Asymptotics of the mean-field Heisenberg model

We consider the mean-field classical Heisenberg model and obtain detailed information about the total spin of the system by studying the model on a complete graph and sending the number of vertices to infinity. In particular, we obtain Cramer- and Sanov-type large deviations principles for the total spin and the empirical spin distribution and demonstrate a second-order phase transition in the Gibbs measures. We also study the asymptotics of the total spin throughout the phase transition using Stein's method, proving central limit theorems in the sub- and supercritical phases and a nonnormal limit theorem at the critical temperature.Comment: 44 page

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

The central limit problem for random vectors with symmetries

Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional random vectors with various types of symmetries. In particular, we obtain results for distributions which are coordinatewise symmetric, uniform in a regular simplex, or spherically symmetric. Our proofs are based on Stein's method of exchangeable pairs; as far as we know, this approach has not previously been used in convex geometry and we give a brief introduction to the classical method. The spherically symmetric case is treated by a variation of Stein's method which is adapted for continuous symmetries.Comment: AMS-LaTeX, uses xy-pic, 23 pages; v3: added new corollary to Theorem

Rate of convergence of linear functions on the unitary group

We study the rate of convergence to a normal random variable of the real and imaginary parts of Tr(AU), where U is an N x N random unitary matrix and A is a deterministic complex matrix. We show that the rate of convergence is O(N^{-2 + b}), with 0 <= b < 1, depending only on the asymptotic behaviour of the singular values of A; for example, if the singular values are non-degenerate, different from zero and O(1) as N -> infinity, then b=0. The proof uses a Berry-Esse'en inequality for linear combinations of eigenvalues of random unitary, matrices, and so appropriate for strongly dependent random variables.Comment: 34 pages, 1 figure; corrected typos, added remark 3.3, added 3 reference

Estudio farmacológico y fitoquímico de dos especies de salandra nativas de México

A pharmacological and phytochemical sreening study of two species of Solandra native of Mexico is reported due to their indigenous use in traditional medicine. Water extracts of flowers of S. nítida and barks of S. guerrerense have marked anticholinergic effectis inhibiting acetiylicholine induced contraction of the smooth muscle of isolated ileum of guinea pig and depressing EEG activity in rats after intraperitoneal injection. By gas chromatography and NMR spectrometry the prodomine is abundant in S. nítida flowers, vhile Hyoscyamine is the mayin alkaloid in S. guerrerense bark. The presence of these tropane alkaloids in Solandra extracts and popular use of the plants for ceremonial and medicinal procedures is discussed.Se realizó un screening farmacológico y fitoquírnico de dos especies de Solandra que se usan en México con propósitos medicinales y rituales. Los extractos de flores de S. nítida y de cortezas de S. guerrerense contienen escopolamina e hiosciamina respectivamente como alcaloides predominantes. El efecto anticolinérgico de los extractos acuosos de estas plantas se estudió en el íleon aislado del cobayo y su efecto sedante del sistema nervioso central en la rata implantada con electrodos y sometida a estímulos dolorosos. El uso como psicotrópico que se hace de estas especies se explica como una consecuencia de la intoxicación que producen los extractos administrados por vía oral. Se discute el papel de la acetilcolina y los alcaloides del tropano en la acción anestésica local atribuida a estas plantas

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

Microparticle-mediated transfer of the viral receptors CAR and CD46, and the CFTR channel in a CHO cell model confers new functions to target cells

Cell microparticles (MPs) released in the extracellular milieu can embark plasma membrane and intracellular components which are specific of their cellular origin, and transfer them to target cells. The MP-mediated, cell-to-cell transfer of three human membrane glycoproteins of different degrees of complexity was investigated in the present study, using a CHO cell model system. We first tested the delivery of CAR and CD46, two monospanins which act as adenovirus receptors, to target CHO cells. CHO cells lack CAR and CD46, high affinity receptors for human adenovirus serotype 5 (HAdV5), and serotype 35 (HAdV35), respectively. We found that MPs derived from CHO cells (MP-donor cells) constitutively expressing CAR (MP-CAR) or CD46 (MP-CD46) were able to transfer CAR and CD46 to target CHO cells, and conferred selective permissiveness to HAdV5 and HAdV35. In addition, target CHO cells incubated with MP-CD46 acquired the CD46-associated function in complement regulation. We also explored the MP-mediated delivery of a dodecaspanin membrane glycoprotein, the CFTR to target CHO cells. CFTR functions as a chloride channel in human cells and is implicated in the genetic disease cystic fibrosis. Target CHO cells incubated with MPs produced by CHO cells constitutively expressing GFP-tagged CFTR (MP-GFP-CFTR) were found to gain a new cellular function, the chloride channel activity associated to CFTR. Time-course analysis of the appearance of GFP-CFTR in target cells suggested that MPs could achieve the delivery of CFTR to target cells via two mechanisms: the transfer of mature, membrane-inserted CFTR glycoprotein, and the transfer of CFTR-encoding mRNA. These results confirmed that cell-derived MPs represent a new class of promising therapeutic vehicles for the delivery of bioactive macromolecules, proteins or mRNAs, the latter exerting the desired therapeutic effect in target cells via de novo synthesis of their encoded proteins

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

Heart-specific immune responses in an animal model of autoimmune-related myocarditis mitigated by an immunoproteasome inhibitor and genetic ablation

BACKGROUND: Immune checkpoint inhibitor (ICI) therapy is often accompanied by immune-related pathology, with an increasing occurrence of high-risk ICI-related myocarditis. Understanding the mechanisms involved in this side effect could enable the development of management strategies. In mouse models, immune checkpoints, such as PD-1, control the threshold of self-antigen responses directed against cardiac troponin I (TnI). Here, we aimed at identifying how the immunoproteasome, the main proteolytic machinery in immune cells harboring three distinct protease activities in the LMP2, LMP7 and MECL1 subunit, affects TnI-directed autoimmune pathology of the heart. METHODS: TnI-directed autoimmune myocarditis (TnI-AM), a CD4(+) T cell-mediated disease, was induced in mice lacking all three immunoproteasome subunits, triple-ip(-/-), or lacking either the LMP2 or LMP7 gene, by immunization with a cardiac TnI peptide. Alternatively, prior to induction of TnI-AM or after establishment of AM, mice were treated with the immunoproteasome inhibitor ONX 0914. Immune parameters defining heart-specific autoimmunity were investigated in both experimental TnI-AM and in two cases of ICI-related myocarditis. RESULTS: All immunoproteasome-deficient strains showed mitigated autoimmune-related cardiac pathology with less inflammation, lower pro-inflammatory and chemotactic cytokines, less IL-17 production, and reduced fibrosis formation. Protection from TnI-directed autoimmune heart pathology with improved cardiac function in LMP7(-/-) mice involved a changed balance between effector and regulatory CD4(+) T cells in the spleen, with CD4(+) T cells from LMP7(-/-) mice showing a higher expression of inhibitory PD-1 molecules. Blocked immunoproteasome proteolysis, by treatment of TLR2 and TLR7/8-engaged CD14(+) monocytes with ONX 0914, diminished pro-inflammatory cytokine responses, thereby reducing the boost for the expansion of self-reactive CD4(+) T cells. Correspondingly, in mice, ONX 0914 treatment reversed cardiac autoimmune pathology, preventing both the induction and progression of TnI-AM, when self-reactive CD4+ T cells were primed. The autoimmune signature during experimental TnI-AM, with high immunoproteasome expression, immunoglobulinG deposition, IL-17 production in heart tissue and TnI-directed humoral autoimmune responses, was also present in two cases of ICI-related myocarditis, thus demonstrating the activation of heart-specific autoimmune reactions by ICI therapy. CONCLUSIONS: By reversing heart-specific autoimmune responses, immunoproteasome inhibitors applied to a mouse model demonstrate their potential to aid in the management of autoimmune myocarditis in humans, possibly including cases with ICI-related heart-specific autoimmunity