Riesz potential operators and inverses via fractional centred derivatives

International Journal of Mathematics and Mathematical Sciences, Vol.2006

New findings on the dynamics of HIV and TB coinfection models

In this paper we study a model for HIV and TB coinfection. We consider the integer order and the fractional order versions of the model. Let α∈[0.78,1.0] be the order of the fractional derivative, then the integer order model is obtained for α=1.0. The model includes vertical transmission for HIV and treatment for both diseases. We compute the reproduction number of the integer order model and HIV and TB submodels, and the stability of the disease free equilibrium. We sketch the bifurcation diagrams of the integer order model, for variation of the average number of sexual partners per person and per unit time, and the tuberculosis transmission rate. We analyze numerical results of the fractional order model for different values of α, including α=1. The results show distinct types of transients, for variation of α. Moreover, we speculate, from observation of the numerical results, that the order of the fractional derivative may behave as a bifurcation parameter for the model. We conclude that the dynamics of the integer and the fractional order versions of the model are very rich and that together these versions may provide a better understanding of the dynamics of HIV and TB coinfection.

Feature Discretization with Relevance and Mutual Information Criteria

Feature discretization (FD) techniques often yield adequate and compact representations of the data, suitable for machine learning and pattern recognition problems. These representations usually decrease the training time, yielding higher classification accuracy while allowing for humans to better understand and visualize the data, as compared to the use of the original features. This paper proposes two new FD techniques. The first one is based on the well-known Linde-Buzo-Gray quantization algorithm, coupled with a relevance criterion, being able perform unsupervised, supervised, or semi-supervised discretization. The second technique works in supervised mode, being based on the maximization of the mutual information between each discrete feature and the class label. Our experimental results on standard benchmark datasets show that these techniques scale up to high-dimensional data, attaining in many cases better accuracy than existing unsupervised and supervised FD approaches, while using fewer discretization intervals.

Spectral and dynamical invariants in a complete clustered network

The main result of this work is a new criterion for the formation of good clusters in a graph. This criterion uses a new dynamical invariant, the performance of a clustering, that characterizes the quality of the formation of clusters. We prove that the growth of the dynamical invariant, the network topological entropy, has the effect of worsening the quality of a clustering, in a process of cluster formation by the successive removal of edges. Several examples of clustering on the same network are presented to compare the behavior of other parameters such as network topological entropy, conductance, coefficient of clustering and performance of a clustering with the number of edges in a process of clustering by successive removal.

Symbolic dynamics and big bang bifurcation in Weibull-Gompertz-Fréchet's growth models

In this paper, motivated by the interest and relevance of the study of tumor growth models, a central point of our investigation is the study of the chaotic dynamics and the bifurcation structure of Weibull-Gompertz-Fréchet's functions: a class of continuousdefined one-dimensional maps. Using symbolic dynamics techniques and iteration theory, we established that depending on the properties of this class of functions in a neighborhood of a bifurcation point PBB, in a two-dimensional parameter space, there exists an order regarding how the infinite number of periodic orbits are born: the Sharkovsky ordering. Consequently, the corresponding symbolic sequences follow the usual unimodal kneading sequences in the topological ordered tree. We verified that under some sufficient conditions, Weibull-Gompertz-Fréchet's functions have a particular bifurcation structure: a big bang bifurcation point PBB. This fractal bifurcations structure is of the so-called "box-within-a-box" type, associated to a boxe ω1, where an infinite number of bifurcation curves issues from. This analysis is done making use of fold and flip bifurcation curves and symbolic dynamics techniques. The present paper is an original contribution in the framework of the big bang bifurcation analysis for continuous maps.

Exploring the long-term associations between adolescents’ music training and academic achievement

There is a positive relationship between learning music and academic achievement, although doubts remain regarding the mechanisms underlying this association. This research analyses the academic performance of music and non-music students from seventh to ninth grade. The study controls for socioeconomic status, intelligence, motivation and prior academic achievement. Data were collected from 110 adolescents at two time points, once when the students were between 11 and 14 years old in the seventh grade, and again 3 years later. Our results show that music students perform better academically than non-music students in the seventh grade (Cohen’s d = 0.88) and in the ninth grade (Cohen’s d = 1.05). This difference is particularly evident in their scores in Portuguese language and natural science; the difference is somewhat weaker in history and geography scores, and is least pronounced in mathematics and English scores (η2 p from .09 to .21). A longitudinal analysis also revealed better academic performance by music students after controlling for prior academic achievement (η2 p = .07). Furthermore, controlling for intelligence, socioeconomic status and motivation did not eliminate the positive association between music learning from the seventh to the ninth grade and students’ academic achievement (η2 p = .06). During the period, music students maintained better and more consistent academic standing. We conclude that, after controlling for intelligence, socioeconomic status and motivation, music training is positively associated with academic achievement.

Morphologic and morphometric evaluation of pancreatic islets in chronic Chagas' disease

PURPOSE: Hyperglycemia and abnormal glucose tolerance tests observed in some patients with chronic Chagas' disease suggest the possibility of morphological changes in pancreatic islets and/or denervation. The purpose of this study was to describe the morphology and morphometry of pancreatic islets in chronic Chagas' disease. METHODS: Morphologic and computerized morphometric studies were performed in fragments of the head, body, and tail regions of the pancreas obtained at necropsies of 8 normal controls and 17 patients with chronic Chagas' disease: 8 with the digestive form (Megas) and 9 with the congestive heart failure form. RESULTS: The Megas group had a larger (p < 0.05) pancreatic islet area in the tail of the pancreas (10649.3 ± 4408.8 µm²) than the normal control (9481.8 ± 3242.4 µm²) and congestive heart failure (9475.1 ± 2104.9 µm²) groups; likewise, the density of the pancreatic islets (PI) was greater (1.2 ± 0.7 vs. 0.9 ± 0.6 vs. 1.9 ± 1.0 PI/mm², respectively). In the tail region of the pancreas of patients with the Megas form, there was a significant and positive correlation (r = +0.73) between the area and density of pancreatic islets. Discrete fibrosis and leukocytic infiltrates were found in pancreatic ganglia and pancreatic islets of the patients with Chagas' disease. Trypanosoma cruzi nests were not observed in the examined sections. Individuals with the Megas form of Chagas' disease showed increased area and density of pancreatic islets in the tail of the pancreas. CONCLUSION: The observed morphometric and morphologic alterations are consistent with functional changes in the pancreas, including glycemia and insulin disturbances.

Daily variation of zooplankton abundance and evenness in the Rosana reservoir, Brazil: biotic and abiotic inferences

The zooplankton community presents stochastic temporal fluctuation and heterogeneous spatial variation determined by the relationships among the organisms and environmental conditions. We predicted that the temporal and spatial zooplankton distribution is heterogeneous and discrete, respectively, and that the daily variation of most abundant species is related to environmental conditions, specifically the availability of resources. Zooplankton samples were collected daily at three sampling stations in a lateral arm of the Rosana Reservoir (SP/PR). The zooplankton did not present significant differences in abundance and evenness among sampling stations, but the temporal variation of these attributes was significant. Abiotic variables and algal resource availability have significantly explained the daily variation of the most abundant species (p<0.001), however, the species distribution makes inferences on biotic relationships between them. Thus, not only the food resource availability is influential on the abundance of principal zooplankton species, but rather a set of factors (abiotic variables and biotic relationships).

Quasi-Potency and Cyclic subgroup separability

We study the profinite topology on discrete groups and in particular the property of cyclic subgroup separability. We investigate the class of quasi-potent, cyclic subgroup separable groups, producing many examples and showing how it behaves with respect to certain group constructions.

Bifurcations of homoclinic tangency in two-dimensional area-preserving and reversible maps

Report for the scientific sojourn at the Research Institute for Applied Mathematics and Cybernetics, Nizhny Novgorod, Russia, from July to September 2006. Within the project, bifurcations of orbit behavior in area-preserving and reversible maps with a homoclinic tangency were studied. Finitely smooth normal forms for such maps near saddle fixed points were constructed and it was shown that they coincide in the main order with the analytical Birkhoff-Moser normal form. Bifurcations of single-round periodic orbits for two-dimensional symplectic maps close to a map with a quadratic homoclinic tangency were studied. The existence of one- and two-parameter cascades of elliptic periodic orbits was proved.

Political alliances and organisational change in political parties: a framework for analysis

This article sets out a theoretical framework for the study of organisational change within political alliances. To achieve this objective it uses as a starting point a series of premises, the most notable of which include the definition of organisational change as a discrete, complex and focussed phenomenon of changes in power within the party. In accordance with these premises, it analyses the synthetic model of organisational change proposed by Panebianco (1988). After examining its limitations, a number of amendments are proposed to adapt it to the way political alliances operate. The above has resulted in the design of four new models. In order to test its validity and explanatory power in a preliminary manner, the second part looks at the organisational change of the UDC within the CiU alliance between 1978 and 2001. The discussion and conclusions reached demonstrate the problems of determinism of the Panebianco model and suggest, tentatively, the importance of the power balance within the alliance as a key factor.

Transition probabilities and duration analysis among disability states: Some evidence from Spanish data

In this paper we study the disability transition probabilities (as well as the mortalityprobabilities) due to concurrent factors to age such as income, gender and education. Althoughit is well known that ageing and socioeconomic status influence the probability ofcausing functional disorders, surprisingly little attention has been paid to the combined effectof those factors along the individuals' life and how this affects the transition from one degreeof disability to another. The assumption that tomorrow's disability state is only a functionof the today's state is very strong, since disability is a complex variable that depends onseveral other elements than time. This paper contributes into the field in two ways: (1) byattending the distinction between the initial disability level and the process that leads tohis course (2) by addressing whether and how education, age and income differentially affectthe disability transitions. Using a Markov chain discrete model and a survival analysis, weestimate the probability by year and individual characteristics that changes the state of disabilityand the duration that it takes its progression in each case. We find that people withan initial state of disability have a higher propensity to change and take less time to transitfrom different stages. Men do that more frequently than women. Education and incomehave negative effects on transition. Moreover, we consider the disability benefits associatedto those changes along different stages of disability and therefore we offer some clues onthe potential savings of preventive actions that may delay or avoid those transitions. Onpure cost considerations, preventive programs for improvement show higher benefits thanthose for preventing deterioration, and in general terms, those focussing individuals below65 should go first. Finally the trend of disability in Spain seems not to change among yearsand regional differences are not found.

Arithmetical problems in number fields, abelian varieties and modular forms

Number theory, a fascinating area in mathematics and one of the oldest, has experienced spectacular progress in recent years. The development of a deep theoretical background and the implementation of algorithms have led to new and interesting interrelations with mathematics in general which have paved the way for the emergence of major theorems in the area. This report summarizes the contribution to number theory made by the members of the Seminari de Teoria de Nombres (UB-UAB-UPC) in Barcelona. These results are presented in connection with the state of certain arithmetical problems, and so this monograph seeks to provide readers with a glimpse of some specific lines of current mathematical research.

Ruin Theory with Excess of Loss Reinsurance and Reinstatements

The present paper studies the probability of ruin of an insurer, if excess of loss reinsurance with reinstatements is applied. In the setting of the classical Cramer-Lundberg risk model, piecewise deterministic Markov processes are used to describe the free surplus process in this more general situation. It is shown that the finite-time ruin probability is both the solution of a partial integro-differential equation and the fixed point of a contractive integral operator. We exploit the latter representation to develop and implement a recursive algorithm for numerical approximation of the ruin probability that involves high-dimensional integration. Furthermore we study the behavior of the finite-time ruin probability under various levels of initial surplus and security loadings and compare the efficiency of the numerical algorithm with the computational alternative of stochastic simulation of the risk process. (C) 2011 Elsevier Inc. All rights reserved.