Interior point solution of fractional Bethe permanent

Many combinatorial problems in fields such as object tracking involve reasoning over correspondence, e.g, calculating the probability that a measurement belongs to a particular track. Recent studies have shown that loopy belief propagation (LBP) provides a highly desirable option in the trade-off between accuracy and computational complexity in this task. LBP can be understood as a particular method for optimising the Bethe free energy (BFE). In this paper, we directly optimise the BFE using an interior point Newton method. Exploiting the structure of the constraints, we arrive at an algorithm offers improvements in computation in cases in which LBP converges very slowly. The method also solves the recently-proposed fractional free energy (FFE); we use this to demonstrate that FFE can offer marginal estimates with improved accuracy.Jason L. William

Approximating the Permanent with Fractional Belief Propagation

We discuss schemes for exact and approximate computations of permanents, and compare them with each other. Specifically, we analyze the Belief Propagation (BP) approach and its Fractional Belief Propagation (FBP) generalization for computing the permanent of a non-negative matrix. Known bounds and conjectures are verified in experiments, and some new theoretical relations, bounds and conjectures are proposed. The Fractional Free Energy (FFE) functional is parameterized by a scalar parameter $\gamma\in[-1;1]$, where $\gamma=-1$ corresponds to the BP limit and $\gamma=1$ corresponds to the exclusion principle (but ignoring perfect matching constraints) Mean-Field (MF) limit. FFE shows monotonicity and continuity with respect to $\gamma$. For every non-negative matrix, we define its special value $\gamma_*\in[-1;0]$ to be the $\gamma$ for which the minimum of the $\gamma$-parameterized FFE functional is equal to the permanent of the matrix, where the lower and upper bounds of the $\gamma$-interval corresponds to respective bounds for the permanent. Our experimental analysis suggests that the distribution of $\gamma_*$ varies for different ensembles but $\gamma_*$ always lies within the $[-1;-1/2]$ interval. Moreover, for all ensembles considered the behavior of $\gamma_*$ is highly distinctive, offering an emprirical practical guidance for estimating permanents of non-negative matrices via the FFE approach.Comment: 42 pages, 14 figure

Approximating the Permanent with Fractional Belief Propagation

We discuss schemes for exact and approximate computations of permanents, and compare them with each other. Specifically, we analyze the belief propagation (BP) approach and its fractional belief propagation (FBP) generalization for computing the permanent of a non-negative matrix. Known bounds and Conjectures are verified in experiments, and some new theoretical relations, bounds and Conjectures are proposed. The fractional free energy (FFE) function is parameterized by a scalar parameter y ∈ [−1;1], where y = −1 corresponds to the BP limit and y = 1 corresponds to the exclusion principle (but ignoring perfect matching constraints) mean-field (MF) limit. FFE shows monotonicity and continuity with respect to g. For every non-negative matrix, we define its special value y∗ ∈ [−1;0] to be the g for which the minimum of the y-parameterized FFE function is equal to the permanent of the matrix, where the lower and upper bounds of the g-interval corresponds to respective bounds for the permanent. Our experimental analysis suggests that the distribution of y∗ varies for different ensembles but y∗ always lies within the [−1;−1/2] interval. Moreover, for all ensembles considered, the behavior of y∗ is highly distinctive, offering an empirical practical guidance for estimating permanents of non-negative matrices via the FFE approach.Los Alamos National Laboratory (Undergraduate Research Assistant Program)United States. National Nuclear Security Administration (Los Alamos National Laboratory Contract DE C52-06NA25396

Noneuclidean Tessellations and their relation to Reggie Trajectories

The coefficients in the confluent hypergeometric equation specify the Regge trajectories and the degeneracy of the angular momentum states. Bound states are associated with real angular momenta while resonances are characterized by complex angular momenta. With a centrifugal potential, the half-plane is tessellated by crescents. The addition of an electrostatic potential converts it into a hydrogen atom, and the crescents into triangles which may have complex conjugate angles; the angle through which a rotation takes place is accompanied by a stretching. Rather than studying the properties of the wave functions themselves, we study their symmetry groups. A complex angle indicates that the group contains loxodromic elements. Since the domain of such groups is not the disc, hyperbolic plane geometry cannot be used. Rather, the theory of the isometric circle is adapted since it treats all groups symmetrically. The pairing of circles and their inverses is likened to pairing particles with their antiparticles which then go one to produce nested circles, or a proliferation of particles. A corollary to Laguerre's theorem, which states that the euclidean angle is represented by a pure imaginary projective invariant, represents the imaginary angle in the form of a real projective invariant.Comment: 27 pages, 4 figure

Solar Neutrino Physics: historical evolution, present status and perspectives

Solar neutrino physics is an exciting and difficult field of research for physicists, where astrophysics, elementary particle and nuclear physics meet. \ The Sun produces the energy that life has been using on Earth for many years, about $10^9$ y, emits a lot of particles: protons, electrons, ions, electromagnetic quanta... among them neutrinos play an important role allowing to us to check our knowledge on solar characteristics. The main aim of this paper is to offer a practical overview of various aspects concerning the solar neutrino physics: after a short historical excursus, the different detection techniques and present experimental results and problems are analysed. Moreover, the status of art of solar modeling, possible solutions to the so called solar neutrino problem (SNP) and planned detectors are reviewed.Comment: 139 pages, 42 figure

Fast synthesis of permanent magnet assisted synchronous reluctance motors

open3This paper describes a procedure for a practical synthesis of both a synchronous reluctance motor and a permanent magnet assisted synchronous reluctance motor. The procedure is completely analytical, yielding a rapid drawing of the motor geometry, taking into account both magnetic and mechanical considerations. From the application requirements, the external volume of the motor is computed. The further practical needs, such as maximum outer space, maximum available length, existing stator lamination, and so on are considered. Then, the design of the rotor geometry is carried out. The PM size is determined considering the demagnetisation limit according to the maximum current loading.openBianchi, Nicola; Mahmoud, Hanafy; Bolognani, SilverioBianchi, Nicola; Mahmoud, Hanafy; Bolognani, Silveri

Progress in Time-Dependent Density-Functional Theory

The classic density-functional theory (DFT) formalism introduced by Hohenberg, Kohn, and Sham in the mid-1960s, is based upon the idea that the complicated N-electron wavefunction can be replaced with the mathematically simpler 1-electron charge density in electronic struc- ture calculations of the ground stationary state. As such, ordinary DFT is neither able to treat time-dependent (TD) problems nor describe excited electronic states. In 1984, Runge and Gross proved a theorem making TD-DFT formally exact. Information about electronic excited states may be obtained from this theory through the linear response (LR) theory formalism. Begin- ning in the mid-1990s, LR-TD-DFT became increasingly popular for calculating absorption and other spectra of medium- and large-sized molecules. Its ease of use and relatively good accuracy has now brought LR-TD-DFT to the forefront for this type of application. As the number and the diversity of applications of TD-DFT has grown, so too has grown our understanding of the strengths and weaknesses of the approximate functionals commonly used for TD-DFT. The objective of this article is to continue where a previous review of TD-DFT in this series [Annu. Rev. Phys. Chem. 55: 427 (2004)] left off and highlight some of the problems and solutions from the point of view of applied physical chemistry. Since doubly-excited states have a particularly important role to play in bond dissociation and formation in both thermal and photochemistry, particular emphasis will be placed upon the problem of going beyond or around the TD-DFT adiabatic approximation which limits TD-DFT calculations to nominally singly-excited states. Posted with permission from the Annual Review of Physical Chemistry, Volume 63 \c{opyright} 2012 by Annual Reviews, http://www.annualreviews.org

Improving the precision of dynamic forest parameter estimates using Landsat

The use of satellite-derived classification maps to improve post-stratified forest parameter estimates is well established.When reducing the variance of post-stratification estimates for forest change parameters such as forest growth, it is logical to use a change-related strata map. At the stand level, a time series of Landsat images is ideally suited for producing such a map. In this study, we generate strata maps based on trajectories of Landsat Thematic Mapper-based normalized difference vegetation index values, with a focus on post-disturbance recovery and recent measurements. These trajectories, from1985 to 2010, are converted to harmonic regression coefficient estimates and classified according to a hierarchical clustering algorithm from a training sample. The resulting strata maps are then used in conjunction with measured plots to estimate forest status and change parameters in an Alabama, USA study area. These estimates and the variance of the estimates are then used to calculate the estimated relative efficiencies of the post-stratified estimates. Estimated relative efficiencies around or above 1.2 were observed for total growth, total mortality, and total removals, with different strata maps being more effective for each. Possible avenues for improvement of the approach include the following: (1) enlarging the study area and (2) using the Landsat images closest to the time of measurement for each plot. Multitemporal satellite-derived strata maps show promise for improving the precision of change parameter estimates