On invariants of graphs related to quantum sl(2)\mathfrak{sl}(2) at roots of unity

We show how to define invariants of graphs related to quantum $\mathfrak{sl}(2)$ when the graph has more then one connected component and components are colored by blocks of representations with zero quantum dimensions

Capabilities and Governance the Rebirth of Production in the Theory of Economic Organization

We argue that since Coase’s seminal 1937 paper on “The Nature of the Firm,” there has been an odd and unjustified separation between price theory and the economics of organization. For example, matters of production has been the domain of the former exclusively. However, a new approach to economic organization, here called “the capabilities approach,” that places production center-stage in the explanation of economic organization, is now emerging. We discuss the sources of this approach and its relation to the mainstream economics of organization.Capability, Theory of the Firm, Price Theory

Introduction to \u3ci\u3eThe Tragedy of Ukraine: What Classical Greek Tragedy Can Teach Us About Conflict Resolution\u3c/i\u3e

Introduction and table of contents to The Tragedy of Ukraine: What Classical Greek Tragedy Can Teach Us About Conflict Resolution by Nicolai N. Petro. Forthcoming, 2023

Entanglement generation in relativistic quantum fields

We present a general, analytic recipe to compute the entanglement that is generated between arbitrary, discrete modes of bosonic quantum fields by Bogoliubov transformations. Our setup allows the complete characterization of the quantum correlations in all Gaussian field states. Additionally, it holds for all Bogoliubov transformations. These are commonly applied in quantum optics for the description of squeezing operations, relate the mode decompositions of observers in different regions of curved spacetimes, and describe observers moving along non-stationary trajectories. We focus on a quantum optical example in a cavity quantum electrodynamics setting: an uncharged scalar field within a cavity provides a model for an optical resonator, in which entanglement is created by non-uniform acceleration. We show that the amount of generated entanglement can be magnified by initial single-mode squeezing, for which we provide an explicit formula. Applications to quantum fields in curved spacetimes, such as an expanding universe, are discussed.Comment: 8 pages, 2 figures, Ivette Fuentes previously published as Ivette Fuentes-Guridi and Ivette Fuentes-Schuller; v2: published version (online), to appear in the J. Mod. Opt. Special Issue on the Physics of Quantum Electronic

Optical properties of apple skin and flesh in the wavelength range from 350 to 2200 nm

Optical measurement of fruit quality is challenging due to the presence of a skin around the fruit flesh and the multiple scattering by the structured tissues. To gain insight in the light-tissue interaction, the optical properties of apple skin and flesh tissue are estimated in the 350-2200nm range for three cultivars. For this purpose, single integrating sphere measurements are combined with inverse adding- doubling. The observed absorption coefficient spectra are dominated by water in the near infrared and by pigments and chlorophyll in the visible region, whose concentrations are much higher in skin tissue. The scattering coefficient spectra show the monotonic decrease with increasing wavelength typical for biological tissues with skin tissue being approximately three times more scattering than flesh tissue. Comparison to the values from time-resolved spectroscopy reported in literature showed comparable profiles for the optical properties, but overestimation of the absorption coefficient values, due to light losses

Vacua of N=10 three dimensional gauged supergravity

We study scalar potentials and the corresponding vacua of N=10 three dimensional gauged supergravity. The theory contains 32 scalar fields parametrizing the exceptional coset space $\frac{E_{6(-14)}}{SO(10)\times U(1)}$. The admissible gauge groups considered in this work involve both compact and non-compact gauge groups which are maximal subgroups of $SO(10)\times U(1)$ and $E_{6(-14)}$, respectively. These gauge groups are given by $SO(p)\times SO(10-p)\times U(1)$ for $p=6,...10$, $SO(5)\times SO(5)$, $SU(4,2)\times SU(2)$, $G_{2(-14)}\times SU(2,1)$ and $F_{4(-20)}$. We find many AdS$_3$ critical points with various unbroken gauge symmetries. The relevant background isometries associated to the maximally supersymmetric critical points at which all scalars vanish are also given. These correspond to the superconformal symmetries of the dual conformal field theories in two dimensions.Comment: 37 pages no figures, typos corrected and a little change in the forma

Estimaci?n de par?metros para un modelo de regresi?n difusa simple

88 p. Recurso Electr?nic

Gradient Representations and Affine Structures in AE(n)

We study the indefinite Kac-Moody algebras AE(n), arising in the reduction of Einstein's theory from (n+1) space-time dimensions to one (time) dimension, and their distinguished maximal regular subalgebras sl(n) and affine A_{n-2}^{(1)}. The interplay between these two subalgebras is used, for n=3, to determine the commutation relations of the `gradient generators' within AE(3). The low level truncation of the geodesic sigma-model over the coset space AE(n)/K(AE(n)) is shown to map to a suitably truncated version of the SL(n)/SO(n) non-linear sigma-model resulting from the reduction Einstein's equations in (n+1) dimensions to (1+1) dimensions. A further truncation to diagonal solutions can be exploited to define a one-to-one correspondence between such solutions, and null geodesic trajectories on the infinite-dimensional coset space H/K(H), where H is the (extended) Heisenberg group, and K(H) its maximal compact subgroup. We clarify the relation between H and the corresponding subgroup of the Geroch group.Comment: 43 page

Modular domain-to-domain translation network

Domain-to-domain translation methods map images from a source domain to corresponding images from a target domain. The two domains contain images from the same classes, but these images look different. Recent approaches use generative adversarial networks in various configurations and architectures to perform the translation. By using GANs, they inevitably inherit their problems like training instability and mode collapse. We propose a novel approach to the problem that does not use a GAN. Instead, it relies on an hierarchical architecture that encapsulates information of the target domain by using individually trained networks. This hierarchical architecture is then trained as one unified deep network. Using this approach, we show that images from the original domain are translated to the target domain both for the case when there is a one-to-one correspondence between the images of the two domains and for the case that such correspondence information is absent. We visualize and evaluate the translation from one information domain to the other and discuss the proposed model's relation to the conditional generative adversarial networks. We further argue that deep learning can benefit from the proposed hierarchical architecture

Is Galactic Structure Compatible with Microlensing Data?

We generalize to elliptical models the argument of Kuijken (1997), which connects the microlensing optical depth towards the Galactic bulge to the Galactic rotation curve. When applied to the latest value from the MACHO collaboration for the optical depth for microlensing of bulge sources, the argument implies that the Galactic bar cannot plausibly reconcile the measured values of the optical depth, the rotation curve and the local mass density. Either there is a problem with the interpretation of the microlensing data, or our line of sight to the Galactic centre is highly atypical in that it passes through a massive structure that wraps only a small distance around the Galactic centre.Comment: Submitted to ApJ Letters. 8 pages LaTeX, 3 figures. Corrected error in description of microlensing observation