Limit theorems for iterated random topical operators

Let A(n) be a sequence of i.i.d. topical (i.e. isotone and additively homogeneous) operators. Let $x(n,x_0)$ be defined by $x(0,x_0)=x_0$ and $x(n,x_0)=A(n)x(n-1,x_0)$. This can modelize a wide range of systems including, task graphs, train networks, Job-Shop, timed digital circuits or parallel processing systems. When A(n) has the memory loss property, we use the spectral gap method to prove limit theorems for $x(n,x_0)$. Roughly speaking, we show that $x(n,x_0)$ behaves like a sum of i.i.d. real variables. Precisely, we show that with suitable additional conditions, it satisfies a central limit theorem with rate, a local limit theorem, a renewal theorem and a large deviations principle, and we give an algebraic condition to ensure the positivity of the variance in the CLT. When A(n) are defined by matrices in the \mp semi-ring, we give more effective statements and show that the additional conditions and the positivity of the variance in the CLT are generic

The Eyes

A young soldier’s father and friends take him hunting, where he confronts the violence of the war behind him. Articles, stories, and other compositions in this archive were written by participants in the Mighty Pen Project. The program, developed by author David L. Robbins, and in partnership with Virginia Commonwealth University and the Virginia War Memorial in Richmond, Virginia, offers veterans and their family members a customized twelve-week writing class, free of charge. The program encourages, supports, and assists participants in sharing their stories and experiences of military experience so both writer and audience may benefit

Practice and the Comparative Study of Mysticism: \u3cem\u3eThe Yoga Sūtra\u3c/em\u3e and \u3cem\u3eThe Cloud of Unknowing\u3c/em\u3e

In his entry for the term “mysticism” in the updated edition of the Encyclopedia of Religion, Peter Moore writes that “the varieties of mystical practice tend to receive less scholarly attention than the varieties of experience or doctrine.”1 Bernard McGinn similarly claims that many studies of mysticism “so emphasize the moment of mystical contact . . . that they neglect the study of the fullness of the via mystica, particularly the ascetical and moral preparation for such contact.”2 Following from suggestions such as these, this article will do a comparative reading of two mystical texts: the Yoga Sūtra, a third-century Indian work attributed to Patañjali, and The Cloud of Unknowing, an anonymous fourteenth-century English treatise. Specifically, it will consider two dimensions of the mystical practices taught in these texts. These are the taking of vows and the contemplative stilling of the mind

A betting interpretation for probabilities and Dempster-Shafer degrees of belief

There are at least two ways to interpret numerical degrees of belief in terms of betting: (1) you can offer to bet at the odds defined by the degrees of belief, or (2) you can judge that a strategy for taking advantage of such betting offers will not multiply the capital it risks by a large factor. Both interpretations can be applied to ordinary additive probabilities and used to justify updating by conditioning. Only the second can be applied to Dempster-Shafer degrees of belief and used to justify Dempster's rule of combination.Comment: 20 page