A note about the isotropy groups of 22-plane bundles over closed surfaces

Let $\xi$ be a $2$-plane bundle over a closed surface $S$. The line bundles $\lambda$ over $S$ such that $\xi\otimes\lambda\cong\xi$ form a group $\mathcal{J}(\xi)$ (the isotropy group of $\xi$); the scope of this paper is to describe $\mathcal{J}(\xi)$

Zeta function regularization for a scalar field in a compact domain

We express the zeta function associated to the Laplacian operator on $S^1_r\times M$ in terms of the zeta function associated to the Laplacian on $M$, where $M$ is a compact connected Riemannian manifold. This gives formulas for the partition function of the associated physical model at low and high temperature for any compact domain $M$. Furthermore, we provide an exact formula for the zeta function at any value of $r$ when $M$ is a $D$-dimensional box or a $D$-dimensional torus; this allows a rigorous calculation of the zeta invariants and the analysis of the main thermodynamic functions associated to the physical models at finite temperature.Comment: 19 pages, no figures, to appear in J. Phys.

Spectral analysis and zeta determinant on the deformed spheres

We consider a class of singular Riemannian manifolds, the deformed spheres $S^N_k$, defined as the classical spheres with a one parameter family $g[k]$ of singular Riemannian structures, that reduces for $k=1$ to the classical metric. After giving explicit formulas for the eigenvalues and eigenfunctions of the metric Laplacian $\Delta_{S^N_k}$, we study the associated zeta functions $\zeta(s,\Delta_{S^N_k})$. We introduce a general method to deal with some classes of simple and double abstract zeta functions, generalizing the ones appearing in $\zeta(s,\Delta_{S^N_k})$. An application of this method allows to obtain the main zeta invariants for these zeta functions in all dimensions, and in particular $\zeta(0,\Delta_{S^N_k})$ and $\zeta'(0,\Delta_{S^N_k})$. We give explicit formulas for the zeta regularized determinant in the low dimensional cases, $N=2,3$, thus generalizing a result of Dowker \cite{Dow1}, and we compute the first coefficients in the expansion of these determinants in powers of the deformation parameter $k$.Comment: 1 figur

Dissecting the regulatory strategies of NF-kB RelA target genes in the inflammatory response reveals differential transactivation logics

Nuclear factor κB (NF-κB) RelA is the potent transcriptional activator of inflammatory response genes. We stringently defined a list of direct RelA target genes by integrating physical (chromatin immunoprecipitation sequencing [ChIP-seq]) and functional (RNA sequencing [RNA-seq] in knockouts) datasets. We then dissected each gene’s regulatory strategy by testing RelA variants in a primary-cell genetic-complementation assay. All endogenous target genes require RelA to make DNA-base-specific contacts, and none are activatable by the DNA binding domain alone. However, endogenous target genes differ widely in how they employ the two transactivation domains. Through model-aided analysis of the dynamic time-course data, we reveal the gene-specific synergy and redundancy of TA1 and TA2. Given that post-translational modifications control TA1 activity and intrinsic affinity for coactivators determines TA2 activity, the differential TA logics suggests context-dependent versus context-independent control of endogenous RelA-target genes. Although some inflammatory initiators appear to require co-stimulatory TA1 activation, inflammatory resolvers are a part of the NF-κB RelA core response

Black hole determinants and quasinormal modes

We derive an expression for functional determinants in thermal spacetimes as a product over the corresponding quasinormal modes. As simple applications we give efficient computations of scalar determinants in thermal AdS, BTZ black hole and de Sitter spacetimes. We emphasize the conceptual utility of our formula for discussing `1/N' corrections to strongly coupled field theories via the holographic correspondence.Comment: 28 pages. v2: slightly improved exposition, references adde

Irregular singularities in Liouville theory

Motivated by problems arising in the study of N=2 supersymmetric gauge theories we introduce and study irregular singularities in two-dimensional conformal field theory, here Liouville theory. Irregular singularities are associated to representations of the Virasoro algebra in which a subset of the annihilation part of the algebra act diagonally. In this paper we define natural bases for the space of conformal blocks in the presence of irregular singularities, describe how to calculate their series expansions, and how such conformal blocks can be constructed by some delicate limiting procedure from ordinary conformal blocks. This leads us to a proposal for the structure functions appearing in the decomposition of physical correlation functions with irregular singularities into conformal blocks. Taken together, we get a precise prediction for the partition functions of some Argyres-Douglas type theories on the four-sphere.Comment: 84 pages, 6 figure

Small Polarons in Transition Metal Oxides

The formation of polarons is a pervasive phenomenon in transition metal oxide compounds, with a strong impact on the physical properties and functionalities of the hosting materials. In its original formulation the polaron problem considers a single charge carrier in a polar crystal interacting with its surrounding lattice. Depending on the spatial extension of the polaron quasiparticle, originating from the coupling between the excess charge and the phonon field, one speaks of small or large polarons. This chapter discusses the modeling of small polarons in real materials, with a particular focus on the archetypal polaron material TiO2. After an introductory part, surveying the fundamental theoretical and experimental aspects of the physics of polarons, the chapter examines how to model small polarons using first principles schemes in order to predict, understand and interpret a variety of polaron properties in bulk phases and surfaces. Following the spirit of this handbook, different types of computational procedures and prescriptions are presented with specific instructions on the setup required to model polaron effects.Comment: 36 pages, 12 figure

Localised analytic torsion and relative analytic torsion for non compact Lie groups of type I

Let $G$ be a (non compact) connected simply connected locally compact second countable Lie group, either abelian or unimodular of type I, and $\rho$ an irreducible unitary representation of $G$. Then, we define the analytic torsion of $G$ localised at the representation $\rho$. Next, let $\Gamma$ a discrete cocompact subgroup of $G$. We use the localised analytic torsion to define the relative analytic torsion of the pair $(G,\Gamma)$, and we prove that it coincides with the Lott $L^2$ analytic torsion of a covering space. We illustrate these constructions analysing in some details two examples: the abelian case, and the case $G=H$, the Heisenberg group

A NEW HANDHELD SCANNER FOR 3D SURVEY OF SMALL ARTIFACTS: THE STONEX F6

Movable heritage preserved in our museums are an invaluable evidence of our past. In order to properly respond to the need of 3D documentation of these significant assets, in the last few years both range-based and image-based solutions have been developed by researchers operating in the framework of Geomatics with a special focus on reaching a high level of detail and on texture radiometric quality, taking into consideration the intrinsic fragility of these kinds of objects which during the survey require a contactless approach. During the presented research a collection of architectural models representing ancient Nubian temples from “Museo Egizio di Torino” had been digitalized using different techniques; in particular, the wooden maquette of the temple of El-Hilla has been acquired using a new structured light handheld laser scanner, the Stonex F6 SR, and applying a close-range photogrammetric approach. In this paper a comparison between the two approaches is proposed as regards acquisition workflow, final results and suitability as regards digitisation of objects belonging to movable heritage and museum collections