Moments of vicious walkers and M\"obius graph expansions

A system of Brownian motions in one-dimension all started from the origin and conditioned never to collide with each other in a given finite time-interval $(0, T]$ is studied. The spatial distribution of such vicious walkers can be described by using the repulsive eigenvalue-statistics of random Hermitian matrices and it was shown that the present vicious walker model exhibits a transition from the Gaussian unitary ensemble (GUE) statistics to the Gaussian orthogonal ensemble (GOE) statistics as the time $t$ is going on from 0 to $T$. In the present paper, we characterize this GUE-to-GOE transition by presenting the graphical expansion formula for the moments of positions of vicious walkers. In the GUE limit $t \to 0$, only the ribbon graphs contribute and the problem is reduced to the classification of orientable surfaces by genus. Following the time evolution of the vicious walkers, however, the graphs with twisted ribbons, called M\"obius graphs, increase their contribution to our expansion formula, and we have to deal with the topology of non-orientable surfaces. Application of the recent exact result of dynamical correlation functions yields closed expressions for the coefficients in the M\"obius expansion using the Stirling numbers of the first kind.Comment: REVTeX4, 11 pages, 1 figure. v.2: calculations of the Green function and references added. v.3: minor additions and corrections made for publication in Phys.Rev.

Evidence for geometry-dependent universal fluctuations of the Kardar-Parisi-Zhang interfaces in liquid-crystal turbulence

We provide a comprehensive report on scale-invariant fluctuations of growing interfaces in liquid-crystal turbulence, for which we recently found evidence that they belong to the Kardar-Parisi-Zhang (KPZ) universality class for 1+1 dimensions [Phys. Rev. Lett. 104, 230601 (2010); Sci. Rep. 1, 34 (2011)]. Here we investigate both circular and flat interfaces and report their statistics in detail. First we demonstrate that their fluctuations show not only the KPZ scaling exponents but beyond: they asymptotically share even the precise forms of the distribution function and the spatial correlation function in common with solvable models of the KPZ class, demonstrating also an intimate relation to random matrix theory. We then determine other statistical properties for which no exact theoretical predictions were made, in particular the temporal correlation function and the persistence probabilities. Experimental results on finite-time effects and extreme-value statistics are also presented. Throughout the paper, emphasis is put on how the universal statistical properties depend on the global geometry of the interfaces, i.e., whether the interfaces are circular or flat. We thereby corroborate the powerful yet geometry-dependent universality of the KPZ class, which governs growing interfaces driven out of equilibrium.Comment: 31 pages, 21 figures, 1 table; references updated (v2,v3); Fig.19 updated & minor changes in text (v3); final version (v4); J. Stat. Phys. Online First (2012

Quantum Interference in Superconducting Wire Networks and Josephson Junction Arrays: Analytical Approach based on Multiple-Loop Aharonov-Bohm Feynman Path-Integrals

We investigate analytically and numerically the mean-field superconducting-normal phase boundaries of two-dimensional superconducting wire networks and Josephson junction arrays immersed in a transverse magnetic field. The geometries we consider include square, honeycomb, triangular, and kagome' lattices. Our approach is based on an analytical study of multiple-loop Aharonov-Bohm effects: the quantum interference between different electron closed paths where each one of them encloses a net magnetic flux. Specifically, we compute exactly the sums of magnetic phase factors, i.e., the lattice path integrals, on all closed lattice paths of different lengths. A very large number, e.g., up to $10^{81}$ for the square lattice, exact lattice path integrals are obtained. Analytic results of these lattice path integrals then enable us to obtain the resistive transition temperature as a continuous function of the field. In particular, we can analyze measurable effects on the superconducting transition temperature, $T_c(B)$, as a function of the magnetic filed $B$, originating from electron trajectories over loops of various lengths. In addition to systematically deriving previously observed features, and understanding the physical origin of the dips in $T_c(B)$ as a result of multiple-loop quantum interference effects, we also find novel results. In particular, we explicitly derive the self-similarity in the phase diagram of square networks. Our approach allows us to analyze the complex structure present in the phase boundaries from the viewpoint of quantum interference effects due to the electron motion on the underlying lattices.Comment: 18 PRB-type pages, plus 8 large figure

Development of a photosynthesis model with an emphasis on ecological applications

A theoretical description of the simultaneous processes of photosynthesis and photorespiration in a single leaf is developed, based on the hypothesis that carbon dioxide and oxygen compete for the active site of ribulose diphosphate carboxylase. Michaelis-Menten kinetics and competitive inhibition at the end of a diffusion path provide the basic structure of the model. Data of Ludwig (1972) from sunflower are analyzed according to the formulation. This description is part of a more general physiological-ecological model of photosynthesis presented previously (Tenhunen et al., 1976a, b) and continues to elaborate sub-processes in terms of physiologically meaningful parameters. The description is considered a working hypothesis. Data on photorespiration from the literature are reviewed as they relate to this working hypothesis. Several lines of investigation are thereby suggested that will help clarify the role of photorespiration in whole leaf photosynthesis and determine the over-all utility of this modeling approach.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47718/1/442_2005_Article_BF01833627.pd

Discovery of widespread transcription initiation at microsatellites predictable by sequence-based deep neural network

Using the Cap Analysis of Gene Expression (CAGE) technology, the FANTOM5 consortium provided one of the most comprehensive maps of transcription start sites (TSSs) in several species. Strikingly, ~72% of them could not be assigned to a specific gene and initiate at unconventional regions, outside promoters or enhancers. Here, we probe these unassigned TSSs and show that, in all species studied, a significant fraction of CAGE peaks initiate at microsatellites, also called short tandem repeats (STRs). To confirm this transcription, we develop Cap Trap RNA-seq, a technology which combines cap trapping and long read MinION sequencing. We train sequence-based deep learning models able to predict CAGE signal at STRs with high accuracy. These models unveil the importance of STR surrounding sequences not only to distinguish STR classes, but also to predict the level of transcription initiation. Importantly, genetic variants linked to human diseases are preferentially found at STRs with high transcription initiation level, supporting the biological and clinical relevance of transcription initiation at STRs. Together, our results extend the repertoire of non-coding transcription associated with DNA tandem repeats and complexify STR polymorphism

Validation of RoboGuide to Support the Emulation of Sporting Movements using an Industrial Robot

AbstractMechanical testing plays an important role in the development of athletic footwear. Typically, these tests do not accurately represent the forces and motions the footwear experiences during human use and there is substantial scope to improve this situation. The purpose of this study was to assess the extent to which RoboGuide software can be used as a virtual environment to support the emulation of the ground contact phase of human locomotion on a FANUCTM six degrees of freedom industrial robot. A series of simple (linear and corner) and complex (sagittal plan heelstrike running) movements were completed on both the robot and RoboGuide using the same input kinematics. The effect of movement velocity, level of robotic smoothing and number of co-ordinate points defining the trajectory were also investigated. The resulting movement and timings on the robot and Roboguide were compared to the input kinematics as well as to each other. The results indicated small differences in the robot and RoboGuide trajectories for simple linear motions (< 30mm), that became much greater for the complex footstrike motion (∼ 100mm). These differences were affected by levels of smoothing and movement velocity and, notably, only with no smoothing did the robot and Roboguide approach the input trajectory. To conclude, RoboGuide does not accurately represent the motion of the FANUCTM robot and therefore only has limited use in supporting the physical emulation of complex sporting movements