A Statistical Convergence Aplication for the Hopfield Networks

When Recurrent Neural Networks (RNN) are going to be used as Pattern Recognition systems, the problem to be considered is how to impose prescribed prototype vectors ξ^1,ξ^2,...,ξ^p as fixed points. The synaptic matrix W should be interpreted as a sort of sign correlation matrix of the prototypes, In the classical approach. The weak point in this approach, comes from the fact that it does not have the appropriate tools to deal efficiently with the correlation between the state vectors and the prototype vectors The capacity of the net is very poor because one can only know if one given vector is adequately correlated with the prototypes or not and we are not able to know what its exact correlation degree. The interest of our approach lies precisely in the fact that it provides these tools. In this paper, a geometrical vision of the dynamic of states is explained. A fixed point is viewed as a point in the Euclidean plane R2. The retrieving procedure is analyzed trough statistical frequency distribution of the prototypes. The capacity of the net is improved and the spurious states are reduced. In order to clarify and corroborate the theoretical results, together with the formal theory, an application is presented

Universal duality in a Luttinger liquid coupled to a generic environment

We study a Luttinger liquid (LL) coupled to a generic environment consisting of bosonic modes with arbitrary density-density and current-current interactions. The LL can be either in the conducting phase and perturbed by a weak scatterer or in the insulating phase and perturbed by a weak link. The environment modes can also be scattered by the imperfection in the system with arbitrary transmission and reflection amplitudes. We present a general method of calculating correlation functions under the presence of the environment and prove the duality of exponents describing the scaling of the weak scatterer and of the weak link. This duality holds true for a broad class of models and is sensitive to neither interaction nor environmental modes details, thus it shows up as the universal property. It ensures that the environment cannot generate new stable fixed points of the renormalization group flow. Thus, the LL always flows toward either conducting or insulating phase. Phases are separated by a sharp boundary which is shifted by the influence of the environment. Our results are relevant, for example, for low-energy transport in (i) an interacting quantum wire or a carbon nanotube where the electrons are coupled to the acoustic phonons scattered by the lattice defect; (ii) a mixture of interacting fermionic and bosonic cold atoms where the bosonic modes are scattered due to an abrupt local change of the interaction; (iii) mesoscopic electric circuits.

Indice de Point Fixe pour les Morphismes de Chaînes

2000 Mathematics Subject Classification: 54H25, 55M20.

Scaling limits of a model for selection at two scales

The dynamics of a population undergoing selection is a central topic in evolutionary biology. This question is particularly intriguing in the case where selective forces act in opposing directions at two population scales. For example, a fast-replicating virus strain outcompetes slower-replicating strains at the within-host scale. However, if the fast-replicating strain causes host morbidity and is less frequently transmitted, it can be outcompeted by slower-replicating strains at the between-host scale. Here we consider a stochastic ball-and-urn process which models this type of phenomenon. We prove the weak convergence of this process under two natural scalings. The first scaling leads to a deterministic nonlinear integro-partial differential equation on the interval $[0,1]$ with dependence on a single parameter, $\lambda$. We show that the fixed points of this differential equation are Beta distributions and that their stability depends on $\lambda$ and the behavior of the initial data around $1$. The second scaling leads to a measure-valued Fleming-Viot process, an infinite dimensional stochastic process that is frequently associated with a population genetics.

Irreducibility of Random Hilbert Schemes

We prove that a random Hilbert scheme that parametrizes the closed subschemes with a fixed Hilbert polynomial in some projective space is irreducible and nonsingular with probability greater than $0.5$. To consider the set of nonempty Hilbert schemes as a probability space, we transform this set into a disjoint union of infinite binary trees, reinterpreting Macaulay's classification of admissible Hilbert polynomials. Choosing discrete probability distributions with infinite support on the trees establishes our notion of random Hilbert schemes. To bound the probability that random Hilbert schemes are irreducible and nonsingular, we show that at least half of the vertices in the binary trees correspond to Hilbert schemes with unique Borel-fixed points.

Casi di aggiunta della διαστολή nel codice Vaticano Gr. 1209

El artículo estudia casos de adición de la διαστολή en el Codex Vaticanus gr. 1209. Esta adición puede advertirse, asimismo, en pasajes del Nuevo Testamento y en la Septuaginta donde se utiliza el pronominal ὅτι. Este artículo sostiene que, en los pasajes examinados, la adición responde a propósitos filológicos en lugar de obedecer a razones de lectura. La διαστολή, de hecho, podría ser una especie de firma involuntaria que ayuda a establecer o confirmar los puntos clave antes de que el codex llegase a la Biblioteca Vaticana en 1475.

Caos e fractais na sala de aula

O objectivo deste trabalho é o estudo do tema Caos e Fractais, com o propósito fundamental da sua implementação na sala de aula ou outro ambiente do Ensino Secundário. Com esse fim, é feita uma abordagem teórica dos conteúdos e são apresentadas algumas actividades a desenvolver com os alunos daquele nível de ensino. A introdução dos conceitos é feita de modo a possibilitar a sua leitura por um público mais geral, onde se incluem os alunos mais interessados e curiosos no tema. O estudo é acompanhado, sempre que possível, de exemplos e ilustrações gráficas. Para tal, foi utilizado o software Maxima (software livre) e outras aplicações interactivas disponíveis na Internet. ABSTRACT: The aim of this work is to study the theme of Chaos and Fractals, with the fundamental purpose of its implementation in the classroom, or in other environments of secondary school education. To carry out this aim a theoretical outlook of the contents will be provided alongside some activities to be undergone with students of that school level. The introduction to these concepts is open to the understanding of a larger audience, where we can include the most interested and curious students in this issue. The study is accompanied, whenever possible, with examples and graphics. To do so, the Maxima software (free software) was used, besides other interactive applications available on the Internet.

What hides behind the fixed-term contracts wage gap?

In Portugal, about 20% of full-time workers are employed under a fixed-term contract. Using a rich longitudinal matched employer-employee dataset for Portugal, with more than 20 million observations and covering the 2002-2012 period, we confirm the common idea that fixed-term contracts are not desirable when compared to permanent ones, by estimating a conditional wage gap of -1.7 log points. Then, we evaluate the sources of that wage penalty by combining a three way high-dimensional fixed effects model with the decomposition of Gelbach (2014), in which the three dimensions considered are the worker’s unobserved ability, the firm’s compensation wage policy and the job title effect. It is shown that the average worker with a fixed-term contract is less productive than his/her permanent counterparts, explaining -3.92 log points of the FTC wage penalty. Additionally, the sorting of workers into lower-paid job titles is also responsible for -0.59 log points of the wage gap. Surprisingly, we found that the allocation of workers among firms mitigates the existing wage penalty (in 4.23 log points), as fixed-term workers are concentrated into firms with a more generous compensation policy. Finally, following Figueiredo et al. (2014), we further control for the worker-firm match characteristics and reach the conclusion that fixed-term employment relationships have an overrepresentation of low quality worker-firm matches, explaining 0.65 log points of the FTC wage penalty.

An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds

For a given self-map f of M, a closed smooth connected and simply-connected manifold of dimension m ≥ 4, we provide an algorithm for estimating the values of the topological invariant Dm r [f], which equals the minimal number of r-periodic points in the smooth homotopy class of f. Our results are based on the combinatorial scheme for computing Dm r [f] introduced by G. Graff and J. Jezierski [J. Fixed Point Theory Appl. 13 (2013), 63–84]. An open-source implementation of the algorithm programmed in C++ is publicly available at http://www.pawelpilarczyk.com/combtop/.

Routine delivery of artemisinin-based combination treatment at fixed health facilities reduces malaria prevalence in Tanzania: an observational study.

BACKGROUND: Artemisinin-based combination therapy (ACT) has been promoted as a means to reduce malaria transmission due to their ability to kill both asexual blood stages of malaria parasites, which sustain infections over long periods and the immature derived sexual stages responsible for infecting mosquitoes and onward transmission. Early studies reported a temporal association between ACT introduction and reduced malaria transmission in a number of ecological settings. However, these reports have come from areas with low to moderate malaria transmission, been confounded by the presence of other interventions or environmental changes that may have reduced malaria transmission, and have not included a comparison group without ACT. This report presents results from the first large-scale observational study to assess the impact of case management with ACT on population-level measures of malaria endemicity in an area with intense transmission where the benefits of effective infection clearance might be compromised by frequent and repeated re-infection. METHODS: A pre-post observational study with a non-randomized comparison group was conducted at two sites in Tanzania. Both sites used sulphadoxine-pyrimethamine (SP) monotherapy as a first-line anti-malarial from mid-2001 through 2002. In 2003, the ACT, artesunate (AS) co-administered with SP (AS + SP), was introduced in all fixed health facilities in the intervention site, including both public and registered non-governmental facilities. Population-level prevalence of Plasmodium falciparum asexual parasitaemia and gametocytaemia were assessed using light microscopy from samples collected during representative household surveys in 2001, 2002, 2004, 2005 and 2006. FINDINGS: Among 37,309 observations included in the analysis, annual asexual parasitaemia prevalence in persons of all ages ranged from 11% to 28% and gametocytaemia prevalence ranged from <1% to 2% between the two sites and across the five survey years. A multivariable logistic regression model was fitted to adjust for age, socioeconomic status, bed net use and rainfall. In the presence of consistently high coverage and efficacy of SP monotherapy and AS + SP in the comparison and intervention areas, the introduction of ACT in the intervention site was associated with a modest reduction in the adjusted asexual parasitaemia prevalence of 5 percentage-points or 23% (p < 0.0001) relative to the comparison site. Gametocytaemia prevalence did not differ significantly (p = 0.30). INTERPRETATION: The introduction of ACT at fixed health facilities only modestly reduced asexual parasitaemia prevalence. ACT is effective for treatment of uncomplicated malaria and should have substantial public health impact on morbidity and mortality, but is unlikely to reduce malaria transmission substantially in much of sub-Saharan Africa where individuals are rapidly re-infected.

The number of planar central configurations for the 4-body problem is finite when 3 mass positions are fixed

In the n{body problem a central con guration is formed when the position vector of each particle with respect to the center of mass is a common scalar multiple of its acceleration vector. Lindstrom showed for n = 3 and for n > 4 that if n ? 1 masses are located at xed points in the plane, then there are only a nite number of ways to position the remaining nth mass in such a way that they de ne a central con guration. Lindstrom leaves open the case n = 4. In this paper we prove the case n = 4 using as variables the mutual distances between the particles.

The sequential analysis of repeated binary responses: a score test for the case of three time points

In this paper a robust method is developed for the analysis of data consisting of repeated binary observations taken at up to three fixed time points on each subject. The primary objective is to compare outcomes at the last time point, using earlier observations to predict this for subjects with incomplete records. A score test is derived. The method is developed for application to sequential clinical trials, as at interim analyses there will be many incomplete records occurring in non-informative patterns. Motivation for the methodology comes from experience with clinical trials in stroke and head injury, and data from one such trial is used to illustrate the approach. Extensions to more than three time points and to allow for stratification are discussed. Copyright © 2005 John Wiley & Sons, Ltd.

Do laws influence the cost of real estate brokerage services? A state fixed effects approach

A FTC-DOJ study argues that state laws and regulations may inhibit the unbundling of real estate brokerage services in response to new technology. Our data show that 18 states have changed laws in ways that promote unbundling since 2000. We model brokerage costs as measured by number of agents in a state-level annual panel vector autoregressive framework, a novel way of analyzing wasteful competition. Our findings support a positive relationship between brokerage costs and lagged house price and transactions. We find that change in full-service brokers responds negatively (by well over two percentage points per year) to legal changes facilitating unbundling

Myeloperoxidase activity is increased in gingival crevicular fluid and whole saliva after fixed orthodontic appliance activation

Introduction: Orthodontic tooth movement uses mechanical forces that result in inflammation in the first days. Myeloperoxidase (MPO) is an enzyme found in polymorphonuclear neutrophil (PMN) granules, and it is used to estimate the number of PMN granules in tissues. So far, MPO has not been used to study the inflammatory alterations after the application of orthodontic tooth movement forces. The aim of this study was to determine MPO activity in the gingival crevicular fluid (GCF) and saliva (whole stimulated saliva) of orthodontic patients at different time points after fixed appliance activation. Methods: MPO was determined in the GCF and collected by means of periopaper from the saliva of 14 patients with orthodontic fixed appliances. GCF and saliva samples were collected at baseline, 2 hours, and 7 and 14 days after application of the orthodontic force. Results: Mean MPO activity was increased in both the GCF and saliva of orthodontic patients at 2 hours after appliance activation (P<0.02 for all comparisons). At 2 hours, PMN infiltration into the periodontal ligament from the orthodontic force probably results in the increased MPO level observed at this time point. Conclusions: MPO might be a good marker to assess inflammation in orthodontic movement; it deserves further studies in orthodontic therapy. (Am J Orthod Dentofacial Orthop 2010;138:613-6)

Genericity of Nondegenerate Critical Points and Morse Geodesic Functionals

We consider a family of variational problems on a Hilbert manifold parameterized by an open subset of a Banach manifold, and we discuss the genericity of the nondegeneracy condition for the critical points. Using classical techniques, we prove an abstract genericity result that employs the infinite dimensional Sard-Smale theorem, along the lines of an analogous result of B. White [29]. Applications are given by proving the genericity of metrics without degenerate geodesics between fixed endpoints in general (non compact) semi-Riemannian manifolds, in orthogonally split semi-Riemannian manifolds and in globally hyperbolic Lorentzian manifolds. We discuss the genericity property also in stationary Lorentzian manifolds.