Front bifurcations in an excitatory neural network

We show how a one-dimensional excitatory neural network can exhibit a symmetry breaking front bifurcation analogous to that found in reaction diffusion systems. This occurs in a homogeneous network when a stationary front undergoes a pitchfork bifurcation leading to bidirectional wave propagation. We analyze the dynamics in a neighborhood of the front bifurcation using perturbation methods, and we establish that a weak input inhomogeneity can induce a Hopf instability of the stationary front, leading to the formation of an oscillatory front or breather. We then carry out a stability analysis of stationary fronts in an exactly solvable model and use this to derive conditions for oscillatory fronts beyond the weak input regime. In particular, we show how wave propagation failure occurs in the presence of a large stationary input due to the pinning of a stationary front; a subsequent reductionin the strength of the input then generates a breather via a Hopf instability of the front. Finally, we derive conditions for the locking of a traveling front to a moving input, and we show how locking depends on both the amplitude and velocity of the input

Stimulus-locked traveling waves and breathers in an excitatory neural network

We analyze the existence and stability of stimulus-locked traveling waves in a one-dimensional synaptically coupled excitatory neural network. The network is modeled in terms of a nonlocal integro-differential equation, in which the integral kernel represents the spatial distribution of synaptic weights, and the output firing rate of a neuron is taken to be a Heaviside function of activity. Given an inhomogeneous moving input of amplitude I0 and velocity v, we derive conditions for the existence of stimulus-locked waves by working in the moving frame of the input. We use this to construct existence tongues in (v,I0 )-parameter space whose tips at I0 = 0 correspond to the intrinsic waves of the homogeneous network. We then determine the linear stability of stimulus-locked waves within the tongues by constructing the associated Evans function and numerically calculating its zeros as a function of network parameters. We show that, as the input amplitude is reduced, a stimulus-locked wave within the tongue of an unstable intrinsic wave can undergo a Hopf bifurcation, leading to the emergence of either a traveling breather or a traveling pulse emitter

Breathers in two-dimensional neural media

In this Letter we show how nontrivial forms of spatially localized oscillations or breathers can occur in two-dimensional excitable neural media with short-range excitation and long-range inhibition. The basic dynamical mechanism involves a Hopf bifurcation of a stationary pulse solution in the presence of a spatially localized input. Such an input could arise from external stimuli or reflect changes in the excitability of local populations of neurons as a precursor for epileptiform activity. The resulting dynamical instability breaks the underlying radial symmetry of the stationary pulse, leading to the formation of a nonradially symmetric breather. The number of breathing lobes is consistent with the order of the dominant unstable Fourier mode associated with perturbations of the stationary pulse boundar

Jim Starnes' Contributions to Residual Strength Analysis Methods for Metallic Structures

A summary of advances in residual strength analyses methods for metallic structures that were realized under the leadership of Dr. James H. Starnes, Jr., is presented. The majority of research led by Dr. Starnes in this area was conducted in the 1990's under the NASA Airframe Structural Integrity Program (NASIP). Dr. Starnes, respectfully referred to herein as Jim, had a passion for studying complex response phenomena and dedicated a significant amount of research effort toward advancing damage tolerance and residual strength analysis methods for metallic structures. Jim's efforts were focused on understanding damage propagation in built-up fuselage structure with widespread fatigue damage, with the goal of ensuring safety in the aging international commercial transport fleet. Jim's major contributions in this research area were in identifying the effects of combined internal pressure and mechanical loads, and geometric nonlinearity, on the response of built-up structures with damage. Analytical and experimental technical results are presented to demonstrate the breadth and rigor of the research conducted in this technical area. Technical results presented herein are drawn exclusively from papers where Jim was a co-author

Traveling pulses and wave propagation failure in inhomogeneous neural media

We use averaging and homogenization theory to study the propagation of traveling pulses in an inhomogeneous excitable neural network. The network is modeled in terms of a nonlocal integro-differential equation, in which the integral kernel represents the spatial distribution of synaptic weights. We show how a spatially periodic modulation of homogeneous synaptic connections leads to an effective reduction in the speed of a traveling pulse. In the case of large amplitude modulations, the traveling pulse represents the envelope of a multibump solution, in which individual bumps are nonpropagating and transient. The appearance (disappearance) of bumps at the leading (trailing) edge of the pulse generates the coherent propagation of the pulse. Wave propagation failure occurs when activity is insufficient to maintain bumps at the leading edge

Synchronization hubs may arise from strong rhythmic inhibition during gamma oscillations in primary visual cortex

Poster presentation from Twentieth Annual Computational Neuroscience Meeting: CNS*2011 Stockholm, Sweden. 23-28 July 2011. Parallel multiunit recordings from V1 in anesthetized cat were collected during the presentation of random sequences of drifting sinusoidal gratings at 12 fixed orientations while gamma oscillations were present. In agreement with the seminal work [1], most units were orientation selective to varying degrees and synchronization was evident in spike train crosscorrelograms computed between units with similar preferred orientations, particularly during the presentation of optimal stimuli. Interestingly, a subset of units, which we refer to as synchronization hubs, were additionally found to synchronize with units having differing preferred orientations which was consistent with a previous study [2]. Moreover, oscillatory patterning in spike train autocorrelograms was also found to be strongest in units denoted as synchronization hubs, and synchronization hubs also tended to have narrower tuning curves relative to other units. We used simplified computational models of small networks of V1 neurons to demonstrate that neurons subject to a sufficiently strong level of inhibitory input can function as synchronization hubs. Neurons were endowed either with integrate-and-fire or conductance-based dynamics and each neuron received a combination of excitatory (AMPA) synaptic inputs that were Poisson-distributed and inhibitory (GABA) inputs that were coherent at a gamma-frequency range. If the strength of rhythmic inhibition was increased for a subset of neurons in the network, and excitation was increased simultaneously to maintain a fixed firing rate, then these neurons produced stronger oscillatory patterning in their discharge probabilities. The oscillations in turn synchronized these neurons with other neurons in the network. Importantly, the strength of synchronization increased with neurons of differing orientation preferences even though no direct synaptic coupling existed between the hubs and the other neurons. Enhanced levels of inhibition account for the emergence of synchronization hubs in the following way: Inhibitory inputs exhibiting a gamma rhythm determine a time window within which a cell is likely to discharge. Increased levels of inhibition narrow down this window further simultaneously leading to (i) even stronger oscillatory patterning of the neuron's activity and (ii) enhanced synchronization with other neurons. This enables synchronization even between cells with differing orientation preferences. Additionally, the same increased levels of inhibition may be responsible for the narrow tuning curves of hub neurons. In conclusion, synchronization hubs may be the cells that interact most strongly with the network of inhibitory interneurons during gamma oscillations in primary visual cortex

Modelado de la singularidad de borde libre en grietas 3D mediante XFEM y armónicos esféricos

Una singularidad que puede aparecer en la mayoría de los problemas de fractura tridimensional bajo comportamiento elástico es la singularidad de esquina o de borde libre, localizada en la intersección del frente de grieta con una frontera libre. Sin embargo, su efecto es habitualmente ignorado. Por otro lado, el método de los elementos finitos extendido, XFEM, es una técnica que permite el modelado numérico eficiente de problemas de fractura, para lo que incorpora la geometría de la grieta a través de funciones de enriquecimiento dentro de un modelo de elementos finitos, cuya malla ya no necesita adaptarse a la geometría de la fisura. Sin embargo, cuando se aplica al estudio de problemas de fractura que presentan singularidad de esquina, esta no se captura adecuadamente. La razón es que las funciones de enriquecimiento del XFEM solo describen la singularidad típicamente asociada al frente de grieta. Por tanto, para poder modelar la singularidad del borde libre es necesario su introducción en el enriquecimiento. En este trabajo presentamos un nuevo conjunto de funciones de enriquecimiento basadas en armónicos esféricos que consiguen introducir el comportamiento asociado a la singularidad de borde libre.One type of singularity that may appear in a three-dimensional fracture problem under elastic behavior is the free corner singularity, which occurs at the intersection of the crack with a free boundary and whose effect is usually ignored. The extended finite element method (XFEM) is a technique that allows the efficient numerical modeling of fracture problems, by using enrichment functions within a finite element model that incorporate the geometry and effect of the crack. However, when applied to the study of a problem with corner singularity, the singular behavior is not properly captured. The reason is that the usual enrichment in the XFEM only describes the typical crack front singularity. Hence, in order to include the effect of the free border singularity, the enrichment has to be modified. In this work, we present a new set of functions which relies on spherical harmonics and is able to capture the behavior of the free border singularity.González Albuixech, VF.; Giner Maravilla, E.; Tarancón Caro, JE. (2015). Modelado de la singularidad de borde libre en grietas 3D mediante XFEM y armónicos esféricos. Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería. 31(1):50-54. doi:10.1016/j.rimni.2013.12.002S505431

Macroscopic coherent structures in a stochastic neural network: from interface dynamics to coarse-grained bifurcation analysis

We study coarse pattern formation in a cellular automaton modelling a spatially-extended stochastic neural network. The model, originally proposed by Gong and Robinson (Phys Rev E 85(5):055,101(R), 2012), is known to support stationary and travelling bumps of localised activity. We pose the model on a ring and study the existence and stability of these patterns in various limits using a combination of analytical and numerical techniques. In a purely deterministic version of the model, posed on a continuum, we construct bumps and travelling waves analytically using standard interface methods from neural field theory. In a stochastic version with Heaviside firing rate, we construct approximate analytical probability mass functions associated with bumps and travelling waves. In the full stochastic model posed on a discrete lattice, where a coarse analytic description is unavailable, we compute patterns and their linear stability using equation-free methods. The lifting procedure used in the coarse time-stepper is informed by the analysis in the deterministic and stochastic limits. In all settings, we identify the synaptic profile as a mesoscopic variable, and the width of the corresponding activity set as a macroscopic variable. Stationary and travelling bumps have similar meso- and macroscopic profiles, but different microscopic structure, hence we propose lifting operators which use microscopic motifs to disambiguate them. We provide numerical evidence that waves are supported by a combination of high synaptic gain and long refractory times, while meandering bumps are elicited by short refractory times

Fabrication and thermal conductivity of CeO2???Ce3Si2 composite

Various compositions of CeO2-Ce3Si2 (0, 10, 30, 50, and 100 wt%Ce3Si2) composites were fabricated using conventional sintering and spark plasma sintering. Lower relative density, enhanced interdiffusion of oxygen and silicon, and silicide agglomerations from the congruent melting of Ce3Si2 at 1390 degrees C were only observed from conventionally-sintered pellets. Thermal conductivity of spark plasma sintered CeO2-Ce3Si2 composites was calculated from the measured thermal diffusivity, specific heat, and density, which exhibited dense (>90 %TD) and homogeneous microstructure. The composite with 50 wt%Ce3Si2 exhibited 55% higher thermal conductivity than CeO2 at 500 degrees C, and 81% higher at 1000 degrees C. (c) 2020 Korean Nuclear Society, Published by Elsevier Korea LLC. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Collaboration of Werner syndrome protein and BRCA1 in cellular responses to DNA interstrand cross-links

Cells deficient in the Werner syndrome protein (WRN) or BRCA1 are hypersensitive to DNA interstrand cross-links (ICLs), whose repair requires nucleotide excision repair (NER) and homologous recombination (HR). However, the roles of WRN and BRCA1 in the repair of DNA ICLs are not understood and the molecular mechanisms of ICL repair at the processing stage have not yet been established. This study demonstrates that WRN helicase activity, but not exonuclease activity, is required to process DNA ICLs in cells and that WRN cooperates with BRCA1 in the cellular response to DNA ICLs. BRCA1 interacts directly with WRN and stimulates WRN helicase and exonuclease activities in vitro. The interaction between WRN and BRCA1 increases in cells treated with DNA cross-linking agents. WRN binding to BRCA1 was mapped to BRCA1 452–1079 amino acids. The BRCA1/BARD1 complex also associates with WRN in vivo and stimulates WRN helicase activity on forked and Holliday junction substrates. These findings suggest that WRN and BRCA1 act in a coordinated manner to facilitate repair of DNA ICLs