Large Deviations of the Free-Energy in Diluted Mean-Field Spin-Glass

Sample-to-sample free energy fluctuations in spin-glasses display a markedly different behaviour in finite-dimensional and fully-connected models, namely Gaussian vs. non-Gaussian. Spin-glass models defined on various types of random graphs are in an intermediate situation between these two classes of models and we investigate whether the nature of their free-energy fluctuations is Gaussian or not. It has been argued that Gaussian behaviour is present whenever the interactions are locally non-homogeneous, i.e. in most cases with the notable exception of models with fixed connectivity and random couplings $J_{ij}=\pm \tilde{J}$. We confirm these expectation by means of various analytical results. In particular we unveil the connection between the spatial fluctuations of the populations of populations of fields defined at different sites of the lattice and the Gaussian nature of the free-energy fluctuations. On the contrary on locally homogeneous lattices the populations do not fluctuate over the sites and as a consequence the small-deviations of the free energy are non-Gaussian and scales as in the Sherrington-Kirkpatrick model

Spin glass transition in a magnetic field: a renormalization group study

We study the transition of short range Ising spin glasses in a magnetic field, within a general replica symmetric field theory, which contains three masses and eight cubic couplings, that is defined in terms of the fields representing the replicon, anomalous and longitudinal modes. We discuss the symmetry of the theory in the limit of replica number n to 0, and consider the regular case where the longitudinal and anomalous masses remain degenerate. The spin glass transitions in zero and non-zero field are analyzed in a common framework. The mean field treatment shows the usual results, that is a transition in zero field, where all the modes become critical, and a transition in non-zero field, at the de Almeida-Thouless (AT) line, with only the replicon mode critical. Renormalization group methods are used to study the critical behavior, to order epsilon = 6-d. In the general theory we find a stable fixed-point associated to the spin glass transition in zero field. This fixed-point becomes unstable in the presence of a small magnetic field, and we calculate crossover exponents, which we relate to zero-field critical exponents. In a finite magnetic field, we find no physical stable fixed-point to describe the AT transition, in agreement with previous results of other authors.Comment: 36 pages with 4 tables. To be published in Phys. Rev.

Analysis of the infinity-replica symmetry breaking solution of the Sherrington-Kirkpatrick model

In this work we analyse the Parisi's infinity-replica symmetry breaking solution of the Sherrington - Kirkpatrick model without external field using high order perturbative expansions. The predictions are compared with those obtained from the numerical solution of the infinity-replica symmetry breaking equations which are solved using a new pseudo-spectral code which allows for very accurate results. With this methods we are able to get more insight into the analytical properties of the solutions. We are also able to determine numerically the end-point x_{max} of the plateau of q(x) and find that lim_{T --> 0} x_{max}(T) > 0.5.Comment: 15 pages, 11 figures, RevTeX 4.

Multifractal Analysis of the Coupling Space of Feed-Forward Neural Networks

Random input patterns induce a partition of the coupling space of feed-forward neural networks into different cells according to the generated output sequence. For the perceptron this partition forms a random multifractal for which the spectrum $f(\alpha)$ can be calculated analytically using the replica trick. Phase transition in the multifractal spectrum correspond to the crossover from percolating to non-percolating cell sizes. Instabilities of negative moments are related to the VC-dimension.Comment: 10 pages, Latex, submitted to PR

On the scaling and ageing behaviour of the alternating susceptibility in spin glasses and local scale-invariance

The frequency-dependent scaling of the dispersive and dissipative parts of the alternating susceptibility is studied for spin glasses at criticality. An extension of the usual $\omega t$-scaling is proposed. Simulational data from the three-dimensional Ising spin glass agree with this new scaling form and moreover reproduce well the scaling functions explicitly calculated for systems satisfying local scale-invariance. There is also a qualitative agreement with existing experimental data.Comment: 19 pages, 2 figures, to appear in special issue of J. Phys. Cond. Matt. dedicated to Lothar Schaefer on the occasion of his 60th birthday, final form with IOP macro

Static chaos and scaling behaviour in the spin-glass phase

We discuss the problem of static chaos in spin glasses. In the case of magnetic field perturbations, we propose a scaling theory for the spin-glass phase. Using the mean-field approach we argue that some pure states are suppressed by the magnetic field and their free energy cost is determined by the finite-temperature fixed point exponents. In this framework, numerical results suggest that mean-field chaos exponents are probably exact in finite dimensions. If we use the droplet approach, numerical results suggest that the zero-temperature fixed point exponent $\theta$ is very close to $\frac{d-3}{2}$. In both approaches $d=3$ is the lower critical dimension in agreement with recent numerical simulations.Comment: 28 pages + 6 figures, LateX, figures uuencoded at the end of fil

The Phase Diagram of an Anisotropic Potts Model

A study is made of an anisotropic Potts model in three dimensions where the coupling depends on both the Potts state on each site but also the direction of the bond between them using both analytical and numerical methods. The phase diagram is mapped out for all values of the exchange interactions. Six distinct phases are identified. Monte Carlo simulations have been used to obtain the order parameter and the values for the energy and entropy in the ground state and also the transition temperatures. Excellent agreement is found between the simulated and analytic results. We find one region where there are two phase transitions with the lines meeting in a triple point. The orbital ordering that occurs in $LaMnO_3$ occurs as one of the ordered phases.Comment: 30 pages, 19 figures, one tabl

Resolving the homology-function relationship through comparative genomics of membrane-trafficking machinery and parasite cell biology

With advances in DNA sequencing technology, it is increasingly common and tractable to informatically look for genes of interest in the genomic databases of parasitic organisms and infer cellular states. Assignment of a putative gene function based on homology to functionally characterized genes in other organisms, though powerful, relies on the implicit assumption of functional homology, i.e. that orthology indicates conserved function. Eukaryotes reveal a dazzling array of cellular features and structural organization, suggesting a concomitant diversity in their underlying molecular machinery. Significantly, examples of novel functions for pre-existing or new paralogues are not uncommon. Do these examples undermine the basic assumption of functional homology, especially in parasitic protists, which are often highly derived? Here we examine the extent to which functional homology exists between organisms spanning the eukaryotic lineage. By comparing membrane trafficking proteins between parasitic protists and traditional model organisms, where direct functional evidence is available, we find that function is indeed largely conserved between orthologues, albeit with significant adaptation arising from the unique biological features within each lineage

Influence of socioeconomic factors on pregnancy outcome in women with structural heart disease

OBJECTIVE: Cardiac disease is the leading cause of indirect maternal mortality. The aim of this study was to analyse to what extent socioeconomic factors influence the outcome of pregnancy in women with heart disease.  METHODS: The Registry of Pregnancy and Cardiac disease is a global prospective registry. For this analysis, countries that enrolled ≥10 patients were included. A combined cardiac endpoint included maternal cardiac death, arrhythmia requiring treatment, heart failure, thromboembolic event, aortic dissection, endocarditis, acute coronary syndrome, hospitalisation for cardiac reason or intervention. Associations between patient characteristics, country characteristics (income inequality expressed as Gini coefficient, health expenditure, schooling, gross domestic product, birth rate and hospital beds) and cardiac endpoints were checked in a three-level model (patient-centre-country).  RESULTS: A total of 30 countries enrolled 2924 patients from 89 centres. At least one endpoint occurred in 645 women (22.1%). Maternal age, New York Heart Association classification and modified WHO risk classification were associated with the combined endpoint and explained 37% of variance in outcome. Gini coefficient and country-specific birth rate explained an additional 4%. There were large differences between the individual countries, but the need for multilevel modelling to account for these differences disappeared after adjustment for patient characteristics, Gini and country-specific birth rate.  CONCLUSION: While there are definite interregional differences in pregnancy outcome in women with cardiac disease, these differences seem to be mainly driven by individual patient characteristics. Adjustment for country characteristics refined the results to a limited extent, but maternal condition seems to be the main determinant of outcome

The development of emergency medical services benefit score: a European Delphi study

BackgroundThe helicopter emergency services (HEMS) Benefit Score (HBS) is a nine-level scoring system developed to evaluate the benefits of HEMS missions. The HBS has been in clinical use for two decades in its original form. Advances in prehospital care, however, have produced demand for a revision of the HBS. Therefore, we developed the emergency medical services (EMS) Benefit Score (EBS) based on the former HBS. As reflected by its name, the aim of the EBS is to measure the benefits produced by the whole EMS systems to patients.MethodsThis is a four-round, web-based, international Delphi consensus study with a consensus definition made by experts from seven countries. Participants reviewed items of the revised HBS on a 5-point Likert scale. A content validity index (CVI) was calculated, and agreement was defined as a 70% CVI. Study included experts from seven European countries. Of these, 18 were prehospital expert panellists and 11 were in-hospital commentary board members.ResultsThe first Delphi round resulted in 1248 intervention examples divided into ten diagnostic categories. After removing overlapping examples, 413 interventions were included in the second Delphi round, which resulted in 38 examples divided into HBS categories 3–8. In the third Delphi round, these resulted in 37 prehospital interventions, examples of which were given revised version of the score. In the fourth and final Delphi round, the expert panel was given an opportunity to accept or comment on the revised scoring system.ConclusionsThe former HBS was revised by a Delphi methodology and EBS developed to represent its structural purpose better. The EBS includes 37 exemplar prehospital interventions to guide its clinical use.Trial registration The study permission was requested and granted by Turku University Hospital (decision number TP2/010/18)