Rates of convergence for empirical spectral measures: a soft approach

Understanding the limiting behavior of eigenvalues of random matrices is the central problem of random matrix theory. Classical limit results are known for many models, and there has been significant recent progress in obtaining more quantitative, non-asymptotic results. In this paper, we describe a systematic approach to bounding rates of convergence and proving tail inequalities for the empirical spectral measures of a wide variety of random matrix ensembles. We illustrate the approach by proving asymptotically almost sure rates of convergence of the empirical spectral measure in the following ensembles: Wigner matrices, Wishart matrices, Haar-distributed matrices from the compact classical groups, powers of Haar matrices, randomized sums and random compressions of Hermitian matrices, a random matrix model for the Hamiltonians of quantum spin glasses, and finally the complex Ginibre ensemble. Many of the results appeared previously and are being collected and described here as illustrations of the general method; however, some details (particularly in the Wigner and Wishart cases) are new. Our approach makes use of techniques from probability in Banach spaces, in particular concentration of measure and bounds for suprema of stochastic processes, in combination with more classical tools from matrix analysis, approximation theory, and Fourier analysis. It is highly flexible, as evidenced by the broad list of examples. It is moreover based largely on "soft" methods, and involves little hard analysis

Central limit theorem for multiplicative class functions on the symmetric group

Hambly, Keevash, O'Connell and Stark have proven a central limit theorem for the characteristic polynomial of a permutation matrix with respect to the uniform measure on the symmetric group. We generalize this result in several ways. We prove here a central limit theorem for multiplicative class functions on symmetric group with respect to the Ewens measure and compute the covariance of the real and the imaginary part in the limit. We also estimate the rate of convergence with the Wasserstein distance.Comment: 23 pages; the mathematics is the same as in the previous version, but there are several improvments in the presentation, including a more intuitve name for the considered function

Oxygen Cost of Performing Selected Adult and Child Care Activities

International Journal of Exercise Science 6(1) : 11-19, 2013. Little is known about the oxygen cost of caring for infants and older adults. Many people perform these activities so it is useful to know the energy cost and if the activities are of sufficient intensity to contribute to meeting physical activity recommendations. The purpose of this study was to assess the oxygen cost of four care-related activities in the Compendium of Physical Activities. Nineteen participants (n = 10 women, n = 9 men; Age = 36.4 ± 13.6 y; % Fat = 34.1 ± 10.5; BMI = 28.1 ± 4.5 kg/m2) performed four activities: 1) pushing an infant in a stroller, 2) pushing an adult in a wheelchair, 3) carrying an infant, and 4) bathing and dressing an infant. The oxygen cost was assessed using a portable metabolic unit. Activities were performed in random order for 8 minutes. The oxygen cost and heart rates, respectively, for healthy adults during care related activities were 3.09 METs and 90 ± 8 beats per minute (bpm) for pushing an infant in a stroller, 3.69 METs and 97 ± 9 bpm for pushing an adult in a wheelchair, 2.37 METs and 85 ± 9 bpm for carrying an infant, and 2.00 METs and 87 ± 9 bpm for bathing and dressing an infant. Carrying an infant and bathing an infant are light-intensity physical activities and pushing a wheelchair or a stroller are moderate intensity activities. The latter activities are of sufficient intensity to meet health-related physical activity recommendations

On Poincare and logarithmic Sobolev inequalities for a class of singular Gibbs measures

This note, mostly expository, is devoted to Poincar{\'e} and log-Sobolev inequalities for a class of Boltzmann-Gibbs measures with singular interaction. Such measures allow to model one-dimensional particles with confinement and singular pair interaction. The functional inequalities come from convexity. We prove and characterize optimality in the case of quadratic confinement via a factorization of the measure. This optimality phenomenon holds for all beta Hermite ensembles including the Gaussian unitary ensemble, a famous exactly solvable model of random matrix theory. We further explore exact solvability by reviewing the relation to Dyson-Ornstein-Uhlenbeck diffusion dynamics admitting the Hermite-Lassalle orthogonal polynomials as a complete set of eigenfunctions. We also discuss the consequence of the log-Sobolev inequality in terms of concentration of measure for Lipschitz functions such as maxima and linear statistics.Comment: Minor improvements. To appear in Geometric Aspects of Functional Analysis -- Israel Seminar (GAFA) 2017-2019", Lecture Notes in Mathematics 225

Monoubiquitination of syntaxin 3 leads to retrieval from the basolateral plasma membrane and facilitates cargo recruitment to exosomes

Syntaxin 3 (Stx3), a SNARE protein located and functioning at the apical plasma membrane of epithelial cells, is required for epithelial polarity. A fraction of Stx3 is localized to late endosomes/lysosomes, although how it traffics there and its function in these organelles is unknown. Here we report that Stx3 undergoes monoubiquitination in a conserved polybasic domain. Stx3 present at the basolateral—but not the apical—plasma membrane is rapidly endocytosed, targeted to endosomes, internalized into intraluminal vesicles (ILVs), and excreted in exosomes. A nonubiquitinatable mutant of Stx3 (Stx3-5R) fails to enter this pathway and leads to the inability of the apical exosomal cargo protein GPRC5B to enter the ILV/exosomal pathway. This suggests that ubiquitination of Stx3 leads to removal from the basolateral membrane to achieve apical polarity, that Stx3 plays a role in the recruitment of cargo to exosomes, and that the Stx3-5R mutant acts as a dominant-negative inhibitor. Human cytomegalovirus (HCMV) acquires its membrane in an intracellular compartment and we show that Stx3-5R strongly reduces the number of excreted infectious viral particles. Altogether these results suggest that Stx3 functions in the transport of specific proteins to apical exosomes and that HCMV exploits this pathway for virion excretion

Modulation of B-cell exosome proteins by gamma herpesvirus infection

Exosomes are released from tumor cells at high levels, and multiple studies have determined that the secreted exosomes enter recipient cells and can affect their biologic and biochemical properties. In this study, the specific effects of the oncogenic herpesviruses, EBV and Kaposi sarcoma-associated virus, on the proteomes of B-cell exosomes were determined using global quantitative proteomics. The data indicate that the viruses greatly impact the protein content of exosomes with common and distinct changes induced by both viruses. It is likely that these alterations in exosome content modulate the tumor environment, potentially to enhance viral infection and promote tumorigenesis

Minimal information for studies of extracellular vesicles 2018 (MISEV2018): a position statement of the International Society for Extracellular Vesicles and update of the MISEV2014 guidelines

The last decade has seen a sharp increase in the number of scientific publications describing physiological and pathological functions of extracellular vesicles (EVs), a collective term covering various subtypes of cell-released, membranous structures, called exosomes, microvesicles, microparticles, ectosomes, oncosomes, apoptotic bodies, and many other names. However, specific issues arise when working with these entities, whose size and amount often make them difficult to obtain as relatively pure preparations, and to characterize properly. The International Society for Extracellular Vesicles (ISEV) proposed Minimal Information for Studies of Extracellular Vesicles (“MISEV”) guidelines for the field in 2014. We now update these “MISEV2014” guidelines based on evolution of the collective knowledge in the last four years. An important point to consider is that ascribing a specific function to EVs in general, or to subtypes of EVs, requires reporting of specific information beyond mere description of function in a crude, potentially contaminated, and heterogeneous preparation. For example, claims that exosomes are endowed with exquisite and specific activities remain difficult to support experimentally, given our still limited knowledge of their specific molecular machineries of biogenesis and release, as compared with other biophysically similar EVs. The MISEV2018 guidelines include tables and outlines of suggested protocols and steps to follow to document specific EV-associated functional activities. Finally, a checklist is provided with summaries of key points