Dynamic BOLD functional connectivity in humans and its electrophysiological correlates

Neural oscillations subserve many human perceptual and cognitive operations. Accordingly, brain functional connectivity is not static in time, but fluctuates dynamically following the synchronization and desynchronization of neural populations. This dynamic functional connectivity has recently been demonstrated in spontaneous fluctuations of the Blood Oxygen Level-Dependent (BOLD) signal, measured with functional Magnetic Resonance Imaging (fMRI). We analyzed temporal fluctuations in BOLD connectivity and their electrophysiological correlates, by means of long (≈50 min) joint electroencephalographic (EEG) and fMRI recordings obtained from two populations: 15 awake subjects and 13 subjects undergoing vigilance transitions. We identified positive and negative correlations between EEG spectral power (extracted from electrodes covering different scalp regions) and fMRI BOLD connectivity in a network of 90 cortical and subcortical regions (with millimeter spatial resolution). In particular, increased alpha (8-12 Hz) and beta (15-30 Hz) power were related to decreased functional connectivity, whereas gamma (30-60 Hz) power correlated positively with BOLD connectivity between specific brain regions. These patterns were altered for subjects undergoing vigilance changes, with slower oscillations being correlated with functional connectivity increases. Dynamic BOLD functional connectivity was reflected in the fluctuations of graph theoretical indices of network structure, with changes in frontal and central alpha power correlating with average path length. Our results strongly suggest that fluctuations of BOLD functional connectivity have a neurophysiological origin. Positive correlations with gamma can be interpreted as facilitating increased BOLD connectivity needed to integrate brain regions for cognitive performance. Negative correlations with alpha suggest a temporary functional weakening of local and long-range connectivity, associated with an idling state

Partial Autoinformation to Characterize Symbolic Sequences

An information-theoretic approach to numerically determine the Markov order of discrete stochastic processes defined over a finite state space is introduced. To measure statistical dependencies between different time points of symbolic time series, two information-theoretic measures are proposed. The first measure is time-lagged mutual information between the random variables Xn and Xn+k, representing the values of the process at time points n and n + k, respectively. The measure will be termed autoinformation, in analogy to the autocorrelation function for metric time series, but using Shannon entropy rather than linear correlation. This measure is complemented by the conditional mutual information between Xn and Xn+k, removing the influence of the intermediate values Xn+k−1, …, Xn+1. The second measure is termed partial autoinformation, in analogy to the partial autocorrelation function (PACF) in metric time series analysis. Mathematical relations with known quantities such as the entropy rate and active information storage are established. Both measures are applied to a number of examples, ranging from theoretical Markov and non-Markov processes with known stochastic properties, to models from statistical physics, and finally, to a discrete transform of an EEG data set. The combination of autoinformation and partial autoinformation yields important insights into the temporal structure of the data in all test cases. For first- and higher-order Markov processes, partial autoinformation correctly identifies the order parameter, but also suggests extended, non-Markovian effects in the examples that lack the Markov property. For three hidden Markov models (HMMs), the underlying Markov order is found. The combination of both quantities may be used as an early step in the analysis of experimental, non-metric time series and can be employed to discover higher-order Markov dependencies, non-Markovianity and periodicities in symbolic time series

On two-particle Anderson localization at low energies

We prove exponential spectral localization in a two-particle lattice Anderson model, with a short-range interaction and external random i.i.d. potential, at sufficiently low energies. The proof is based on the multi-particle multi-scale analysis developed earlier by Chulaevsky and Suhov (2009) in the case of high disorder. Our method applies to a larger class of random potentials than in Aizenman and Warzel (2009) where dynamical localization was proved with the help of the fractional moment method

Two examples of ungrading in higher education from the United States and from Germany

In this paper the authors discuss their experiences with ungrading at a small public university in the U.S. as well as a large public university in Germany. The courses described are Calculus 1, Mathematics for Liberal Arts, and courses for pre-service secondary teachers of mathematics. We outline and compare our approaches, discuss student performance and feedback and present some interesting patterns relating to gender. A shortened and revised version of this paper appeared in PRIMUS 33 (2023), no. 9, 1035-1054, DOI: 10.1080/10511970.2023.2229819.Comment: 23 page

Wegner bounds for a two-particle tight binding model

We consider a quantum two-particle system on a d-dimensional lattice with interaction and in presence of an IID external potential. We establish Wegner-typer estimates for such a model. The main tool used is Stollmann's lemma

Flupenthixol in relapse prevention in schizophrenics with comorbid alcoholism: Results from an open clinical study

Substance use, especially alcoholism, has been recognized as a significant problem in schizophrenic patients, though only a few studies on the effects of pharmacotherapy in these patients have been conducted so far. The thioxanthene neuroleptic flupenthixol, which can be given intramuscularly (i.m.) for improving compliance, has been studied as a possible anti-craving drug both in animal models of alcoholism and some clinical studies. Pilot studies suggest that comorbid schizophrenics with substance use may benefit from treatment with flupenthixol. Efficacy of flupenthixol (10-60 mg i.m.) in reducing alcohol consumption of dual diagnosis patients was studied in an open 6-month clinical trial in 27 schizophrenics with comorbid alcoholism. Twenty-one patients entered the intention-to-treat analysis. Fourteen subjects were completers, 13 dropped out. Six patients completely abstained from alcohol during treatment. Alcohol consumption was significantly reduced compared to baseline (4 weeks before treatment as measured by timeline follow-back interview). In general, while patients showed a marked improvement concerning alcohol consumption, only a slight improvement in psychopathology was recorded. Overall tolerability was good. These data indicate a probable beneficial effect of flupenthixol in schizophrenic patients with comorbid alcoholism. Although the efficacy of flupenthixol as an anti-craving drug in dual diagnosis patients has to be explored in further studies, the drug may be considered a promising medication for these patients. Copyright (C) 2003 S. Karger AG, Basel

Exploiting environmental resonances to enhance qubit quality factors

We discuss dephasing times for a two-level system (including bias) coupled to a damped harmonic oscillator. This system is realized in measurements on solid-state Josephson qubits. It can be mapped to a spin-boson model with a spectral function with an approximately Lorentzian resonance. We diagonalize the model by means of infinitesimal unitary transformations (flow equations), and calculate correlation functions, dephasing rates, and qubit quality factors. We find that these depend strongly on the environmental resonance frequency $\Omega$; in particular, quality factors can be enhanced significantly by tuning $\Omega$ to lie below the qubit frequency $\Delta$.Comment: 5 psges, 5 figure

Renormalization Group Derivation of the Localization Length Exponent in the Integer Quantum Hall Effect

We compute, neglecting possible effects of subleading irrelevant couplings, the localization length exponent in the integer quantum Hall effect, for the case of white noise random potentials. The result obtained is $\nu=2$ for all Landau levels. Our approach consists in a renormalization group transformation of Landau orbitals, which iterates the generating functional of Green's functions for the localization problem. The value of $\nu$ is obtained from the asymptotic form of the renormalization group mapping. The basic assumptions in our derivation are the existence of a scaling law for the localization length and the absence of Landau level mixing.Comment: Computations are discussed in a more detailed wa

Exact and Approximate Stochastic Simulation of Intracellular Calcium Dynamics

In simulations of chemical systems, the main task is to find an exact or approximate solution of the chemical master equation (CME) that satisfies certain constraints with respect to computation time and accuracy. While Brownian motion simulations of single molecules are often too time consuming to represent the mesoscopic level, the classical Gillespie algorithm is a stochastically exact algorithm that provides satisfying results in the representation of calcium microdomains. Gillespie's algorithm can be approximated via the tau-leap method and the chemical Langevin equation (CLE). Both methods lead to a substantial acceleration in computation time and a relatively small decrease in accuracy. Elimination of the noise terms leads to the classical, deterministic reaction rate equations (RRE). For complex multiscale systems, hybrid simulations are increasingly proposed to combine the advantages of stochastic and deterministic algorithms. An often used exemplary cell type in this context are striated muscle cells (e.g., cardiac and skeletal muscle cells). The properties of these cells are well described and they express many common calcium-dependent signaling pathways. The purpose of the present paper is to provide an overview of the aforementioned simulation approaches and their mutual relationships in the spectrum ranging from stochastic to deterministic algorithms

Mott--Hubbard transition vs. Anderson localization of correlated, disordered electrons

The phase diagram of correlated, disordered electrons is calculated within dynamical mean--field theory using the geometrically averaged (''typical'') local density of states. Correlated metal, Mott insulator and Anderson insulator phases, as well as coexistence and crossover regimes are identified. The Mott and Anderson insulators are found to be continuously connected.Comment: 4 pages, 4 figure