Spectral invariants of periodic nonautonomous discrete dynamical systems

For an interval map, the poles of the Artin-Mazur zeta function provide topological invariants which are closely connected to topological entropy. It is known that for a time-periodic nonautonomous dynamical system F with period p, the p-th power [zeta(F) (z)](p) of its zeta function is meromorphic in the unit disk. Unlike in the autonomous case, where the zeta function zeta(f)(z) only has poles in the unit disk, in the p-periodic nonautonomous case [zeta(F)(z)](p) may have zeros. In this paper we introduce the concept of spectral invariants of p-periodic nonautonomous discrete dynamical systems and study the role played by the zeros of [zeta(F)(z)](p) in this context. As we will see, these zeros play an important role in the spectral classification of these systems.

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.

Analysis of UV spectral bands using multidimensional scaling

This study describes the change of the ultraviolet spectral bands starting from 0.1 to 5.0 nm slit width in the spectral range of 200–400 nm. The analysis of the spectral bands is carried out by using the multidimensional scaling (MDS) approach to reach the latent spectral background. This approach indicates that 0.1 nm slit width gives higher-order noise together with better spectral details. Thus, 5.0 nm slit width possesses the higher peak amplitude and lower-order noise together with poor spectral details. In the above-mentioned conditions, the main problem is to find the relationship between the spectral band properties and the slit width. For this aim, the MDS tool is to used recognize the hidden information of the ultraviolet spectra of sildenafil citrate by using a Shimadzu UV–VIS 2550, which is in the world the best double monochromator instrument. In this study, the proposed mathematical approach gives the rich findings for the efficient use of the spectrophotometer in the qualitative and quantitative studies.

Efficient Legendre spectral tau algorithm for solving two-sided space-time Caputo fractional advection-dispersion equation

In this paper we present the operational matrices of the left Caputo fractional derivative, right Caputo fractional derivative and Riemann–Liouville fractional integral for shifted Legendre polynomials. We develop an accurate numerical algorithm to solve the two-sided space–time fractional advection–dispersion equation (FADE) based on a spectral shifted Legendre tau (SLT) method in combination with the derived shifted Legendre operational matrices. The fractional derivatives are described in the Caputo sense. We propose a spectral SLT method, both in temporal and spatial discretizations for the two-sided space–time FADE. This technique reduces the two-sided space–time FADE to a system of algebraic equations that simplifies the problem. Numerical results carried out to confirm the spectral accuracy and efficiency of the proposed algorithm. By selecting relatively few Legendre polynomial degrees, we are able to get very accurate approximations, demonstrating the utility of the new approach over other numerical methods.

A Review of Operational Matrices and Spectral Techniques for Fractional Calculus

Recently, operational matrices were adapted for solving several kinds of fractional differential equations (FDEs). The use of numerical techniques in conjunction with operational matrices of some orthogonal polynomials, for the solution of FDEs on finite and infinite intervals, produced highly accurate solutions for such equations. This article discusses spectral techniques based on operational matrices of fractional derivatives and integrals for solving several kinds of linear and nonlinear FDEs. More precisely, we present the operational matrices of fractional derivatives and integrals, for several polynomials on bounded domains, such as the Legendre, Chebyshev, Jacobi and Bernstein polynomials, and we use them with different spectral techniques for solving the aforementioned equations on bounded domains. The operational matrices of fractional derivatives and integrals are also presented for orthogonal Laguerre and modified generalized Laguerre polynomials, and their use with numerical techniques for solving FDEs on a semi-infinite interval is discussed. Several examples are presented to illustrate the numerical and theoretical properties of various spectral techniques for solving FDEs on finite and semi-infinite intervals.

Deciding Kleene Algebra Terms Equivalence in Coq

This paper presents a mechanically verified implementation of an algorithm for deciding the equivalence of Kleene algebra terms within the Coq proof assistant. The algorithm decides equivalence of two given regular expressions through an iterated process of testing the equivalence of their partial derivatives and does not require the construction of the corresponding automata. Recent theoretical and experimental research provides evidence that this method is, on average, more efficient than the classical methods based on automata. We present some performance tests, comparisons with similar approaches, and also introduce a generalization of the algorithm to decide the equivalence of terms of Kleene algebra with tests. The motivation for the work presented in this paper is that of using the libraries developed as trusted frameworks for carrying out certified program verification.

Adaptive modeling and high quality spectral estimation for speech enhancement

In this work an adaptive modeling and spectral estimation scheme based on a dual Discrete Kalman Filtering (DKF) is proposed for speech enhancement. Both speech and noise signals are modeled by an autoregressive structure which provides an underlying time frame dependency and improves time-frequency resolution. The model parameters are arranged to obtain a combined state-space model and are also used to calculate instantaneous power spectral density estimates. The speech enhancement is performed by a dual discrete Kalman filter that simultaneously gives estimates for the models and the signals. This approach is particularly useful as a pre-processing module for parametric based speech recognition systems that rely on spectral time dependent models. The system performance has been evaluated by a set of human listeners and by spectral distances. In both cases the use of this pre-processing module has led to improved results.

Spectral and homogenization problems

Dissertation for the Degree of Doctor of Philosophy in Mathematics

Spectral and coherence estimates on electroencephalogram recordings during arithmetical tasks

Dissertação apresentada na Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa para obtenção do Grau de Mestre em Engenharia Biomédica

Electrohysterogram signal component cataloging with spectral and time-frequency methods

The Electrohysterogram (EHG) is a new instrument for pregnancy monitoring. It measures the uterine muscle electrical signal, which is closely related with uterine contractions. The EHG is described as a viable alternative and a more precise instrument than the currently most widely used method for the description of uterine contractions: the external tocogram. The EHG has also been indicated as a promising tool in the assessment of preterm delivery risk. This work intends to contribute towards the EHG characterization through the inventory of its components which are: • Contractions; • Labor contractions; • Alvarez waves; • Fetal movements; • Long Duration Low Frequency Waves; The instruments used for cataloging were: Spectral Analysis, parametric and non-parametric, energy estimators, time-frequency methods and the tocogram annotated by expert physicians. The EHG and respective tocograms were obtained from the Icelandic 16-electrode Electrohysterogram Database. 288 components were classified. There is not a component database of this type available for consultation. The spectral analysis module and power estimation was added to Uterine Explorer, an EHG analysis software developed in FCT-UNL. The importance of this component database is related to the need to improve the understanding of the EHG which is a relatively complex signal, as well as contributing towards the detection of preterm birth. Preterm birth accounts for 10% of all births and is one of the most relevant obstetric conditions. Despite the technological and scientific advances in perinatal medicine, in developed countries, prematurity is the major cause of neonatal death. Although various risk factors such as previous preterm births, infection, uterine malformations, multiple gestation and short uterine cervix in second trimester, have been associated with this condition, its etiology remains unknown [1][2][3].

Using relational algebra on the specification of real world ETL processes

Modeling Extract-Transform-Load (ETL) processes of a Data Warehousing System has always been a challenge. The heterogeneity of the sources, the quality of the data obtained and the conciliation process are some of the issues that must be addressed in the design phase of this critical component. Commercial ETL tools often provide proprietary diagrammatic components and modeling languages that are not standard, thus not providing the ideal separation between a modeling platform and an execution platform. This separation in conjunction with the use of standard notations and languages is critical in a system that tends to evolve through time and which cannot be undermined by a normally expensive tool that becomes an unsatisfactory component. In this paper we demonstrate the application of Relational Algebra as a modeling language of an ETL system as an effort to standardize operations and provide a basis for uncommon ETL execution platforms.

A relational algebra approach to ETL modeling

The MAP-i Doctoral Programme in Informatics, of the Universities of Minho, Aveiro and Porto

Recurrence relations for Clifford algebra-valued orthogonal polynomials

The theory of orthogonal polynomials of one real or complex variable is well established as well as its generalization for the multidimensional case. Hypercomplex function theory (or Clifford analysis) provides an alternative approach to deal with higher dimensions. In this context, we study systems of orthogonal polynomials of a hypercomplex variable with values in a Clifford algebra and prove some of their properties.

A linear algebra approach to OLAP

Inspired by the relational algebra of data processing, this paper addresses the foundations of data analytical processing from a linear algebra perspective. The paper investigates, in particular, how aggregation operations such as cross tabulations and data cubes essential to quantitative analysis of data can be expressed solely in terms of matrix multiplication, transposition and the Khatri–Rao variant of the Kronecker product. The approach offers a basis for deriving an algebraic theory of data consolidation, handling the quantitative as well as qualitative sides of data science in a natural, elegant and typed way. It also shows potential for parallel analytical processing, as the parallelization theory of such matrix operations is well acknowledged.

An R package for the integrated analysis of metabolomics and spectral data

Recently, there has been a growing interest in the field of metabolomics, materialized by a remarkable growth in experimental techniques, available data and related biological applications. Indeed, techniques as Nuclear Magnetic Resonance, Gas or Liquid Chromatography, Mass Spectrometry, Infrared and UV-visible spectroscopies have provided extensive datasets that can help in tasks as biological and biomedical discovery, biotechnology and drug development. However, as it happens with other omics data, the analysis of metabolomics datasets provides multiple challenges, both in terms of methodologies and in the development of appropriate computational tools. Indeed, from the available software tools, none addresses the multiplicity of existing techniques and data analysis tasks. In this work, we make available a novel R package, named specmine, which provides a set of methods for metabolomics data analysis, including data loading in different formats, pre-processing, metabolite identification, univariate and multivariate data analysis, machine learning, and feature selection. Importantly, the implemented methods provide adequate support for the analysis of data from diverse experimental techniques, integrating a large set of functions from several R packages in a powerful, yet simple to use environment. The package, already available in CRAN, is accompanied by a web site where users can deposit datasets, scripts and analysis reports to be shared with the community, promoting the efficient sharing of metabolomics data analysis pipelines.