Dynamic heterogeneities in critical coarsening: Exact results for correlation and response fluctuations in finite-sized spherical models

We study dynamic heterogeneities in the out-of-equilibrium coarsening dynamics of the spherical ferromagnet after a quench from infinite temperature to its critical point. A standard way of probing such heterogeneities is by monitoring the fluctuations of correlation and susceptibility, coarse-grained over mesoscopic regions. We discuss how to define fluctuating coarse-grained correlations (C) and susceptibilities (Chi) in models where no quenched disorder is present. Our focus for the spherical model is on coarse-graining over the whole volume of $N$ spins, which requires accounting for N^{-1/2} non-Gaussian fluctuations of the spin. The latter are treated as a perturbation about the leading order Gaussian statistics. We obtain exact results for these quantities, which enable us to characterise the joint distribution of C and Chi fluctuations. We find that this distribution is qualitatively different, even for equilibrium above criticality, from the spin-glass scenario where C and Chi fluctuations are linked in a manner akin to the fluctuation-dissipation relation between the average C and Chi. Our results show that coarsening at criticality is clearly heterogeneous for d>4 and suggest that, as in other glassy systems, there is a well-defined timescale on which fluctuations across thermal histories are largest. Surprisingly, however, neither this timescale nor the amplitude of the heterogeneities increase with the age of the system, as would be expected from the growing correlation length. For d<4, the strength of the fluctuations varies on a timescale proportional to the age of the system; the corresponding amplitude also grows with age, but does not scale with the correlation volume as might have been expected naively.Comment: 39 pages, 9 figures, version for publication in J. Stat. Mech. Shortened by cutting all technical details in section 6, with minor corrections elsewher

Evolution of Binary Stars in Multiple-Population Globular Clusters - II. Compact Binaries

We present the results of a survey of N-body simulations aimed at exploring the evolution of compact binaries in multiple-population globular clusters.We show that as a consequence of the initial differences in the structural properties of the first-generation (FG) and the second-generation (SG) populations and the effects of dynamical processes on binary stars, the SG binary fraction decreases more rapidly than that of the FG population. The difference between the FG and SG binary fraction is qualitatively similar to but quantitatively smaller than that found for wider binaries in our previous investigations.The evolution of the radial variation of the binary fraction is driven by the interplay between binary segregation, ionization and ejection. Ionization and ejection counteract in part the effects of mass segregation but for compact binaries the effects of segregation dominate and the inner binary fraction increases during the cluster evolution. We explore the variation of the difference between the FG and the SG binary fraction with the distance from the cluster centre and its dependence on the binary binding energy and cluster structural parameters. The difference between the binary fraction in the FG and the SG populations found in our simulations is consistent with the results of observational studies finding a smaller binary fraction in the SG population.Comment: 9 pages, 12 figures. Accepted for publication in MNRA

Evolution of Binary Stars in Multiple-Population Globular Clusters

The discovery of multiple stellar populations in globular clusters has implications for all the aspects of the study of these stellar systems. In this paper, by means of N-body simulations, we study the evolution of binary stars in multiple-population clusters and explore the implications of the initial differences in the spatial distribution of different stellar populations for the evolution and survival of their binary stars. Our simulations show that initial differences between the spatial distribution of first-generation (FG) and second-generation (SG) stars can leave a fingerprint in the current properties of the binary population. SG binaries are disrupted more efficiently than those of the FG population resulting in a global SG binary fraction smaller than that of the FG. As for surviving binaries, dynamical evolution produces a difference between the SG and the FG binary binding energy distribution with the SG population characterized by a larger fraction of high binding energy (more bound) binaries. We have also studied the dependence of the binary properties on the distance from the cluster centre. Although the global binary fraction decreases more rapidly for the SG population, the local binary fraction measured in the cluster inner regions may still be dominated by SG binaries. The extent of the differences between the surviving FG and SG binary binding energy distribution also varies radially within the cluster and is larger in the cluster inner regions.Comment: 10 pages, 12 figures. Accepted for publication in MNRA

Coexistence of supersymmetric and supersymmetry-breaking states in spherical spin-glasses

The structure of states of the perturbed p-spin spherical spin-glass is analyzed. At low enough free energy metastable states have a supersymmetric structure, while at higher free energies the supersymmetry is broken. The transition between the supersymmetric and the supersymmetry-breaking phase is triggered by a change in the stability of states

Occurrence of exocrine pancreatic insufficiency in patients with advanced neuroendocrine tumors treated with somatostatin analogs

Background: Although exocrine pancreatic insufficiency (EPI) has been described in patients with neuroendocrine neoplasia (NEN) treated with somatostatin analogs (SSAs), its role in the therapeutic management of these patients is not well established. Aim: To determine the frequency of EPI in patients with NEN long-term treated with SSAs. Methods: This is a prospective single-center study evaluating 35 patients treated with SSAs for &gt;12 months due to unresectable/advanced nonpancreatic well-differentiated NEN. Clinical evaluation, biochemical parameters, and fecal elastases 1 (FE-1) were assessed to diagnose EPI. Results: A total of 7 patients (20%) had EPI, given the presence of abdominal symptoms and a median FE-1 value of 180 mcg/g stool (150–198). No patient had severe EPI, defined as FE-1 &lt; 100 mcg/g stool. Elevated glycated Hb levels were a significant predictor for developing EPI (OR 4.81, p = 0.01). No significant difference in terms of duration of SSA treatment was observed between patients with or without EPI diagnosed (84 months and 72 months, respectively; p = 0.950). Conclusions: Mild-moderate EPI is a relatively common condition in patients receiving long-term treatment with SSAs. Specific clinical and biochemical evaluations, including FE-1, should be planned in these patients to diagnose this relevant condition early, which may deteriorate quality of life and cause malnutrition

Tailored graph ensembles as proxies or null models for real networks I: tools for quantifying structure

We study the tailoring of structured random graph ensembles to real networks, with the objective of generating precise and practical mathematical tools for quantifying and comparing network topologies macroscopically, beyond the level of degree statistics. Our family of ensembles can produce graphs with any prescribed degree distribution and any degree-degree correlation function, its control parameters can be calculated fully analytically, and as a result we can calculate (asymptotically) formulae for entropies and complexities, and for information-theoretic distances between networks, expressed directly and explicitly in terms of their measured degree distribution and degree correlations.Comment: 25 pages, 3 figure

Relationship between Persistent Gastrointestinal Symptoms and Duodenal Histological Findings after Adequate Gluten-Free Diet. A Gray Area of Celiac Disease Management in Adult Patients

A gluten-free diet (GFD) leads to a rapid improvement in gastrointestinal (GI) symptoms, biochemical alterations and duodenal histological damage in the majority of celiac disease (CD) patients. This study aimed to assess the frequency and factors associated with the persistence of GI symptoms/malabsorption signs and their relationship with duodenal histological findings among CD patients on an adequate GFD (mean duration 16 months, range 12-28 months). This longitudinal cohort study included 102 adult CD patients (median age 38.5 years, range 18-76 years, F = 71.6%) diagnosed between 2012 and 2018. A total of 36.3% of the included patients had persistent GI symptoms and/or malabsorption signs (Group 1), while the remaining patients had complete GI well-being without malabsorption signs (Group 2) at the time of histological re-evaluation. The persistence of GI symptoms/signs was associated with a long duration of symptoms/signs before CD diagnosis (&gt;= 5 years) (OR 5.3; 95% CI 1.3-21.8) and the presence of constipation at the time of CD diagnosis (OR 7.5; 95% CI 1.3-42) while for other variables, including age at CD diagnosis, sex, duration of GFD, comorbidities, CD serology positivity and severity of duodenal damage at histological re-evaluation, no association was found. According to our results, the persistence of symptoms/signs is not associated with histological findings, and their relationship could be a gray area in CD management

Dynamic crossover in the global persistence at criticality

We investigate the global persistence properties of critical systems relaxing from an initial state with non-vanishing value of the order parameter (e.g., the magnetization in the Ising model). The persistence probability of the global order parameter displays two consecutive regimes in which it decays algebraically in time with two distinct universal exponents. The associated crossover is controlled by the initial value m_0 of the order parameter and the typical time at which it occurs diverges as m_0 vanishes. Monte-Carlo simulations of the two-dimensional Ising model with Glauber dynamics display clearly this crossover. The measured exponent of the ultimate algebraic decay is in rather good agreement with our theoretical predictions for the Ising universality class.Comment: 5 pages, 2 figure

Critical aging of a ferromagnetic system from a completely ordered state

We adapt the non-linear $\sigma$ model to study the nonequilibrium critical dynamics of O(n) symmetric ferromagnetic system. Using the renormalization group analysis in $d=2+\epsilon$ dimensions we investigate the pure relaxation of the system starting from a completely ordered state. We find that the average magnetization obeys the long-time scaling behavior almost immediately after the system starts to evolve while the correlation and response functions demonstrate scaling behavior which is typical for aging phenomena. The corresponding fluctuation-dissipation ratio is computed to first order in $\epsilon$ and the relation between transverse and longitudinal fluctuations is discussed.Comment: 5 pages, revtex