Building effective models from sparse but precise data

A common approach in computational science is to use a set of of highly precise but expensive calculations to parameterize a model that allows less precise, but more rapid calculations on larger scale systems. Least-squares fitting on a model that underfits the data is generally used for this purpose. For arbitrarily precise data free from statistic noise, e.g. ab initio calculations, we argue that it is more appropriate to begin with a ensemble of models that overfit the data. Within a Bayesian framework, a most likely model can be defined that incorporates physical knowledge, provides error estimates for systems not included in the fit, and reproduces the original data exactly. We apply this approach to obtain a cluster expansion model for the Ca[Zr,Ti]O3 solid solution.Comment: 10 pages, 3 figures, submitted to Physical Review Letter

James van Allen and his namesake NASA mission

Abstract In many ways, James A. Van Allen defined and “invented” modern space research. His example showed the way for government-university partners to pursue basic research that also served important national and international goals. He was a tireless advocate for space exploration and for the role of space science in the spectrum of national priorities

Supersymmetric and Shape-Invariant Generalization for Nonresonant and Intensity-Dependent Jaynes-Cummings Systems

A class of shape-invariant bound-state problems which represent transition in a two-level system introduced earlier are generalized to include arbitrary energy splittings between the two levels as well as intensity-dependent interactions. We show that the couple-channel Hamiltonians obtained correspond to the generalizations of the nonresonant and intensity-dependent nonresonant Jaynes-Cummings Hamiltonians, widely used in quantized theories of laser. In this general context, we determine the eigenstates, eigenvalues, the time evolution matrix and the population inversion matrix factor.Comment: A combined version of quant-ph/0005045 and quant-ph/0005046. 24 pages, LATE

Escort mean values and the characterization of power-law-decaying probability densities

Escort mean values (or $q$-moments) constitute useful theoretical tools for describing basic features of some probability densities such as those which asymptotically decay like {\it power laws}. They naturally appear in the study of many complex dynamical systems, particularly those obeying nonextensive statistical mechanics, a current generalization of the Boltzmann-Gibbs theory. They recover standard mean values (or moments) for $q=1$. Here we discuss the characterization of a (non-negative) probability density by a suitable set of all its escort mean values together with the set of all associated normalizing quantities, provided that all of them converge. This opens the door to a natural extension of the well known characterization, for the $q=1$ instance, of a distribution in terms of the standard moments, provided that {\it all} of them have {\it finite} values. This question would be specially relevant in connection with probability densities having {\it divergent} values for all nonvanishing standard moments higher than a given one (e.g., probability densities asymptotically decaying as power-laws), for which the standard approach is not applicable. The Cauchy-Lorentz distribution, whose second and higher even order moments diverge, constitutes a simple illustration of the interest of this investigation. In this context, we also address some mathematical subtleties with the aim of clarifying some aspects of an interesting non-linear generalization of the Fourier Transform, namely, the so-called $q$-Fourier Transform.Comment: 20 pages (2 Appendices have been added

Supersymmetric Jaynes-Cummings model and its exact solutions

The super-algebraic structure of a generalized version of the Jaynes-Cummings model is investigated. We find that a Z2 graded extension of the so(2,1) Lie algebra is the underlying symmetry of this model. It is isomorphic to the four-dimensional super-algebra u(1/1) with two odd and two even elements. Differential matrix operators are taken as realization of the elements of the superalgebra to which the model Hamiltonian belongs. Several examples with various choices of superpotentials are presented. The energy spectrum and corresponding wavefunctions are obtained analytically.Comment: 12 pages, no figure

What's wrong with this rebuttal?

A recent rebuttal to criticism of Bell's analysis is shown to be defective by fault of failure to consider all hypothetical conditions input into the derivation of Bell Inequalitites.Comment: 2 page

Configurational entropy of Wigner crystals

We present a theoretical study of classical Wigner crystals in two- and three-dimensional isotropic parabolic traps aiming at understanding and quantifying the configurational uncertainty due to the presence of multiple stable configurations. Strongly interacting systems of classical charged particles confined in traps are known to form regular structures. The number of distinct arrangements grows very rapidly with the number of particles, many of these arrangements have quite low occurrence probabilities and often the lowest-energy structure is not the most probable one. We perform numerical simulations on systems containing up to 100 particles interacting through Coulomb and Yukawa forces, and show that the total number of metastable configurations is not a well defined and representative quantity. Instead, we propose to rely on the configurational entropy as a robust and objective measure of uncertainty. The configurational entropy can be understood as the logarithm of the effective number of states; it is insensitive to the presence of overlooked low-probability states and can be reliably determined even within a limited time of a simulation or an experiment.Comment: 12 pages, 8 figures. This is an author-created, un-copyedited version of an article accepted for publication in J. Phys.: Condens. Matter. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The definitive publisher-authenticated version is available online at 10.1088/0953-8984/23/7/075302.

An entropy-based class assignment detection approach for RDF data

The RDF-style Knowledge Bases usually contain a certain level of noises known as Semantic Web data quality issues. This paper has introduced a new Semantic Web data quality issue called Incorrect Class Assignment problem that shows the incorrect assignment between instances in the instance-level and corresponding classes in an ontology. We have proposed an approach called CAD (Class Assignment Detector) to find the correctness and incorrectness of relationships between instances and classes by analyzing features of classes in an ontology. Initial experiments conducted on a dataset demonstrate the effectiveness of CAD

Entanglement purification of unknown quantum states

A concern has been expressed that ``the Jaynes principle can produce fake entanglement'' [R. Horodecki et al., Phys. Rev. A {\bf 59}, 1799 (1999)]. In this paper we discuss the general problem of distilling maximally entangled states from $N$ copies of a bipartite quantum system about which only partial information is known, for instance in the form of a given expectation value. We point out that there is indeed a problem with applying the Jaynes principle of maximum entropy to more than one copy of a system, but the nature of this problem is classical and was discussed extensively by Jaynes. Under the additional assumption that the state $\rho^{(N)}$ of the $N$ copies of the quantum system is exchangeable, one can write down a simple general expression for $\rho^{(N)}$. We show how to modify two standard entanglement purification protocols, one-way hashing and recurrence, so that they can be applied to exchangeable states. We thus give an explicit algorithm for distilling entanglement from an unknown or partially known quantum state.Comment: 20 pages RevTeX 3.0 + 1 figure (encapsulated Postscript) Submitted to Physical Review

Chaos for Liouville probability densities

Using the method of symbolic dynamics, we show that a large class of classical chaotic maps exhibit exponential hypersensitivity to perturbation, i.e., a rapid increase with time of the information needed to describe the perturbed time evolution of the Liouville density, the information attaining values that are exponentially larger than the entropy increase that results from averaging over the perturbation. The exponential rate of growth of the ratio of information to entropy is given by the Kolmogorov-Sinai entropy of the map. These findings generalize and extend results obtained for the baker's map [R. Schack and C. M. Caves, Phys. Rev. Lett. 69, 3413 (1992)].Comment: 26 pages in REVTEX, no figures, submitted to Phys. Rev.