Distribution of spiking and bursting in Rulkov’s neuron model

Large-scale brain simulations require the investigation of large networks of realistic neuron models, usually represented by sets of differential equations. Here we report a detailed fine-scale study of the dynamical response over extended parameter ranges of a computationally inexpensive model, the two-dimensional Rulkov map, which reproduces well the spiking and spiking-bursting activity of real biological neurons. In addition, we provide evidence of the existence of nested arithmetic progressions among periodic pulsing and bursting phases of Rulkov’s neuron. We find that specific remarkably complex nested sequences of periodic neural oscillations can be expressed as simple linear combinations of pairs of certain basal periodicities. Moreover, such nested progressions are robust and can be observed abundantly in diverse control parameter planes which are described in detail. We believe such findings to add significantly to the knowledge of Rulkov neuron dynamics and to be potentially helpful in large-scale simulations of the brain and other complex neuron networks.

Supply Chain Networking Models Under Fuzzy Uncertainty

In decision-making model, the techniques of numerical analysis have been widely adopted. It is rare for someone to solve a linear program by hand — except perhaps in a class-room. Large-scale simulations would be all but impossible without the aid of a computer. For many people, numerical techniques have superseded analytic techniques as a tool for solving mathematical problems. This paper proposed Generalized LUExponential Trapezoidal Fuzzy Number and their ranking based on numerical integration. In this ranking method, the values are calculated with left and right spreads at some 𝜶 −level of generalized LU-exponential trapezoidal fuzzy numbers and Weddle‘s rule for numerical integration. To illustrate the proposed methods, a fuzzy four dimensional transportation problem (FDTP) is proposed and solved. This ranking approach is very simple and useful for the real life inequality based decision making problems.

Rheology of crossbridge ensembles

Muscle rheology, or the characterization of a muscle's response to external mechanical perturbations, is crucial to an animal's motor control and locomotive abilities. How the rheology emerges from the ensemble dynamics of microscopic actomyosin crossbridges known to underlie muscle forces is however a longstanding question. Classical descriptions in terms of force-length and force-velocity relationships capture only part of the rheology, namely under steady but not dynamical conditions. Although much is known about the actomyosin machinery, current mathematical models that describe the behavior of a population or an ensemble of crossbridges are plagued by an excess of parameters and computational complexity that limits their usage in large-scale musculoskeletal simulations. In this paper, we examine models of crossbridge dynamics of varying complexity and show that the emergent rheology of an ensemble of crossbridges can be simplified to a few dominant time-constants associated with intrinsic dynamical processes. For Huxley's classical two-state crossbridge model, we derive exact analytical expressions for the emergent ensemble rheology and find that it is characterized by a single time-constant. For more complex models with up to five crossbridge states, we show that at most three time-constants are needed to capture the ensemble rheology. Our results thus yield simplified models comprising of a few time-constants for muscle's bulk rheological response that can be readily used in large-scale simulations without sacrificing the model's interpretability in terms of the underlying actomyosin crossbridge dynamics.

Spectroscopic analysis of M- and N-intrashell transitions in Co-like to Na-like Yb ions

The M-intrashell spectra from Co-like Yb43+ through Na-like Yb59+ ions produced in an electron beam ion trap (EBIT) at the National Institute of Standards and Technology have been studied in the extreme ultraviolet (EUV) range. A few N-intrashell transitions for Co-like Yb43+ and Fe-like Yb44+ are also reported. The EUV radiation was observed with a flat-field grazing incidence spectrometer in the wavelength region of about 7.5 nm to 26.2 nm. The electron beam energies were varied between 3.6 keV and 18 keV to produce the ionization stages of interest. The line identifications were based on the large-scale simulations of the EBIT plasma emission using the non-Maxwellian collisional-radiative code NOMAD. A total of 76 previously unobserved spectral lines corresponding to electric-dipole and magnetic-dipole transitions in the above mentioned ions were identified and discussed. In particular, our accurate wavelength of 24.3855±0.0005 nm for a magnetic-dipole (M1) transition in the ground configuration of Co-like ion presents a solid benchmark for comparisons with the most advanced theories of atomic structure.

MEAM interatomic potentials of Ni, Re, and Ni-Re alloys for atomistic fracture simulations

Second nearest neighbor modified embedded atom method (2NN-MEAM) interatomic potentials are developed for the Ni, Re, and Ni-Re binaries. To construct the potentials, density functional theory (DFT) calculations have been employed to calculate fundamental physical properties that play a dominant role in fracture. The potentials are validated to accurately reproduce material properties that correlate with material’s fracture behavior. The thus constructed potentials were applied to perform large scale simulations of mode I fracture in Ni and Ni-Re binaries with low Re content. Substitutional Re did not alter the ductile nature of crack propagation, though it resulted in a monotonous increase of the critical stress intensity factor with Re content.

Dopaminergic and Cholinergic Modulation of Large Scale Networks in silico Using Snudda

Neuromodulation is present throughout the nervous system and serves a critical role for circuit function and dynamics. The computational investigations of neuromodulation in large scale networks require supportive software platforms. Snudda is a software for the creation and simulation of large scale networks of detailed microcircuits consisting of multicompartmental neuron models. We have developed an extension to Snudda to incorporate neuromodulation in large scale simulations. The extended Snudda framework implements neuromodulation at the level of single cells incorporated into large-scale microcircuits. We also developed Neuromodcell, a software for optimizing neuromodulation in detailed multicompartmental neuron models. The software adds parameters within the models modulating the conductances of ion channels and ionotropic receptors. Bath application of neuromodulators is simulated and models which reproduce the experimentally measured effects are selected. In Snudda, we developed an extension to accommodate large scale simulations of neuromodulation. The simulator has two modes of simulation – denoted replay and adaptive. In the replay mode, transient levels of neuromodulators can be defined as a time-varying function which modulates the receptors and ion channels within the network in a cell-type specific manner. In the adaptive mode, spiking neuromodulatory neurons are connected via integrative modulating mechanisms to ion channels and receptors. Both modes of simulating neuromodulation allow for simultaneous modulation by several neuromodulators that can interact dynamically with each other. Here, we used the Neuromodcell software to simulate dopaminergic and muscarinic modulation of neurons from the striatum. We also demonstrate how to simulate different neuromodulatory states with dopamine and acetylcholine using Snudda. All software is freely available on Github, including tutorials on Neuromodcell and Snudda-neuromodulation.

A GPU-Accelerated Linear Solver for Massively Parallel Underground Simulations

Modern engineering applications require the solution of linear systems of millions or even billions of equations. The solution of the linear system takes most of the simulation for large scale simulations, and represent the bottleneck in developing scientific and technical software. Usually, preconditioned iterative solvers are preferred because of their low memory requirements and they can have a high level of parallelism. Approximate inverses have been proven to be robust and effective preconditioners in several contexts. In this communication, we present an adaptive Factorized Sparse Approximate Inverse (FSAI) preconditioner with a very high level of parallelism in both set-up and application. Its inherent parallelism makes FSAI an ideal candidate for a GPU-accelerated implementation, even if taking advantage of this hardware is not a trivial task, especially in the set-up stage. An extensive numerical experimentation has been performed on industrial underground applications. It is shown that the proposed approach outperforms more traditional preconditioners in challenging underground simulation, greatly reducing time-to-solution.

Cortex-Like Complex Systems: What Occurs Within?

We consider cortex-like complex systems in the form of strongly connected, directed networks-of-networks. In such a network, there are spiking dynamics at each of the nodes (modelling neurones), together with non-trivial time-lags associated with each of the directed edges (modelling synapses). The connections of the outer network are sparse, while the many inner networks, called modules, are dense. These systems may process various incoming stimulations by producing whole-system dynamical responses. We specifically discuss a generic class of systems with up to 10 billion nodes simulating the human cerebral cortex. It has recently been argued that such a system’s responses to a wide range of stimulations may be classified into a number of latent, internal dynamical modes. The modes might be interpreted as focussing and biasing the system’s short-term dynamical system responses to any further stimuli. In this work, we illustrate how latent modes may be shown to be both present and significant within very large-scale simulations for a wide and appropriate class of complex systems. We argue that they may explain the inner experience of the human brain.

On the Upper Bounds of Test Statistics for a Single Outlier Test in Linear Regression Models

A bewildering large number of test statistics have been found for testing the presence of an outlier in multiple linear regression models. Exact critical values of these test statistics are not available, and approximate ones are usually obtained by the first-order Bonferroni upper bound or large-scale simulations. In this paper, we show that the upper bound values of two of these test statistics are algebraically the same. An application to real data for multiple linear regression is used to demonstrate the procedure.