On Convergence Properties of Shannon Entropy

Convergence properties of Shannon Entropy are studied. In the differential setting, it is shown that weak convergence of probability measures, or convergence in distribution, is not enough for convergence of the associated differential entropies. A general result for the desired differential entropy convergence is provided, taking into account both compactly and uncompactly supported densities. Convergence of differential entropy is also characterized in terms of the Kullback-Liebler discriminant for densities with fairly general supports, and it is shown that convergence in variation of probability measures guarantees such convergence under an appropriate boundedness condition on the densities involved. Results for the discrete setting are also provided, allowing for infinitely supported probability measures, by taking advantage of the equivalence between weak convergence and convergence in variation in this setting.Comment: Submitted to IEEE Transactions on Information Theor

Offline to Online Conversion

We consider the problem of converting offline estimators into an online predictor or estimator with small extra regret. Formally this is the problem of merging a collection of probability measures over strings of length 1,2,3,... into a single probability measure over infinite sequences. We describe various approaches and their pros and cons on various examples. As a side-result we give an elementary non-heuristic purely combinatoric derivation of Turing's famous estimator. Our main technical contribution is to determine the computational complexity of online estimators with good guarantees in general.Comment: 20 LaTeX page

Dark Energy Content of Nonlinear Electromagnetism

Quasi-constant external fields in nonlinear electromagnetism generate a contribution to the energy-momentum tensor with the form of dark energy. To provide a thorough understanding of the origin and strength of the effects, we undertake a complete theoretical and numerical study of the energy-momentum tensor $T^{\mu\nu}$ for nonlinear electromagnetism. The Euler-Heisenberg nonlinearity due to quantum fluctuations of spinor and scalar matter fields is considered and contrasted with the properties of classical nonlinear Born-Infeld electromagnetism. We also address modifications of charged particle kinematics by strong background fields.Comment: 16 pages, 12 figures; reorganized introduction and sections 4 and 5, added further numerical results and discussion, updated references, fixed typo

Ewald methods for polarizable surfaces with application to hydroxylation and hydrogen bonding on the (012) and (001) surfaces of alpha-Fe2O3

We present a clear and rigorous derivation of the Ewald-like method for calculation of the electrostatic energy of the systems infinitely periodic in two-dimensions and of finite size in the third dimension (slabs) which is significantly faster than existing methods. Molecular dynamics simulations using the transferable/polarizable model by Rustad et al. were applied to study the surface relaxation of the nonhydroxylated, hydroxylated, and solvated surfaces of alpha-Fe2O3 (hematite). We find that our nonhydroxylated structures and energies are in good agreement with previous LDA calculations on alpha-alumina by Manassidis et al. [Surf. Sci. Lett. 285, L517, 1993]. Using the results of molecular dynamics simulations of solvated interfaces, we define end-member hydroxylated-hydrated states for the surfaces which are used in energy minimization calculations. We find that hydration has a small effect on the surface structure, but that hydroxylation has a significant effect. Our calculations, both for gas-phase and solution-phase adsorption, predict a greater amount of hydroxylation for the (012) surface than for the (001) surface. Our simulations also indicate the presence of four-fold coordinated iron ions on the (001) surface.Comment: 23 pages, REVTeX (LaTeX), 8 figures not included, e-mail to [email protected], paper accepted in Surface Scienc

Real-Time Onboard Global Nonlinear Aerodynamic Modeling from Flight Data

Flight test and modeling techniques were developed to accurately identify global nonlinear aerodynamic models onboard an aircraft. The techniques were developed and demonstrated during piloted flight testing of an Aermacchi MB-326M Impala jet aircraft. Advanced piloting techniques and nonlinear modeling techniques based on fuzzy logic and multivariate orthogonal function methods were implemented with efficient onboard calculations and flight operations to achieve real-time maneuver monitoring and analysis, and near-real-time global nonlinear aerodynamic modeling and prediction validation testing in flight. Results demonstrated that global nonlinear aerodynamic models for a large portion of the flight envelope were identified rapidly and accurately using piloted flight test maneuvers during a single flight, with the final identified and validated models available before the aircraft landed

Calabi-Yau Duals of Torus Orientifolds

We study a duality that relates the T^6/Z_2 orientifold with N=2 flux to standard fluxless Calabi-Yau compactifications of type IIA string theory. Using the duality map, we show that the Calabi-Yau manifolds that arise are abelian surface (T^4) fibrations over P^1. We compute a variety of properties of these threefolds, including Hodge numbers, intersection numbers, discrete isometries, and H_1(X,Z). In addition, we show that S-duality in the orientifold description becomes T-duality of the abelian surface fibers in the dual Calabi-Yau description. The analysis is facilitated by the existence of an explicit Calabi-Yau metric on an open subset of the geometry that becomes an arbitrarily good approximation to the actual metric (at most points) in the limit that the fiber is much smaller than the base.Comment: 39 pages; uses harvmac.tex, amssym.tex; v4: minor correction

The Value of Information for Populations in Varying Environments

The notion of information pervades informal descriptions of biological systems, but formal treatments face the problem of defining a quantitative measure of information rooted in a concept of fitness, which is itself an elusive notion. Here, we present a model of population dynamics where this problem is amenable to a mathematical analysis. In the limit where any information about future environmental variations is common to the members of the population, our model is equivalent to known models of financial investment. In this case, the population can be interpreted as a portfolio of financial assets and previous analyses have shown that a key quantity of Shannon's communication theory, the mutual information, sets a fundamental limit on the value of information. We show that this bound can be violated when accounting for features that are irrelevant in finance but inherent to biological systems, such as the stochasticity present at the individual level. This leads us to generalize the measures of uncertainty and information usually encountered in information theory

Spiral Galaxies as Chiral Objects?

Spiral galaxies show axial symmetry and an intrinsic 2D-chirality. Environmental effects can influence the chirality of originally isolated stellar systems and a progressive loss of chirality can be recognised in the Hubble sequence. We point out a preferential modality for genetic galaxies as in microscopic systems like aminoacids, sugars or neutrinos. This feature could be the remnant of a primordial symmetry breaking characterizing systems at all scales.Comment: 10 pages, 3 figure

Scalable Massively Parallel Artificial Neural Networks

There is renewed interest in computational intelligence, due to advances in algorithms, neuroscience, and computer hardware. In addition there is enormous interest in autonomous vehicles (air, ground, and sea) and robotics, which need significant onboard intelligence. Work in this area could not only lead to better understanding of the human brain but also very useful engineering applications. The functioning of the human brain is not well understood, but enormous progress has been made in understanding it and, in particular, the neocortex. There are many reasons to develop models of the brain. Artificial Neural Networks (ANN), one type of model, can be very effective for pattern recognition, function approximation, scientific classification, control, and the analysis of time series data. ANNs often use the back-propagation algorithm for training, and can require large training times especially for large networks, but there are many other types of ANNs. Once the network is trained for a particular problem, however, it can produce results in a very short time. Parallelization of ANNs could drastically reduce the training time. An object-oriented, massively-parallel ANN (Artificial Neural Network) software package SPANN (Scalable Parallel Artificial Neural Network) has been developed and is described here. MPI was use