Comparison of perturbative and non-perturbative methods in f(R) gravity

In this work, we investigate the structure and properties of neutron stars in $$R^2$$ R 2 gravity using two approaches, viz: the perturbative and non-perturbative methods. For this purpose, we consider NS with several nucleonic, as well as strange EoS generated in the framework of relativistic mean field models. The strange particles in the core of NS are in the form of $$\Lambda $$ Λ hyperons and quarks, in addition to the nucleons and leptons. In both the approaches, we obtain mass–radius relation for a wide range of values of the extra degree of freedom parameter a arising due to modification of gravity at large scales. The mass–radius relation of the chosen equation of states lies well within the observational limit in the case of GR. We identify the changes in the property of neutron star in the background of f(R) gravity, and compare the results in both the methods. We also identify the best suited method to study the modified gravity using the astrophysical observations.

Beta Equilibrium Under Neutron Star Merger Conditions

We calculate the nonzero-temperature correction to the beta equilibrium condition in nuclear matter under neutron star merger conditions, in the temperature range 1MeV<T≲5MeV. We improve on previous work using a consistent description of nuclear matter based on the IUF and SFHo relativistic mean field models. This includes using relativistic dispersion relations for the nucleons, which we show is essential in these models. We find that the nonzero-temperature correction can be of order 10 to 20 MeV, and plays an important role in the correct calculation of Urca rates, which can be wrong by factors of 10 or more if it is neglected.

Assembly formation is stabilized by Parvalbumin neurons and accelerated by Somatostatin neurons

Learning entails preserving the features of the external world in the neuronal representations of the brain, and manifests itself in the form of strengthened interactions between neurons within assemblies. Hebbian synaptic plasticity is thought to be one mechanism by which correlations in spiking promote assembly formation during learning. While spike timing dependent plasticity (STDP) rules for excitatory synapses have been well characterized, inhibitory STDP rules remain incomplete, particularly with respect to sub-classes of inhibitory interneurons. Here, we report that in layer 2/3 of the orbitofrontal cortex of mice, inhibition from parvalbumin (PV) interneurons onto excitatory (E) neurons follows a symmetric STDP function and mediates homeostasis in E-neuron firing rates. However, inhibition from somatostatin (SOM) interneurons follows an asymmetric, Hebbian STDP rule. We incorporate these findings in both large scale simulations and mean-field models to investigate how these differences in plasticity impact network dynamics and assembly formation. We find that plasticity of SOM inhibition builds lateral inhibitory connections and increases competition between assemblies. This is reflected in amplified correlations between neurons within assembly and anti-correlations between assemblies. An additional finding is that the emergence of tuned PV inhibition depends on the interaction between SOM and PV STDP rules. Altogether, we show that incorporation of differential inhibitory STDP rules promotes assembly formation through competition, while enhanced inhibition both within and between assemblies protects new representations from degradation after the training input is removed.

Cluster mean-field theory accurately predicts statistical properties of large-scale DNA methylation patterns

The accurate establishment and maintenance of DNA methylation patterns is vital for mammalian development and disruption to these processes causes human disease. Our understanding of DNA methylation mechanisms has been facilitated by mathematical modelling, particularly stochastic simulations. Mega-base scale variation in DNA methylation patterns is observed in development, cancer and ageing and the mechanisms generating these patterns are little understood. However, the computational cost of stochastic simulations prevents them from modelling such large genomic regions. Here we test the utility of three different mean-field models to predict large-scale DNA methylation patterns. By comparison to stochastic simulations, we show that a cluster mean-field model accurately predicts the statistical properties of steady-state DNA methylation patterns, including the mean and variance of methylation levels calculated across a system of CpG sites, as well as the covariance and correlation of methylation levels between neighbouring sites. We also demonstrate that a cluster mean-field model can be used within an approximate Bayesian computation framework to accurately infer model parameters from data. As mean-field models can be solved numerically in a few seconds, our work demonstrates their utility for understanding the processes underpinning large-scale DNA methylation patterns.