Extensions of discrete triangular distributions and boundary bias in kernel estimation for discrete functions

Asymmetric discrete triangular distributions are introduced in order to extend the symmetric ones serving for discrete associated kernels in the nonparametric estimation for discrete functions. The extension from one to two orders around the mode provides a large family of discrete distributions having a finite support. Establishing a bridge between Dirac and discrete uniform distributions, some different shapes are also obtained and their properties are investigated. In particular, the mean and variance are pointed out. Applications to discrete kernel estimators are given with a solution to a boundary bias problem. (C) 2010 Elsevier B.V. All rights reserved.

The pareto-stability concept is a natural solution concept for discrete matching markets with indifferences

In a decentralized setting the game-theoretical predictions are that only strong blockings are allowed to rupture the structure of a matching. This paper argues that, under indifferences, also weak blockings should be considered when these blockings come from the grand coalition. This solution concept requires stability plus Pareto optimality. A characterization of the set of Pareto-stable matchings for the roommate and the marriage models is provided in terms of individually rational matchings whose blocking pairs, if any, are formed with unmatched agents. These matchings always exist and give an economic intuition on how blocking can be done by non-trading agents, so that the transactions need not be undone as agents reach the set of stable matchings. Some properties of the Pareto-stable matchings shared by the Marriage and Roommate models are obtained.

Discrete dimorphism among castes of the bald-faced hornet Dolichovespula maculata (Hymenoptera: Vespidae) in different phases of the colony cycle

Morphological and physiological caste differences were compared from colonies of Dolichovespula maculata in middle and late phases of the colony cycle. The females showed three patterns of ovarian development and only females classified as queens were inseminated. In both phases, queens were larger than workers for most measures. Discriminant analyses showed high distinction of caste in both phases. We also found highly pronounced qualitative differences: workers had hairs covering the entire body whereas queens had no hair and also some colour differences in the gaster. These results indicate that D. maculata presents pre-imaginal differentiation as seen in other Vespinae, and that size variation occurs from colony to colony such that queens of one colony may be comparable to workers of a different colony although the castes are always distinguishable within colonies.

Hypo- and hyperthyroidism affect NEI concentration in discrete brain areas of adult male rats

To date, there has been only one in vitro study of the relationship between neuropeptide EI (NEI) and the hypothalamic-pituitary-thyroid (HPT) axis. To investigate the possible relationship between NEI and the HPT axis, we developed a rat model of hypothyroidism and hyperthyroidism that allows us to determine whether NEI content is altered in selected brain areas after treatment, as well as whether such alterations are related to the time of day. Hypothyroidism and hyperthyroidism, induced in male rats, with 6-propyl-1-thiouracil and L-thyroxine, respectively, were confirmed by determination of triiodothyronine, total thyroxine, and thyrotropin levels. All groups were studied at the morning and the afternoon. In rats with hypothyroidism, NEI concentration, evaluated on postinduction days 7 and 24, was unchanged or slightly elevated on day 7 but was decreased on day 24. In rats with hyperthyroidism, NEI content, which was evaluated after 4 days of L-thyroxine administration, was slightly elevated, principally in the preoptic area in the morning and in the median eminence-arcuate nucleus and pineal gland in the afternoon, the morning and afternoon NEI contents being similar in the controls. These results provide the bases to pursue the study of the interaction between NEI and the HPT axis. (C) 2011 Elsevier Inc. All rights reserved.

Discrete retinal input to the parabrachial complex of a new-world primate, the common marmoset (Callithrix jacchus)

Traditional retinal projections target three functionally complementary systems it) the brain of mammals: the primary visual system, the visuomotor integration systems and the circadian timing system. In recent years, studies in several animals have been conducted to investigate the retinal projections to these three systems, despite some evidence of additional targets. The aim of this study was to disclose a previously unknown connection between the retina and the parabrachial complex of the common marmoset, by means of the intraocular injection of cholera toxin Subunit b. A few labeled retinal fibers/terminals that are detected in the medial parabrachial portion of the marmoset brain show clear varicosities, Suggesting terminal fields. Although the possible role of these projections remains unknown, they may provide a modulation of the cholinergic parabrachial neurons which project to the thalamic dorsal lateral geniculate nucleus. (c) 2008 Elsevier Ireland Ltd. All rights reserved.

UNIFORM DISSIPATIVENESS, ROBUST SYNCHRONIZATION AND LOCATION OF THE ATTRACTOR OF PARAMETRIZED NONAUTONOMOUS DISCRETE SYSTEMS

In this series of papers, we study issues related to the synchronization of two coupled chaotic discrete systems arising from secured communication. The first part deals with uniform dissipativeness with respect to parameter variation via the Liapunov direct method. We obtain uniform estimates of the global attractor for a general discrete nonautonomous system, that yields a uniform invariance principle in the autonomous case. The Liapunov function is allowed to have positive derivative along solutions of the system inside a bounded set, and this reduces substantially the difficulty of constructing a Liapunov function for a given system. In particular, we develop an approach that incorporates the classical Lagrange multiplier into the Liapunov function method to naturally extend those Liapunov functions from continuous dynamical system to their discretizations, so that the corresponding uniform dispativeness results are valid when the step size of the discretization is small. Applications to the discretized Lorenz system and the discretization of a time-periodic chaotic system are given to illustrate the general results. We also show how to obtain uniform estimation of attractors for parametrized linear stable systems with nonlinear perturbation.

Continuum, Discrete, and Explicit Solvation Models for Describing the Low-Lying Absorption Spectrum of the Pterin Acid in Aqueous Environment

The absorption spectrum of the acid form of pterin in water was investigated theoretically. Different procedures using continuum, discrete, and explicit models were used to include the solvation effect on the absorption spectrum, characterized by two bands. The discrete and explicit models used Monte Carlo simulation to generate the liquid structure and time-dependent density functional theory (B3LYP/6-31G+(d)) to obtain the excitation energies. The discrete model failed to give the correct qualitative effect on the second absorption band. The continuum model, in turn, has given a correct qualitative picture and a semiquantitative description. The explicit use of 29 solvent molecules, forming a hydration shell of 6 angstrom, embedded in the electrostatic field of the remaining solvent molecules, gives absorption transitions at 3.67 and 4.59 eV in excellent agreement with the S(0)-S(1) and S(0)-S(2) absorption bands at of 3.66 and 4.59 eV, respectively, that characterize the experimental spectrum of pterin in water environment. (C) 2010 Wiley Periodicals, Inc. Int J Quantum Chem 110: 2371-2377, 2010

Solvent effects on the electronic absorption spectrum of camphor using continuum, discrete or explicit approaches

We address the effect of solvation on the lowest electronic excitation energy of camphor. The solvents considered represent a large variation in-solvent polarity. We consider three conceptually different ways of accounting for the solvent using either an implicit, a discrete or an explicit solvation model. The solvatochromic shifts in polar solvents are found to be in good agreement with the experimental data for all three solvent models. However, both the implicit and discrete solvation models are less successful in predicting solvatochromic shifts for solvents of low polarity. The results presented suggest the importance of using explicit solvent molecules in the case of nonpolar solvents. (C) 2009 Elsevier B.V. All rights reserved.

From decoherence-free channels to decoherence-free and quasi-free subspaces within bosonic dissipative networks

We present a technique to build, within a dissipative bosonic network, decoherence-free channels (DFCs): a group of normal-mode oscillators with null effective damping rates. We verify that the states protected within the DFC define the well-known decoherence-free subspaces (DFSs) when mapped back into the natural network oscillators. Therefore, our technique to build protected normal-mode channels turns out to be an alternative way to build DFSs, which offers advantages over the conventional method. It enables the computation of all the network-protected states at once, as well as leading naturally to the concept of the decoherence quasi-free subspace (DQFS), inside which a superposition state is quasi-completely protected against decoherence. The concept of the DQFS, weaker than that of the DFS, may provide a more manageable mechanism to control decoherence. Finally, as an application of the DQFSs, we show how to build them for quasi-perfect state transfer in networks of coupled quantum dissipative oscillators.

A note on a practical relationship between filter coefficients and scaling and wavelet functions of Discrete Wavelet Transforms

In this paper, the relationship between the filter coefficients and the scaling and wavelet functions of the Discrete Wavelet Transform is presented and exemplified from a practical point-of-view. The explanations complement the wavelet theory, that is well documented in the literature, being important for researchers who work with this tool for time-frequency analysis. (c) 2011 Elsevier Ltd. All rights reserved.

A Bayesian Semiparametric Approach for Solving the Discrete Calibration Problem

In this article, we introduce a semi-parametric Bayesian approach based on Dirichlet process priors for the discrete calibration problem in binomial regression models. An interesting topic is the dosimetry problem related to the dose-response model. A hierarchical formulation is provided so that a Markov chain Monte Carlo approach is developed. The methodology is applied to simulated and real data.

SPECIAL CHARACTERIZATIONS OF STANDARD DISCRETE MODELS

This article presents important properties of standard discrete distributions and its conjugate densities. The Bernoulli and Poisson processes are described as generators of such discrete models. A characterization of distributions by mixtures is also introduced. This article adopts a novel singular notation and representation. Singular representations are unusual in statistical texts. Nevertheless, the singular notation makes it simpler to extend and generalize theoretical results and greatly facilitates numerical and computational implementation.

Banach spaces without minimal subspaces

We prove three new dichotomies for Banach spaces a la W.T. Gowers` dichotomies. The three dichotomies characterise respectively the spaces having no minimal subspaces, having no subsequentially minimal basic sequences, and having no subspaces crudely finitely representable in all of their subspaces. We subsequently use these results to make progress on Gowers` program of classifying Banach spaces by finding characteristic spaces present in every space. Also, the results are used to embed any partial order of size K I into the subspaces of any space without a minimal subspace ordered by isomorphic embeddability. (c) 2009 Elsevier Inc. All fights reserved.

Dually discrete spaces

A neighbourhood assignment in a space X is a family O = {O-x: x is an element of X} of open subsets of X such that X is an element of O-x for any x is an element of X. A set Y subset of X is a kernel of O if O(Y) = U{O-x: x is an element of Y} = X. We obtain some new results concerning dually discrete spaces, being those spaces for which every neighbourhood assignment has a discrete kernel. This is a strictly larger class than the class of D-spaces of [E.K. van Douwen, W.F. Pfeffer, Some properties of the Sorgenfrey line and related spaces, Pacific J. Math. 81 (2) (1979) 371-377]. (c) 2008 Elsevier B.V. All rights reserved.

Examples from trees, related to discrete subsets, pseudo-radiality and omega-boundedness

We construct some examples using trees. Some of them are consistent counterexamples for the discrete reflection of certain topological properties. All the properties dealt with here were already known to be non-discretely reflexive if we assume CH and we show that the same is true assuming the existence of a Suslin tree. In some cases we actually get some ZFC results. We construct also, using a Suslin tree, a compact space that is pseudo-radial but it is not discretely generated. With a similar construction, but using an Aronszajn tree, we present a ZFC space that is first countable, omega-bounded but is not strongly w-bounded, answering a question of Peter Nyikos. (C) 2008 Elsevier B.V. All rights reserved.