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We obtain several extensions of Talagrand’s lower bound for the small deviation probability using metric entropy. For Gaussian processes, our investigations are focused on processes with sub-polynomial and, respectively, exponential behaviour of covering numbers. The corresponding results are also proved for non-Gaussian symmetric stable processes, both for the cases of critically small and cri...

Although all manifest skew deviations appear the same for the clinician, skew deviation can result from different combinations of dysconjugate vertical ocular deviations. Evidence is presented for three different types of skew deviation when it occurs as a feature of an ocular tilt reaction. In type 1 (utricle) there is upward deviation of both eyes with different amplitudes, as described for o...

In these notes, we survey developments on the asymptotic behavior of the largest eigenvalues of random matrix and random growth models, and describe the corresponding known non-asymptotic exponential bounds. We then discuss some elementary and accessible tools from measure concentration and functional analysis to reach some of these quantitative inequalities at the correct small deviation rate ...

Why process at all? Of course, the answer is ultimately feed efficiency, producing the most milk, eggs, meat or fiber at the lowest possible cost. Particle size reduction as the first step in the feed manufacturing process works toward the goal of improved feed efficiency by increasing the surface area of the materials being processed. This increases the amount of materials exposed to the anima...

We study the dynamic selection of governments. A government consists of a subset of the individuals in the society. The competence level of the government in o ce determines collective utilities (e.g., by determining the amount and quality of public goods), and each individual derives additional utility from being part of the government (e.g., corruption or rents from holding o ce). We characte...

Do the eldery use the political system to get benefits from Swedish municipal spending at the expense of the young, and vice versa? If so, to what extent? These are the basic questions asked in this paper. To analyze this question a median voter model with altruism within families is used. The answer given by the empirical investigation is that these the effects of the intergenerational conflic...

In an election, voting power—the probability that a single vote is decisive—is affected by the rule for aggregating votes into a single outcome. Voting power is important for studying political representation, fairness and strategy, and has been much discussed in political science. Although power indexes are often considered as mathematical definitions, they ultimately depend on statistical mod...

We here provide a comprehensive study of the utility-deviation-risk portfolio selectionproblem. By considering the first-order condition for the corresponding objective function, we firstderive the necessary condition that the optimal terminal wealth satisfying two mild regularity con-ditions solves for a primitive static problem, called Nonlinear Moment Problem. We then illustrate<...