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

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

Fungi colonizing the soil and roots of tomato (Lycopersicum esculentum Mill.) plants treated with biological control agents

Tomato plants, cv. Rumba Ożarowska, grown in the greenhouse of the University of Warmia and Mazury, were protected in the form of alternate spraying (twice) and watering (twice) with 5% aqueous extracts of the following plant species: Aloe vulgaris Lam., Achillea millefolium L., Mentha piperita L., Polygonum aviculare L., Equisetum arvense L., Juglans regia L. and Urtica dioica L. Plants not treated with the extracts served as control. After fruit harvest, samples of roots and soil were collected. The roots were disinfected and next placed on PDA medium. Soil-colonizing fungi were cultured on Martin medium. Fungi were identified microscopically after incubation. Pathogenic fungal species, Colletotrichum coccodes, Fusarium equiseti, F. oxysporum and F. poae, accounted for over 60% of all isolates obtained from the roots of tomato plants. The soil fungal community was dominated by yeast-like fungi (75.4%), whereas pathogenic fungi were present in low numbers. The applied 5% aqueous plant extracts effectively reduced the abundance of fungi, including pathogenic species, colonizing tomato plants and soil. The extract from P. aviculare showed the highest efficacy, while the extract from J. regia was least effective. Fungi showing antagonistic activity against pathogens (Paecilomyces roseum and species of the genus Trichoderma) were isolated in greatest abundance from the soil and the roots of tomato plants treated with A. millefolium, M. piperita and U. dioica extracts

Modelling and optimisation of the operation of a radiant warmer

This paper presents numerical calculations of the temperature field obtained for the case of a neonate placed under a radiant warmer. The results of the simulations show a very non-uniform temperature distribution on the skin of the neonate, which may cause increased evaporation leading to severe dehydration. For this reason, we propose some modifications on the geometry and operation of the radiant warmer, in order to make the temperature distribution more uniform and prevent the high temperature gradients observed on the surface of the neonate. It is concluded that placing a high conductivity blanket over the neonate and introducing additional screens along the side of the mattress, thus recovering the radiation heat escaping through the side boundaries, helped providing more uniform temperature fields.The European Union for the Marie Curie Fellowship grant awarded to the Centre for CFD, University of Leeds

A combined study of heat and mass transfer in an infant incubator with an overhead screen

The main objective of this study is to investigate the major physical processes taking place inside an infant incubator, before and after modifications have been made to its interior chamber. The modification involves the addition of an overhead screen to decrease radiation heat losses from the infant placed inside the incubator. The present study investigates the effect of these modifications on the convective heat flux from the infant’s body to the surrounding environment inside the incubator. A combined analysis of airflow and heat transfer due to conduction, convection, radiation and evaporation has been performed, in order to calculate the temperature and velocity fields inside the incubator before and after the design modification. Due to the geometrical complexity of the model, Computer-Aided Design (CAD) applications were used to generate a computer-based model. All numerical calculations have been performed using the commercial Computational Fluid Dynamics (CFD) package FLUENT, together with in-house routines used for managing purposes and User-Defined Functions (UDFs) which extend the basic solver capabilities. Numerical calculations have been performed for three different air inlet temperatures: 32, 34 and 36ºC. The study shows a decrease of the radiative and convective heat losses when the overhead screen is present. The results obtained were numerically verified as well as compared with results available in the literature from investigations of dry heat losses from infant manikins

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

Spectral density of generalized Wishart matrices and free multiplicative convolution

We investigate the level density for several ensembles of positive random matrices of a Wishart--like structure, $W=XX^{\dagger}$, where $X$ stands for a nonhermitian random matrix. In particular, making use of the Cauchy transform, we study free multiplicative powers of the Marchenko-Pastur (MP) distribution, ${\rm MP}^{\boxtimes s}$, which for an integer $s$ yield Fuss-Catalan distributions corresponding to a product of $s$ independent square random matrices, $X=X_1\cdots X_s$. New formulae for the level densities are derived for $s=3$ and $s=1/3$. Moreover, the level density corresponding to the generalized Bures distribution, given by the free convolution of arcsine and MP distributions is obtained. We also explain the reason of such a curious convolution. The technique proposed here allows for the derivation of the level densities for several other cases.Comment: 10 latex pages including 4 figures, Ver 4, minor improvements and references updat

Chiral Disorder in QCD

Using the Gell-Mann-Oakes-Renner (GOR) relation and semi-classical arguments, we show that the bulk quark spectrum in QCD exhibits a variety of regimes including the ergodic one described by random matrix theory. We analyze the quark spectral form-factor in the diffusive and ballistic regime. We suggest that a class of chiral transitions in QCD is possibly of the metal-insulator type, with a universal spectral statistics at the mobility edge