Faces of matrix models

Partition functions of eigenvalue matrix models possess a number of very different descriptions: as matrix integrals, as solutions to linear and non-linear equations, as tau-functions of integrable hierarchies and as special-geometry prepotentials, as result of the action of W-operators and of various recursions on elementary input data, as gluing of certain elementary building blocks. All this explains the central role of such matrix models in modern mathematical physics: they provide the basic "special functions" to express the answers and relations between them, and they serve as a dream model of what one should try to achieve in any other field.Comment: 10 page

Calcium phosphate particles stimulate interleukin-1β release from human vascular smooth muscle cells: A role for spleen tyrosine kinase and exosome release

Aims: Calcium phosphate (CaP) particle deposits are found in several inflammatory diseases including atherosclerosis and osteoarthritis. CaP, and other forms of crystals and particles, can promote inflammasome formation in macrophages leading to caspase-1 activation and secretion of mature interleukin-1β (IL-1β). Given the close association of small CaP particles with vascular smooth muscle cells (VSMCs) in atherosclerotic fibrous caps, we aimed to determine if CaP particles affected pro-inflammatory signalling in human VSMCs. Methods and results: Using ELISA to measure IL-1β release from VSMCs, we demonstrated that CaP particles stimulated IL-1β release from proliferating and senescent human VSMCs, but with substantially greater IL-1β release from senescent cells; this required caspase-1 activity but not LPS-priming of cells. Potential inflammasome agonists including ATP, nigericin and monosodium urate crystals did not stimulate IL-1β release from VSMCs. Western blot analysis demonstrated that CaP particles induced rapid activation of spleen tyrosine kinase (SYK) (increased phospho-Y525/526). The SYK inhibitor R406 reduced IL-1β release and caspase-1 activation in CaP particle-treated VSMCs, indicating that SYK activation occurs upstream of and is required for caspase-1 activation. In addition, IL-1β and caspase-1 colocalised in intracellular endosome-like vesicles and we detected IL-1β in exosomes isolated from VSMC media. Furthermore, CaP particle treatment stimulated exosome secretion by VSMCs in a SYK-dependent manner, while the exosome-release inhibitor spiroepoxide reduced IL-1β release. Conclusions: CaP particles stimulate SYK and caspase-1 activation in VSMCs, leading to the release of IL-1β, at least in part via exosomes. These novel findings in human VSMCs highlight the pro-inflammatory and procalcific potential of microcalcification

Non-linear Integral Equations and Determinant Formulae of the Open XXZ Spin Chain

We derive a non-linear integral equation for the Bethe-ansatz solvable open XXZ spin chain of arbitrary length describing the lowest lying state with zero magnetization. For this case we show how to combine the integral representation with the known determinant formula of norms and scalar products.Comment: final versio

Dualities in Quantum Hall System and Noncommutative Chern-Simons Theory

We discuss different dualities of QHE in the framework of the noncommutative Chern-Simons theory. First, we consider the Morita or T-duality transformation on the torus which maps the abelian noncommutative CS description of QHE on the torus into the nonabelian commutative description on the dual torus. It is argued that the Ruijsenaars integrable many-body system provides the description of the QHE with finite amount of electrons on the torus. The new IIB brane picture for the QHE is suggested and applied to Jain and generalized hierarchies. This picture naturally links 2d $\sigma$-model and 3d CS description of the QHE. All duality transformations are identified in the brane setup and can be related with the mirror symmetry and S duality. We suggest a brane interpretation of the plateu transition in IQHE in which a critical point is naturally described by $SL(2,R)$ WZW model.Comment: 31 pages, 4 figure

Hadronic Invariant Mass Spectrum in B -> X_u l nu Decay with Lepton Energy Cut

We discuss the implications of charged lepton energy cut to the hadronic invariant mass spectrum in charmless semileptonic B decays. Charged-lepton energy cut is inevitable in order to remove secondary leptonic events such as b -> c, tau -> l, and to identify the chaged leptons at detectors experimentally. We consider three possible lepton energy cuts, E_l^{cuts} = 0.6,1.5,2.3 GeV, and found that with the most probable cuts E_l^{cut} = 1.5 GeV and M_X^{max} = 1.5~(1.86) GeV, 45 ~ 60 % ~(58 ~ 67 %) of decay events survive. Therefore, B -> X_u l nu decay events can be efficiently distinguished from B -> X_c l nu decay events. We also discuss the possible model dependence on the results.Comment: 19 pages, 3 figure

Ucma/GRP inhibits phosphate-induced vascular smooth muscle cell calcification via SMAD-dependent BMP signalling

Vascular calcification (VC) is the process of deposition of calcium phosphate crystals in the blood vessel wall, with a central role for vascular smooth muscle cells (VSMCs). VC is highly prevalent in chronic kidney disease (CKD) patients and thought, in part, to be induced by phosphate imbalance. The molecular mechanisms that regulate VC are not fully known. Here we propose a novel role for the mineralisation regulator Ucma/GRP (Upper zone of growth plate and Cartilage Matrix Associated protein/Gla Rich Protein) in phosphate-induced VSMC calcification. We show that Ucma/GRP is present in calcified atherosclerotic plaques and highly expressed in calcifying VSMCs in vitro. VSMCs from Ucma/GRP(-/-) mice showed increased mineralisation and expression of osteo/chondrogenic markers (BMP-2, Runx2, beta-catenin, p-SMAD1/5/8, ALP, OCN), and decreased expression of mineralisation inhibitor MGP, suggesting that Ucma/GRP is an inhibitor of mineralisation. Using BMP signalling inhibitor noggin and SMAD1/5/8 signalling inhibitor dorsomorphin we showed that Ucma/GRP is involved in inhibiting the BMP-2-SMAD1/5/8 osteo/chondrogenic signalling pathway in VSMCs treated with elevated phosphate concentrations. Additionally, we showed for the first time evidence of a direct interaction between Ucma/GRP and BMP-2. These results demonstrate an important role of Ucma/GRP in regulating osteo/chondrogenic differentiation and phosphate-induced mineralisation of VSMCs.NWO ZonMw [MKMD 40-42600-98-13007]; FCT [SFRH/BPD/70277/2010]info:eu-repo/semantics/publishedVersio

UK–Russia Researcher Links Workshop: extracellular vesicles – mechanisms of biogenesis and roles in disease pathogenesis, M.V. Lomonosov Moscow State University, Moscow, Russia, 1–5 March 2015

The UK–Russia extracellular vesicles (EVs) workshop was held at the Medical Center of the M.V. Lomonosov Moscow State University, Moscow, Russia, with 56 attendees from UK and Russian universities and research institutes. The program consisted of 6 research sessions and was focused on studies of EVs isolated from in vitro model systems or biological fluids, including blood and urine. The multidisciplinary program included presentations on mechanisms of EV biogenesis, the role of EVs in disease pathogenesis, the diagnostic value of EVs, including their quantitation and cargo load, as well as the clinical use of EVs in regenerative medicine. Methodological challenges imposed by the nanoscale size of EVs as well as targeted delivery approaches for therapeutics were considered in a separate session on technologies. The main aim of the workshop was to overview challenges confronting EV researchers and to facilitate knowledge exchange between researchers with different backgrounds and skills. Given the lack of definitive EV nomenclature, specific terms (exosomes or microvesicles) were only applied in the meeting report to studies that carried out full EV characterization, including differential ultracentrifugation isolation approaches, comprehensive protein marker characterization, and single vesicle analysis (electron microscopy and nanoparticle analysis), to ascertain EV size and morphology following the International Society for Extracellular Vesicles standardization recommendations (1,2). In studies where characterization was not conclusive, the term EV is used

K-Decompositions and 3d Gauge Theories

This paper combines several new constructions in mathematics and physics. Mathematically, we study framed flat PGL(K,C)-connections on a large class of 3-manifolds M with boundary. We define a space L_K(M) of framed flat connections on the boundary of M that extend to M. Our goal is to understand an open part of L_K(M) as a Lagrangian in the symplectic space of framed flat connections on the boundary, and as a K_2-Lagrangian, meaning that the K_2-avatar of the symplectic form restricts to zero. We construct an open part of L_K(M) from data assigned to a hypersimplicial K-decomposition of an ideal triangulation of M, generalizing Thurston's gluing equations in 3d hyperbolic geometry, and combining them with the cluster coordinates for framed flat PGL(K)-connections on surfaces. Using a canonical map from the complex of configurations of decorated flags to the Bloch complex, we prove that any generic component of L_K(M) is K_2-isotropic if the boundary satisfies some topological constraints (Theorem 4.2). In some cases this implies that L_K(M) is K_2-Lagrangian. For general M, we extend a classic result of Neumann-Zagier on symplectic properties of PGL(2) gluing equations to reduce the K_2-Lagrangian property to a combinatorial claim. Physically, we use the symplectic properties of K-decompositions to construct 3d N=2 superconformal field theories T_K[M] corresponding (conjecturally) to the compactification of K M5-branes on M. This extends known constructions for K=2. Just as for K=2, the theories T_K[M] are described as IR fixed points of abelian Chern-Simons-matter theories. Changes of triangulation (2-3 moves) lead to abelian mirror symmetries that are all generated by the elementary duality between N_f=1 SQED and the XYZ model. In the large K limit, we find evidence that the degrees of freedom of T_K[M] grow cubically in K.Comment: 121 pages + 2 appendices, 80 figures; Version 2: reorganized mathematical perspective, swapped Sections 3 and