Pinning of dislocations in disordered alloys: effects of dislocation orientation

The current interest in compositionally complex alloys including so called high entropy alloys has caused renewed interest in the general problem of solute hardening. It has been suggested that this problem can be addressed by treating the alloy as an effective medium containing a random distribution of dilatation and compression centers representing the volumetric misfit of atoms of different species. The mean square stresses arising from such a random distribution can be calculated analytically, their spatial correlations are strongly anisotropic and exhibit long-range tails with third-order power law decay (Geslin and Rodney 2021; Geslin et al. 2021). Here we discuss implications of the anisotropic and long-range nature of the correlation functions for the pinning of dislocations of arbitrary orientation. While edge dislocations are found to follow the standard pinning paradigm, for dislocations of near screw orientation we demonstrate the co-existence of two types of pinning energy minima.

International trade distributions and their relation with random fragmentation processes

A study of the distribution of the value of traded goods under the Harmonized System is presented. The ramifications of this classification system are found to exhibit an approximate power law decay, indicating complexity and self-organization in the nomenclature of traded merchandises. For almost all countries with available data, log-values of annually imported and exported goods are well described by three-parameter Weibull distributions. This distribution commonly appears in particles size distributions, suggesting a connection between random fragmentation processes and the mechanisms behind the international trade of merchandises. Analysis of the resulting values for the fitting parameters from 1995 to 2018 shows a nearly constant linear relationship between the parameters of the Weibull distributions, so that, for each country, the distribution of log-values can be approximately characterized by a single shape parameter [Formula: see text]. The empirical findings of this paper suggest that specialization on trading a constant set of goods prevents the values of all traded merchandises from growing/decreasing simultaneously.

Differences in running performance of single- and group-housed mice

Mice are one of several common animal models in neuroscience and mouse behavior is becoming increasingly relevant. Mice are housed either in groups or alone in standard cages during which they show a variety of different behaviors. Moreover, housing conditions might alter the behavior of the mice as do social interactions. When given access to running wheels as an environmental enrichment, mice tend to run long distances preferentially during their dark cycle. However, it is currently not well understood whether and how mice utilize running wheels when single-housed or group-housed. Here we developed a low-cost running wheel data acquisition system to study running in adult C57BL/6 mice at high temporal resolution under different social conditions. As expected, adult C57BL/6 mice prefer to run in stretches during the dark cycle and mostly rest during the light cycle. When single-housed, running bouts occur independent from each other as indicated by an exponential decaying autocorrelation. In contrast, mice run ~50% less when housed in groups of n = 3 and their temporal pattern of running exhibits a power law decay in the autocorrelation indicative of potential social interactions. Our results demonstrate that running wheels are a limited resource for which mice compete for when they are group-housed, thereby reducing their overall running activity.

The Spatial Reach of Neuronal Coherence and Spike-field Coupling across the Human Neocortex

Neuronal coherence is thought to be a fundamental mechanism of communication in the brain, where synchronized field potentials coordinate synaptic and spiking events to support plasticity and learning. Although the spread of field potentials has garnered great interest, little is known about the spatial reach of phase synchronization, or neuronal coherence. Functional connectivity between different brain regions is known to occur across long distances, but the locality of coherence within a brain region is understudied. Here we used simultaneous recordings from electrocorticography (ECoG) grids and high-density microelectrode arrays to estimate the spatial reach of neuronal coherence and spike-field coherence (SFC) across frontal, temporal, and occipital cortices during cognitive tasks in humans. We observed the strongest coherence within a 2-3 cm distance from the microelectrode arrays, potentially defining an effective range for local communication. This range was relatively consistent across brain regions, spectral frequencies, and cognitive tasks. The magnitude of coherence showed power law decay with increasing distance from the microelectrode arrays, where the highest coherence occurred between ECoG contacts, followed by coherence between ECoG and deep cortical LFP, and then SFC (i.e., ECoG > LFP > SFC). The spectral frequency of coherence also affected its magnitude. Alpha coherence (8-14 Hz) was generally higher than other frequencies for signals nearest the microelectrode arrays, whereas delta coherence (1-3 Hz) was higher for signals that were farther away. Action potentials in all brain regions were most coherent with the phase of alpha oscillations, which suggests that alpha waves could play a larger, more spatially local role in spike timing than other frequencies. These findings provide a deeper understanding of the spatial and spectral dynamics of neuronal coherence, further advancing knowledge about how activity propagates across the human brain.

Analysis of visual processing capabilities and neural coding strategies of a detailed model for laminar cortical microcircuits in mouse V1

The neocortex is a network of rather stereotypical cortical microcircuits that share an exquisite genetically encoded architecture: Neurons of a fairly large number of different types are distributed over several layers (laminae), with specific probabilities of synaptic connections that depend on the neuron types involved and their spatial locations. Most available knowledge about this structure has been compiled into a detailed model [Billeh et al., 2020] for a generic cortical microcircuit in the primary visual cortex, consisting of 51,978 neurons of 111 different types. We add a noise model to the network that is based on experimental data, and analyze the results of network computations that can be extracted by projection neurons on layer 5. We show that the resulting model acquires through alignment of its synaptic weights via gradient descent training the capability to carry out a number of demanding visual processing tasks. Furthermore, this weight-alignment induces specific neural coding features in the microcircuit model that match those found in the living brain: High dimensional neural codes with an arguably close to optimal power-law decay of explained variance of PCA components, specific relations between signal- and noise-coding dimensions, and network dynamics in a critical regime. Hence these important features of neural coding and dynamics of cortical microcircuits in the brain are likely to emerge from aspects of their genetically encoded architecture that are captured by this data-based model in combination with learning processes. In addition, the model throws new light on the relation between visual processing capabilities and details of neural coding.

Stochastic Adsorption of Diluted Solute Molecules at Interfaces

<div> <p>Here an analytical solution of Fick’s 2^nd law is used to predict the diffusion and the stochastic adsorption of single diluted solute molecules on flat and patterned surfaces. The equations are then compared to the results of several numerical Monte Carlo simulations using a random walk model. The 1D diffusion simulations clarify that the dependence of the solute-surface collision rate on the observation-time (measurement time resolution) is because of the multiple collisions of the same molecules over different time regions. It also surprisingly suggests that due to the self-mimetic fractal function of diffusion, the equation should be corrected by a factor of two. The absorption rate of solute on an adsorptive surface is found to follow a power-law decay function due to an evolving concentration gradient near the surface along with the depletion of the bulk solute molecules on the surface, for example, in a self-assembled monolayer adsorption kinetics. Thus, the analytical equations developed to calculate the collision at a fixed measuring frequency can be extended to map the whole curve over time. In the last section of this work, 3D diffusion simulations suggest that the analytical solution is valid to predict the adsorption rate of the bulk solute to a small group of adsorptive target molecules/area on a bouncing surface, which is a critical process in analyzing the kinetics of many bio-sensing platforms.</p> </div>

Localised Waves: Tightest Focus, Lorentz Transformation, and Polarization Singularities of Non-Paraxial Beams

<p>I explore the limits of how tightly a beam can be focused, and derive a focal parameter for scalar beams that can be symbolically evaluated for most beams, and is guaranteed to be convergent for physical beams, that compares peak in- tensity to the total intensity in the beam profile. I argue that this parameter is superior to spot size, and use this to derive a rigorous limit of focusing for scalar beams. A particular beam known as the proto-beam achieves this tight- est focus possible. I show the generalisation of this measure to electromagnetic beams, and place a lower bound on the focal extent of electromagnetic beams. I also propose the use of exponential regulators as alternatives to moment based measures, as a solution to the convergence issues created by the power law decay of exact solutions. I explore the Doppler shift for finite beams, and how monochromatic beams become polychromatic under a Lorentz boost. The local frequency is also explored, and I show that a deviation of the local frequency from the Doppler frequency will occur due to wavelength broadening near the focus. Lekner and I examine a beam that closely approximates a paraxial Gaussian beam radially, and examine the phase singularities for optical beams that occur near the zeros of the beams wavefunction. We also investigate attempts to find exact solutions with Gaussian profiles, and show that this is impossible; any such beam will be evanescent and exponentially grow. Finally, I investigate the property of finite classical electromagnetic pulses having a zero momentum frame, and show that for quantum single photon pulses this property holds for the expectation value. I show that any individual measurement however, still measures a light-like four-momentum for the photon.</p>

Localised Waves: Tightest Focus, Lorentz Transformation, and Polarization Singularities of Non-Paraxial Beams

<p>I explore the limits of how tightly a beam can be focused, and derive a focal parameter for scalar beams that can be symbolically evaluated for most beams, and is guaranteed to be convergent for physical beams, that compares peak in- tensity to the total intensity in the beam profile. I argue that this parameter is superior to spot size, and use this to derive a rigorous limit of focusing for scalar beams. A particular beam known as the proto-beam achieves this tight- est focus possible. I show the generalisation of this measure to electromagnetic beams, and place a lower bound on the focal extent of electromagnetic beams. I also propose the use of exponential regulators as alternatives to moment based measures, as a solution to the convergence issues created by the power law decay of exact solutions. I explore the Doppler shift for finite beams, and how monochromatic beams become polychromatic under a Lorentz boost. The local frequency is also explored, and I show that a deviation of the local frequency from the Doppler frequency will occur due to wavelength broadening near the focus. Lekner and I examine a beam that closely approximates a paraxial Gaussian beam radially, and examine the phase singularities for optical beams that occur near the zeros of the beams wavefunction. We also investigate attempts to find exact solutions with Gaussian profiles, and show that this is impossible; any such beam will be evanescent and exponentially grow. Finally, I investigate the property of finite classical electromagnetic pulses having a zero momentum frame, and show that for quantum single photon pulses this property holds for the expectation value. I show that any individual measurement however, still measures a light-like four-momentum for the photon.</p>

Trapping-influenced photoluminescence intensity decay in semiconductor nanoplatelets

We present a diffusion-based simulation model for explanation of long time power-law decay of photoluminescence (PL) emission intensity in semiconductor nanoplatelets. In our model the shape of emission curves is an outcome of interplay of recombination, diffusion and trapping of excitons. At short times the excitons diffuse freely following the normal diffusion behaviour. The emission decay is purely exponential and is defined by recombination. At long times the transition into the subdiffusive motion happens and the emission occurs due to the release of excitons from surface traps. A power-law tail for intensity is a consequence of the release. The crossover from onelimit to another is controlled by diffusion properties. The approach reproduces the properties of experimental curves measured for different nanoplatelet systems.

NEO: NEuro-Inspired Optimization—A Fractional Time Series Approach

Solving optimization problems is a recurrent theme across different fields, including large-scale machine learning systems and deep learning. Often in practical applications, we encounter objective functions where the Hessian is ill-conditioned, which precludes us from using optimization algorithms utilizing second-order information. In this paper, we propose to use fractional time series analysis methods that have successfully been used to model neurophysiological processes in order to circumvent this issue. In particular, the long memory property of fractional time series exhibiting non-exponential power-law decay of trajectories seems to model behavior associated with the local curvature of the objective function at a given point. Specifically, we propose a NEuro-inspired Optimization (NEO) method that leverages this behavior, which contrasts with the short memory characteristics of currently used methods (e.g., gradient descent and heavy-ball). We provide evidence of the efficacy of the proposed method on a wide variety of settings implicitly found in practice.