Maximal Entropy Random Walk: solvable cases of dynamics

We focus on the study of dynamics of two kinds of random walk: generic random walk (GRW) and maximal entropy random walk (MERW) on two model networks: Cayley trees and ladder graphs. The stationary probability distribution for MERW is given by the squared components of the eigenvector associated with the largest eigenvalue \lambda_0 of the adjacency matrix of a graph, while the dynamics of the probability distribution approaching to the stationary state depends on the second largest eigenvalue \lambda_1. Firstly, we give analytic solutions for Cayley trees with arbitrary branching number, root degree, and number of generations. We determine three regimes of a tree structure that result in different statics and dynamics of MERW, which are due to strongly, critically, and weakly branched roots. We show how the relaxation times, generically shorter for MERW than for GRW, scale with the graph size. Secondly, we give numerical results for ladder graphs with symmetric defects. MERW shows a clear exponential growth of the relaxation time with the size of defective regions, which indicates trapping of a particle within highly entropic intact region and its escaping that resembles quantum tunneling through a potential barrier. GRW shows standard diffusive dependence irrespective of the defects.Comment: 13 pages, 6 figures, 24th Marian Smoluchowski Symposium on Statistical Physics (Zakopane, Poland, September 17-22, 2011

From synaptic interactions to collective dynamics in random neuronal networks models: critical role of eigenvectors and transient behavior

The study of neuronal interactions is currently at the center of several neuroscience big collaborative projects (including the Human Connectome, the Blue Brain, the Brainome, etc.) which attempt to obtain a detailed map of the entire brain matrix. Under certain constraints, mathematical theory can advance predictions of the expected neural dynamics based solely on the statistical properties of such synaptic interaction matrix. This work explores the application of free random variables (FRV) to the study of large synaptic interaction matrices. Besides recovering in a straightforward way known results on eigenspectra of neural networks, we extend them to heavy-tailed distributions of interactions. More importantly, we derive analytically the behavior of eigenvector overlaps, which determine stability of the spectra. We observe that upon imposing the neuronal excitation/inhibition balance, although the eigenvalues remain unchanged, their stability dramatically decreases due to strong non-orthogonality of associated eigenvectors. It leads us to the conclusion that the understanding of the temporal evolution of asymmetric neural networks requires considering the entangled dynamics of both eigenvectors and eigenvalues, which might bear consequences for learning and memory processes in these models. Considering the success of FRV analysis in a wide variety of branches disciplines, we hope that the results presented here foster additional application of these ideas in the area of brain sciences.Comment: 24 pages + 4 pages of refs, 8 figure

Revisiting non-linear functional brain co-activations: directed, dynamic and delayed

The center stage of neuro-imaging is currently occupied by studies of functional correlations between brain regions. These correlations define the brain functional networks, which are the most frequently used framework to represent and interpret a variety of experimental findings. In previous work we first demonstrated that the relatively stronger BOLD activations contain most of the information relevant to understand functional connectivity and subsequent work confirmed that a large compression of the original signals can be obtained without significant loss of information. In this work we revisit the correlation properties of these epochs to define a measure of nonlinear dynamic directed functional connectivity (nldFC) across regions of interest. We show that the proposed metric provides at once, without extensive numerical complications, directed information of the functional correlations, as well as a measure of temporal lags across regions, overall offering a different perspective in the analysis of brain co-activation patterns. In this paper we provide for a proof of concept, based on replicating and completing existing results on an Autism database, to discuss the main features and advantages of the proposed strategy for the study of brain functional correlations. These results show new interpretations of the correlations found on this sample.Comment: 12 pages, 8 figure

How we move is universal: scaling in the average shape of human activity

Human motor activity is constrained by the rhythmicity of the 24 hours circadian cycle, including the usual 12-15 hours sleep-wake cycle. However, activity fluctuations also appear over a wide range of temporal scales, from days to a few seconds, resulting from the concatenation of a myriad of individual smaller motor events. Furthermore, individuals present different propensity to wakefulness and thus to motor activity throughout the circadian cycle. Are activity fluctuations across temporal scales intrinsically different, or is there a universal description encompassing them? Is this description also universal across individuals, considering the aforementioned variability? Here we establish the presence of universality in motor activity fluctuations based on the empirical study of a month of continuous wristwatch accelerometer recordings. We study the scaling of average fluctuations across temporal scales and determine a universal law characterized by critical exponents $\alpha$, $\tau$ and $1/{\mu}$. Results are highly reminiscent of the universality described for the average shape of avalanches in systems exhibiting crackling noise. Beyond its theoretical relevance, the present results can be important for developing objective markers of healthy as well as pathological human motor behavior.Comment: Communicated to the Granada Seminar, "Physics Meets the Social Sciences: Emergent cooperative phenomena, from bacterial to human group behavior". June 14-19, 2015. La Herradura, Spai

Revisiting nonlinear functional brain co-activations: Directed, dynamic, and delayed

The center stage of neuro-imaging is currently occupied by studies of functional correlations between brain regions. These correlations define the brain functional networks, which are the most frequently used framework to represent and interpret a variety of experimental findings. In the previous study, we first demonstrated that the relatively stronger blood oxygenated level dependent (BOLD) activations contain most of the information relevant to understand functional connectivity, and subsequent work confirmed that a large compression of the original signals can be obtained without significant loss of information. In this study, we revisit the correlation properties of these epochs to define a measure of nonlinear dynamic directed functional connectivity (nldFC) across regions of interest. We show that the proposed metric provides at once, without extensive numerical complications, directed information of the functional correlations, as well as a measure of temporal lags across regions, overall offering a different and complementary perspective in the analysis of brain co-activation patterns. In this study, we provide further details for the computations of these measures and for a proof of concept based on replicating existing results from an Autistic Syndrome database, and discuss the main features and advantages of the proposed strategy for the study of brain functional correlations.Fil: Cifre, Ignacio. Universitat Ramon Llull; España. Universidad Nacional de San Martin. Escuela de Ciencia y Tecnologia. Centro de Estudios Multidisciplinarios En Sistemas Complejos y Ciencias del Cerebro.; ArgentinaFil: Miller Flores, Maria T.. Universidad Nacional de San Martin. Escuela de Ciencia y Tecnologia. Centro de Estudios Multidisciplinarios En Sistemas Complejos y Ciencias del Cerebro.; ArgentinaFil: Penalba, Lucia. Universitat Ramon Llull; EspañaFil: Ochab, Jeremi K.. Jagiellonian University; PoloniaFil: Chialvo, Dante Renato. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de San Martin. Escuela de Ciencia y Tecnologia. Centro de Estudios Multidisciplinarios En Sistemas Complejos y Ciencias del Cerebro.; Argentin

Non-linear Functional Brain Co-activations in Short-Term Memory Distortion Tasks

Recent works shed light on the neural correlates of true and false recognition and the influence of time of day on cognitive performance. The current study aimed to investigate the modulation of the false memory formation by the time of day using a non-linear correlation analysis originally designed for fMRI resting-state data. Fifty-four young and healthy participants (32 females, mean age: 24.17 ± 3.56 y.o.) performed in MRscanner the modified Deese-Roediger-McDermott paradigm in short-term memory during one session in the morning and another in the evening. Subjects’ responses were modeled with a general linear model, which includes as a predictor the nonlinear correlations of regional BOLD activity with the stimuli, separately for encoding and retrieval phases. The results show the dependence of the non-linear correlations measures with the time of day and the type of the probe. In addition, the results indicate differences in the correlations measures with hippocampal regions between positive and lure probes. Besides confirming previous results on the influence of time-of-day on cognitive performance, the study demonstrates the effectiveness of the non-linear correlation analysis method for the characterization of fMRI task paradigms.Fil: Ceglarek, Anna. Jagiellonian University; PoloniaFil: Ochab, Jeremi K.. Jagiellonian University; PoloniaFil: Cifre, Ignacio. Universitat Ramon Llull; EspañaFil: Fafrowicz, Magdalena. Jagiellonian University; PoloniaFil: Sikora Wachowicz, Barbara. Jagiellonian University; PoloniaFil: Lewandowska, Koryna. Jagiellonian University; PoloniaFil: Bohaterewicz, Bartosz. Jagiellonian University; PoloniaFil: Marek, Tadeusz. Jagiellonian University; PoloniaFil: Chialvo, Dante Renato. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Ciencias Físicas. - Universidad Nacional de San Martín. Instituto de Ciencias Físicas; Argentin

Observing changes in human functioning during induced sleep deficiency and recovery periods

Prolonged periods of sleep restriction seem to be common in the contemporary world. Sleep loss causes perturbations of circadian rhythmicity and degradation of waking alertness as reflected in attention, cognitive efficiency and memory. Understanding whether and how the human brain recovers from chronic sleep loss is important not only from a scientific but also from a public health perspective. In this work we report on behavioral, motor, and neurophysiological correlates of sleep loss in healthy adults in an unprecedented study conducted in natural conditions and comprising 21 consecutive days divided into periods of 4 days of regular life (a baseline), 10 days of chronic partial sleep restriction (30% reduction relative to individual sleep need) and 7 days of recovery. Throughout the whole experiment we continuously measured the spontaneous locomotor activity by means of actigraphy with 1-minute resolution. On a daily basis the subjects were undergoing EEG measurements (64-electrodes with 500 Hz sampling frequency): resting state with eyes open and closed (8 minutes long each) followed by Stroop task lasting 22 minutes. Altogether we analyzed actigraphy (distributions of rest and activity durations), behavioral measures (reaction times and accuracy from Stroop task) and EEG (amplitudes, latencies and scalp maps of event-related potentials from Stroop task and power spectra from resting states). We observed unanimous deterioration in all the measures during sleep restriction. Further results indicate that a week of recovery subsequent to prolonged periods of sleep restriction is insufficient to recover fully. Only one measure (mean reaction time in Stroop task) reverted to baseline values, while the others did not.Fil: Ochab, Jeremi K.. Jagiellonian University. Marian Smoluchowski Institute of Physics; Polonia. Jagiellonian University. Mark Kac Complex Systems Research Centre; PoloniaFil: Szwed, Jerzy. Jagiellonian University. Marian Smoluchowski Institute of Physics; Polonia. Jagiellonian University. Mark Kac Complex Systems Research Centre; PoloniaFil: Oles, Katarzyna. Jagiellonian University. Marian Smoluchowski Institute of Physics; PoloniaFil: Beres, Anna. Jagiellonian University. Department of Cognitive Neuroscience and Neuroergonomics; PoloniaFil: Chialvo, Dante Renato. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de San Martin. Escuela de Ciencia y Tecnologia. Centro de Estudios Multidisciplinarios En Sistemas Complejos y Ciencias del Cerebro.; ArgentinaFil: Domagalik, Aleksandra. Jagiellonian University. Department of Cognitive Neuroscience and Neuroergonomics; PoloniaFil: Frafrowicz, Magdalena. Jagiellonian University. Department of Cognitive Neuroscience and Neuroergonomics; PoloniaFil: Oginska, Halszka. Jagiellonian University. Department of Cognitive Neuroscience and Neuroergonomics; PoloniaFil: Gudowska-Nowak, Ewa. Jagiellonian University. Marian Smoluchowski Institute of Physics; Polonia. Jagiellonian University. Małopolska Center of Biotechnology ; PoloniaFil: Marek, Tadeusz. Jagiellonian University. Department of Cognitive Neuroscience and Neuroergonomic; Polonia. Jagiellonian University. Małopolska Center of Biotechnology; ArgentinaFil: Nowak, Maciej A.. Jagiellonian University. Marian Smoluchowski Institute of Physics; Polonia. Jagiellonian University. Mark Kac Complex Systems Research Centre; Poloni