Anatomical origins of ocular dominance in mouse primary visual cortex

Ocular dominance (OD) plasticity is a classic paradigm for studying the effect of experience and deprivation on cortical development, and is manifested as shifts in the relative strength of binocular inputs to primary visual cortex (V1). The mouse has become an increasingly popular model for mechanistic studies of OD plasticity and, consequently, it is important that we understand how binocularity is constructed in this species. One puzzling feature of the mouse visual system is the gross disparity between the physiological strength of each eye in V1 and their anatomical representation in the projection from retina to the dorsal lateral geniculate nucleus (dLGN). While the contralateral-to-ipsilateral (C/I) ratio of visually evoked responses in binocular V1 is approximately 2:1, the ipsilateral retinal projection is weakly represented in terms of retinal ganglion cell (RGC) density where the C/I ratio is approximately 9:1. The structural basis for this relative amplification of ipsilateral eye responses between retina and V1 is not known. Here we employed neuroanatomical tracing and morphometric techniques to quantify the relative magnitude of each eye's input to and output from the binocular segment of dLGN. Our data are consistent with the previous suggestion that a point in space viewed by both eyes will activate 9 times as many RGCs in the contralateral retina as in the ipsilateral retina. Nonetheless, the volume of the dLGN binocular segment occupied by contralateral retinogeniculate inputs is only 2.4 times larger than the volume occupied by ipsilateral retinogeniculate inputs and recipient relay cells are evenly distributed among the input layers. The results from our morphometric analyses show that this reduction in input volume can be accounted for by a three-to-one convergence of contralateral eye RGC inputs to dLGN neurons. Together, our findings establish that the relative density of feed-forward dLGN inputs determines the C/I response ratio of mouse binocular V1

Testing, Verification and Improvements of Timeliness in ROS Processes

This paper addresses the problem improving response times of robots implemented in the Robotic Operating System (ROS) using formal verification of computational-time feasibility. In order to verify the real time behaviour of a robot under uncertain signal processing times, methods of formal verification of timeliness properties are proposed for data flows in a ROS-based control system using Probabilistic Timed Programs (PTPs). To calculate the probability of success under certain time limits, and to demonstrate the strength of our approach, a case study is implemented for a robotic agent in terms of operational times verification using the PRISM model checker, which points to possible enhancements to the operation of the robotic agent

Order statistics of the trapping problem

When a large number N of independent diffusing particles are placed upon a site of a d-dimensional Euclidean lattice randomly occupied by a concentration c of traps, what is the m-th moment of the time t_{j,N} elapsed until the first j are trapped? An exact answer is given in terms of the probability Phi_M(t) that no particle of an initial set of M=N, N-1,..., N-j particles is trapped by time t. The Rosenstock approximation is used to evaluate Phi_M(t), and it is found that for a large range of trap concentracions the m-th moment of t_{j,N} goes as x^{-m} and its variance as x^{-2}, x being ln^{2/d} (1-c) ln N. A rigorous asymptotic expression (dominant and two corrective terms) is given for for the one-dimensional lattice.Comment: 11 pages, 7 figures, to be published in Phys. Rev.

Evaluation of rate law approximations in bottom-up kinetic models of metabolism.

BackgroundThe mechanistic description of enzyme kinetics in a dynamic model of metabolism requires specifying the numerical values of a large number of kinetic parameters. The parameterization challenge is often addressed through the use of simplifying approximations to form reaction rate laws with reduced numbers of parameters. Whether such simplified models can reproduce dynamic characteristics of the full system is an important question.ResultsIn this work, we compared the local transient response properties of dynamic models constructed using rate laws with varying levels of approximation. These approximate rate laws were: 1) a Michaelis-Menten rate law with measured enzyme parameters, 2) a Michaelis-Menten rate law with approximated parameters, using the convenience kinetics convention, 3) a thermodynamic rate law resulting from a metabolite saturation assumption, and 4) a pure chemical reaction mass action rate law that removes the role of the enzyme from the reaction kinetics. We utilized in vivo data for the human red blood cell to compare the effect of rate law choices against the backdrop of physiological flux and concentration differences. We found that the Michaelis-Menten rate law with measured enzyme parameters yields an excellent approximation of the full system dynamics, while other assumptions cause greater discrepancies in system dynamic behavior. However, iteratively replacing mechanistic rate laws with approximations resulted in a model that retains a high correlation with the true model behavior. Investigating this consistency, we determined that the order of magnitude differences among fluxes and concentrations in the network were greatly influential on the network dynamics. We further identified reaction features such as thermodynamic reversibility, high substrate concentration, and lack of allosteric regulation, which make certain reactions more suitable for rate law approximations.ConclusionsOverall, our work generally supports the use of approximate rate laws when building large scale kinetic models, due to the key role that physiologically meaningful flux and concentration ranges play in determining network dynamics. However, we also showed that detailed mechanistic models show a clear benefit in prediction accuracy when data is available. The work here should help to provide guidance to future kinetic modeling efforts on the choice of rate law and parameterization approaches

Critical dimensions for random walks on random-walk chains

The probability distribution of random walks on linear structures generated by random walks in $d$-dimensional space, $P_d(r,t)$, is analytically studied for the case $\xi\equiv r/t^{1/4}\ll1$. It is shown to obey the scaling form $P_d(r,t)=\rho(r) t^{-1/2} \xi^{-2} f_d(\xi)$, where $\rho(r)\sim r^{2-d}$ is the density of the chain. Expanding $f_d(\xi)$ in powers of $\xi$, we find that there exists an infinite hierarchy of critical dimensions, $d_c=2,6,10,\ldots$, each one characterized by a logarithmic correction in $f_d(\xi)$. Namely, for $d=2$, $f_2(\xi)\simeq a_2\xi^2\ln\xi+b_2\xi^2$; for $3\le d\le 5$, $f_d(\xi)\simeq a_d\xi^2+b_d\xi^d$; for $d=6$, $f_6(\xi)\simeq a_6\xi^2+b_6\xi^6\ln\xi$; for $7\le d\le 9$, $f_d(\xi)\simeq a_d\xi^2+b_d\xi^6+c_d\xi^d$; for $d=10$, $f_{10}(\xi)\simeq a_{10}\xi^2+b_{10}\xi^6+c_{10}\xi^{10}\ln\xi$, {\it etc.\/} In particular, for $d=2$, this implies that the temporal dependence of the probability density of being close to the origin $Q_2(r,t)\equiv P_2(r,t)/\rho(r)\simeq t^{-1/2}\ln t$.Comment: LATeX, 10 pages, no figures submitted for publication in PR

Retarding Sub- and Accelerating Super-Diffusion Governed by Distributed Order Fractional Diffusion Equations

We propose diffusion-like equations with time and space fractional derivatives of the distributed order for the kinetic description of anomalous diffusion and relaxation phenomena, whose diffusion exponent varies with time and which, correspondingly, can not be viewed as self-affine random processes possessing a unique Hurst exponent. We prove the positivity of the solutions of the proposed equations and establish the relation to the Continuous Time Random Walk theory. We show that the distributed order time fractional diffusion equation describes the sub-diffusion random process which is subordinated to the Wiener process and whose diffusion exponent diminishes in time (retarding sub-diffusion) leading to superslow diffusion, for which the square displacement grows logarithmically in time. We also demonstrate that the distributed order space fractional diffusion equation describes super-diffusion phenomena when the diffusion exponent grows in time (accelerating super-diffusion).Comment: 11 pages, LaTe

Order statistics for d-dimensional diffusion processes

We present results for the ordered sequence of first passage times of arrival of N random walkers at a boundary in Euclidean spaces of d dimensions

The unexpectedly short Holocene Humid Period in Northern Arabia

The early to middle Holocene Humid Period led to a greening of today's arid Saharo-Arabian desert belt. While this phase is well defined in North Africa and the Southern Arabian Peninsula, robust evidence from Northern Arabia is lacking. Here we fill this gap with unprecedented annually to sub-decadally resolved proxy data from Tayma, the only known varved lake sediments in Northern Arabia. Based on stable isotopes, micro-facies analyses and varve and radiocarbon dating, we distinguish five phases of lake development and show that the wet phase in Northern Arabia from 8800-7900 years BP is considerably shorter than the commonly defined Holocene Humid Period (similar to 11,000-5500 years BP). Moreover, we find a two century-long peak humidity at times when a centennial-scale dry anomaly around 8200 years BP interrupted the Holocene Humid Period in adjacent regions. The short humid phase possibly favoured Neolithic migrations into Northern Arabia representing a strong human response to environmental changes

Sublocalization, superlocalization, and violation of standard single parameter scaling in the Anderson model

We discuss the localization behavior of localized electronic wave functions in the one- and two-dimensional tight-binding Anderson model with diagonal disorder. We find that the distributions of the local wave function amplitudes at fixed distances from the localization center are well approximated by log-normal fits which become exact at large distances. These fits are consistent with the standard single parameter scaling theory for the Anderson model in 1d, but they suggest that a second parameter is required to describe the scaling behavior of the amplitude fluctuations in 2d. From the log-normal distributions we calculate analytically the decay of the mean wave functions. For short distances from the localization center we find stretched exponential localization ("sublocalization") in both, 1d and 2d. In 1d, for large distances, the mean wave functions depend on the number of configurations N used in the averaging procedure and decay faster that exponentially ("superlocalization") converging to simple exponential behavior only in the asymptotic limit. In 2d, in contrast, the localization length increases logarithmically with the distance from the localization center and sublocalization occurs also in the second regime. The N-dependence of the mean wave functions is weak. The analytical result agrees remarkably well with the numerical calculations.Comment: 12 pages with 9 figures and 1 tabl