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

Linked Data approach for selection process automation in Systematic Reviews

Background: a systematic review identifies, evaluates and synthesizes the available literature on a given topic using scientific and repeatable methodologies. The significant workload required and the subjectivity bias could affect results. Aim: semi-automate the selection process to reduce the amount of manual work needed and the consequent subjectivity bias. Method: extend and enrich the selection of primary studies using the existing technologies in the field of Linked Data and text mining. We define formally the selection process and we also develop a prototype that implements it. Finally, we conduct a case study that simulates the selection process of a systematic literature published in literature. Results: the process presented in this paper could reduce the work load of 20% with respect to the work load needed in the fully manually selection, with a recall of 100%. Conclusions: the extraction of knowledge from scientific studies through Linked Data and text mining techniques could be used in the selection phase of the systematic review process to reduce the work load and subjectivity bia

Interacting dark energy from the joint analysis of the power spectrum and bispectrum multipoles with the EFTofLSS

Interacting dark energy models have been suggested as alternatives to the standard cosmological model, $\Lambda$CDM. We focus on a phenomenologically interesting class of dark scattering models that is characterised by pure momentum exchange between dark energy and dark matter. This model extends the parameter space with respect to $\Lambda$CDM by two parameters, $w$ and $A$, which define the dark energy equation of state and the strength of the coupling between dark energy and dark matter, respectively. In order to test non-standard cosmologies with Stage-IV galaxy clustering surveys, it is crucial to model mildly nonlinear scales and perform precision vs accuracy tests. We use the Effective Field Theory of Large-Scale Structure, and we perform validation tests by means of an MCMC analysis using a large set of N-body simulations. We find that adding the bispectrum monopole to the power spectrum multipoles improves the constraints on the dark energy parameters by $\sim 30 \%$ for $k_{\mathrm{max}, B}^{l=0} = 0.11$ $h$ Mpc$^{-1}$ without introducing biases in the parameter estimation. We also find that the same improvement can be achieved with more moderate scale cuts and the use of bias relations, or with the addition of the bispectrum quadrupole. Finally, we study degeneracies between the dark energy parameters and the scalar amplitude $A_\mathrm{s}$ and discuss the corresponding projection effects, as well as degeneracies with other cosmological parameters.Comment: 22 pages, 13 figures; V2: Matches version accepted for publication in MNRAS, includes a new analysis of degeneracies with cosmological parameter

Male breast cancer.

Male breast cancer (MaleBC) is a rare disease, accounting for <1% of all male tumors. During the last few years, there has been an increase in the incidence of this disease, along with the increase in female breast cancer (FBC). Little is known about the etiology of MaleBC: hormonal, environmental and genetic factors have been reported to be involved in its pathogenesis. Major risk factors include clinical disorders carrying hormonal imbalances, radiation exposure and, in particular, a positive family history (FH) for BC, the latter suggestive of genetic susceptibility. Rare mutations in high-penetrance genes (BRCA1 and BRCA2) confer a high risk of BC development; low-penetrance gene mutations (i.e. CHEK-2) are more common but involve a lower risk increase. About 90% of all male breast tumors have proved to be invasive ductal carcinomas, expressing high levels of hormone receptors with evident therapeutic returns. The most common clinical sign of BC onset in men is a painless palpable retroareolar lump, which should be evaluated by means of mammography, ultrasonography and core biopsy or fine needle aspiration (FNA). To date, there are no published data from prospective randomized trials supporting a specific therapeutic approach in MaleBC. Tumor size together with the number of axillary nodes involved are the main prognostic factors and should guide the treatment choice. Locoregional approaches include surgery and radiotherapy (RT), depending upon the initial clinical presentation. When systemic treatment (adjuvant, neoadjuvant and metastatic) is delivered, the choice between hormonal and or chemotherapy (CT) should depend upon the clinical and biological features, according to the FBC management guidelines. However great caution is required because of high rates of age-related comorbidities

A very fast inference algorithm for finite-dimensional spin glasses: Belief Propagation on the dual lattice

Starting from a Cluster Variational Method, and inspired by the correctness of the paramagnetic Ansatz (at high temperatures in general, and at any temperature in the 2D Edwards-Anderson model) we propose a novel message passing algorithm --- the Dual algorithm --- to estimate the marginal probabilities of spin glasses on finite dimensional lattices. We show that in a wide range of temperatures our algorithm compares very well with Monte Carlo simulations, with the Double Loop algorithm and with exact calculation of the ground state of 2D systems with bimodal and Gaussian interactions. Moreover it is usually 100 times faster than other provably convergent methods, as the Double Loop algorithm.Comment: 23 pages, 12 figures. v2: improved introductio