly predicted with species distribution models that build upon the statistical relationships between observed species presence data and climate data. We used field observations, climate station data, and Maximum Entropy species distribution models for 13 invasive plant species in the United States, and then compared the models with inputs from a General Circulation Model （hereafter GCM-based models） and a downscaled Regional Climate Model （hereafter, RCM-based models）. We also compared species distributions based on either GCM-based or RCM-based models for the present （1990-1999） to the future （2046- 2055）. RCM-based species distribution models replicated observed distributions remarkably better than GCM- based models for all invasive species under the current climate. This was shown for the presence locations of the species, and by using four common statistical metrics to compare modeled distributions. For two widespread invasive taxa （Bromus tectorum or cheatgrass, and Tamarix spp. or tamarisk）, GCM-based models failed miserably to reproduce observed species distributions. In contrast, RCM-based species distribution models closely matched observations. Future species distributions may be significantly affected by using GCM-based inputs. Because invasive plants species often show high resilience and low rates of local extinction, RCM-based species distribution models may perform better than GCM-based species distribution models for planning containment programs for invasive species.
