A Criterion for the Critical Number of Fermions and Chiral Symmetry Breaking in Anisotropic QED(2+1)

By analyzing the strength of a photon-fermion coupling using basic scattering processes we calculate the effect of a velocity anisotropy on the critical number of fermions at which mass is dynamically generated in planar QED. This gives a quantitative criterion which can be used to locate a quantum critical point at which fermions are gapped and confined out of the physical spectrum in a phase diagram of various condensed matter systems. We also discuss the mechanism of relativity restoration within the symmetric, quantum-critical phase of the theory.Comment: To appear in Physical Review

Constructive Field Theory and Applications: Perspectives and Open Problems

In this paper we review many interesting open problems in mathematical physics which may be attacked with the help of tools from constructive field theory. They could give work for future mathematical physicists trained with the constructive methods well within the 21st century

Exploring the Use of Computer Simulations in Unraveling Research and Development Governance Problems

Understanding Research and Development (R&D) enterprise relationships and processes at a governance level is not a simple task, but valuable decision-making insight and evaluation capabilities can be gained from their exploration through computer simulations. This paper discusses current Modeling and Simulation (M&S) methods, addressing their applicability to R&D enterprise governance. Specifically, the authors analyze advantages and disadvantages of the four methodologies used most often by M&S practitioners: System Dynamics (SO), Discrete Event Simulation (DES), Agent Based Modeling (ABM), and formal Analytic Methods (AM) for modeling systems at the governance level. Moreover, the paper describes nesting models using a multi-method approach. Guidance is provided to those seeking to employ modeling techniques in an R&D enterprise for the purposes of understanding enterprise governance. Further, an example is modeled and explored for potential insight. The paper concludes with recommendations regarding opportunities for concentration of future work in modeling and simulating R&D governance relationships and processes

Chemical Graphs. XXXII. Constitutional and Steric Isomers of Substituted Cycloalkanes

Polya\u27s theorem was applied to cycloalkanes in order to obtain the numbers of stereoisomers, enantiomers, and constitutional isomers of substituted derivatives. Whereas the stereoisomers result from the actual constitutional graphs of the flexible cycloalkanes, special graphs must be devised for ignoring stereoisomerism or enantiomerism

The Global Renormalization Group Trajectory in a Critical Supersymmetric Field Theory on the Lattice Z^3

We consider an Euclidean supersymmetric field theory in $Z^3$ given by a supersymmetric $\Phi^4$ perturbation of an underlying massless Gaussian measure on scalar bosonic and Grassmann fields with covariance the Green's function of a (stable) L\'evy random walk in $Z^3$. The Green's function depends on the L\'evy-Khintchine parameter $\alpha={3+\epsilon\over 2}$ with $0<\alpha<2$. For $\alpha ={3\over 2}$ the $\Phi^{4}$ interaction is marginal. We prove for $\alpha-{3\over 2}={\epsilon\over 2}>0$ sufficiently small and initial parameters held in an appropriate domain the existence of a global renormalization group trajectory uniformly bounded on all renormalization group scales and therefore on lattices which become arbitrarily fine. At the same time we establish the existence of the critical (stable) manifold. The interactions are uniformly bounded away from zero on all scales and therefore we are constructing a non-Gaussian supersymmetric field theory on all scales. The interest of this theory comes from the easily established fact that the Green's function of a (weakly) self-avoiding L\'evy walk in $Z^3$ is a second moment (two point correlation function) of the supersymmetric measure governing this model. The control of the renormalization group trajectory is a preparation for the study of the asymptotics of this Green's function. The rigorous control of the critical renormalization group trajectory is a preparation for the study of the critical exponents of the (weakly) self-avoiding L\'evy walk in $Z^3$.Comment: 82 pages, Tex with macros supplied. Revision includes 1. redefinition of norms involving fermions to ensure uniqueness. 2. change in the definition of lattice blocks and lattice polymer activities. 3. Some proofs have been reworked. 4. New lemmas 5.4A, 5.14A, and new Theorem 6.6. 5.Typos corrected.This is the version to appear in Journal of Statistical Physic

An Efficient Algorithm for Enumerating Chordless Cycles and Chordless Paths

A chordless cycle (induced cycle) $C$ of a graph is a cycle without any chord, meaning that there is no edge outside the cycle connecting two vertices of the cycle. A chordless path is defined similarly. In this paper, we consider the problems of enumerating chordless cycles/paths of a given graph $G=(V,E),$ and propose algorithms taking $O(|E|)$ time for each chordless cycle/path. In the existing studies, the problems had not been deeply studied in the theoretical computer science area, and no output polynomial time algorithm has been proposed. Our experiments showed that the computation time of our algorithms is constant per chordless cycle/path for non-dense random graphs and real-world graphs. They also show that the number of chordless cycles is much smaller than the number of cycles. We applied the algorithm to prediction of NMR (Nuclear Magnetic Resonance) spectra, and increased the accuracy of the prediction

When memory falls short: The effect of suggestibility and repeated questioning on 3- to 5-year-old children’s recognition of event details

The present study investigated children’s event recognition as a function of feedback, suggestible question type, and repeated questioning. Forty-three 3- to 5-year-old children read a book and were asked twelve positive-leaning, negative-leaning, and additive-misinformation questions. After six and twelve questions, children were presented with positive or negative feedback and asked the same questions again. Feedback did not affect response accuracy; however, children’s likelihood of changing their answer when questioned a second time varied as a function of question type. Children answered negative-leaning questions more accurately the second time, additive-misinformation questions less accurately the second time, and showed no change with positive-leaning questions. These findings extend prior knowledge of factors that influence children’s recollection of an event