Data Accuracy Dependence on Number of Bins in Stochastic Series Expansion for Spin-1/2 Antiferromagnetic Heisenberg Chains

Background: Antiferromagnetic systems exhibit complex quantum behaviours that require accurate numerical methods to analyse. The Stochastic Series Expansion (SSE) is a quantum Monte Carlo technique that simulates these systems. This study examines the effect of the number of bins on the accuracy of physical property measurements using SSE. Materials and Methods: The SSE simulations were performed using Fortran 90 on a Ryzen 7 processor. The system was initialised with varying lattice sizes (64, 128, 256, and 1024) and dimensionless temperatures (1/32, 1/16, 1/2, and 4) to analyse different configurations. Nbins and Monte Carlo steps were adjusted systematically to investigate their impact on the results. Results were visualised in Origin Lab. Results: Increasing the number of bins (Nbins) reduced fluctuations, leading to reliable results, especially at low temperatures. Lower temperatures lead to higher fluctuations in susceptibility and specific heat of the system. The Neel temperatures were observed around dimensionless temperature.  Indicating phase transitions. Conclusions:   The study shows that Nbins are crucial for accurate results in SSE simulations. Although the method is effective for most properties, specific heat calculations require higher computational costs and present limitations in precision. &nbsp

Renormalization Group Approach to Generalized Cosmological models

We revisit here the problem of generalized cosmology using renormalization group approach. A complete analysis of these cosmologies, where specific models appear as asymptotic fixed-points, is given here along with their linearized stability analysis.Comment: 10 pages, to appear in the International Journal of Theoretical Physic

Chitosan-Graft-Branched Polyethylenimine Copolymers: Influence of Degree of Grafting on Transfection Behavior

BACKGROUND: Successful non-viral gene delivery currently requires compromises to achieve useful transfection levels while minimizing toxicity. Despite high molecular weight (MW) branched polyethylenimine (bPEI) is considered the gold standard polymeric transfectant, it suffers from high cytotoxicity. Inversely, its low MW counterpart is less toxic and effective in transfection. Moreover, chitosan is a highly biocompatible and biodegradable polymer but characterized by very low transfection efficiency. In this scenario, a straightforward approach widely exploited to develop effective transfectants relies on the synthesis of chitosan-graft-low MW bPEIs (Chi-g-bPEI(x)) but, despite the vast amount of work that has been done in developing promising polymeric assemblies, the possible influence of the degree of grafting on the overall behavior of copolymers for gene delivery has been largely overlooked. METHODOLOGY/PRINCIPAL FINDINGS: With the aim of providing a comprehensive evaluation of the pivotal role of the degree of grafting in modulating the overall transfection effectiveness of copolymeric vectors, we have synthesized seven Chi-g-bPEI(x) derivatives with a variable amount of bPEI grafts (minimum: 0.6%; maximum: 8.8%). Along the Chi-g-bPEI(x) series, the higher the degree of grafting, the greater the ζ-potential and the cytotoxicity of the resulting polyplexes. Most important, in all cell lines tested the intermediate degree of grafting of 2.7% conferred low cytotoxicity and higher transfection efficiency compared to other Chi-g-bPEI(x) copolymers. We emphasize that, in transfection experiments carried out in primary articular chondrocytes, Chi-g-bPEI(2.7%) was as effective as and less cytotoxic than the gold standard 25 kDa bPEI. CONCLUSIONS/SIGNIFICANCE: This work underlines for the first time the pivotal role of the degree of grafting in modulating the overall transfection effectiveness of Chi-g-bPEI(x) copolymers. Crucially, we have demonstrated that, along the copolymer series, the fine tuning of the degree of grafting directly affected the overall charge of polyplexes and, altogether, had a direct effect on cytotoxicity

Simulation of Postsynaptic Glutamate Receptors Reveals Critical Features of Glutamatergic Transmission

Activation of several subtypes of glutamate receptors contributes to changes in postsynaptic calcium concentration at hippocampal synapses, resulting in various types of changes in synaptic strength. Thus, while activation of NMDA receptors has been shown to be critical for long-term potentiation (LTP) and long term depression (LTD) of synaptic transmission, activation of metabotropic glutamate receptors (mGluRs) has been linked to either LTP or LTD. While it is generally admitted that dynamic changes in postsynaptic calcium concentration represent the critical elements to determine the direction and amplitude of the changes in synaptic strength, it has been difficult to quantitatively estimate the relative contribution of the different types of glutamate receptors to these changes under different experimental conditions. Here we present a detailed model of a postsynaptic glutamatergic synapse that incorporates ionotropic and mGluR type I receptors, and we use this model to determine the role of the different receptors to the dynamics of postsynaptic calcium with different patterns of presynaptic activation. Our modeling framework includes glutamate vesicular release and diffusion in the cleft and a glutamate transporter that modulates extracellular glutamate concentration. Our results indicate that the contribution of mGluRs to changes in postsynaptic calcium concentration is minimal under basal stimulation conditions and becomes apparent only at high frequency of stimulation. Furthermore, the location of mGluRs in the postsynaptic membrane is also a critical factor, as activation of distant receptors contributes significantly less to calcium dynamics than more centrally located ones. These results confirm the important role of glutamate transporters and of the localization of mGluRs in postsynaptic sites in their signaling properties, and further strengthen the notion that mGluR activation significantly contributes to postsynaptic calcium dynamics only following high-frequency stimulation. They also provide a new tool to analyze the interactions between metabotropic and ionotropic glutamate receptors

Hopf bifurcation analysis for a ratio-dependent predator-prey system involving two delays

The aim of this paper is to give a detailed analysis of Hopf bifurcation of a ratio-dependent predator–prey system involving two discrete delays. A delay parameter is chosen as the bifurcation parameter for the analysis. Stability of the bifurcating periodic solutions is determined by using the centre manifold theorem and the normal form theory introduced by Hassard et al. Some of the bifurcation properties including the direction, stability and period are given. Finally, our theoretical results are supported by some numerical simulations. doi:10.1017/S144618111400005

Hopf bifurcation analysis of a system of coupled delayed-differential equations

In this paper, we have considered a system of delay differential equations. The system without delayed arises in the Lengyel-Epstein model. Its dynamics are studied in terms of local analysis and Hopf bifurcation analysis. Linear stability is investigated and existence of Hopf bifurcation is demonstrated via analyzing the associated characteristic equation. For the Hopf bifurcation analysis, the delay parameter is chosen as a bifurcation parameter. The stability of the bifurcating periodic solutions is determined by using the center manifold theorem and the normal form theory introduced by Hassard et al. (1981) [7]. Furthermore, the direction of the bifurcation, the stability and the period of periodic solutions are given. Finally, the theoretical results are supported by some numerical simulations. (C) 2013 Elsevier Inc. All rights reserved