We introduce and study the main properties of a class convex risk measures that refine Expected Shortfall by simultaneously controlling expected losses associated with different portions tail distribution. The corresponding adjusted Shortfalls quantify as minimum amount capital has to be raised injected into financial position X ensure ES p ( ) does not exceed pre-specified threshold g for ever...

Tornado occurrence rates computed from the available reports are biased low relative to unknown true rates. To correct for this bias, authors demonstrate a method estimate annual probability of being struck by tornado that uses average report density estimated as function distance nearest city/town center. The is demonstrated on Kansas and then applied 15 other tornado-prone states Nebraska Ten...

We introduce a new technique that adopts the halo occupation framework for understanding the origin of QSO absorption-line systems. Our initial study focuses specifically on Mg II absorbers. We construct a model of the gaseous content in which the absorption equivalent width Wr is determined by the the amount of cold gas, in the form of discrete clouds, along a sightline through a halo. The two...

A sector condition for two connected deadzone nonlinearities is provided. By introducing an additional non-square operator which exploits their connectivity, a more general set of sector-like matrix inequalities is obtained. This “non-square” matrix inequality condition is applied to an anti-windup (AW) problem in which the AW compensator is not activated until the unconstrained control signal ...

Adaptively weighted Sub-pattern PCA (Aw-SpPCA) for face recognition is presented in this paper. Unlike PCA based on a whole image pattern, Aw-SpPCA operates directly on its sub-patterns partitioned from an original whole pattern and separately extracts features from them. Moreover, unlike both SpPCA and mPCA that neglect different contributions made by different parts of the human face in face ...

The Adjusted Winner procedure is an important fair division mechanism proposed by Brams and Taylor for allocating goods between two parties. It has been used in practice for divorce settlements and analyzing political disputes. Assuming truthful declaration of the valuations, it computes an allocation that is envy-free, equitable and Pareto optimal. We show that Adjusted Winner admits several e...

Inspired by the theory of P -and Q-polynomial association schemes we consider the following situation in linear algebra. Let F denote a field, and let V denote a vector space over F with finite positive dimension. We consider a pair of linear transformations A : V → V and A : V → V satisfying the following four conditions. (i) A and A are both diagonalizable on V . (ii) There exists an ordering...

Let K denote a field and let V denote a vector space over K with finite positive dimension. Let End(V ) denote the K-algebra consisting of all K-linear transformations from V to V . We consider a pair A,A ∈ End(V ) that satisfy (i)–(iv) below: (i) Each of A,A is diagonalizable. (ii) There exists an ordering {Vi} d i=0 of the eigenspaces of A such that A Vi ⊆ Vi−1+ Vi + Vi+1 for 0 ≤ i ≤ d, where...