Simulation Investigation of Bulk and Surface Properties of Liquid Benzonitrile: Ring Stacking  Assessment and Deconvolution

This manuscript is devoted to classical molecular dynamics (MD) simulation studies of the bulk and surface properties of liquid benzonitrile (BZN) in the temperature range of 293-323K. The content and the simulation-analysis are inspired by our recent ab initio calculation on benzonitrile, whereas present results are to expand and develop macroscopic documentation involving data verification. We investigate the molecular stacking that involves phenyl ring, which is notably absent in the counterpart acetonitrile solvent. MD simulations of the bulk liquid unravel the hydrogen bond (C≡N⋯H) formation and strength, in the order of ortho-H >> meta-H ~>para-H. The possibility for ortho-H’s to get involved in the formation of two bonds simultaneously confirms each having - and -bonding features. The singularity centered at about 313 K found in the trend of the simulated temperature-dependent viscosity and diffusion coefficient of liquid BZN goes alongside the reported experiment, and the phenomenon may root from a change in the internal frictional motion of the molecular cluster in stacking modes. Accordingly, we used vast efforts for analysis particularly based on the deconvolution of the corresponding complex correlation functions. Specific angle-dependent correlation functions led to the recognition of the stacking molecules and their strict orientational character by utilizing relative molecular twist angles. Recognition of the strict orientational character of the stacking molecules, as a clue to the singularity in the viscosity trend, will be discussed based on specific angle-dependent correlation functions.

Generalized-hydrodynamic approach to inhomogeneous quenches: correlations, entanglement and quantum effects

We give a pedagogical introduction to the generalized hydrodynamic approach to inhomogeneous quenches in integrable many-body quantum systems. We review recent applications of the theory, focusing in particular on two classes of problems: bipartitioning protocols and trap quenches, which represent two prototypical examples of broken translational symmetry in either the system initial state or post-quench Hamiltonian. We report on exact results that have been obtained for generic time-dependent correlation functions and entanglement evolution, and discuss in detail the range of applicability of the theory. Finally, we present some open questions and suggest perspectives on possible future directions.

The Heston Model with Time-Dependent Correlation Driven by Isospectral Flows

In this work, we extend the Heston stochastic volatility model by including a time-dependent correlation that is driven by isospectral flows instead of a constant correlation, being motivated by the fact that the correlation between, e.g., financial products and financial institutions is hardly a fixed constant. We apply different numerical methods, including the method for backward stochastic differential equations (BSDEs) for a fast computation of the extended Heston model. An example of calibration to market data illustrates that our extended Heston model can provide a better volatility smile than the Heston model with other considered extensions.

On the existence of soliton-like collective modes in liquid water at the viscoelastic crossover

The problem of large-density variations in supercooled and ambient water has been widely discussed in the past years. Recent studies have indicated the possibility of nanometer-sized density variations on the subpicosecond and picosecond time scales. The nature of fluctuating density heterogeneities remains a highly debated issue. In the present work, we address the problem of possible association of such density variations with the dynamics of terahertz longitudinal acoustic-like modes in liquid water. Our study is based on the fact that the subpicosecond dynamics of liquid water are essentially governed by the structural relaxation. Using a mode coupling theory approach, we found that for typical values of parameters of liquid water, the dynamic mechanism coming from the combination of the structural relaxation process and the finiteness of the amplitude of terahertz longitudinal acoustic-like mode gives rise to a soliton-like collective mode on a temperature-dependent nanometer length scale. The characteristics of this mode are consistent with the estimates of the amplitudes and temperature-dependent correlation lengths of density fluctuations in liquid water obtained in experiments and simulations. Thus, the fully dynamic mechanism could contribute to the formation and dynamics of fluctuating density heterogeneities. The soliton-like collective excitations suggested by our analysis may be relevant to different phenomena connected with supercooled water and can be expected to be associated with some ultrafast biological processes.

Open Markov Chains: Cumulant Dynamics, Fluctuations and Correlations

In this work we propose a model for open Markov chains that can be interpreted as a system of non-interacting particles evolving according to the rules of a Markov chain. The number of particles in the system is not constant, because we allow the particles to arrive or leave the state space according to prescribed protocols. We describe this system by looking at the population of particles on every state by establishing the rules of time-evolution of the distribution of particles. We show that it is possible to describe the distribution of particles over the state space through the corresponding moment generating function. This description is given through the dynamics ruling the behavior of such a moment generating function and we prove that the system is able to attain the stationarity under some conditions. We also show that it is possible to describe the dynamics of the two first cumulants of the distribution of particles, which in some way is a simpler technique to obtain useful information of the open Markov chain for practical purposes. Finally we also study the behavior of the time-dependent correlation functions of the number of particles present in the system. We give some simple examples of open chains that either, can be fully described through the moment generating function or partially described through the exact solution of the cumulant dynamics.

Approximating Correlation Matrices Using Stochastic Lie Group Methods

Specifying time-dependent correlation matrices is a problem that occurs in several important areas of finance and risk management. The goal of this work is to tackle this problem by applying techniques of geometric integration in financial mathematics, i.e., to combine two fields of numerical mathematics that have not been studied yet jointly. Based on isospectral flows we create valid time-dependent correlation matrices, so called correlation flows, by solving a stochastic differential equation (SDE) that evolves in the special orthogonal group. Since the geometric structure of the special orthogonal group needs to be preserved we use stochastic Lie group integrators to solve this SDE. An application example is presented to illustrate this novel methodology.

Abnormal Levels of Metal Micronutrients and Autism Spectrum Disorder: A Perspective Review

The aim of the present review is to summarize the prevalence of abnormal levels of various metal micronutrients including copper (Cu), iron (Fe), magnesium (Mg), zinc (Zn), and selenium (Se) in Autism Spectrum Disorder (ASD) using hair, nail and serum samples. A correlation of selected abnormal metal ions with known neurodevelopmental processes using Gene Ontology (GO) term was also conducted. Data included in this review are derived from ASD clinical studies performed globally. Metal ion disparity data is also analyzed and discussed based on gender (Male/Female) to establish any gender dependent correlation. Finally, a rational perspective and possible path to better understand the role of metal micronutrients in ASD is suggested.