Frontal Solutions: an Information Technology Transfer to Abstract Mathematics

The paper introduces a method for dependencies discovery during human-machine interaction. It is based on an analysis of numerical data sets in knowledge-poor environments. The driven procedures are independent and they interact on a competitive principle. The research focuses on seven of them. The application is in Number Theory.

Lattice approach to the dynamics of the DPSK-encoded soliton trains

We study the dynamical properties of the RZ-DPSK encoded sequences, focusing on the instabilities in the soliton train leading to the distortions of the information transmitted. The problem is reformulated within the framework of complex Toda chain model which allows one to carry out the simplified description of the optical soliton dynamics. We elucidate how the bit composition of the pattern affects the initial (linear) stage of the train dynamics and explain the general mechanisms of the appearance of unstable collective soliton modes. Then we discuss the nonlinear regime using asymptotic properties of the pulse stream at large propagation distances and analyze the dynamical behavior of the train classifying different scenarios for the pattern instabilities. Both approaches are based on the machinery of Hermitian and non-Hermitian lattice analysis. © 2010 IEEE.

The NumbersWithNames Program

We present the NumbersWithNames program which performs data-mining on the Encyclopedia of Integer Sequences to find interesting conjectures in number theory. The program forms conjectures by finding empirical relationships between a sequence chosen by the user and those in the Encyclopedia. Furthermore, it transforms the chosen sequence into another set of sequences about which conjectures can also be formed. Finally, the program prunes and sorts the conjectures so that themost plausible ones are presented first. We describe here the many improvements to the previous Prolog implementation which have enabled us to provide NumbersWithNames as an online program. We also present some new results from using NumbersWithNames, including details of an automated proof plan of a conjecture NumbersWithNames helped to discover.

A singular function and its relation with the number systems involved in its definition

Minkowski's ?(x) function can be seen as the confrontation of two number systems: regular continued fractions and the alternated dyadic system. This way of looking at it permits us to prove that its derivative, as it also happens for many other non-decreasing singular functions from [0,1] to [0,1], when it exists can only attain two values: zero and infinity. It is also proved that if the average of the partial quotients in the continued fraction expansion of x is greater than k* =5.31972, and ?'(x) exists then ?'(x)=0. In the same way, if the same average is less than k**=2 log2(F), where F is the golden ratio, then ?'(x)=infinity. Finally some results are presented concerning metric properties of continued fraction and alternated dyadic expansions.

Some non- linear problems in theoretical physics

An immense variety of problems in theoretical physics are of the non-linear type. Non~linear partial differential equations (NPDE) have almost become the rule rather than an exception in diverse branches of physics such as fluid mechanics, field theory, particle physics, statistical physics and optics, and the construction of exact solutions of these equations constitutes one of the most vigorous activities in theoretical physics today. The thesis entitled ‘Some Non-linear Problems in Theoretical Physics’ addresses various aspects of this problem at the classical level. For obtaining exact solutions we have used mathematical tools like the bilinear operator method, base equation technique and similarity method with emphasis on its group theoretical aspects. The thesis deals with certain methods of finding exact solutions of a number of non-linear partial differential equations of importance to theoretical physics. Some of these new solutions are of relevance from the applications point of view in diverse branches such as elementary particle physics, field theory, solid state physics and non-linear optics and give some insight into the stable or unstable behavior of dynamical Systems The thesis consists of six chapters.

Evaluation of survey methods for sampling anuran species richness in the neotropics.

Species richness is central to ecological theory, with practical applications in conservation, environmental management and monitoring. Several techniques are available for measuring species richness and composition of amphibians in breeding pools, but the relative efficacy of these methods for sampling high-diversity Neotropical amphibian fauna is poorly understood. I evaluated seven studies from south and south-eastern Brazil to compare the relative and combined effectiveness of two methods for measuring species richness at anuran breeding pools: acoustic surveys with visual encounter of adults and dipnet surveys of larvae. I also compared the relative efficacy of each survey method in detecting species with different reproductive modes. Results showed that both survey methods underestimated the number of species when used separately; however, a close approximation of the actual number of species in each breeding pool was obtained when the methods were combined. There was no difference between survey methods in detecting species with different reproductive modes. These results indicate that researchers should employ multiple survey methods that target both adult and larval life history stages in order to accurately assess anuran species richness at breeding pools in the Neotropics.

RIEMANN ZETA ZEROS AND PRIME NUMBER SPECTRA IN QUANTUM FIELD THEORY

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Higher-order molecular properties and excitation energies in single-reference and multireference coupled-cluster theory

Coupled-cluster (CC) theory is one of the most successful approaches in high-accuracy quantum chemistry. The present thesis makes a number of contributions to the determination of molecular properties and excitation energies within the CC framework. The multireference CC (MRCC) method proposed by Mukherjee and coworkers (Mk-MRCC) has been benchmarked within the singles and doubles approximation (Mk-MRCCSD) for molecular equilibrium structures. It is demonstrated that Mk-MRCCSD yields reliable results for multireference cases where single-reference CC methods fail. At the same time, the present work also illustrates that Mk-MRCC still suffers from a number of theoretical problems and sometimes gives rise to results of unsatisfactory accuracy. To determine polarizability tensors and excitation spectra in the MRCC framework, the Mk-MRCC linear-response function has been derived together with the corresponding linear-response equations. Pilot applications show that Mk-MRCC linear-response theory suffers from a severe problem when applied to the calculation of dynamic properties and excitation energies: The Mk-MRCC sufficiency conditions give rise to a redundancy in the Mk-MRCC Jacobian matrix, which entails an artificial splitting of certain excited states. This finding has established a new paradigm in MRCC theory, namely that a convincing method should not only yield accurate energies, but ought to allow for the reliable calculation of dynamic properties as well. In the context of single-reference CC theory, an analytic expression for the dipole Hessian matrix, a third-order quantity relevant to infrared spectroscopy, has been derived and implemented within the CC singles and doubles approximation. The advantages of analytic derivatives over numerical differentiation schemes are demonstrated in some pilot applications.

Modern elementary theory of numbers

Mode of access: Internet.

Access to better education: The school choice experience of families served by low-performing elementary public schools in Miami-Dade County

Public school choice education policy attempts to create an education marketplace. Although school choice research has focused on the parent role in the school choice process, little is known about parents served by low-performing schools. Following market theory, students attending low-performing schools should be the primary students attempting to use school choice policy to access high performing schools rather than moving to a better school. However, students remain in these low-performing schools. This study took place in Miami-Dade County, which offers a wide variety of school choice options through charter schools, magnet schools, and open-choice schools. ^ This dissertation utilized a mixed-methods design to examine the decision-making process and school choice options utilized by the parents of students served by low-performing elementary schools in Miami-Dade County. Twenty-two semi-structured interviews were conducted with the parents of students served by low-performing schools. Binary logistic regression models were fitted to the data to compare the demographic characteristics, academic achievement and distance from alternative schooling options between transfers and non-transfers. Multinomial logistic regression models were fitted to the data to evaluate how demographic characteristics, distance to transfer school, and transfer school grade influenced the type of school a transfer student chose. A geographic analysis was conducted to determine how many miles students lived from alternative schooling options and the miles transfer students lived away from their transfer school. ^ The findings of the interview data illustrated that parents’ perceived needs are not being adequately addressed by state policy and county programs. The statistical analysis found that students from higher socioeconomic social groups were not more likely to transfer than students from lower socioeconomic social groups. Additionally, students who did transfer were not likely to end up at a high achieving school. The findings of the binary logistic regression demonstrated that transfer students were significantly more likely to live near alternative school options.^

Access to Better Education: The School Choice Experience of Families Served by Low-Performing Elementary Public Schools in Miami-Dade County

Public school choice education policy attempts to create an education marketplace. Although school choice research has focused on the parent role in the school choice process, little is known about parents served by low-performing schools. Following market theory, students attending low-performing schools should be the primary students attempting to use school choice policy to access high performing schools rather than moving to a better school. However, students remain in these low-performing schools. This study took place in Miami-Dade County, which offers a wide variety of school choice options through charter schools, magnet schools, and open-choice schools. This dissertation utilized a mixed-methods design to examine the decision-making process and school choice options utilized by the parents of students served by low-performing elementary schools in Miami-Dade County. Twenty-two semi-structured interviews were conducted with the parents of students served by low-performing schools. Binary logistic regression models were fitted to the data to compare the demographic characteristics, academic achievement and distance from alternative schooling options between transfers and non-transfers. Multinomial logistic regression models were fitted to the data to evaluate how demographic characteristics, distance to transfer school, and transfer school grade influenced the type of school a transfer student chose. A geographic analysis was conducted to determine how many miles students lived from alternative schooling options and the miles transfer students lived away from their transfer school. The findings of the interview data illustrated that parents’ perceived needs are not being adequately addressed by state policy and county programs. The statistical analysis found that students from higher socioeconomic social groups were not more likely to transfer than students from lower socioeconomic social groups. Additionally, students who did transfer were not likely to end up at a high achieving school. The findings of the binary logistic regression demonstrated that transfer students were significantly more likely to live near alternative school options.

ADHD in a representative sample of the Brazilian population: estimated prevalence and comparative adequacy of criteria between adolescents and adults according to the item response theory

Background: Attention deficit hyperactivity disorder (ADHD) is a clinically significant disorder in adulthood, but current diagnostic criteria and instruments do not seem to adequately capture the complexity of the disorder in this developmental phase. Accordingly, there are limited data on the proportion of adults affected by the disorder, specially in developing countries. Method: We assessed a representative household sample of the Brazilian population for ADHD with the Adult ADHD Self-report Scale (ASRS) Screener, and evaluated the instrument according to the Rasch model of item response theory. Results: The sample was comprised by 3007 individuals, and the overal prevalence of positive screeners for ADHD was 5.8% [95% confidence interval (CI), 4.8-7.0]. Rasch analyses revealed the misfitt of the overall sample to expectations of the model. The evaluation of the sample stratified by age revealed that data for adolescents showed a signficant fittnes to the model expectations, while items completed by adults were not adequated. Conclusions: The lack of fitness to the model for adult respondents challenges the possibility of a linear transformation of the ordinal data into interval measures and the utilization of parametric analyses of data. This result suggests that diagnostic criteria and instruments for adult ADHD must take into account a developmental perspective. Moreover, it calls for further evaluation of currently employed research methods in light of modern theories of psychometrics. Copyright (C) 2010 John Wiley & Sons, Ltd.

Efficiency of sampling methods and effort to assess arthropod diversity in Azorean native forests

The BALA project (Biodiversity of Arthropods of Laurisilva of the Azores) is a research initiative to quantify the spatial distribution of arthropod biodiversity in native forests of the Azores archipelago. Arthropods were collected using a combination of two techniques, targeting epigean (ground dwelling) and canopy (arboreal) arthropods: pitfall traps (with Turquin and Ethylene solutions) and beating samples (using the three most dominant plant species). A total of 109 transects distributed amongst 18 forest fragments in seven of the nine Azorean islands were used in this study. The performance of alternative sampling methods and effort were tested. No significant differences were found in the accumulated number of species captured whether an alternative method was used or whether another transect with similar effort was established in another location within the same fragment. A combination of Ethylene and Turquin traps captured more species per individual, Turquin and beating captured more species per sample, and Turquin captured more species per unit time. An optimization exercise was performed and we found that the protocol applied during recent years is very close to optimal, allowing its future replication with confidence. The minimum combinations of sampling effort and methods, in order to monitor or to inventory diversity, taking into account different proportions of sample completeness are discussed.

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/.

Periprocedural Hemodynamic Depression Is Associated With a Higher Number of New Ischemic Brain Lesions After Stenting in the International Carotid Stenting Study-MRI Substudy.

BACKGROUND AND PURPOSE: Carotid artery stenting (CAS) is associated with a higher risk of both hemodynamic depression and new ischemic brain lesions on diffusion-weighted imaging than carotid endarterectomy (CEA). We assessed whether the occurrence of hemodynamic depression is associated with these lesions in patients with symptomatic carotid stenosis treated by CAS or CEA in the randomized International Carotid Stenting Study (ICSS)-MRI substudy. METHODS: The number and total volume of new ischemic lesions on diffusion-weighted imaging 1 to 3 days after CAS or CEA was measured in the ICSS-MRI substudy. Hemodynamic depression was defined as periprocedural bradycardia, asystole, or hypotension requiring treatment. The number of new ischemic lesions was the primary outcome measure. We calculated risk ratios and 95% confidence intervals per treatment with Poisson regression comparing the number of lesions in patients with or without hemodynamic depression. RESULTS: A total of 229 patients were included (122 allocated CAS; 107 CEA). After CAS, patients with hemodynamic depression had a mean of 13 new diffusion-weighted imaging lesions, compared with a mean of 4 in those without hemodynamic depression (risk ratio, 3.36; 95% confidence interval, 1.73-6.50). The number of lesions after CEA was too small for reliable analysis. Lesion volumes did not differ between patients with or without hemodynamic depression. CONCLUSIONS: In patients treated by CAS, periprocedural hemodynamic depression is associated with an excess of new ischemic lesions on diffusion-weighted imaging. The findings support the hypothesis that hypoperfusion increases the susceptibility of the brain to embolism. CLINICAL TRIAL REGISTRATION URL: http://www.controlled-trials.com. Unique identifier: ISRCTN25337470.