Combinatorial Assortment Optimization

Assortment optimization refers to the problem of designing a slate of products to offer potential customers, such as stocking the shelves in a convenience store. The price of each product is fixed in advance, and a probabilistic choice function describes which product a customer will choose from any given subset. We introduce the combinatorial assortment problem, where each customer may select a bundle of products. We consider a model of consumer choice where the relative value of different bundles is described by a valuation function, while individual customers may differ in their absolute willingness to pay, and study the complexity of the resulting optimization problem. We show that any sub-polynomial approximation to the problem requires exponentially many demand queries when the valuation function is XOS, and that no FPTAS exists even for succinctly-representable submodular valuations. On the positive side, we show how to obtain constant approximations under a "well-priced" condition, where each product's price is sufficiently high. We also provide an exact algorithm for $k$-additive valuations, and show how to extend our results to a learning setting where the seller must infer the customers' preferences from their purchasing behavior

Kinetic Theory of Collisionless Self-Gravitating Gases: II. Relativistic Corrections in Galactic Dynamics

In this paper we study the kinetic theory of many-particle astrophysical systems imposing axial symmetry and extending our previous analysis in Phys. Rev. D 83, 123007 (2011). Starting from a Newtonian model describing a collisionless self-gravitating gas, we develop a framework to include systematically the first general relativistic corrections to the matter distribution and gravitational potentials for general stationary systems. Then, we use our method to obtain particular solutions for the case of the Morgan & Morgan disks. The models obtained are fully analytical and correspond to the post-Newtonian generalizations of classical ones. We explore some properties of the models in order to estimate the importance of post-Newtonian corrections and we find that, contrary to the expectations, the main modifications appear far from the galaxy cores. As a by-product of this investigation we derive the corrected version of the tensor virial theorem. For stationary systems we recover the same result as in the Newtonian theory. However, for time dependent backgrounds we find that there is an extra piece that contributes to the variation of the inertia tensor.Comment: 30 pages, 8 figures. v2: Minor corrections and references added. Conclusions unchanged. v3: Version published in PR

On the evaluation of some three-body variational integrals

Stable recursive relations are presented for the numerical computation of the integrals $$\int d{\bf r}_1 d{\bf r}_2 r_1^{l-1} r_2^{m-1} r_{12}^{n-1} \exp{\{-\alpha r_1 -\beta r_2 -\gamma r_{12}\}}$$ ($l$, $m$ and $n$ integer, $\alpha$, $\beta$ and $\gamma$ real) when the indices $l$, $m$ or $n$ are negative. Useful formulas are given for particular values of the parameters $\alpha$, $\beta$ and $\gamma$.Comment: 12 pages, 1 figure (PS) and 3 tables. Old figures 2 and 3 replaced by Tables I and III. A further table added. Paper enlarged giving some tips on the convergence of quadrature

Androgenetic alopecia: a review

Androgenetic alopecia, commonly known as male pattern baldness, is the most common type of progressive hair loss disorder in men. The aim of this paper is to review recent advances in understanding the pathophysiology and molecular mechanism of androgenetic alopecia.Using the PubMed database, we conducted a systematic review of the literature, selecting studies published from 1916 to 2016.The occurrence and development of androgenetic alopecia depends on the interaction of endocrine factors and genetic predisposition. Androgenetic alopecia is characterized by progressive hair follicular miniaturization, caused by the actions of androgens on the epithelial cells of genetically susceptible hair follicles in androgen-dependent areas. Although the exact pathogenesis of androgenetic alopecia remains to be clarified, research has shown that it is a polygenetic condition. Numerous studies have unequivocally identified two major genetic risk loci for androgenetic alopecia, on the X-chromosome ARa"EDA2R locus and the chromosome 20p11 locus.Candidate gene and genome-wide association studies have reported that single-nucleotide polymorphisms at different genomic loci are associated with androgenetic alopecia development. A number of genes determine the predisposition for androgenetic alopecia in a polygenic fashion. However, further studies are needed before the specific genetic factors of this polygenic condition can be fully explained

Kinetic Theory of Collisionless Self-Gravitating Gases: Post-Newtonian Polytropes

In this paper we study the kinetic theory of many-particle astrophysical systems and we present a consistent version of the collisionless Boltzmann equation in the 1PN approximation. We argue that the equation presented by Rezania and Sobouti in A&A 354 1110 (2000) is not the correct expression to describe the evolution of a collisionless self-gravitating gas. One of the reasons that account for the previous statement is that the energy of a free-falling test particle, obeying the 1PN equations of motion for static gravitational fields, is not a static solution of the mentioned equation. The same statement holds for the angular momentum, in the case of spherical systems. We provide the necessary corrections and obtain an equation that is consistent with the corresponding equations of motion and the 1PN conserved quantities. We suggest some potential relevance for the study of high density astrophysical systems and as an application we construct the corrected version of the post-Newtonian polytropes.Comment: 23 pages, 24 figures. Accepted for publication in PR

Recent expansion of dengue virus serotype 3 in West Africa

Due to non-existing or limited surveillance in Africa, little is known about the epidemiology of dengue illness in the continent. Serological and virological data obtained from returning European travellers is a key complement to this often flawed information. In the past years, dengue 3 virus has emerged in West Africa and has been detected in travellers returning to Europe. The first dengue epidemic in Cape Verde with more than 17,000 cases from September to December 2009 demonstrated that dengue virus is still expanding worldwide to new territories.S

Do patients’ information needs decrease over the course of radiotherapy?

PURPOSE: We aimed to investigate if cancer patients’ information needs decrease during radiotherapy and if so, which patient, consultation and radiation oncologist characteristics are associated with a decrease in information needs over time. METHODS: In this longitudinal study, patients (n = 104) completed a baseline questionnaire a week before the initial radiotherapy consultation, immediately following this initial consultation, and 1 week prior to the first follow-up visit, which took place on average 3–5 weeks after the initial visit. Besides information needs, measured by the Information Preference for Radiotherapy Patients scale, the questionnaire assessed patient, consultation and radiation oncologist characteristics. RESULTS: Information needs decreased over time, but remained at a high level. Being religious, being male, having low health literacy and higher perceived involvement during the consultation were all statistically significantly associated to a decrease in information needs on specific domains (e.g. procedures or side effects). CONCLUSIONS: Cancer patients’ information needs decline between the initial consultation and the first follow-up visit, but remain high. It is therefore advised to investigate the patients’ information needs at every radiotherapy visit and not rely on giving information just once. Furthermore, radiation oncologists should check if the information given at first consultation is understood and remembered. By those means, tailored information giving becomes possible

Numerical studies towards practical large-eddy simulation

Large-eddy simulation developments and validations are presented for an improved simulation of turbulent internal flows. Numerical methods are proposed according to two competing criteria: numerical qualities (precision and spectral characteristics), and adaptability to complex configurations. First, methods are tested on academic test-cases, in order to abridge with fundamental studies. Consistent results are obtained using adaptable finite volume method, with higher order advection fluxes, implicit grid filtering and "low-cost" shear-improved Smagorinsky model. This analysis particularly focuses on mean flow, fluctuations, two-point correlations and spectra. Moreover, it is shown that exponential averaging is a promising tool for LES implementation in complex geometry with deterministic unsteadiness. Finally, adaptability of the method is demonstrated by application to a configuration representative of blade-tip clearance flow in a turbomachine