Time Consistent Dynamic Risk Measures

We introduce the time-consistency concept that is inspired by the so-called “principle of optimality” of dynamic programming and demonstrate – via an example – that the conditional value-at-risk (CVaR) need not be time-consistent in a multi-stage case. Then, we give the formulation of the target-percentile risk measure which is time-consistent and hence more suitable in the multi-stage investment context. Finally, we also generalize the value-at-risk and CVaR to multi-stage risk measures based on the theory and structure of the target-percentile risk measure.     

Reconstruction of the Point-Spread Function of the Human Eye Using a New Phase-Retrieval Algorithm

The double-pass method is thought to obtain the point spread function (PSF) in human eyes based on two techniques: the symmetric double-pass method using the same pupil size and the asymmetric double-pass method using a different pupil size. The symmetric double-pass method provides autocorrelation of the retinal PSF and, thus, the modulation transfer function. The asymmetric double-pass method provides low-frequency partial-phase information and the partial phase-retrieval algorithm is applied to obtain the complete-phase information, and to estimate the PSF. The partial phase-retrieval algorithm is based on the iteration method proposed by Fineup and Kowalczyk and requires a lengthy computation. In this study, we propose a new high-speed phase-retrieval algorithm based on the property that the real and imaginary parts of optical transfer functions (OTFs) continuously change in value.     

Bubble point pressure estimates from Gibbs ensemble simulations

Bubble pressure points of ethanol–1,1,1,2,3,3,3-heptafluoropropane (HFC-227ea refrigerant) mixtures from the third Industrial Fluid Properties Simulation Challenge are computed using publicly available molecular simulation software. Several published force fields are compared against the known answers provided in the contest guidelines and the best force fields are used to make predictions for the unknown results.     

Fixed point theorems for multivalued nonexpansive mappings satisfying inwardness conditions

Let X be a Banach space whose characteristic of noncompact convexity is less than 1 and satisfies the nonstrict Opial condition. Let C be a bounded closed convex subset of X, KC(X) the family of all compact convex subsets of X and T a nonexpansive mapping from C into KC(X) with bounded range. We prove that T has a fixed point. The nonstrict Opial condition can be removed if, in addition, T is an 1-χ-contractive mapping.     

On the number of full levels in tries

We study the asymptotic distribution of the fill‐up level in a binary trie built over n independent strings generated by a biased memoryless source. The fill‐up level is the number of full levels in a tree. A level is full if it contains the maximum allowable number of nodes (e.g., in a binary tree level k can have up to 2^k nodes). The fill‐up level finds many interesting applications, e.g., in the internet IP lookup problem and in the analysis of level compressed tries (LC tries). In this paper, we present a complete asymptotic characterization of the fill‐up distribution. In particular, we prove that this distribution concentrates on one or two points around the most probably value k = ?log_1/qn ? log log log n + 1 + log log(p/q)?, where p > q = 1 ? p is the probability of generating the more likely symbol (while q = 1 ? p is the probability of the less likely symbol). We derive our results by analytic methods such as generating functions, Mellin transform, the saddle point method, and analytic depoissonization. We also present some numerical verification of our results. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004     

Isotone relations revisited

We propose a new approach towards proving that the fixed point property for ordered sets is preserved by products. This approach uses a characterization of fixed points in products via isotone relations. First explorations of classes of isotone relations are presented. These first explorations give us hope that this approach could lead to advances on the Product Problem.     

An approximate proximal-extragradient type method for monotone variational inequalities

Proximal point algorithms (PPA) are attractive methods for monotone variational inequalities. The approximate versions of PPA are more applicable in practice. A modified approximate proximal point algorithm (APPA) presented by Solodov and Svaiter [Math. Programming, Ser. B 88 (2000) 371–389] relaxes the inexactness criterion significantly. This paper presents an extended version of Solodov–Svaiter's APPA. Building the direction from current iterate to the new iterate obtained by Solodov–Svaiter's APPA, the proposed method improves the profit at each iteration by choosing the optimal step length along this direction. In addition, the inexactness restriction is relaxed further. Numerical example indicates the improvement of the proposed method.     

On the existence of positive solutions for a class of singular boundary value problems

In this paper, by the use of a fixed point theorem, many new necessary and sufficient conditions for the existence of positive solutions in C[0,1]∩C¹[0,1]∩C²(0,1) or C[0,1]∩C²(0,1) are presented for singular superlinear and sublinear second-order boundary value problems. Singularities at t=0, t=1 will be discussed.     

Existence of two solutions of m-point boundary value problem for second order dynamic equations on time scales

In this paper, by means of a new twin fixed-point theorem in a cone, the existence of at least two positive solutions of m-point boundary value problem for second order dynamic equations on time scales is considered.