arXiv subjects

Randy Kobes

Publications and source records attributed to Randy Kobes.

10 recordsLinked to original sources

arXiv2010

Generating and solving the mean field and pair approximation equations in epidemiological models

The pair approximation is a simple, low-order method to incorporate effects of local spatial structure in epidemiological models. However, since for K state variables in a model there are K(K+1)/2 equations in the pair approximation, generating these equations, although straightforward, can become tedious. In this paper we describe two programs written in Perl to simplify this process - one to construct the equations, and the other to generate Matlab/Octave functions to numerically integrate the equations using a positivity-preserving method. A third utility program is also included which generates a Maple file that can be used within the Maple symbolic manipulation program to simplify algebraically some of the terms in the generated file describing the equations, as well as to check that the usual combination of equations sum up to zero, which is expected in cases where the total population sizes are conserved.

physics.soc-ph↗

arXiv2010

Expansion of the conditional probability function in a network with nearest-neighbour degree correlations

A useful property of a network that can be used to characterize many systems is the degree distribution. However, many complex networks exhibit higher--order degree correlations that must be studied through other means, such as clustering coefficients, the Newman r factor, and the average nearest neighbour degree (ANND). In this paper we develop an expansion of the conditional probability that can be used to parameterize such degree correlations. The measures of degree correlations associated with this expansion can be used to signal the presence of non--linear correlations.

physics.soc-ph↗

arXiv2003

Energy and Efficiency of Adiabatic Quantum Search Algorithms

We present the results of a detailed analysis of a general, unstructured adiabatic quantum search of a data base of $N$ items. In particular we examine the effects on the computation time of adding energy to the system. We find that by increasing the lowest eigenvalue of the time dependent Hamiltonian {\it temporarily} to a maximum of $\propto \sqrt{N}$, it is possible to do the calculation in constant time. This leads us to derive the general theorem which provides the adiabatic analogue of the $\sqrt{N}$ bound of conventional quantum searches. The result suggests that the action associated with the oracle term in the time dependent Hamiltonian is a direct measure of the resources required by the adiabatic quantum search.

quant-ph↗

arXiv2002

Adiabatic Quantum Computation and Deutsch's Algorithm

We show that by a suitable choice of a time dependent Hamiltonian, Deutsch's algorithm can be implemented by an adiabatic quantum computer. We extend our analysis to the Deutsch-Jozsa problem and estimate the required running time for both global and local adiabatic evolutions.

quant-ph↗

arXiv2002

Rapid Data Search using Adiabatic Quantum Computation

We show that by a suitable choice of time-dependent Hamiltonian, the search for a marked item in an unstructured database can be achieved in unit time, using Adiabatic Quantum Computation. This is a considerable improvement over the O(sqrt(N)) time required in previous algorithms. The trade-off is that in the intermediate stages of the computation process, the ground state energy of the computer increases to a maximum of O(sqrt(N)), before returning to zero at the end of the process.

quant-ph↗

arXiv2002

Structured Adiabatic Quantum Search

We examine the use of adiabatic quantum algorithms to solve structured, or nested, search problems. We construct suitable time dependent Hamiltonians and derive the computation times for a general class of nested searches involving n qubits. As expected, we find that as additional structure is included, the Hamiltonians become more local and the computation times decrease.

quant-ph↗

arXiv2000

Analysis of a Parametrically Driven Pendulum

We study in this paper the behavior of a periodically driven nonlinear mechanical system. Bifurcation diagrams are found which locate regions of quasiperiodic, periodic and chaotic behavior within the parameter space of the system. We also conduct a symbolic analysis of the model, which demonstrates that the symbolic dynamics of two-dimensional maps can be applied effectively to the study of ordinary differential equations in order to gain global knowledge about them.

nlin.CD↗

arXiv1999

Two-loop Compton and annihilation processes in thermal QCD

We calculate the Compton and annihilation production of a soft static lepton pair in a quark-gluon plasma in the two-loop approximation. We work in the context of the effective perturbative expansion based on the resummation of hard thermal loops. Double counting is avoided by subtracting appropriate counterterms. It is found that the two-loop diagrams give contributions of the same order as the one-loop diagram. Furthermore, these contributions are necessary to obtain agreement with the naive perturbative expansion in the limit of vanishing thermal masses.

hep-ph↗

arXiv1995

Hard thermal loop resummation techniques in hot gauge theories

A review is given of the hard thermal loop resummation methods initiated by Braaten, Pisarski, and others. We describe some successes of these techniques as well as instances where modifications are necessary. Some possible directions where these modifications may lead are also discussed. [Review talk given at the 4th workshop on thermal field theories held in Dalian, China]

hep-ph↗

arXiv1994

The Thermal Beta-Function in Yang-Mills Theory

Previous calculations of the thermal beta-function in a hot Yang--Mills gas at the one--loop level have exposed problems with the gauge dependence and with the sign, which is opposite to what one would expect for asymptotic freedom. We show that inclusion of higher--loop effects through a static Braaten--Pisarski resummation is necessary to consistently obtain the leading term, but alters the results only quantitatively. The sign, in particular, remains the same. We also explore, by a crude parameterization, the effects a (non--perturbative) magnetic mass may have on these results.

hep-ph↗