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

Finite-size scaling above the upper critical dimension in Ising models with long-range interactions

The correlation length plays a pivotal role in finite-size scaling and hyperscaling at continuous phase transitions. Below the upper critical dimension, where the correlation length is proportional to the system length, both finite-size scaling and hyperscaling take conventional forms. Above the upper critical dimension these forms break down and a new scaling scenario appears. Here we investigate this scaling behaviour in one-dimensional Ising ferromagnets with long-range interactions. We show that the correlation length scales as a non-trivial power of the linear system size and investigate the scaling forms. For interactions of sufficiently long range, the disparity between the correlation length and the system length can be made arbitrarily large, while maintaining the new scaling scenarios. We also investigate the behavior of the correlation function above the upper critical dimension and the modifications imposed by the new scaling scenario onto the associated Fisher relation.Comment: 16 pages, 5 figure

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

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

ON THE FRACTIONAL RICCATI DIFFERENTIAL EQUATION

In this paper, We tried to find an analytical solution of nonlinear Riccati conformable fractional differential equation. Fractional derivatives are described in the conformable derivative. The behavior of the solutions and the effects of different values of fractional order ? are presented graphically and table. The results obtained by the CFD(conformable fractional derivative) are compared with homotopy perturbation method(HPM), fractional variational iteration method(FVIM). © 2016 Academic Publications, Ltd

MODELING DISEASE TRANSMISSION DYNAMICS WITH RANDOM DATA AND HEAVY TAILED RANDOM EFFECTS: THE ZIKA CASE

In this study, we investigate a compartmental model of Zika Virus transmission under random effects. Random effects enable the analysis of random numerical characteristics of transmission, which cannot be modeled through deterministic equations. Data obtained from Zika studies in the literature are used along with heavy tailed random effects to obtain new random variables for the parameters of the deterministic model. Finally, simulations of the model are carried out to analyze the random dynamics of Zika Virus transmission. Deterministic results are compared with results from the simulations of the random system to underline the advantages of a random modeling approach. It is shown that the random model provides additional results for disease transmission dynamics such as results for standard deviation and coefficients of variation, making it a valuable alternative to deterministic modeling. Random results suggest around 90% - 120% coefficient of variation for the random model underlining the fact that the randomness should not be ignored for the transmission of this disease. © Işık University, Department of Mathematics, 2023; all rights reserved.1 Department of Mathematics, Recep Tayyip Erdogan University, Rize, Turkey. e-mail: [email protected]; ORCID: https://orcid.org/0000-0001-5671-9995. ∗ Corresponding author. 2 Department of Mathematics, Karadeniz Technical University, Trabzon, Turkey. e-mail: [email protected]; ORCID: https://orcid.org/ 0000-0002-8807-5677. 3 Department of Mathematical Engineering, Gumushane University, Gumushane, Turkey. e-mail: [email protected]; ORCID: https://orcid.org/ 0000-0002-8509-3044. 4 Department of Industrial Engineering, TOBB University of Economics and Technology, Ankara, Turkey. The Center of Digital Economics, Azerbaijan State University of Economics, Baku, Azerbaijan. e-mail: [email protected]; ORCID: https://orcid.org/0000-0003-1974-0140. § Manuscript received: September 10, 2021; accepted: July 01, 2022. TWMS Journal of Applied and Engineering Mathematics, Vol.13, No.4 © I¸sık University, Department of Mathematics, 2023; all rights reserved. This work was supported by Research Fund of the Recep Tayyip Erdogan University. Project Number: FBA-2019-992.Recep Tayyip Erdogan Üniversitesi, RTEU: FBA-2019-99

Transmission of Cholera Disease With Laplacian and Triangular Parameters

A mathematical model has been introduced for the transmission dynamics of cholera disease by GQ Sun et al. recently. In this study, we add Laplacian and Triangular random effects to this model and analyze the variation of results for both cases. The expectations and co-efficients of variation are compared for the random models and the results are used to comment on the differences and similarities between the effects of these probability distributions. The randomness of the model itself is also investigated through comparison of the random and deterministic outcomes. © 2022 Academic Center for Education, Culture and Research TMU