Russia: A Eurasian Anomaly

From the Washington University Office of Undergraduate Research Digest (WUURD), Vol. 13, 05-01-2018. Published by the Office of Undergraduate Research. Joy Zalis Kiefer, Director of Undergraduate Research and Associate Dean in the College of Arts & Sciences; Lindsey Paunovich, Editor; Helen Human, Programs Manager and Assistant Dean in the College of Arts and Sciences Mentor(s): James Wertsc

On the geometry of Hamiltonian chaos

We show that Gutzwiller's characterization of chaotic Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor in the structure of the Hamiltonian can be extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce the Hamilton equations of the original potential model when a transition is made to the dual manifold, and the geodesics in the dual space coincide with the orbits of the Hamiltonian potential model. We therefore find a direct geometrical description of the time development of a Hamiltonian potential model. The second covariant derivative of the geodesic deviation in this dual manifold generates a dynamical curvature, resulting in (energy dependent) criteria for unstable behavior different from the usual Lyapunov criteria. We discuss some examples of unstable Hamiltonian systems in two dimensions giving, in particular, detailed results for a potential obtained from a fifth order expansion of a Toda lattice Hamiltonian.Comment: 7 pages TeX, Figure captions, 4 figures (eps). Some clarifications, added reference

Self-Wiring of Neural Networks

In order to form the intricate network of synaptic connections in the brain, the growth cones migrate through the embryonic environment to their targets using chemical communication. As a first step to study self-wiring, 2D model systems of neurons have been used. We present a simple model to reproduce the salient features of the 2D systems. The model incorporates random walkers representing the growth cones, which migrate in response to chemotaxis substances extracted by the soma and communicate with each other and with the soma by means of attractive chemotactic "feedback".Comment: 10 pages, 10 PostScript figures. Originally submitted to the neuro-dev archive which was never publicly announced (was 9710001

Entropy measures as geometrical tools in the study of cosmology

Classical chaos is often characterized as exponential divergence of nearby trajectories. In many interesting cases these trajectories can be identified with geodesic curves. We define here the entropy by $S = \ln \chi (x)$ with $\chi(x)$ being the distance between two nearby geodesics. We derive an equation for the entropy which by transformation to a Ricatti-type equation becomes similar to the Jacobi equation. We further show that the geodesic equation for a null geodesic in a double warped space time leads to the same entropy equation. By applying a Robertson-Walker metric for a flat three-dimensional Euclidian space expanding as a function of time, we again reach the entropy equation stressing the connection between the chosen entropy measure and time. We finally turn to the Raychaudhuri equation for expansion, which also is a Ricatti equation similar to the transformed entropy equation. Those Ricatti-type equations have solutions of the same form as the Jacobi equation. The Raychaudhuri equation can be transformed to a harmonic oscillator equation, and it has been shown that the geodesic deviation equation of Jacobi is essentially equivalent to that of a harmonic oscillator. The Raychaudhuri equations are strong geometrical tools in the study of General Relativity and Cosmology. We suggest a refined entropy measure applicable in Cosmology and defined by the average deviation of the geodesics in a congruence.Comment: Final Versio

Gene Essentiality Analyzed by In Vivo Transposon Mutagenesis and Machine Learning in a Stable Haploid Isolate of Candida albicans

This work was supported by European Research Council Advanced Award 340087 (RAPLODAPT) to J.B., the Dahlem Centre of Plant Sciences (DCPS) of the Freie Universität Berlin (R.K.), Israel Science Foundation grant no. 715/18 (R.S.), the Wellcome Trust (grants 086827, 075470, 101873, and 200208) and the MRC Centre for Medical Mycology (N006364/1) (N.A.R.G.). Data availability.All of the code and required dependencies for analysis of the TnSeq data are available at https://github.com/berman-lab/transposon-pipeline. Library insertion sequences are available at NCBI under project PRJNA490565 (https://www.ncbi.nlm.nih.gov/bioproject/PRJNA490565). Datasets S1 through S9 are available at https://doi.org/10.6084/m9.figshare.c.4251182.Peer reviewedPublisher PD

Immunocytochemical localization of the GABAA/benzodiazepine receptor in the guinea pig cochlear nucleus: evidence for receptor localization heterogeneity

Immunocytochemistry with a monoclonal antibody against the GABAA/benzodiazepine receptor showed labeled axo-dendritic synapses in the anteroventral cochlear nucleus. In the dorsal cochlear nucleus, label was seen apposing both axo-somatic and axo-dendritic terminals. The results suggest a heterogeneous distribution of GABA receptors, together with a possible segregation of receptor subtypes between somata and dendrites in certain neurons. The presence of cytoplasmic labeling in some neurons might reflect a higher receptor turnover rate in these neurons.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/27639/1/0000015.pd