A Preference Order Dynamic Program for a Knapsack Problem with Stochastic Rewards

In this paper, we extend the knapsack problem to include more realistic situations by treating the rewards (or values) associated with each item included in the solution as random variables with distributions that are known (or may be estimated) rather than known integers, as in the usual formulation. We propose a dynamic programming solution methodology where the usual real-valued return function is replaced by a preference ordering on the distributions of returns from the items selected. In addition to extending previous solutions to the knapsack problem, we demonstrate the selection of a preference ordering criterion and illustrate the conditions required of the ordering to guarantee optimality of the procedure. A sample problem is shown to demonstrate the algorithm, and results of computational experience with 459 problems of varying sizes and parameters are presented.     

On Aperiodic Relational Morphisms

We characterize aperiodic relational morphisms as those that are injective on regular $\H$-classes. This result is applied to obtain simple proofs and generalizations of McAlisters results on joins of aperiodic semigroups and groups. Also, we show that if $\pv H$ is a proper, non-trivial pseudovariety of groups, then \[\pv A\ast \pv H\subsetneq (\pv A\ast \pv G)\cap \ov {\pv H}.\] We provide coordinate-free formulations and proofs of Rhodess Presentation Lemma and generalizations. As an application, we give simpler proofs of Tilsons theorem on the complexity of semigroups with at most $2$ non-zero $\J$-classes and Rhodess theorem that complexity is not local.     

Multiple solutions to the equation of the law of mass action

The appearance of multiple solutions to the equation of the law of mass action indicates a chemical instability where a system, as a result of the first order phase transition, breaks down into several phases. In each phase the reactant concentrations are different.     

Coherence freeze in an optical lattice investigated via pump-probe spectroscopy

Motivated by our observation of fast echo decay and a surprising coherence freeze, we have developed a pump-probe spectroscopy technique for vibrational states of 85Rb atoms in an optical lattice to gain information about the memory dynamics of the system. We monitor the time-dependent changes of frequencies experienced by atoms and characterize the probability distribution of these frequency trajectories. We show that the inferred distribution, unlike a naive microscopic model of the lattice, correctly predicts the main features of the observed echo decay.     

The Capacity Region of the Degraded Multiple-Input Multiple-Output Compound Broadcast Channel

The capacity region of a compound multiple-antenna broadcast channel is characterized when the users exhibit a certain degradedness order. The channel under consideration has two users, each user has a finite set of possible realizations. The transmitter transmits two messages, one for each user, in such a manner that regardless of the actual realizations, both users will be able to decode their messages correctly. An alternative view of this channel is that of a broadcast channel with two common messages, each common message is intended to a different set of users. The degradedness order between the two sets of realizations/users is defined through an additional, fictitious, user whose channel is degraded with respect to all realizations/users from one set while all realizations/users from the other set are degraded with respect to him.     

A Matched Asymptotic Expansions Approach to Continuity Corrections for Discretely Sampled Options. Part 1: Barrier Options

We propose a general framework to model equity volatility for a firm financed by equity and additional non-equity sources of funds. The stochastic nature of equity volatility is endogenous, and comes from the impact of a change in the value of the firm's assets on the financial leverage. We first present the basic model, which is an extension of the Black-Scholes model, to value corporate securities. Second, we show for the first time in the option literature, that instantaneous equity volatility is a solution of a partial differential equation similar to Black-Scholes', although it is non-linear and in general does not have any analytical solution. However, analytical approximations for equity volatility are proposed for different capital structures: (1) equity and debt, (2) equity and warrants, and (3) equity, debt and warrants. They are shown to be very accurate.     

Skin Microbiome Compositional Changes in Atopic Dermatitis Accompany Dead Sea Climatotherapy

Dead Sea climatotherapy (DSC) is a well‐established therapeutic modality for the treatment of several diseases, including atopic dermatitis. Skin microbiome studies have shown that skin microbiome diversity is anticorrelated with both atopic dermatitis severity and concurrent Staphylococcus aureus overgrowth. This study aimed to determine whether DSC induces skin microbiome changes concurrent with clinical improvements in atopic dermatitis. We sampled 35 atopic dermatitis patients and ten healthy controls on both the antecubital and popliteal fossa. High‐resolution microbial community profiling was attained by sequencing multiple regions of the 16S rRNA gene. Dysbiosis was observed in both lesional and nonlesional sites, which was partially attenuated following treatment. Severe AD skin underwent the most significant community shifts, and Staphylococcus epidermidis, Streptococcus mitis and Micrococcus luteus relative abundance were significantly affected by Dead Sea climatotherapy. Our study highlights the temporal shifts of the AD skin microbiome induced by Dead Sea climatotherapy and offers potential explanations for the success of climatotherapy on a variety of skin diseases, including AD.     

Structural response of different Lewis number premixed flames interacting with a toroidal vortex

Simultaneous measurements of temperature, CH* and OH* chemiluminescent species are carried out to explore the impact of stretch rate and curvature on the structure of premixed flames. The configuration of an initially flat premixed flame interacting with a toroidal vortex is selected for the present study and reasons for this choice are discussed. Lewis number effects are assessed by comparing methane and propane flames. It is emphasized that the flame structure experiences very strong variations. In particular, the flame is shrunk (broadened) in the initial (final) period of the interaction with the vortex where strain rate (curvature) contribution of the stretch rate is predominant. By further analysing independently the thickness of the preheat and reaction zones, it is shown that for propane flames, not only the former but also the latter is significantly altered in zones where the flame curvature is negative. Changes in the reaction zone properties are further emphasized using CH* and OH* radicals. It is demonstrated that higher thermal diffusivity plays a significant role around curved regions, in which the enhanced diffusion of heat leads to a strong increase of CH* compared to OH* intensity. As an overall conclusion, this study suggests that it would be interesting to reassess the internal flame structure at lower and moderate Karlovitz numbers since changes might appear for a moderate vortex intensity with typical size much larger than the flame thickness.