Weak violation of universality for Polyelectrolyte Chains: Variational Theory and Simulations

A variational approach is considered to calculate the free energy and the conformational properties of a polyelectrolyte chain in $d$ dimensions. We consider in detail the case of pure Coulombic interactions between the monomers, when screening is not present, in order to compute the end-to-end distance and the asymptotic properties of the chain as a function of the polymer chain length $N$. We find $R \simeq N^{\nu}(\log N)^{\gamma}$ where $\nu = \frac{3}{\lambda+2}$ and $\lambda$ is the exponent which characterize the long-range interaction $U \propto 1/r^{\lambda}$. The exponent $\gamma$ is shown to be non-universal, depending on the strength of the Coulomb interaction. We check our findings, by a direct numerical minimization of the variational energy for chains of increasing size $2^4<N<2^{15}$. The electrostatic blob picture, expected for small enough values of the interaction strength, is quantitatively described by the variational approach. We perform a Monte Carlo simulation for chains of length $2^4<N<2^{10}$. The non universal behavior of the exponent $\gamma$ previously derived within the variational method, is also confirmed by the simulation results. Non-universal behavior is found for a polyelectrolyte chain in $d=3$ dimension. Particular attention is devoted to the homopolymer chain problem, when short range contact interactions are present.Comment: to appear in European Phys. Journal E (soft matter

Polymer chain in a quenched random medium: slow dynamics and ergodicity breaking

The Langevin dynamics of a self - interacting chain embedded in a quenched random medium is investigated by making use of the generating functional method and one - loop (Hartree) approximation. We have shown how this intrinsic disorder causes different dynamical regimes. Namely, within the Rouse characteristic time interval the anomalous diffusion shows up. The corresponding subdiffusional dynamical exponents have been explicitly calculated and thoroughly discussed. For the larger time interval the disorder drives the center of mass of the chain to a trap or frozen state provided that the Harris parameter, $(\Delta/b^d) N^{2 - \nu d} \ge 1$, where $\Delta$ is a disorder strength, $b$ is a Kuhnian segment length, $N$ is a chain length and $\nu$ is the Flory exponent. We have derived the general equation for the non - ergodicity function $f(p)$ which characterizes the amplitude of frozen Rouse modes with an index $p = 2\pi j/N$. The numerical solution of this equation has been implemented and shown that the different Rouse modes freeze up at the same critical disorder strength $\Delta_c \sim N^{-\gamma}$ where the exponent $\gamma \approx 0.25$ and does not depend from the solvent quality.Comment: 17 pages, 6 figures, submitted to EPJB (condensed matter

The Fully Frustrated Hypercubic Model is Glassy and Aging at Large DD

We discuss the behavior of the fully frustrated hypercubic cell in the infinite dimensional mean-field limit. In the Ising case the system undergoes a glass transition, well described by the random orthogonal model. Under the glass temperature aging effects show clearly. In the $XY$ case there is no sign of a phase transition, and the system is always a paramagnet.Comment: Figures added in uufiles format, and epsf include

Replica Field Theory for Deterministic Models (II): A Non-Random Spin Glass with Glassy Behavior

We introduce and study a model which admits a complex landscape without containing quenched disorder. Continuing our previous investigation we introduce a disordered model which allows us to reconstruct all the main features of the original phase diagram, including a low $T$ spin glass phase and a complex dynamical behavior.Comment: 35 pages with uu figures, Roma 102

Myocarditis Mimicking an Acute Coronary Syndrome: A Case Related to Salmonella enteritis

Infective myocarditis is most commonly due to a viral infection; occasionally it has been related to bacteria. Gastrointestinal infections associated with myocarditis have only rarely been described in young people, and the pathogenesis is unclear. We report a case of myocarditis mimicking an acute coronary syndrome (ACS) in a patient hospitalized for fever and diarrhoea. Salmonella enteritidis was isolated from stool, and no other pathogens were found. The coronary angiography was normal, and there were not other coronary artery risk factors, other than hypertension. The patient was treated with ciprofloxacin, acetylsalicylate acid, and ramipril with rapid clinical improvement and normalization of cardiac abnormalities. Final diagnosis of Salmonella enteritis and related myocarditis was made based on clinical, laboratory, ECG and echocardiographical findings

Throughput-optimal Resource Allocation in LTE-Advanced with Distributed Antennas

Distributed antennas are envisaged for LTE-Advanced deployments in order to improve the coverage and increase the cell throughput. The latter in turn depends on how resources are allocated to the User Equipments (UEs) at the MAC layer. In this paper we discuss how to allocate resources to UEs so as to maximize the cell throughput, given that UEs may re-ceive from several antennas simultaneously. We first show that the problem is both NP-hard and APX-hard, i.e. no polynomial-time algorithm exists that approximates the opti-mum within a constant factor. Hence, we pro-pose and evaluate two polynomial-time heuristics whose complexity is feasible for practical purposes. Our simulative analysis shows that, in practical scenarios, the two heuristics are highly accurate

What makes spatial data big? A discussion on how to partition spatial data

The amount of available spatial data has significantly increased in the last years so that traditional analysis tools have become inappropriate to effectively manage them. Therefore, many attempts have been made in order to define extensions of existing MapReduce tools, such as Hadoop or Spark, with spatial capabilities in terms of data types and algorithms. Such extensions are mainly based on the partitioning techniques implemented for textual data where the dimension is given in terms of the number of occupied bytes. However, spatial data are characterized by other features which describe their dimension, such as the number of vertices or the MBR size of geometries, which greatly affect the performance of operations, like the spatial join, during data analysis. The result is that the use of traditional partitioning techniques prevents to completely exploit the benefit of the parallel execution provided by a MapReduce environment. This paper extensively analyses the problem considering the spatial join operation as use case, performing both a theoretical and an experimental analysis for it. Moreover, it provides a solution based on a different partitioning technique, which splits complex or extensive geometries. Finally, we validate the proposed solution by means of some experiments on synthetic and real datasets

Dynamical Behaviour of Low Autocorrelation Models

We have investigated the nature of the dynamical behaviour in low autocorrelation binary sequences. These models do have a glass transition $T_G$ of a purely dynamical nature. Above the glass transition the dynamics is not fully ergodic and relaxation times diverge like a power law $\tau\sim (T-T_G)^{-\gamma}$ with $\gamma$ close to $2$. Approaching the glass transition the relaxation slows down in agreement with the first order nature of the dynamical transition. Below the glass transition the system exhibits aging phenomena like in disordered spin glasses. We propose the aging phenomena as a precise method to determine the glass transition and its first order nature.Comment: 19 pages + 14 figures, LateX, figures uuencoded at the end of the fil