Properties of Classical and Quantum Jensen-Shannon Divergence

Jensen-Shannon divergence (JD) is a symmetrized and smoothed version of the most important divergence measure of information theory, Kullback divergence. As opposed to Kullback divergence it determines in a very direct way a metric; indeed, it is the square of a metric. We consider a family of divergence measures (JD_alpha for alpha>0), the Jensen divergences of order alpha, which generalize JD as JD_1=JD. Using a result of Schoenberg, we prove that JD_alpha is the square of a metric for alpha lies in the interval (0,2], and that the resulting metric space of probability distributions can be isometrically embedded in a real Hilbert space. Quantum Jensen-Shannon divergence (QJD) is a symmetrized and smoothed version of quantum relative entropy and can be extended to a family of quantum Jensen divergences of order alpha (QJD_alpha). We strengthen results by Lamberti et al. by proving that for qubits and pure states, QJD_alpha^1/2 is a metric space which can be isometrically embedded in a real Hilbert space when alpha lies in the interval (0,2]. In analogy with Burbea and Rao's generalization of JD, we also define general QJD by associating a Jensen-type quantity to any weighted family of states. Appropriate interpretations of quantities introduced are discussed and bounds are derived in terms of the total variation and trace distance.Comment: 13 pages, LaTeX, expanded contents, added references and corrected typo

L\'evy-Schr\"odinger wave packets

We analyze the time--dependent solutions of the pseudo--differential L\'evy--Schr\"odinger wave equation in the free case, and we compare them with the associated L\'evy processes. We list the principal laws used to describe the time evolutions of both the L\'evy process densities, and the L\'evy--Schr\"odinger wave packets. To have self--adjoint generators and unitary evolutions we will consider only absolutely continuous, infinitely divisible L\'evy noises with laws symmetric under change of sign of the independent variable. We then show several examples of the characteristic behavior of the L\'evy--Schr\"odinger wave packets, and in particular of the bi-modality arising in their evolutions: a feature at variance with the typical diffusive uni--modality of both the L\'evy process densities, and the usual Schr\"odinger wave functions.Comment: 41 pages, 13 figures; paper substantially shortened, while keeping intact examples and results; changed format from "report" to "article"; eliminated Appendices B, C, F (old names); shifted Chapters 4 and 5 (old numbers) from text to Appendices C, D (new names); introduced connection between Relativistic q.m. laws and Generalized Hyperbolic law

On the behaviour of spatial Wilson loops in the high temperature phase of Lattice Gauge Theories

The behaviour of the space-like string tension in the high temperature phase is studied. Data obtained in the $Z_2$ gauge model in (2+1) dimensions are compared with predictions of a simple model of a fluctuating flux tube with finite thickness. It is shown that in the high temperature phase contributions coming from the fluctuations of the flux tube vanish. As a consequence we also show that in (2+1) dimensional gauge theories the thickness of the flux tube coincides with the inverse of the deconfinement temperature.Comment: 16 pages, 4 ps-figures included, (Latex), DFTT 57/9

Propagators in Noncommutative Instantons

We explicitly construct Green functions for a field in an arbitrary representation of gauge group propagating in noncommutative instanton backgrounds based on the ADHM construction. The propagators for spinor and vector fields can be constructed in terms of those for the scalar field in noncommutative instanton background. We show that the propagators in the adjoint representation are deformed by noncommutativity while those in the fundamental representation have exactly the same form as the commutative case.Comment: 28 pages, Latex, v2: A few typos correcte

Strategies for fitting nonlinear ecological models in R, AD Model Builder, and BUGS

Summary: 1. Ecologists often use nonlinear fitting techniques to estimate the parameters of complex ecological models, with attendant frustration. This paper compares three open-source model fitting tools and discusses general strategies for defining and fitting models. 2. R is convenient and (relatively) easy to learn, AD Model Builder is fast and robust but comes with a steep learning curve, while BUGS provides the greatest flexibility at the price of speed. 3. Our model-fitting suggestions range from general cultural advice (where possible, use the tools and models that are most common in your subfield) to specific suggestions about how to change the mathematical description of models to make them more amenable to parameter estimation. 4. A companion web site (https://groups.nceas.ucsb.edu/nonlinear-modeling/projects) presents detailed examples of application of the three tools to a variety of typical ecological estimation problems; each example links both to a detailed project report and to full source code and data

The a-theorem and conformal symmetry breaking in holographic RG flows

We study holographic models describing an RG flow between two fixed points driven by a relevant scalar operator. We show how to introduce a spurion field to restore Weyl invariance and compute the anomalous contribution to the generating functional in even dimensional theories. We find that the coefficient of the anomalous term is proportional to the difference of the conformal anomalies of the UV and IR fixed points, as expected from anomaly matching arguments in field theory. For any even dimensions the coefficient is positive as implied by the holographic a-theorem. For flows corresponding to spontaneous breaking of conformal invariance, we also compute the two-point functions of the energy-momentum tensor and the scalar operator and identify the dilaton mode. Surprisingly we find that in the simplest models with just one scalar field there is no dilaton pole in the two-point function of the scalar operator but a stronger singularity. We discuss the possible implications.Comment: 50 pages. v2: minor changes, added references, extended discussion. v3: we have clarified some of the calculations and assumptions, results unchanged. v4: published version in JHE

Recognition of Face Identity and Emotion in Expressive Specific Language Impairment

Objective: To study face and emotion recognition in children with mostly expressive specific language impairment (SLI-E). Subjects and Methods: A test movie to study perception and recognition of faces and mimic-gestural expression was applied to 24 children diagnosed as suffering from SLI-E and an age-matched control group of normally developing children. Results: Compared to a normal control group, the SLI-E children scored significantly worse in both the face and expression recognition tasks with a preponderant effect on emotion recognition. The performance of the SLI-E group could not be explained by reduced attention during the test session. Conclusion: We conclude that SLI-E is associated with a deficiency in decoding non-verbal emotional facial and gestural information, which might lead to profound and persistent problems in social interaction and development. Copyright (C) 2012 S. Karger AG, Base

Can One Trust Quantum Simulators?

Various fundamental phenomena of strongly-correlated quantum systems such as high-$T_c$ superconductivity, the fractional quantum-Hall effect, and quark confinement are still awaiting a universally accepted explanation. The main obstacle is the computational complexity of solving even the most simplified theoretical models that are designed to capture the relevant quantum correlations of the many-body system of interest. In his seminal 1982 paper [Int. J. Theor. Phys. 21, 467], Richard Feynman suggested that such models might be solved by "simulation" with a new type of computer whose constituent parts are effectively governed by a desired quantum many-body dynamics. Measurements on this engineered machine, now known as a "quantum simulator," would reveal some unknown or difficult to compute properties of a model of interest. We argue that a useful quantum simulator must satisfy four conditions: relevance, controllability, reliability, and efficiency. We review the current state of the art of digital and analog quantum simulators. Whereas so far the majority of the focus, both theoretically and experimentally, has been on controllability of relevant models, we emphasize here the need for a careful analysis of reliability and efficiency in the presence of imperfections. We discuss how disorder and noise can impact these conditions, and illustrate our concerns with novel numerical simulations of a paradigmatic example: a disordered quantum spin chain governed by the Ising model in a transverse magnetic field. We find that disorder can decrease the reliability of an analog quantum simulator of this model, although large errors in local observables are introduced only for strong levels of disorder. We conclude that the answer to the question "Can we trust quantum simulators?" is... to some extent.Comment: 20 pages. Minor changes with respect to version 2 (some additional explanations, added references...