Asymptotics of Generalized Bessel Functions and Weight Multiplicities via Large Deviations of Radial Dunkl Processes

This paper studies the asymptotic behavior of several central objects in Dunkl theory as the dimension of the underlying space grows large. Our starting point is the observation that a recent result from the random matrix theory literature implies a large deviations principle for the hydrodynamic limit of radial Dunkl processes. Using this fact, we prove a variational formula for the large-$N$ asymptotics of generalized Bessel functions, as well as a large deviations principle for the more general family of radial Heckman-Opdam processes. As an application, we prove a theorem on the asymptotic behavior of weight multiplicities of irreducible representations of compact or complex simple Lie algebras in the limit of large rank. The theorems in this paper generalize several known results describing analogous asymptotics for Dyson Brownian motion, spherical matrix integrals, and Kostka numbers.Comment: 44 pages, no figures. This version: Minor corrections to scaling of variables in Sections 3.2, 4 and 6. Significant updates to presentatio

Sparse metric learning via smooth optimization

Copyright © 2009 NIPS Foundation23rd Annual Conference on Advances in Neural Information Processing Systems (NIPS 2009), Vancouver, Canada, 7-10 December 2009In this paper we study the problem of learning a low-rank (sparse) distance matrix. We propose a novel metric learning model which can simultaneously conduct dimension reduction and learn a distance matrix. The sparse representation involves a mixed-norm regularization which is non-convex. We then show that it can be equivalently formulated as a convex saddle (min-max) problem. From this saddle representation, we develop an efficient smooth optimization approach [15] for sparse metric learning, although the learning model is based on a non-differentiable loss function. This smooth optimization approach has an optimal convergence rate of O(1=t2) for smooth problems where t is the iteration number. Finally, we run experiments to validate the effectiveness and efficiency of our sparse metric learning model on various datasets

Large Angle Magnetic Suspension Test Fixture

Progress in the areas of eddy current computations, modelling and analysis, design optimization methods, wind tunnel Magnetic Suspension and Balance Systems (MSBS), payload pointing and vibration isolation systems, and system identification is reported. Research accomplishments facilitated the demonstration of several new developments in the field of magnetic suspension technology

Specialist alcohol inpatient treatment admissions and non-specialist hospital admissions for alcohol withdrawal in England: an inverse relationship

© The Author(s) 2020. Medical Council on Alcohol and Oxford University Press. AIMS: We assessed the relationship between specialist and non-specialist admissions for alcohol withdrawal since the introduction of the UK government Health and Social Care Act in 2012. METHODS: Using publicly available national data sets from 2009 to 2019, we compared the number of alcohol withdrawal admissions and estimated costs in specialist and non-specialist treatment settings. RESULTS: A significant negative correlation providing strong evidence of an association was observed between the fall in specialist and rise in non-specialist admissions. Significant cost reductions within specialist services were displaced to non-specialist settings. CONCLUSIONS: The shift in demand from specialist to non-specialist alcohol admissions due to policy changes in England should be reversed by specialist workforce investment to improve outcomes. In the meantime, non-specialist services and staff must be resourced and equipped to meet the complex needs of these service users

Odd elasticity in driven granular matter

Odd elasticity describes the unusual elastic response of solids whose stress-strain relationship is not compatible with an elastic potential. Here, we present a study of odd elasticity in a driven granular matter system composed of grains with ratchet-like interparticle friction and activated by oscillatory shear. We find that the system permits a time-averaged elasticity theory featuring nonzero odd elastic coefficients. These coefficients are explicitly measured using molecular dynamics simulations and can be predicted and tuned from microscopics. In the presence of disorder, our driven granular material displays distinctive properties ranging from self-healing grain boundaries in polycrystalline systems to chiral plastic vortices and force chain deflection in amorphous packings. Beyond granular matter, our work motivates the search for microscopic transduction mechanisms that convert periodic nonuniform drive into uniform elastic properties of active solids.Comment: See supplementary movies at https://home.uchicago.edu/~vitelli/videos.htm

Large angle magnetic suspension test fixture

Good progress is being made in several major areas. These include eddy current modelling and analysis, design optimization methods, wind tunnel Magnetic Suspension and Balance Systems (MSBS), payload pointing and vibration isolation systems, and system identification. In addition, another successful International Symposium has been completed, with the Proceedings being printed at the time of writing. These activities continue current work under this Grant and extend previous work on magnetic suspension systems and devices in the Guidance and Control Branch and will permit the demonstration of several new developments in the field of magnetic suspension technology

MEMS 411: Mini-Golf Robot Vehicle

The primary objective of the project is to develop a remote-controlled vehicle capable of completing a round of mini golf as part of the ASME Student Design Competition. The vehicle’s functionalities are categorized into driving and golf-ball striking. Our group is specifically responsible for the former aspect. The remote-controlled vehicle is expected to traverse through the designated competition field and exhibit the ability to maneuver between and over obstacles, including a high wall and a low platform. Our design should adhere to the competition regulations set forth by ASME SDC, which include specific criteria for the vehicle such as size limitations, battery restrictions, and the prescribed method of remote control. Successful completion of this project also necessitates collaboration with a striking group. This collaborative effort is crucial for the development of a multifunctional vehicle capable of accomplishing a wide range of tasks as demanded

The relationship between maternal personality disorder and early birth outcomes: A systematic review and meta-analysis

Title: Systematic review and meta-analysis of the relationship between maternal personality disorder and early birth outcomes.Background: Women with personality disorder are at risk of social and emotional problems which impact deleteriously on everyday functioning. Moreover, a personality disorder diagnosis has been established to have an adverse impact upon pregnancy outcomes and child health. Understanding this impact is critical to improving both maternal and child outcomes. This systematic review and meta-analysis will evaluate the contemporary evidence regarding these relationships.Methods: Prospero and Cochrane were searched for any systematic reviews already completed on this topic. Academic Search Premier, CINAHL Complete, MEDLINE, PsycARTICLES, PsycINFO via the EBSCO host, and Web of Science Core Collection were searched to include research articles published between 1980 and 2019. 158 records were identified; 105 records were screened by reviewing the abstract. 99 records were excluded. 6 full text articles were assessed for eligibility. 5 records were included in the review. Results: All the included studies reported on preterm birth. The meta-analysis indicates significant risk of preterm birth in women with personality disorder (overall OR 2.62; CI 2.24-3.06