Detecting scaling in phase transitions on the truncated Heisenberg algebra

We construct and analyze a phase diagram of a self-interacting matrix field coupled to curvature of the non-commutative truncated Heisenberg space. The model reduces to the renormalizable Grosse-Wulkenhaar model in an infinite matrix size limit and exhibits a purely non-commutative non-uniformly ordered phase. Particular attention is given to scaling of model’s parameters. We additionally provide the infinite matrix size limit for the disordered to ordered phase transition line

Friction and Stiffness Dependent Dynamics of Accumulation Landslides with Delayed Failure

We propose a new model for landslide dynamics under the assumption of a delay failure mechanism. Delay failure is simulated as a delayed interaction between adjacent blocks, which mimics the relationship between the accumulation and feeder part of the accumulation slope. The conducted research consisted of three phases. Firstly, the real observed movements of the landslide were examined to exclude the existence or the statistically significant presence of background noise. Secondly, we propose a new mechanical model of an accumulation landslide dynamics, with introduced delay failure, and with variable friction law. Results obtained indicate the onset of a transition from an equilibrium state to an oscillatory regime if delayed failure is assumed for different cases of slope stiffness and state of homogeneity/heterogeneity of the slope. At the end, we examine the influence of different frictional properties (along the sliding surface) on the conditions for the onset of instability. Results obtained indicate that the increase of friction parameters leads to stabilization of sliding for homogeneous geological environment. Moreover, increase of certain friction parameters leads to the occurrence of irregular aperiodic behavior, which could be ascribed to the regime of fast irregular sliding along the slope

Instability Induced by Random Background Noise in a Delay Model of Landslide Dynamics

In the present paper, we propose a new model for landslide dynamics, in the form of the spring-block mechanical model, with included delayed interaction and the effect of the background seismic noise. The introduction of the random noise in the model of landslide dynamics is confirmed by the surrogate data testing of the recorded ambient noise within the existing landslide in Serbia. The performed research classified the analyzed recordings as linear stationary stochastic processes with Gaussian inputs. The proposed mechanical model is described in the form of a nonlinear dynamical system: a set of stochastic delay-differential equations. The solution of such a system is enabled by the introduction of mean-field approximation, which resulted in a mean-field approximated model whose dynamics are qualitatively the same as the dynamics of the starting stochastic system. The dynamics of the approximated model are analyzed numerically, with rather unexpected results, implying the positive effect of background noise on landslide dynamics. Particularly, the increase of the noise intensity requires higher values of spring stiffness and displacement delay for the occurrence of bifurcation. This confirms the positive stabilizing effect of the increase in noise intensity on the dynamics of the analyzed landslide model. Present research confirms the significant role of noise in landslides near the bifurcation point (e.g., creeping landslides)

Triggered dynamics in a model of different fault creep regimes

The study is focused on the effect of transient external force induced by a passing seismic wave on fault motion in different creep regimes. Displacement along the fault is represented by the movement of a spring-block model, whereby the uniform and oscillatory motion correspond to the fault dynamics in post-seismic and inter-seismic creep regime, respectively. The effect of the external force is introduced as a change of block acceleration in the form of a sine wave scaled by an exponential pulse. Model dynamics is examined for variable parameters of the induced acceleration changes in reference to periodic oscillations of the unperturbed system above the supercritical Hopf bifurcation curve. The analysis indicates the occurrence of weak irregular oscillations if external force acts in the post-seismic creep regime. When fault motion is exposed to external force in the inter-seismic creep regime, one finds the transition to quasiperiodic-or chaos-like motion, which we attribute to the precursory creep regime and seismic motion, respectively. If the triggered acceleration changes are of longer duration, a reverse transition from inter-seismic to post-seismic creep regime is detected on a larger time scale

Should MTHFR 1298 A>C be tested together with MTHFR 677 C>T polymorphism in women with reproductive challenges?

Methylenetetrahydrofolate reductase (MTHFR) plays a critical role in the folate metabolism. The polymorphism 677C > T of the MTHFR gene, producing thermolabile enzyme with decreased function, is widely studied and associated with many conditions. Additionally, it has been shown that another polymorphism, 1298A > C, also reduces the activity of this enzyme, although to a lesser extent. The aim of this study is to evaluate the clinical informativeness of testing both MTHFR polymorphisms. Genomic DNA, were extracted from peripheral blood of 180 female patients with pregnancy complications and 183 healthy female controls, and genotyped for MTHFR 677C > T and 1298A > C loci, using TaqMan assays. Our study found similar frequency of alleles and genotypes between two groups. Based on MTHFR 677C > T genotype, 11.7% of patients homozygous for this mutation were under the possible risk. When the position 1298 was included in the testing, 22.8% of the patients were heterozygous for both polymorphisms. Additionally, 8.9% of the patients were homozygous only for the MTHFR 1298 mutation. Although, there was no differences compared to healthy control (p > 0.05), 43% of patients were found to have elevated risk which is about four time higher than results with only MTHFR 677C > T genotyping. After obtaining information for the 677 position, testing for the second polymorphism (1298A > C) should be considered, since we have shown that it dramatically increases the rate of detection of patients who are potentially at risk for MTHFR associated conditions

Mean field approximation for noisy delay coupled excitable neurons

Mean field approximation of a large collection of FitzHugh-Nagumo excitable neurons with noise and all-to-all coupling with explicit time-delays, modelled by $N\gg 1$ stochastic delay-differential equations is derived. The resulting approximation contains only two deterministic delay-differential equations but provides excellent predictions concerning the stability and bifurcations of the averaged global variables of the exact large system.Comment: 15 pages, 3 figure

Reward-related impulsivity as a possible surrogate marker of motivation in aging Sprague-Dawley rats

Introduction: Impulsivity is an umbrella term that encompasses many subdomains, most of which rely on the decision-making processes. It is reported that in the process of healthy aging, the two dimensions of impulse control, cognition and motivation, are preserved or even improved. On the other hand, the attentive efficiency seems to decrease with age. Therefore, we aimed to investigate the effects of healthy aging on impulsivity in rats and the influence of food deprivation on impulsivity in aged rats as a strategy to enhance motivation. Additionally, we wanted to assess the gene expression for the alpha5 GABAA receptor subunit during aging, which plays a role in cognitive processes. Methodology: The variable-delay-to-signal (VDS) paradigm adapted to a touchscreen environment was used to assess impulsivity and attention in Sprague-Dawley rats at 2, 3, 5, 8, and 14 months of age. After one week of training, animals were tested at different ages in 3-stage testing protocol. Additionally, prior to testing, animals were fed a restricted diet (16 g/animal). The first stage included 20 trials with inter-trial interval of 6s (ITI6si) that reflected motor impulsivity. The second stage, with 60 randomly distributed trials of ITI9s or 15s, was related to delay intolerance, while the final stage (ITI6sf), similar to the first, was related to reflection impulsivity. The strict 3-day restriction diet (24h food deprivation followed by 10g/day/animal and 8g/day/animal) was applied to 14-month-old animals before testing. Gabra5 expression in the hippocampus was determined by qPCR. Results were analyzed by one-way ANOVA with or without repeated measures, followed by Sidak post-hoc test for impulsivity and attention parameters and by t-test for PCR parameters. Results: Animals aged 8 and 14 months had reduced motor impulsivity (p<0.01 for both groups) and delay intolerance (p<0.05 for both groups) and higher number of omissions (p<0.05 for both groups) compared to animals aged 2, 3 and 5 months of age. In addition, half of the animals were unable to successfully complete a task after 14 months. After rigorous food restriction in 14-month-old animals, the level of impulsivity (ITI9s and ITI15s) and attention (number of omissions) returned to the control level (2 and 3 months of age) compared to the performance of 14-month-old animals prior to rigorous food restriction (p<0.05). Further, the peak of reflection impulsivity (ITI6sf) was reached at 5 months compared to all other groups (p<0.01). No changes in Gabra5 expression in hippocampus were detected in 14-month-old compared to 3-month-old animals. Conclusion: From 8 months of age onwards, rats showed reduced impulsivity in the VDS stages where motor impulsivity and delay intolerance were tested, followed by attention deficits. After strict food restriction in 14-month-old animals, delay intolerance and attention were restored, suggesting the prominent role of motivation in controlling these processes, independently of Gabra5 expression levels in the hippocampus. Since the VDS paradigm aims to assess reward-related impulsivity based on cognition and motivation, it is suspected that results related to impaired cognition in older animals in other cognitive tests should be interpreted with caution, and with additional observation of motivation