Insight into Thermal Modifications of Quarkonia From a Comparison of Continuum-Extrapolated Lattice Results to Perturbative QCD

In this work, we strive to gain insight into thermal modifications of charmonium and bottomonium bound states as well as the heavy quark diffusion coefficient. The desired information is contained in the spectral function which can not be calculated on the lattice directly. Instead, the correlator given by an integration over the spectral function times an integration kernel is obtained. Extracting the spectral function is an ill-posed inversion problem and various different solutions have been proposed. We focus on a comparison to a spectral function obtained from combining perturbative and pNRQCD calculations. In order to get precise results, continuum extrapolated correlators originating from large and fine lattices are used. We first analyze the pseudoscalar channel since the absence of a transport peak simplifies the analysis. The knowledge gained from this is then used to extend the analysis to the vector channel, where information on heavy quark transport is encoded in the low frequency regime of the spectral function. The comparison shows a qualitatively good agreement between perturbative and lattice correlators. Quantitative differences can be explained by systematic uncertainties.

A divisive model of evidence accumulation explains uneven weighting of evidence over time

SummaryDivisive normalization has long been used to account for computations in various neural processes and behaviours. The model proposes that inputs into a neural system are divisively normalized by the total activity of the system. More recently, dynamical versions of divisive normalization have been shown to account for how neural activity evolves over time in value-based decision making. Despite its ubiquity, divisive normalization has not been studied in decisions that require evidence to be integrated over time. Such decisions are important when we do not have all the information available at once. A key feature of such decisions is how evidence is weighted over time, known as the integration ‘kernel’. Here we provide a formal expression for the integration kernel in divisive normalization, and show that divisive normalization can quantitatively account for the perceptual decision making behaviour of 133 human participants, performing as well as the state-of-the-art Drift Diffusion Model, the predominant model for perceptual evidence accumulation.

Fractional Prabhakar Derivative in Diffusion Equation with Non-Static Stochastic Resetting

In this work, we investigate a series of mathematical aspects for the fractional diffusion equation with stochastic resetting. The stochastic resetting process in Evans–Majumdar sense has several applications in science, with a particular emphasis on non-equilibrium physics and biological systems. We propose a version of the stochastic resetting theory for systems in which the reset point is in motion, so the walker does not return to the initial position as in the standard model, but returns to a point that moves in space. In addition, we investigate the proposed stochastic resetting model for diffusion with the fractional operator of Prabhakar. The derivative of Prabhakar consists of an integro-differential operator that has a Mittag–Leffler function with three parameters in the integration kernel, so it generalizes a series of fractional operators such as Riemann–Liouville–Caputo. We present how the generalized model of stochastic resetting for fractional diffusion implies a rich class of anomalous diffusive processes, i.e., ⟨ ( Δ x ) 2 ⟩ ∝ t α , which includes sub-super-hyper-diffusive regimes. In the sequence, we generalize these ideas to the fractional Fokker–Planck equation for quadratic potential U ( x ) = a x 2 + b x + c . This work aims to present the generalized model of Evans–Majumdar’s theory for stochastic resetting under a new perspective of non-static restart points.

Regulation of evidence accumulation by pupil-linked arousal processes

Integrating evidence over time is crucial for effective decision making. For simple perceptual decisions, a large body of work suggests that humans and animals are capable of integrating evidence over time fairly well, but that their performance is far from optimal. This suboptimality is thought to arise from a number of different sources including: (1) noise in sensory and motor systems, (2) unequal weighting of evidence over time, (3) order effects from previous trials and (4) irrational side biases for one choice over another. In this work we investigated these di.erent sources of suboptimality and how they are related to pupil dilation, a putative correlate of norepinephrine tone. In particular, we measured pupil response in humans making a series of decisions based on rapidly-presented auditory information in an evidence accumulation task. We found that people exhibited all four types of suboptimality, and that some of these suboptimalities covaried with each other across participants. Pupillometry showed that only noise and the uneven weighting of evidence over time, the ‘integration kernel’, were related to the change in pupil response during the stimulus. Moreover, these two different suboptimalities were related to different aspects of the pupil signal, with the individual differences in pupil response associated with individual differences in integration kernel, while trial-by-trial fluctuations in pupil response were associated with trial-by-trial fluctuations in noise. These results suggest that di.erent sources of suboptimality in human perceptual decision making are related to distinct pupil-linked processes possibly related to tonic and phasic norepinephrine activity.

The force on a sphere in a uniform flow with small-amplitude oscillations at finite Reynolds number

The unsteady force acting on a sphere that is held fixed in a steady uniform flow with small-amplitude oscillations is evaluated to O(Re) for small Reynolds number Re. Good agreement is shown with the numerical results of Mei, Lawrence & Adrian (1991) up to Re ≈ 0.5. The analytical result is transformed by Fourier inversion to allow for an arbitrary time-dependent motion which is small relative to the steady uniform flow. This yields a history-dependent force which has an integration kernel that decays exponentially for large time.