Spectral density method in quantum nonextensive thermostatistics and magnetic systems with long-range interactions

Motived by the necessity of explicit and reliable calculations, as a valid contribution to clarify the effectiveness and, possibly, the limits of the Tsallis thermostatistics, we formulate the Two-Time Green Functions Method in nonextensive quantum statistical mechanics within the optimal Lagrange multiplier framework, focusing on the basic ingredients of the related Spectral Density Method. Besides, to show how the SDM works we have performed, to the lowest order of approximation, explicit calculations of the low-temperature properties for a quantum $d$-dimensional spin-1/2 Heisenberg ferromagnet with long-range interactions decaying as $1/r^{p}$ ($r$ is the distance between spins in the lattice)Comment: Contribution to Next-SigmaPhi conference in Kolymbari, Crete, Greece, August 13-18, 2005, 9 page

Two-time Green's functions and spectral density method in nonextensive quantum statistical mechanics

We extend the formalism of the thermodynamic two-time Green's functions to nonextensive quantum statistical mechanics. Working in the optimal Lagrangian multipliers representation, the $q$-spectral properties and the methods for a direct calculation of the two-time $q$% -Green's functions and the related $q$-spectral density ($q$ measures the nonextensivity degree) for two generic operators are presented in strict analogy with the extensive ($q=1$) counterpart. Some emphasis is devoted to the nonextensive version of the less known spectral density method whose effectiveness in exploring equilibrium and transport properties of a wide variety of systems has been well established in conventional classical and quantum many-body physics. To check how both the equations of motion and the spectral density methods work to study the $q$-induced nonextensivity effects in nontrivial many-body problems, we focus on the equilibrium properties of a second-quantized model for a high-density Bose gas with strong attraction between particles for which exact results exist in extensive conditions. Remarkably, the contributions to several thermodynamic quantities of the $q$-induced nonextensivity close to the extensive regime are explicitly calculated in the low-temperature regime by overcoming the calculation of the $q$ grand-partition function.Comment: 48 pages, no figure

The Classical Spectral Density Method at Work: The Heisenberg Ferromagnet

In this article we review a less known unperturbative and powerful many-body method in the framework of classical statistical mechanics and then we show how it works by means of explicit calculations for a nontrivial classical model. The formalism of two-time Green functions in classical statistical mechanics is presented in a form parallel to the well known quantum counterpart, focusing on the spectral properties which involve the important concept of spectral density. Furthermore, the general ingredients of the classical spectral density method (CSDM) are presented with insights for systematic nonperturbative approximations to study conveniently the macroscopic properties of a wide variety of classical many-body systems also involving phase transitions. The method is implemented by means of key ideas for exploring the spectrum of elementary excitations and the damping effects within a unified formalism. Then, the effectiveness of the CSDM is tested with explicit calculations for the classical $d$-dimensional spin-$S$ Heisenberg ferromagnetic model with long-range exchange interactions decaying as $r^{-p}$ ($p>d$) with distance $r$ between spins and in the presence of an external magnetic field. The analysis of the thermodynamic and critical properties, performed by means of the CSDM to the lowest order of approximation, shows clearly that nontrivial results can be obtained in a relatively simple manner already to this lower stage. The basic spectral density equations for the next higher order level are also presented and the damping of elementary spin excitations in the low temperature regime is studied. The results appear in reasonable agreement with available exact ones and Monte Carlo simulations and this supports the CSDM as a promising method of investigation in classical many-body theory.Comment: Latex, 58 pages, 12 figure

Phase separation in coupled chaotic maps on fractal networks

The phase ordering dynamics of coupled chaotic maps on fractal networks are investigated. The statistical properties of the systems are characterized by means of the persistence probability of equivalent spin variables that define the phases. The persistence saturates and phase domains freeze for all values of the coupling parameter as a consequence of the fractal structure of the networks, in contrast to the phase transition behavior previously observed in regular Euclidean lattices. Several discontinuities and other features found in the saturation persistence curve as a function of the coupling are explained in terms of changes of stability of local phase configurations on the fractals.Comment: (4 pages, 4 Figs, Submitted to PRE

A SspI PCR-RFLP detecting a silent allele at the goat CSN2 locus

The comparison between the cDNA sequence obtained and the published sequences of the goat CSN2 alleles showed a new single nucleotide polymorphism (SNP) (transition C-T) at the 180th nucleotide of the ninth exon. This mutation, which took place at 124 nt from the polyadenylation site, identifies a silent allele at the CSN2 locus named CSN2 A1. Since the 9th exon C-T transition creates a SspI endonuclease restriction site, the SspI digestion of a PCR product of 360 bp spanning the 9th exon and flanking regions, would allow carriers for the presence of thymine to be identified. The allelic frequency of the CSN2 A1 allele, determined in 170 goats belonging to an undefined genetic type reared in the province of Naples (Italy), was 0.23 It has been observed that the sequences in the 3’ untranslated regions (UTR), proximal to the polyadenylation site, can affect the mechanism of mRNA deadenylation and degradation. Therefore, it is reasonable to hypothesize that the C-T transition might, directly or indirectly, influence the stability of the mRNA and, consequently, the amount of protein produced

Emergence and persistence of communities in coevolutionary networks

We investigate the emergence and persistence of communities through a recently proposed mechanism of adaptive rewiring in coevolutionary networks. We characterize the topological structures arising in a coevolutionary network subject to an adaptive rewiring process and a node dynamics given by a simple voterlike rule. We find that, for some values of the parameters describing the adaptive rewiring process, a community structure emerges on a connected network. We show that the emergence of communities is associated to a decrease in the number of active links in the system, i.e. links that connect two nodes in different states. The lifetime of the community structure state scales exponentially with the size of the system. Additionally, we find that a small noise in the node dynamics can sustain a diversity of states and a community structure in time in a finite size system. Thus, large system size and/or local noise can explain the persistence of communities and diversity in many real systems.Comment: 6 pages, 5 figures, Accepted in EPL (2014

Genetic polymorphism of goat CSN1S1 and CSN1S2 genes and their impact on milk composition

by means of selection based on parent genotyping at the DNA level it will be possible to obtain goat populations producing milk characterised by the absence of either as1-casein, or s2-casein or -casein. Such milk could be useful for specific technological processes of transformation or for specific nutritional or dietary purposes in order to attenuate the negative consequence of some metabolic deficiencies and allergies and to contribute to the prevention of some diseases Considering the remarkable quantitative polymorphism characterizing the main protein fractions encoding gene, some goat milk types are more similar to the woman milk and, therefore, could be used, with better results, in the human feeding. In fact, the woman milk possess particular characteristics. It is lacking in the -lactoglobulin fraction and it is characterized by a general low content in casein, in particular, as2 casein absence and as1 casein traces, similar to the milk produced by goats with genotype CSN1S2 0/0

A point mutation in the splice donor site of intron 7 in the as2-casein encoding gene of the Mediterranean River buffalo results in an allele-specific exon skipping

The CSN1S2 cDNA of 10 unrelated Mediterranean River Buffaloes reared in Southern Italy was amplified by RT-PCR, while the region from the 6th to the 8th exon of the CSN1S2 gene was amplified from genomic template. cDNA sequence comparisons showed that five individuals had a normal transcript only (named CSN1S2A), one had a deleted transcript only (named CSN1S2B), because of the splicing out of the 27-bp of exon 7, and the remaining four had a heterozygous pattern. Analysis of the genomic sequences revealed a FM865620: g.773G>C transversion that caused inactivation of the intron 7 splice donor site and, consequently, the allele-specific exon skipping characteristic of the CSN1S2B allele. The g.773G>C mutation creates a new AluI restriction site enabling a PCR– RFLP rapid genotyping assay. The cDNA sequences showed three additional exonic mutations forming an extended haplotype with the g.773G>C polymorphism: FM865618: c.459C>T, c.484A>T and c.568A>G homozygous and heterozygous respectively in the CSN1S2BB and CSN1S2AB buffaloes. The first is silent, while the remaining two are non-conservative (p.Ile162Phe and p.Thp200Ala respectively). The genotype frequencies (37 CSN1S2A/A, 15 CSN1S2A/B and one CSN1S2B/B) are in agreement with Hardy–Weinberg equilibrium, with the frequency of the deleted B allele being 0.16. The predicted bubaline as2B protein is 198 aa long instead of 207 aa and would also be characterized by the presence of Phe at position 147 and Ala at 185