Espaço de Hilbert e quantificação de emaranhamento via entropia não extensiva

Pós-graduação em Matemática - IBILCE

Análise funcional e aplicações

Pós-graduação em Matemática Universitária - IGCE

Terceiro problema de Hilbert e Teorema de Dehn

Pós-graduação em Matemática em Rede Nacional - IBILCE

Combining word semantics within complex Hilbert space for information retrieval

Complex numbers are a fundamental aspect of the mathematical formalism of quantum physics. Quantum-like models developed outside physics often overlooked the role of complex numbers. Specifically, previous models in Information Retrieval (IR) ignored complex numbers. We argue that to advance the use of quantum models of IR, one has to lift the constraint of real-valued representations of the information space, and package more information within the representation by means of complex numbers. As a first attempt, we propose a complex-valued representation for IR, which explicitly uses complex valued Hilbert spaces, and thus where terms, documents and queries are represented as complex-valued vectors. The proposal consists of integrating distributional semantics evidence within the real component of a term vector; whereas, ontological information is encoded in the imaginary component. Our proposal has the merit of lifting the role of complex numbers from a computational byproduct of the model to the very mathematical texture that unifies different levels of semantic information. An empirical instantiation of our proposal is tested in the TREC Medical Record task of retrieving cohorts for clinical studies.

Calculate excess mortality during heatwaves using Hilbert-Huang transform algorithm

Background Heatwaves could cause the population excess death numbers to be ranged from tens to thousands within a couple of weeks in a local area. An excess mortality due to a special event (e.g., a heatwave or an epidemic outbreak) is estimated by subtracting the mortality figure under ‘normal’ conditions from the historical daily mortality records. The calculation of the excess mortality is a scientific challenge because of the stochastic temporal pattern of the daily mortality data which is characterised by (a) the long-term changing mean levels (i.e., non-stationarity); (b) the non-linear temperature-mortality association. The Hilbert-Huang Transform (HHT) algorithm is a novel method originally developed for analysing the non-linear and non-stationary time series data in the field of signal processing, however, it has not been applied in public health research. This paper aimed to demonstrate the applicability and strength of the HHT algorithm in analysing health data. Methods Special R functions were developed to implement the HHT algorithm to decompose the daily mortality time series into trend and non-trend components in terms of the underlying physical mechanism. The excess mortality is calculated directly from the resulting non-trend component series. Results The Brisbane (Queensland, Australia) and the Chicago (United States) daily mortality time series data were utilized for calculating the excess mortality associated with heatwaves. The HHT algorithm estimated 62 excess deaths related to the February 2004 Brisbane heatwave. To calculate the excess mortality associated with the July 1995 Chicago heatwave, the HHT algorithm needed to handle the mode mixing issue. The HHT algorithm estimated 510 excess deaths for the 1995 Chicago heatwave event. To exemplify potential applications, the HHT decomposition results were used as the input data for a subsequent regression analysis, using the Brisbane data, to investigate the association between excess mortality and different risk factors. Conclusions The HHT algorithm is a novel and powerful analytical tool in time series data analysis. It has a real potential to have a wide range of applications in public health research because of its ability to decompose a nonlinear and non-stationary time series into trend and non-trend components consistently and efficiently.

Figuras de Espaço na Arquitectura de um Vazio [Figures of space in the architecture of a void]

This text discusses the production of space as performance, space as the architecture of a void in relation to Fernanda Fragateiro's art work 'Caixa para Guardar o Vazio'

Paisagem e Escassez : espaço e experimentação

The text elaborates on the creation of Candlestick Park and Parque de la Pedra Tosca as landscape architectural productions that integrated cultural and ecological processes in its spatialization as a response to scarcity and memory

Resonances, scattering theory, and rigged Hilbert spaces

The problem of decaying states and resonances is examined within the framework of scattering theory in a rigged Hilbert space formalism. The stationary free,''in,'' and ''out'' eigenvectors of formal scattering theory, which have a rigorous setting in rigged Hilbert space, are considered to be analytic functions of the energy eigenvalue. The value of these analytic functions at any point of regularity, real or complex, is an eigenvector with eigenvalue equal to the position of the point. The poles of the eigenvector families give origin to other eigenvectors of the Hamiltonian: the singularities of the ''out'' eigenvector family are the same as those of the continued S matrix, so that resonances are seen as eigenvectors of the Hamiltonian with eigenvalue equal to their location in the complex energy plane. Cauchy theorem then provides for expansions in terms of ''complete'' sets of eigenvectors with complex eigenvalues of the Hamiltonian. Applying such expansions to the survival amplitude of a decaying state, one finds that resonances give discrete contributions with purely exponential time behavior; the background is of course present, but explicitly separated. The resolvent of the Hamiltonian, restricted to the nuclear space appearing in the rigged Hilbert space, can be continued across the absolutely continuous spectrum; the singularities of the continuation are the same as those of the ''out'' eigenvectors. The free, ''in'' and ''out'' eigenvectors with complex eigenvalues and those corresponding to resonances can be approximated by physical vectors in the Hilbert space, as plane waves can. The need for having some further physical information in addition to the specification of the total Hamiltonian is apparent in the proposed framework. The formalism is applied to the Lee–Friedrichs model and to the scattering of a spinless particle by a local central potential. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Unitary Processes with Independent Increments and Representations of Hilbert Tensor Algebras

The aim of this article is to characterize unitary increment process by a quantum stochastic integral representation on symmetric Fock space. Under certain assumptions we have proved its unitary equivalence to a Hudson-Parthasarathy flow.