Central limit theorems for Gaussian polytopes

Choose $n$ random, independent points in $\R^d$ according to the standard normal distribution. Their convex hull $K_n$ is the {\sl Gaussian random polytope}. We prove that the volume and the number of faces of $K_n$ satisfy the central limit theorem, settling a well known conjecture in the field.Comment: to appear in Annals of Probabilit

Kinetic-Ion Simulations Addressing Whether Ion Trapping Inflates Stimulated Brillouin Backscattering Reflectivities

An investigation of the possible inflation of stimulated Brillouin backscattering (SBS) due to ion kinetic effects is presented using electromagnetic particle simulations and integrations of three-wave coupled-mode equations with linear and nonlinear models of the nonlinear ion physics. Electrostatic simulations of linear ion Landau damping in an ion acoustic wave, nonlinear reduction of damping due to ion trapping, and nonlinear frequency shifts due to ion trapping establish a baseline for modeling the electromagnetic SBS simulations. Systematic scans of the laser intensity have been undertaken with both one-dimensional particle simulations and coupled-mode-equations integrations, and two values of the electron-to-ion temperature ratio (to vary the linear ion Landau damping) are considered. Three of the four intensity scans have evidence of SBS inflation as determined by observing more reflectivity in the particle simulations than in the corresponding three-wave mode-coupling integrations with a linear ion-wave model, and the particle simulations show evidence of ion trapping.Comment: 56 pages, 20 figure

Human flourishing from eudaimonic balance of values in entrepreneurs

Much of the focus in the entrepreneurial literature is on the primacy of financial values but in this paper, we argue that this is misplaced. Instead, we propose that entrepreneurs pursue an eudaimonic balance of values to achieve human flourishing. Using insights from the institutional logics perspective, we present findings from an empirical, qualitative, cross-cultural, multi-case study in Taiwan and Vietnam. We show how entrepreneurs strive for a range of goals from different facets of life, demonstrating the importance of non-financial goals for eudaimonia, or human flourishing. We contribute insights from outside the commonly studied North American and European contexts, showing the importance of culture and tradition in shaping the influences operating upon individuals and the value-laden objectives they pursue. Consequently, we illustrate the need for a more complex and complete framing of entrepreneurial values that contradicts much of the literature employing rational-actor theory, economic models, and quantitative analysis

On the theory of the vortex state in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase

We demonstrate that the vortex state in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase may be very different depending on the field orientation relative to the crystalline axes. We calculate numerically the upper critical field near the tricritical point taking into account the modulation of the order parameter along the magnetic field as well as the higher Landau levels. For s-wave superconductors with the anisotropy described by an elliptical Fermi surface we propose a general scheme of the analysis of the angular dependence of upper critical field at all temperatures on the basis of the exact solution for the order parameter. Our results show that the transitions (with tilting magnetic field) between different types of mixed states may be a salient feature of the FFLO phase. Moreover we discuss the reasons for the first-order phase transition into the FFLO state in the case of CeCoIn5 compound.Comment: 7 figure

Inferring Networks of Substitutable and Complementary Products

In a modern recommender system, it is important to understand how products relate to each other. For example, while a user is looking for mobile phones, it might make sense to recommend other phones, but once they buy a phone, we might instead want to recommend batteries, cases, or chargers. These two types of recommendations are referred to as substitutes and complements: substitutes are products that can be purchased instead of each other, while complements are products that can be purchased in addition to each other. Here we develop a method to infer networks of substitutable and complementary products. We formulate this as a supervised link prediction task, where we learn the semantics of substitutes and complements from data associated with products. The primary source of data we use is the text of product reviews, though our method also makes use of features such as ratings, specifications, prices, and brands. Methodologically, we build topic models that are trained to automatically discover topics from text that are successful at predicting and explaining such relationships. Experimentally, we evaluate our system on the Amazon product catalog, a large dataset consisting of 9 million products, 237 million links, and 144 million reviews.Comment: 12 pages, 6 figure

Quantum mechanics in multiply connected spaces

This paper analyses quantum mechanics in multiply connected spaces. It is shown that the multiple connectedness of the configuration space of a physical system can determine the quantum nature of physical observables, such as the angular momentum. In particular, quantum mechanics in compactified Kaluza-Klein spaces is examined. These compactified spaces give rise to an additional angular momentum which can adopt half-integer values and, therefore, may be identified with the intrinsic spin of a quantum particle.Comment: Latex 15 page

The burden and characteristics of enteric fever at a healthcare facility in a densely populated area of Kathmandu

Enteric fever, caused by Salmonella enterica serovars Typhi and Paratyphi A (S. Typhi and S. Paratyphi A) remains a major public health problem in many settings. The disease is limited to locations with poor sanitation which facilitates the transmission of the infecting organisms. Efficacious and inexpensive vaccines are available for S. Typhi, yet are not commonly deployed to control the disease. Lack of vaccination is due partly to uncertainty of the disease burden arising from a paucity of epidemiological information in key locations. We have collected and analyzed data from 3,898 cases of blood culture-confirmed enteric fever from Patan Hospital in Lalitpur Sub-Metropolitan City (LSMC), between June 2005 and May 2009. Demographic data was available for a subset of these patients (n = 527) that were resident in LSMC and who were enrolled in trials. We show a considerable burden of enteric fever caused by S. Typhi (2,672; 68.5%) and S. Paratyphi A (1,226; 31.5%) at this Hospital over a four year period, which correlate with seasonal fluctuations in rainfall. We found that local population density was not related to incidence and we identified a focus of infections in the east of LSMC. With data from patients resident in LSMC we found that the median age of those with S. Typhi (16 years) was significantly less than S. Paratyphi A (20 years) and that males aged 15 to 25 were disproportionately infected. Our findings provide a snapshot into the epidemiological patterns of enteric fever in Kathmandu. The uneven distribution of enteric fever patients within the population suggests local variation in risk factors, such as contaminated drinking water. These findings are important for initiating a vaccination scheme and improvements in sanitation. We suggest any such intervention should be implemented throughout the LSMC area.This work was supported by The Wellcome Trust, Euston Road, London, United Kingdom. MFB is supported by the Medical Research Council (grant G0600718). SB is supported by an OAK foundation fellowship through Oxford University