In this paper we work in the framework of a k-dimensional vector of log-linear risks. Under weak conditions on the marginal tails and the dependence structure of a vector of positive risks, we derive the asymptotic tail behaviour of the aggregated risk and present an application concerning log-normal risks with stochastic volatility.

In the paper we study closures of classes of log–concave measures under taking weak limits, linear transformations and tensor products. We consider what uniform measures on convex bodies can one obtain starting from some class K. In particular we prove that if one starts from one–dimensional log–concave measures, one obtains no non– trivial uniform mesures on convex bodies.

In this work we shall investigate quantum query complexity of weak PARITY problem. Weak Parity is the following natural query problem: What is the minimum number of queries necessary to compute PARITY(x1, x2, x3, . . . , xn) on at least 1 2 + fraction of the inputs. For randomized classical or exact quantum machines this relaxed PARITY problem remains as hard as original PARITY problem. Althoug...

In this paper we work in the framework of a k-dimensional vector of log-linear risks. Under weak conditions on the marginal tails and the dependence structure of a vector of positive risks we derive the asymptotic tail behaviour of the aggregated risk and present an application concerning log-normal risks with stochastic volatility.

A run-relaxed weak queue by Elmasry et al. (2005) is a priority queue data structure with insert and decrease-key in O(1) as well as delete and delete-min in O(log n) worst-case time. One further advantage is the small space consumption of 3n+O(log n) pointers. In this paper we propose rank-relaxed weak queues, reducing the number of rank violations nodes for each level to a constant, while pro...

We present an algorithm to self-consistently generate mock weak gravitational lensing convergence fields and galaxy distributions in redshift space. three-dimensional cosmic density that follow a log-normal distribution, ray-trace them produce maps. As we the distribution from same manner consistent with ray-tracing, galaxy-convergence cross-power spectrum measured agrees theoretical expectatio...

In Rogerson and Restall’s (J Philos Log 36, 2006, p. 435), the “class of implication formulas known to trivialize (NC)” (NC abbreviates “naïve comprehension”) is recorded. The aim of this paper is to show how to invalidate any member in this class by using “weak relevant model structures”. Weak relevant model structures verify deep relevant logics only.

We introduce the weak gap property for directed graphs whose vertex set S is a metric space of size n. We prove that, if the doubling dimension of S is a constant, any directed graph satisfying the weak gap property has O(n) edges and total weight O(log n) · wt(MST (S)), where wt(MST (S)) denotes the weight of a minimum spanning tree of S. We show that 2-optimal TSP tours and greedy spanners sa...

We introduce the notion of \partial Occam algorithm". A partial Oc-cam algorithm produces a succinct hypothesis that is partially consistent with given examples, where the proportion of consistent examples is a bit more than half. By using this new notion, we propose one approach for obtaining a PAC learning algorithm. First, as shown in this paper, a partial Occam algorithm is equivalent to a ...

We prove the existence and uniqueness of the weak Kähler-Ricci flow on projective varieties with log terminal singularities. It is also shown that the weak Kähler-Ricci flow can be uniquely continued through divisorial contractions and flips if they exist. We then propose an analytic version of the Minimal Model Program with Ricci flow.