One-loop diagrams in the Random Euclidean Matching Problem

The matching problem is a notorious combinatorial optimization problem that has attracted for many years the attention of the statistical physics community. Here we analyze the Euclidean version of the problem, i.e. the optimal matching problem between points randomly distributed on a $d$-dimensional Euclidean space, where the cost to minimize depends on the points' pairwise distances. Using Mayer's cluster expansion we write a formal expression for the replicated action that is suitable for a saddle point computation. We give the diagrammatic rules for each term of the expansion, and we analyze in detail the one-loop diagrams. A characteristic feature of the theory, when diagrams are perturbatively computed around the mean field part of the action, is the vanishing of the mass at zero momentum. In the non-Euclidean case of uncorrelated costs instead, we predict and numerically verify an anomalous scaling for the sub-sub-leading correction to the asymptotic average cost.Comment: 17 pages, 7 figure

Scaling hypothesis for the Euclidean bipartite matching problem

We propose a simple yet very predictive form, based on a Poisson's equation, for the functional dependence of the cost from the density of points in the Euclidean bipartite matching problem. This leads, for quadratic costs, to the analytic prediction of the large $N$ limit of the average cost in dimension $d=1,2$ and of the subleading correction in higher dimension. A non-trivial scaling exponent, $\gamma_d=\frac{d-2}{d}$, which differs from the monopartite's one, is found for the subleading correction. We argue that the same scaling holds true for a generic cost exponent in dimension $d>2$.Comment: 11 page

Finite size corrections to disordered Ising models on Random Regular Graphs

We derive the analytical expression for the first finite size correction to the average free energy of disordered Ising models on random regular graphs. The formula can be physically interpreted as a weighted sum over all non self-intersecting loops in the graph, the weight being the free-energy shift due to the addition of the loop to an infinite tree

Loop expansion around the Bethe approximation through the MM-layer construction

For every physical model defined on a generic graph or factor graph, the Bethe $M$-layer construction allows building a different model for which the Bethe approximation is exact in the large $M$ limit and it coincides with the original model for $M=1$. The $1/M$ perturbative series is then expressed by a diagrammatic loop expansion in terms of so-called fat-diagrams. Our motivation is to study some important second-order phase transitions that do exist on the Bethe lattice but are either qualitatively different or absent in the corresponding fully connected case. In this case the standard approach based on a perturbative expansion around the naive mean field theory (essentially a fully connected model) fails. On physical grounds, we expect that when the construction is applied to a lattice in finite dimension there is a small region of the external parameters close to the Bethe critical point where strong deviations from mean-field behavior will be observed. In this region, the $1/M$ expansion for the corrections diverges and it can be the starting point for determining the correct non-mean-field critical exponents using renormalization group arguments. In the end, we will show that the critical series for the generic observable can be expressed as a sum of Feynman diagrams with the same numerical prefactors of field theories. However, the contribution of a given diagram is not evaluated associating Gaussian propagators to its lines as in field theories: one has to consider the graph as a portion of the original lattice, replacing the internal lines with appropriate one-dimensional chains, and attaching to the internal points the appropriate number of infinite-size Bethe trees to restore the correct local connectivity of the original model

NUCLEAR SAFETY OF RBMK REACTORS

This PhD thesis is evaluating the safety level of the graphite-moderated boiling water cooled nuclear power reactors (RBMK reactors) by the use of best estimate three dimensional neutron kinetics coupled thermal-hydraulics codes. The availability of such sophisticated tools has allowed detailed and realistic analyses of these kind of reactors, also known as “Chernobyl-type” reactors. Chernobyl is the name of a RBMK reactor where, in 1986, a severe accident occurred, leading to the destruction of the plant and to a major release of radioactivity into the environment. Parts of the activities of this PhD thesis were developed in the framework of the European Union funded TACIS Project R2.03/97 “Software development for the RBMK and WWER reactors”. This project was awarded to the “Gruppo di Ricerca Nucleare San Piero a Grado” of the University of Pisa and managed by it in collaboration with the RBMK designers (NIKIET, Kurchatov Insititute) and the licensee (RosEnergoAtom, now EnergoAtom Concern OJSC). The research activities dealt with the development and the validation of a sophisticated thermal-hydraulic nodalization of the Smolensk-3 Nuclear Power Plant. This thermal-hydraulic model was then coupled with a three dimensional neutron kinetics model of the core. The code used was RELAP5-3D system code. Suitable RBMK cross sections libraries were developed in collaboration with the Pennsylvania State University, using the deterministic lattice physics code HELIOS. After the validation of the developed models, the most relevant transients for the plant safety at full power were calculated, e.g. the group distribution header rupture, the break of the control and protection system cooling circuit. A special emphasis was put in the simulation of the single fuel channel transient, using also the Monte Carlo code MCNP5. The last part of the PhD activities concerned the analysis of a low power transient. In particular, the Chernobyl extreme scenario was reconstructed. Xenon fuel cell cross sections were calculated using the deterministic transport code DRAGON. Finally, all the analyses performed in the framework of this PhD confirmed the upgraded level of nuclear safety of the RBMK reactors, obtained also as a consequence of the relevant hardware modifications implemented in the aftermath of the Chernobyl accident

Bell lysaker emotion recognition test: a contribution for the italian validation

INTRODUCTION: Emotion recognition deficits in psychopathology have been extensively studied with a variety of measures. The Bell Lysaker Emotion Recognition Test (BLERT; Bell et al., 1997) is an effective method to assess emotion recognition by presenting affect stimuli which may have greater verisimilitude with real life events. Indeed, BLERT combines facial expressions with affective information transmitted in prosody or body posture. This method has allowed the study of emotion recognition deficit in psychotic patients, as well as its relationships with other aspects of psychopathology (Vohs et al., 2014). OBJECTIVES: We aimed at testing the validity and reliability of an Italian version of the BLERT. AIMS: First, a group-comparison was carried out between clinical and nonclinical participants. Then, correlations among BLERT scores and other indices of psychological functioning were explored. METHODS: We recruited 12 inpatients with psychotic disorders (mean age= 54.75; 58.3% female) and 45 nonclinical participants (mean age= 24.04; 75.6% female). We administered the BLERT (Bell et al., 1997), along with the following measures: Empathy Quotient (Lawrence et al., 2004), Interpersonal Reactivity Index (Davis, 1980), Difficulties in Emotion Regulation Scale (Gratz & Roemer, 2004), and the Inventory of Interpersonal Problems-47 (Pilkonis et al., 1996). RESULTS: Clinical participants resulted impaired in all indices of the BLERT. Further, the construct validity of the BLERT was confirmed by associations with measures of empathy, emotion dysregulation, and interpersonal problems. CONCLUSIONS: The use of the Italian version of the BLERT seemed promising for the study of emotion recognition in both clinical and nonclinical samples

La Camera Oscura: teorie e metafore della coscienza nella filosofia del seicento

Nella mia tesi ho analizzato lo sviluppo del concetto filosofico di coscienza nella filosofia del seicento, allo scopo di mostrare come la prima, compiuta, articolazione di questo concetto non si possa reperire in Cartesio, come vorrebbe la storiografia tradizionale, ma piuttosto nell'opera di John Locke. Pertanto, muovendo da un'analisi dei testi cartesiani ho mostrato come la stessa struttura concettuale della sua filosofia impedisse la nascita di un concetto di coscienza inteso nei termini di ciò che caratterizza propriamente lo spazio del mentale e, dunque, concetto chiave per lo sviluppo di un sapere sull'interiorità che si vuole scientifico e rigoroso: in altri termini non in Cartesio ma in alcuni problemi che emergono all'interno della sua filosofia - in particolare la questione del rapporto tra la mente e il corpo - determineranno, nell'opera dei suoi successori, un ricorso massivo a tale concetto. Si è trattato, dunque, in secondo luogo, di analizzare il dibattito post-cartesiano, con particolare attenzione per le figure di La Forge, Malebranche e Arnauld, per cogliere le tensioni al cui intenro il concetto di coscienza trova la sua matrice. Si è analizzato il ricorso malebranchiano alla "coscienza" per descrivere un originario fenomeno di occultamento e di oscurità della mente a se stessa allo scopo però di evidenziare come il tenore dell'opera dell'oratoriano fosse ancora quello "morale" legato al dibattito della Riforma e non quello, propriamente epistemologico, elaborato da Locke. Analizzando alcune questioni centrali della tradizione empirista inglese e in particolare, di Bacone, si è cercato di delineare il contesto al cui interno Locke ha proposto la sua innovativa teoria della coscienza. In particolare la messa tra parentesi delle questioni propriamente metafisiche sulla sostanzialità dell'anima, ha reso disponibile il concetto di coscienza per la descrizione e la definizione dell'identità personal

Quantum Pattern Retrieval by Qubit Networks with Hebb Interactions

Qubit networks with long-range interactions inspired by the Hebb rule can be used as quantum associative memories. Starting from a uniform superposition, the unitary evolution generated by these interactions drives the network through a quantum phase transition at a critical computation time, after which ferromagnetic order guarantees that a measurement retrieves the stored memory. The maximum memory capacity p of these qubit networks is reached at a memory density p/n=1.Comment: To appear in Physical Review Letter

The Random Fractional Matching Problem

We consider two formulations of the random-link fractional matching problem, a relaxed version of the more standard random-link (integer) matching problem. In one formulation, we allow each node to be linked to itself in the optimal matching configuration. In the other one, on the contrary, such a link is forbidden. Both problems have the same asymptotic average optimal cost of the random-link matching problem on the complete graph. Using a replica approach and previous results of W\"{a}stlund [Acta Mathematica 204, 91-150 (2010)], we analytically derive the finite-size corrections to the asymptotic optimal cost. We compare our results with numerical simulations and we discuss the main differences between random-link fractional matching problems and the random-link matching problem.Comment: 24 pages, 3 figure