New spin Calogero-Sutherland models related to B_N-type Dunkl operators

We construct several new families of exactly and quasi-exactly solvable BC_N-type Calogero-Sutherland models with internal degrees of freedom. Our approach is based on the introduction of two new families of Dunkl operators of B_N type which, together with the original B_N-type Dunkl operators, are shown to preserve certain polynomial subspaces of finite dimension. We prove that a wide class of quadratic combinations involving these three sets of Dunkl operators always yields a spin Calogero-Sutherland model, which is (quasi-)exactly solvable by construction. We show that all the spin Calogero-Sutherland models obtainable within this framework can be expressed in a unified way in terms of a Weierstrass P function with suitable half-periods. This provides a natural spin counterpart of the well-known general formula for a scalar completely integrable potential of BC_N type due to Olshanetsky and Perelomov. As an illustration of our method, we exactly compute several energy levels and their corresponding wavefunctions of an elliptic quasi-exactly solvable potential for two and three particles of spin 1/2.Comment: 18 pages, typeset in LaTeX 2e using revtex 4.0b5 and the amslatex package Minor changes in content, one reference adde

Finding Game Levels with the Right Difficulty in a Few Trials through Intelligent Trial-and-Error

Methods for dynamic difficulty adjustment allow games to be tailored to particular players to maximize their engagement. However, current methods often only modify a limited set of game features such as the difficulty of the opponents, or the availability of resources. Other approaches, such as experience-driven Procedural Content Generation (PCG), can generate complete levels with desired properties such as levels that are neither too hard nor too easy, but require many iterations. This paper presents a method that can generate and search for complete levels with a specific target difficulty in only a few trials. This advance is enabled by through an Intelligent Trial-and-Error algorithm, originally developed to allow robots to adapt quickly. Our algorithm first creates a large variety of different levels that vary across predefined dimensions such as leniency or map coverage. The performance of an AI playing agent on these maps gives a proxy for how difficult the level would be for another AI agent (e.g. one that employs Monte Carlo Tree Search instead of Greedy Tree Search); using this information, a Bayesian Optimization procedure is deployed, updating the difficulty of the prior map to reflect the ability of the agent. The approach can reliably find levels with a specific target difficulty for a variety of planning agents in only a few trials, while maintaining an understanding of their skill landscape.Comment: To be presented in the Conference on Games 202

Exactly solvable D_N-type quantum spin models with long-range interaction

We derive the spectra of the D_N-type Calogero (rational) su(m) spin model, including the degeneracy factors of all energy levels. By taking the strong coupling limit of this model, in which its spin and dynamical degrees of freedom decouple, we compute the exact partition function of the su(m) Polychronakos-Frahm spin chain of D_N type. With the help of this partition function we study several statistical properties of the chain's spectrum, such as the density of energy levels and the distribution of spacings between consecutive levels.Comment: 12 pages, 2 figure

A universal model for mobility and migration patterns

Introduced in its contemporary form by George Kingsley Zipf in 1946, but with roots that go back to the work of Gaspard Monge in the 18th century, the gravity law is the prevailing framework to predict population movement, cargo shipping volume, inter-city phone calls, as well as bilateral trade flows between nations. Despite its widespread use, it relies on adjustable parameters that vary from region to region and suffers from known analytic inconsistencies. Here we introduce a stochastic process capturing local mobility decisions that helps us analytically derive commuting and mobility fluxes that require as input only information on the population distribution. The resulting radiation model predicts mobility patterns in good agreement with mobility and transport patterns observed in a wide range of phenomena, from long-term migration patterns to communication volume between different regions. Given its parameter-free nature, the model can be applied in areas where we lack previous mobility measurements, significantly improving the predictive accuracy of most of phenomena affected by mobility and transport processes.Comment: Main text and supplementary informatio

Integrating microalgae production with anaerobic digestion: a biorefinery approach

This is the peer reviewed version of the following article: [Uggetti, E. , Sialve, B. , Trably, E. and Steyer, J. (2014), Integrating microalgae production with anaerobic digestion: a biorefinery approach. Biofuels, Bioprod. Bioref, 8: 516-529. doi:10.1002/bbb.1469], which has been published in final form at https://doi.org/10.1002/bbb.1469. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-ArchivingIn the energy and chemical sectors, alternative production chains should be considered in order to simultaneously reduce the dependence on oil and mitigate climate change. Biomass is probably the only viable alternative to fossil resources for production of liquid transportation fuels and chemicals since, besides fossils, it is one of the only available sources of carbon-rich material on Earth. Over recent years, interest in microalgae biomass has grown in both fundamental and applied research fields. The biorefinery concept includes different technologies able to convert biomass into added-value chemicals, products (food and feed) and biofuels (biodiesel, bioethanol, biohydrogen). As in oil refinery, a biorefinery aims at producing multiple products, maximizing the value derived from differences in biomass components, including microalgae. This paper provides an overview of the various microalgae-derived products, focusing on anaerobic digestion for conversion of microalgal biomass into methane. Special attention is paid to the range of possible inputs for anaerobic digestion (microalgal biomass and microalgal residue after lipid extraction) and the outputs resulting from the process (e.g. biogas and digestate). The strong interest in microalgae anaerobic digestion lies in its ability to mineralize microalgae containing organic nitrogen and phosphorus, resulting in a flux of ammonium and phosphate that can then be used as substrate for growing microalgae or that can be further processed to produce fertilizers. At present, anaerobic digestion outputs can provide nutrients, CO2 and water to cultivate microalgae, which in turn, are used as substrate for methane and fertilizer generation.Peer ReviewedPostprint (author's final draft

Modeling the scaling properties of human mobility

While the fat tailed jump size and the waiting time distributions characterizing individual human trajectories strongly suggest the relevance of the continuous time random walk (CTRW) models of human mobility, no one seriously believes that human traces are truly random. Given the importance of human mobility, from epidemic modeling to traffic prediction and urban planning, we need quantitative models that can account for the statistical characteristics of individual human trajectories. Here we use empirical data on human mobility, captured by mobile phone traces, to show that the predictions of the CTRW models are in systematic conflict with the empirical results. We introduce two principles that govern human trajectories, allowing us to build a statistically self-consistent microscopic model for individual human mobility. The model not only accounts for the empirically observed scaling laws but also allows us to analytically predict most of the pertinent scaling exponents

Towards Intelligent Lower Limb Prostheses with Activity Recognition

User’s volitional control of lower limb prostheses is still challenging task despite technological advancements. There is still a need for amputees to impose their will upon the prosthesis to drive in an accurate and interactive fashion. This study represents a brief review on control strategies using different sensor modalities for the purpose of phases/events detection and activity recognition. The preliminary work that is associated with middle-level control shows a simple and reliable method for event detection in real-time using a single inertial measurement unit. The outcome shows promising results

Inozemtsev's hyperbolic spin model and its related spin chain

In this paper we study Inozemtsev's su(m) quantum spin model with hyperbolic interactions and the associated spin chain of Haldane-Shastry type introduced by Frahm and Inozemtsev. We compute the spectrum of Inozemtsev's model, and use this result and the freezing trick to derive a simple analytic expression for the partition function of the Frahm-Inozemtsev chain. We show that the energy levels of the latter chain can be written in terms of the usual motifs for the Haldane-Shastry chain, although with a different dispersion relation. The formula for the partition function is used to analyze the behavior of the level density and the distribution of spacings between consecutive unfolded levels. We discuss the relevance of our results in connection with two well-known conjectures in quantum chaos.Comment: 22 pages, RevTeX, 7 figure

Thermodynamics of spin chains of Haldane-Shastry type and one-dimensional vertex models

We study the thermodynamic properties of spin chains of Haldane-Shastry type associated with the A_{N-1} root system in the presence of a uniform external magnetic field. To this end, we exactly compute the partition function of these models for an arbitrary finite number of spins. We then show that these chains are equivalent to a suitable inhomogeneous classical Ising model in a spatially dependent magnetic field, generalizing the results of Basu-Mallick et al. for thezero magnetic field case. Using the standard transfer matrix approach, we are able to compute in closed form the free energy per site in the thermodynamic limit. We perform a detailed analysis of the chains' thermodynamics in a unified way, with special emphasis on the zero field and zero temperature limits. Finally, we provide a novel interpretation of the thermodynamic quantities of spin chains of Haldane-Shastry type as weighted averages of the analogous quantities over an ensemble of classical Ising models.Comment: LaTeX, 39 pages, 13 figure

Long-term Follow-up after Feminizing Genital Reconstruction in Patients with Ambiguous Genitalia and High Vaginal Confluence

We evaluated the long-term results of feminizing genital reconstruction in patients with genital ambiguity with high vaginal confluence. The medical records of 10 consecutive patients with ambiguous genitalia and high vaginal confluence who underwent feminizing genital reconstruction from 1996 to 2007 were reviewed. Seven patients had congenital adrenal hyperplasia, one had mixed gonadal dysgenesis, one had partial androgen insensitivity, and one had 5-alpha reductase deficiency syndrome. Median age at operation was 21 months (range, 2-47 months). Median follow up was 7.7 yr. Of the six patients who underwent feminizing genital reconstruction with the Gonzalez method, three had good results. Of the other three patients, one had a urethrovaginal fistula and underwent fistula repair 9 yr after, one had distal vaginal stenosis and underwent revision vaginoplasty 9 yr after, and one had a urethrovaginal fistula and urethral stricture. The patient with urogenital mobilization had persistent urogenital sinus. Feminizing genitoplasty using the Gonzalez method showed good long-term results in patients with ambiguous genitalia and Congenital adrenal hyperplasia. The procedure is less invasive than other approaches and results in excellent cosmetic outcomes; and complications can be corrected by relatively simple procedures