P.A.M. Dirac and the Discovery of Quantum Mechanics

Dirac's contributions to the discovery of non-relativistic quantum mechanics and quantum electrodynamics, prior to his discovery of the relativistic wave equation, are described

Euclidean versus hyperbolic congestion in idealized versus experimental networks

This paper proposes a mathematical justification of the phenomenon of extreme congestion at a very limited number of nodes in very large networks. It is argued that this phenomenon occurs as a combination of the negative curvature property of the network together with minimum length routing. More specifically, it is shown that, in a large n-dimensional hyperbolic ball B of radius R viewed as a roughly similar model of a Gromov hyperbolic network, the proportion of traffic paths transiting through a small ball near the center is independent of the radius R whereas, in a Euclidean ball, the same proportion scales as 1/R^{n-1}. This discrepancy persists for the traffic load, which at the center of the hyperbolic ball scales as the square of the volume, whereas the same traffic load scales as the volume to the power (n+1)/n in the Euclidean ball. This provides a theoretical justification of the experimental exponent discrepancy observed by Narayan and Saniee between traffic loads in Gromov-hyperbolic networks from the Rocketfuel data base and synthetic Euclidean lattice networks. It is further conjectured that for networks that do not enjoy the obvious symmetry of hyperbolic and Euclidean balls, the point of maximum traffic is near the center of mass of the network.Comment: 23 pages, 4 figure

New concept of relativistic invariance in NC space-time: twisted Poincar\'e symmetry and its implications

We present a systematic framework for noncommutative (NC) QFT within the new concept of relativistic invariance based on the notion of twisted Poincar\'e symmetry (with all 10 generators), as proposed in ref. [7]. This allows to formulate and investigate all fundamental issues of relativistic QFT and offers a firm frame for the classification of particles according to the representation theory of the twisted Poincar\'e symmetry and as a result for the NC versions of CPT and spin-statistics theorems, among others, discussed earlier in the literature. As a further application of this new concept of relativism we prove the NC analog of Haag's theorem.Comment: 15 page

Spectral properties of entanglement witnesses

Entanglement witnesses are observables which when measured, detect entanglement in a measured composed system. It is shown what kind of relations between eigenvectors of an observable should be fulfilled, to allow an observable to be an entanglement witness. Some restrictions on the signature of entaglement witnesses, based on an algebraic-geometrical theorem will be given. The set of entanglement witnesses is linearly isomorphic to the set of maps between matrix algebras which are positive, but not completely positive. A translation of the results to the language of positive maps is also given. The properties of entanglement witnesses and positive maps express as special cases of general theorems for $k$-Schmidt witnesses and $k$-positive maps. The results are therefore presented in a general framework.Comment: published version, some proofs are more detailed, mistakes remove

Spectral plots and the representation and interpretation of biological data

It is basic question in biology and other fields to identify the char- acteristic properties that on one hand are shared by structures from a particular realm, like gene regulation, protein-protein interaction or neu- ral networks or foodwebs, and that on the other hand distinguish them from other structures. We introduce and apply a general method, based on the spectrum of the normalized graph Laplacian, that yields repre- sentations, the spectral plots, that allow us to find and visualize such properties systematically. We present such visualizations for a wide range of biological networks and compare them with those for networks derived from theoretical schemes. The differences that we find are quite striking and suggest that the search for universal properties of biological networks should be complemented by an understanding of more specific features of biological organization principles at different scales.Comment: 15 pages, 7 figure

The geometry of thermodynamic control

A deeper understanding of nonequilibrium phenomena is needed to reveal the principles governing natural and synthetic molecular machines. Recent work has shown that when a thermodynamic system is driven from equilibrium then, in the linear response regime, the space of controllable parameters has a Riemannian geometry induced by a generalized friction tensor. We exploit this geometric insight to construct closed-form expressions for minimal-dissipation protocols for a particle diffusing in a one dimensional harmonic potential, where the spring constant, inverse temperature, and trap location are adjusted simultaneously. These optimal protocols are geodesics on the Riemannian manifold, and reveal that this simple model has a surprisingly rich geometry. We test these optimal protocols via a numerical implementation of the Fokker-Planck equation and demonstrate that the friction tensor arises naturally from a first order expansion in temporal derivatives of the control parameters, without appealing directly to linear response theory

Spectral Properties and Synchronization in Coupled Map Lattices

Spectral properties of Coupled Map Lattices are described. Conditions for the stability of spatially homogeneous chaotic solutions are derived using linear stability analysis. Global stability analysis results are also presented. The analytical results are supplemented with numerical examples. The quadratic map is used for the site dynamics with different coupling schemes such as global coupling, nearest neighbor coupling, intermediate range coupling, random coupling, small world coupling and scale free coupling.Comment: 10 pages with 15 figures (Postscript), REVTEX format. To appear in PR

Hamiltonian equation of motion and depinning phase transition in two-dimensional magnets

Based on the Hamiltonian equation of motion of the $\phi^4$ theory with quenched disorder, we investigate the depinning phase transition of the domain-wall motion in two-dimensional magnets. With the short-time dynamic approach, we numerically determine the transition field, and the static and dynamic critical exponents. The results show that the fundamental Hamiltonian equation of motion belongs to a universality class very different from those effective equations of motion.Comment: 6 pages, 7 figures, have been accept by EP

Previous Emergency Department Use Among Homicide Victims and Offenders: A Case-Control Study

We differentiate risk factors for future homicide victimization and offending, and we measure emergency department (ED) use among homicide victims, offenders, and controls. The design was a matched case-control study conducted in Bernalillo County, NM, and its university-affiliated health sciences center and hospital. All Bernalillo County homicide victims (N=124) and offenders (N=138) identified between January 1996 and December 2001 who were linked to university physician billing records and who had health care use during the 3 years before the homicide incident were included as cases. Randomly selected age-matched (±1 year) and sex-matched subjects with health care use within 3 years of their matched pair’s homicide were included as controls. Main outcome measures were the number and type of ED visits by cases and controls. Patients with ED visits for assault, firearm injuries, and substance abuse are at increased risk for homicide and often have an escalating number of visits leading up to the homicide event. ED-based identification and referral programs similar to those used for intimate partner violenc

Modulated Scale-free Network in the Euclidean Space

A random network is grown by introducing at unit rate randomly selected nodes on the Euclidean space. A node is randomly connected to its $i$-th predecessor of degree $k_i$ with a directed link of length $\ell$ using a probability proportional to $k_i \ell^{\alpha}$. Our numerical study indicates that the network is Scale-free for all values of $\alpha > \alpha_c$ and the degree distribution decays stretched exponentially for the other values of $\alpha$. The link length distribution follows a power law: $D(\ell) \sim \ell^{\delta}$ where $\delta$ is calculated exactly for the whole range of values of $\alpha$.Comment: 4 pages, 4 figures. To be published in Physical Review