Functional Renormalisation Group Approach for Tensorial Group Field Theory: a Rank-3 Model

We set up the Functional Renormalisation Group formalism for Tensorial Group Field Theory in full generality. We then apply it to a rank-3 model over U(1) x U(1) x U(1), endowed with a linear kinetic term and nonlocal interactions. The system of FRG equations turns out to be non-autonomous in the RG flow parameter. This feature is explained by the existence of a hidden scale, the radius of the group manifold. We investigate in detail the opposite regimes of large cut-off (UV) and small cut-off (IR) of the FRG equations, where the system becomes autonomous, and we find, in both case, Gaussian and non-Gaussian fixed points. We derive and interpret the critical exponents and flow diagrams associated with these fixed points, and discuss how the UV and IR regimes are matched at finite N. Finally, we discuss the evidence for a phase transition from a symmetric phase to a broken or condensed phase, from an RG perspective, finding that this seems to exist only in the approximate regime of very large radius of the group manifold, as to be expected for systems on compact manifolds.Comment: 27 pages, 14 figures; v2: some clarifications added, minor changes, matches published versio

Hecke cycles on moduli of vector bundles and orbital degeneracy loci

Given a smooth genus two curve $C$, the moduli space SU$_C(3)$ of rank three semi-stable vector bundles on $C$ with trivial determinant is a double cover in $\mathbb{P}^8$ branched over a sextic hypersurface, whose projective dual is the famous Coble cubic, the unique cubic hypersurface that is singular along the Jacobian of $C$. In this paper we continue our exploration of the connections of such moduli spaces with the representation theory of $GL_9$, initiated in \cite{GSW} and pursued in \cite{GS, sam-rains1, sam-rains2, bmt}. Starting from a general trivector $v$ in $\wedge^3\mathbb{C}^9$, we construct a Fano manifold $D_{Z_{10}}(v)$ in $G(3,9)$ as a so-called orbital degeneracy locus, and we prove that it defines a family of Hecke lines in SU$_C(3)$. We deduce that $D_{Z_{10}}(v)$ is isomorphic to the odd moduli space SU$_C(3, \mathcal{O}_C(c))$ of rank three stable vector bundles on $C$ with fixed effective determinant of degree one. We deduce that the intersection of $D_{Z_{10}}(v)$ with a general translate of $G(3,7)$ in $G(3,9)$ is a K3 surface of genus $19$

In silico screening of mutational effects on enzyme-proteic inhibitor affinity: a docking-based approach

<p>Abstract</p> <p>Background</p> <p>Molecular recognition between enzymes and proteic inhibitors is crucial for normal functioning of many biological pathways. Mutations in either the enzyme or the inhibitor protein often lead to a modulation of the binding affinity with no major alterations in the 3D structure of the complex.</p> <p>Results</p> <p>In this study, a rigid body docking-based approach has been successfully probed in its ability to predict the effects of single and multiple point mutations on the binding energetics in three enzyme-proteic inhibitor systems. The only requirement of the approach is an accurate structural model of the complex between the wild type forms of the interacting proteins, with the assumption that the architecture of the mutated complexes is almost the same as that of the wild type and no major conformational changes occur upon binding. The method was applied to 23 variants of the ribonuclease inhibitor-angiogenin complex, to 15 variants of the barnase-barstar complex, and to 8 variants of the bovine pancreatic trypsin inhibitor-β Trypsin system, leading to thermodynamic and kinetic estimates consistent with in vitro data. Furthermore, simulations with and without explicit water molecules at the protein-protein interface suggested that they should be included in the simulations only when their positions are well defined both in the wild type and in the mutants and they result to be relevant for the modulation of mutational effects on the association process.</p> <p>Conclusion</p> <p>The correlative models built in this study allow for predictions of mutational effects on the thermodynamics and kinetics of association of three substantially different systems, and represent important extensions of our computational approach to cases in which it is not possible to estimate the absolute free energies. Moreover, this study is the first example in the literature of an extensive evaluation of the correlative weights of the single components of the ZDOCK score on the thermodynamics and kinetics of binding of protein mutants compared to the native state.</p> <p>Finally, the results of this study corroborate and extend a previously developed quantitative model for in silico predictions of absolute protein-protein binding affinities spanning a wide range of values, i.e. from -10 up to -21 kcal/mol.</p> <p>The computational approach is simple and fast and can be used for structure-based design of protein-protein complexes and for in silico screening of mutational effects on protein-protein recognition.</p

An albumin-derived peptide scaffold capable of binding and catalysis

We have identified a 101-amino-acid polypeptide derived from the sequence surrounding the IIA binding site of human albumin. The polypeptide contains residues that make contact with ligands as warfarin in the parent protein, and eight cysteine residues to form disulfide bridges, which stabilize the polypeptide structure. Seventy-four amino acids are located in six [alpha]-helical regions, with the remaining amino acids forming six connecting coil/loop regions. Codon usage optimization was used to express a GST fusion protein in E. coli in yields as high as 4 mg/l. This fusion protein retains its structural integrity and aldolase activity, the ability to direct the stereochemical outcome of a diketone reduction, and its binding capacity to warfarin and efavirenz. Notably, this newly cloned polypeptide represents a valuable starting point for the construction of libraries of binders and catalysts with improved proficiency

Opposite effects of suicidality and lithium on gray matter volumes in bipolar depression

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Effect of early stress on hippocampal gray matter is influenced by a functional polymorphism in EAAT2 in bipolar disorder

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Widespread changes of white matter microstructure in obsessive-compulsive disorder: Effect of drug status.

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State-of-the-art of small-scale biomass gasification systems: An extensive and unique monitoring review

Abstract During the last few years, there has been an increasing interest in small-scale biomass gasification in Central and Northern Europe. Since 2011, almost fifty small-scale biomass gasification plants have been authorized and built in the South Tyrolean region (Italy), and most of them are currently operating. Within this framework, an extensive survey was performed by means of questionnaires to the plant owners for assessing the biomass and char flows in the region. Moreover, a comprehensive monitoring campaign was carried out onsite on representative plants of almost all the available operating technologies. For each of the monitored plants, the feedstock and the gasification products were characterized and their fluxes quantified, leading to energy and mass balances. This allowed collecting an extended set of data and drawing up a unique overview of the reference values for the ranges of operation of small-scale biomass gasification systems currently available in the European market, in terms of equivalence ratio, dry gas composition and heating value, specific electricity production, and conversion efficiencies. Moreover, samples of chars were deeply characterized, providing an insight into possible utilization pathways for the valorization of this by-product that is currently disposed of, representing an economical and environmental burden

Caudate Gray Matter Volume in Obsessive-Compulsive Disorder Is Influenced by Adverse Childhood Experiences and Ongoing Drug Treatment

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