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

Emergence of order in selection-mutation dynamics

We characterize the time evolution of a d-dimensional probability distribution by the value of its final entropy. If it is near the maximally-possible value we call the evolution mixing, if it is near zero we say it is purifying. The evolution is determined by the simplest non-linear equation and contains a d times d matrix as input. Since we are not interested in a particular evolution but in the general features of evolutions of this type, we take the matrix elements as uniformly-distributed random numbers between zero and some specified upper bound. Computer simulations show how the final entropies are distributed over this field of random numbers. The result is that the distribution crowds at the maximum entropy, if the upper bound is unity. If we restrict the dynamical matrices to certain regions in matrix space, for instance to diagonal or triangular matrices, then the entropy distribution is maximal near zero, and the dynamics typically becomes purifying.Comment: 8 pages, 8 figure

Aerothermal tests of a 12.5 percent cone at Mach 6.7 for various Reynolds numbers, angles of attack and nose shapes

The effects of free-stream unit Reynolds number, angle of attack, and nose shape on the aerothermal environment of a 3-ft basediameter, 12.5 deg half-angle cone were investigated in the Langley 8-foot high temperature tunnel at Mach 6.7. The average total temperature was 3300 R, the freestream unit Reynolds number ranged from 400,000 to 1,400,000 per foot, and the angle of attack ranged from 0 deg to 10 deg. Three nose configurations were tested on the cone: a 3-in-radius tip, a 1-in-radius tip on an ogive frustum, and a sharp tip on an ogive frustum. Surface-pressure and cold-wall heating-rate distributions were obtained for laminar, transitional temperature in the shock layer were obtained. The location of the start of transition moved forward both on windward and leeward sides with increasing free-stream Reynolds numbers, increasing angle of attack, and decreasing nose bluntness

Constrained Monte Carlo Method and Calculation of the Temperature Dependence of Magnetic Anisotropy

We introduce a constrained Monte Carlo method which allows us to traverse the phase space of a classical spin system while fixing the magnetization direction. Subsequently we show the method's capability to model the temperature dependence of magnetic anisotropy, and for bulk uniaxial and cubic anisotropies we recover the low-temperature Callen-Callen power laws in M. We also calculate the temperature scaling of the 2-ion anisotropy in L10 FePt, and recover the experimentally observed M^2.1 scaling. The method is newly applied to evaluate the temperature dependent effective anisotropy in the presence of the N'eel surface anisotropy in thin films with different easy axis configurations. In systems having different surface and bulk easy axes, we show the capability to model the temperature-induced reorientation transition. The intrinsic surface anisotropy is found to follow a linear temperature behavior in a large range of temperatures

Modeling the X-ray Contribution of X-ray Binary Jets

Astrophysical jets exist in both XRBs and AGN, and seem to share common features, particularly in the radio. While AGN jets are known to emit X-rays, the situation for XRB jets is not so clear. Radio jets have been resolved in several XRBs in the low/hard state, establishing that some form of outflow is routinely present in this state. Interestingly, the flat-to-inverted radio synchrotron emission associated with these outflows strongly correlates with the X-ray emission in several sources, suggesting that the jet plasma plays a role at higher frequencies. In this same state, there is increasing evidence for a turnover in the IR/optical where the flat-to-inverted spectrum seems to connect to an optically thin component extending into the X-rays. We discuss how jet synchrotron emission is likely to contribute to the X-rays, in addition to inverse Compton up-scattering, providing a natural explanation for these correlations and the turnover in the IR/optical band. We present model parameters for fits to several sources, and address some common misconceptions about the jet model.Comment: 4 pages, 1 Table, conference proceedings for "The Physics of Relativistic Jets in the Chandra and XMM Era, Bologna, 2002", Eds. G. Brunetti, D. E. Harris, R. M. Sambruna & G. Sett

Orientation and temperature dependence of domain wall properties in FePt

An investigation of the orientation and temperature dependence of domain wall properties in FePt is presented. The authors use a microscopic, atomic model for the magnetic interactions within an effective, classical spin Hamiltonian constructed on the basis of spin-density functional calculations. They find a significant dependence of the domain wall width as well as the domain wall energy on the orientation of the wall with respect to the crystal lattice. Investigating the temperature dependence, they demonstrate the existence of elliptical domain walls in FePt at room temperature. The consequences of their findings for a micromagnetic continuum theory are discussed. (c) 2007 American Institute of Physics

Exchange Bias driven by Dzyaloshinskii-Moriya interactions

The exchange bias effect in compensated IrMn3/Co(111) system is studied using multiscale modeling from "ab initio" to atomistic calculations. We evaluate numerically the out-of-plane hysteresis loops of the bi-layer for different thickness of the ferromagnetic layer. The results show the existence of a perpendicular exchange bias field and an enhancement of the coercivity of the system. In order to elucidate the possible origin of the exchange bias, we analyze the hysteresis loops of a selected bi-layer by tuning the different contributions to the exchange interactions across the interface. Our results indicate that the exchange bias is primarily induced by the Dzyaloshinskii-Moriya interactions, while the coercivity is increased mainly due to a spin-flop mechanism

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