Duality between Spin networks and the 2D Ising model

The goal of this paper is to exhibit a deep relation between the partition function of the Ising model on a planar trivalent graph and the generating series of the spin network evaluations on the same graph. We provide respectively a fermionic and a bosonic Gaussian integral formulation for each of these functions and we show that they are the inverse of each other (up to some explicit constants) by exhibiting a supersymmetry relating the two formulations. We investigate three aspects and applications of this duality. First, we propose higher order supersymmetric theories which couple the geometry of the spin networks to the Ising model and for which supersymmetric localization still holds. Secondly, after interpreting the generating function of spin network evaluations as the projection of a coherent state of loop quantum gravity onto the flat connection state, we find the probability distribution induced by that coherent state on the edge spins and study its stationary phase approximation. It is found that the stationary points correspond to the critical values of the couplings of the 2D Ising model, at least for isoradial graphs. Third, we analyze the mapping of the correlations of the Ising model to spin network observables, and describe the phase transition on those observables on the hexagonal lattice. This opens the door to many new possibilities, especially for the study of the coarse-graining and continuum limit of spin networks in the context of quantum gravity.Comment: 35 page

Nonlinear envelope equation for broadband optical pulses in quadratic media

We derive a nonlinear envelope equation to describe the propagation of broadband optical pulses in second order nonlinear materials. The equation is first order in the propagation coordinate and is valid for arbitrarily wide pulse bandwidth. Our approach goes beyond the usual coupled wave description of $\chi^{(2)}$ phenomena and provides an accurate modelling of the evolution of ultra-broadband pulses also when the separation into different coupled frequency components is not possible or not profitable

Flexible investment planning for water distribution networks

Abstract The present work focuses on the planning of water distribution networks (WDNs). The research proposes an innovative strategy which aims at helping water managers formulate flexible investment plans while allowing for adaptive management under the increasing unawareness of medium–long term planning. This innovative strategy differs from existing strategies accounting for flexibility in WDN design. It allows for developing flexible investment plans without assuming that statistic or deterministic assumptions can account for all unawareness. The strategy introduces the key idea of technical contiguity of actions/solutions by post-processing a Pareto front obtained by a classic optimization technique in order to obtain sequential actions. This means retrieval of a set of 'technically contiguous' actions from the Paretian solutions, namely, by increasing the investment each action needs to contain the previous one. The application to the Apulian network allows discussion of the need for post-processing the Pareto front of solutions returned by the classic multi-objective design optimization and presenting the general strategy to obtain adaptive and flexible investment plans. We discuss further perspectives of the proposed strategy based on the integration of different flexible plans, each obtained with different assumptions, which could be statistic or deterministic, for the system boundary conditions

Non semi-simple sl(2) quantum invariants, spin case

Invariants of 3-manifolds from a non semi-simple category of modules over a version of quantum sl(2) were obtained by the last three authors in [arXiv:1404.7289]. In their construction the quantum parameter $q$ is a root of unity of order $2r$ where $r>1$ is odd or congruent to $2$ modulo $4$. In this paper we consider the remaining cases where $r$ is congruent to zero modulo $4$ and produce invariants of $3$-manifolds with colored links, equipped with generalized spin structure. For a given $3$-manifold $M$, the relevant generalized spin structures are (non canonically) parametrized by $H^1(M;\mathbb C/2\mathbb Z)$.Comment: 13 pages, 16 figure

New Multifunctional Lanthanide and Zr(IV) Phosphonates Derived from the 5-(dihydroxyphosphoryl) Isophthalate Ligand as Proton Conductors

Metal phosphonates are essentially acidic solids featured by groups such as P-OH, -COOH, etc. Moreover, the presence of coordination and lattice water molecules favors the formation of H-bond networks, which make these compounds appropriate as proton conductors, attractive for proton exchange membranes (PEMs) of fuel Cells.1 We report here, general characteristics of metal phosphonate derivatives composed of the polyfunctional 5-(dihydroxyphosphoryl) isophthalate ligand2 and lanthanides or zirconium ions. In the case of the lanthanide derivatives, crystalline compounds were synthesized under hydrothermal conditions. Preliminary results suggest that at least three isostructural series of compounds are formed. One of them, with La3+ derivative as prototype, is characterized by an orthorhombic unit cell (a = 12.7745(6) Å, b = 11.8921(4) Å, c = 7.2193(5) Å). Pr3+, Eu3+ and Gd3+ compounds, displays a monoclinic unit cell likewise the Yb3+ solid, the latter exhibiting different crystallographic parameters. Zr(IV) = compound, with formula Zr[(HO3P-C6H3-(COO)2H)2]·8H2O; was obtained at 80 ºC in the presence of HF as mineralizing agent. This solid crystallizes in an orthorhombic unit cell (a = 21.9306 Å, b = 16.6169 Å, c = 3.6462 Å). All these compounds contain in their frameworks water molecules that contribute to the formation of H-bond networks, making them prone as proton conductor candidates. Structural and proton conductivity are underway.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. Plan Propio de Investigación de la UMA MAT2016-77648

The extension problem for partial Boolean structures in Quantum Mechanics

Alternative partial Boolean structures, implicit in the discussion of classical representability of sets of quantum mechanical predictions, are characterized, with definite general conclusions on the equivalence of the approaches going back to Bell and Kochen-Specker. An algebraic approach is presented, allowing for a discussion of partial classical extension, amounting to reduction of the number of contexts, classical representability arising as a special case. As a result, known techniques are generalized and some of the associated computational difficulties overcome. The implications on the discussion of Boole-Bell inequalities are indicated.Comment: A number of misprints have been corrected and some terminology changed in order to avoid possible ambiguitie

EOQ inventory model for perishable products under uncertainty

Perishable products require accurate inventory control models as their effect on operations management can be critical. This assumption is particularly relevant in highly uncertain and dynamic markets, as for the ones generated by the pandemic era. This paper presents an inventory control model for perishable items with a demand rate variable over time, and dependent on the inventory rate. The model also considers the potential for backlogging and lost sales. Imperfect product quality is included, and deterioration is modelled as a time-dependent variable. The framework envisages the possibility to define variables affected by uncertainty in terms of probability distribution functions, which are then jointly managed via a Monte Carlo simulation. This paper is intended to provide an analytical formulation to deal with uncertainty and time-dependent inventory functions to be used for a variety of perishable products. The formulation is designed to support decision-making for the identification of the optimal order quantity. A numerical example exemplifies the outcomes of the paper and provides a cost-based sensitivity analysis to understand the role of main parameters

Anodal tDCS and High-Frequency tRNS Targeting the Occipitotemporal Cortex Do Not Always Enhance Face Perception

There has been increasing interest in the utility of transcranial electrical stimulation as a tool to enhance cognitive abilities. In the domain of face perception, enhancements have been reported for both transcranial direct current stimulation (tDCS) and high-frequency transcranial random noise stimulation (tRNS) targeting the occipitotemporal cortex. In a series of two experiments, we attempted to replicate these findings for face identity perception, and extend on previous studies, to determine if similar enhancements are also observed for object and facial expression perception. In Experiment 1, using a single blind, between-subjects design in healthy volunteers (N = 53), we examined whether anodal tDCS over the occipitotemporal cortex enhanced performance on tasks involving perception of face identity, facial expression, and object stimuli, when compared to sham stimulation. We failed to replicate previous findings of enhanced performance on face and object perception, nor extend findings to facial expression perception. In Experiment 2, using a single blind, between-subjects design (N = 39), we examined the effect of high-frequency tRNS over the occipitotemporal cortex using the same three tasks employed in Experiment 1. We failed to replicate previous findings of enhanced face perception following high-frequency tRNS over the occipitotemporal cortex, relative to sham stimulation (although we used different stimulation parameters to that employed in a previous study). We also found no evidence of enhanced facial expression and object perception following high-frequency tRNS. The findings align with a growing body of studies that have failed to replicate previously reported enhancements following administration of tDCS and hint for different efficacy of, on first sight, related stimulation protocols. Future studies should explore the foundation of these differential effects in greater detail

The cardiac torsion as a sensitive index of heart pathology: A model study.

The torsional behaviour of the heart (i.e. the mutual rotation of the cardiac base and apex) was proved to be sensitive to alterations of some cardiovascular parameters, i.e. preload, afterload and contractility. Moreover, pathologies which affect the fibers architecture and cardiac geometry were proved to alter the cardiac torsion pattern. For these reasons, cardiac torsion represents a sensitive index of ventricular performance. The aim of this work is to provide further insight into physiological and pathological alterations of the cardiac torsion by means of computational analyses, combining a structural model of the two ventricles with simple lumped parameter models of both the systemic and the pulmonary circulations. Starting from diagnostic images, a 3D anatomy based geometry of the two ventricles was reconstructed. The myocytes orientation in the ventricles was assigned according to literature data and the myocardium was modelled as an anisotropic hyperelastic material. Both the active and the passive phases of the cardiac cycle were modelled, and different clinical conditions were simulated. The results in terms of alterations of the cardiac torsion in the presence of pathologies are in agreement with experimental literature data. The use of a computational approach allowed the investigation of the stresses and strains in the ventricular wall as well as of the global hemodynamic parameters in the presence of the considered pathologies. Furthermore, the model outcomes highlight how for specific pathological conditions, an altered torsional pattern of the ventricles can be present, encouraging the use of the ventricular torsion in the clinical practice.This is the author accepted manuscript. The final version is available from Elsevier via http://dx.doi.org/10.1016/j.jmbbm.2015.10.00

Anti-Angiogenic and Anti-Cancer Effects by Targeting the Protein Kinase G Type-Iα (PKG-Iα) Signaling Pathway and its Downstream Effects on Expression of Inhibitor of Apoptosis Proteins, C-IAP1, Livin and Survivin

Ovarian cancer is often difficult to treat because of the development of resistance to many of the currently-used therapeutic agents (i.e. chemoresistance). The progression and chemoresistance of ovarian cancer can involve tumor angiogenesis, the development of new blood vessels bringing more blood and nutrients to the growing tumor. Tumor angiogenesis also involves the vascular endothelium-induced stimulation of cancer cell growth (1) and the higher expression levels of certain “cell survival proteins”, such as the Inhibitor of Apoptosis Proteins (IAPs, including c-IAP1, Livin and Survivin), which are expressed in both the proliferating cancer cells (2, 3) and the vascular endothelial cells involved in tumor angiogenesis (4)