Adaptive estimation of the density matrix in quantum homodyne tomography with noisy data

In the framework of noisy quantum homodyne tomography with efficiency parameter $1/2 < \eta \leq 1$, we propose a novel estimator of a quantum state whose density matrix elements $\rho_{m,n}$ decrease like $Ce^{-B(m+n)^{r/ 2}}$, for fixed $C\geq 1$, $B>0$ and $0<r\leq 2$. On the contrary to previous works, we focus on the case where $r$, $C$ and $B$ are unknown. The procedure estimates the matrix coefficients by a projection method on the pattern functions, and then by soft-thresholding the estimated coefficients. We prove that under the $\mathbb{L}_2$ -loss our procedure is adaptive rate-optimal, in the sense that it achieves the same rate of conversgence as the best possible procedure relying on the knowledge of $(r,B,C)$. Finite sample behaviour of our adaptive procedure are explored through numerical experiments

Derivatives with respect to metrics and applications: subgradient marching algorithm

This paper introduces a subgradient descent algorithm to compute a Riemannian metric that minimizes an energy involving geodesic distances. The heart of the method is the Subgradient Marching Algorithm to compute the derivative of the geodesic distance with respect to the metric. The geodesic distance being a concave function of the metric, this algorithm computes an element of the subgradient in O(N 2 log(N)) operations on a discrete grid of N points. It performs a front propagation that computes a subgradient of a discrete geodesic distance. We show applications to landscape modeling and to traffic congestion. Both applications require the maximization of geodesic distances under convex constraints, and are solved by subgradient descent computed with our Subgradient Marching. We also show application to the inversion of travel time tomography, where the recovered metric is the local minimum of a non-convex variational problem involving geodesic distance

Adaptive Measurement Network for CS Image Reconstruction

Conventional compressive sensing (CS) reconstruction is very slow for its characteristic of solving an optimization problem. Convolu- tional neural network can realize fast processing while achieving compa- rable results. While CS image recovery with high quality not only de- pends on good reconstruction algorithms, but also good measurements. In this paper, we propose an adaptive measurement network in which measurement is obtained by learning. The new network consists of a fully-connected layer and ReconNet. The fully-connected layer which has low-dimension output acts as measurement. We train the fully-connected layer and ReconNet simultaneously and obtain adaptive measurement. Because the adaptive measurement fits dataset better, in contrast with random Gaussian measurement matrix, under the same measuremen- t rate, it can extract the information of scene more efficiently and get better reconstruction results. Experiments show that the new network outperforms the original one.Comment: 11pages,8figure

Sub-Riemannian Fast Marching in SE(2)

We propose a Fast Marching based implementation for computing sub-Riemanninan (SR) geodesics in the roto-translation group SE(2), with a metric depending on a cost induced by the image data. The key ingredient is a Riemannian approximation of the SR-metric. Then, a state of the art Fast Marching solver that is able to deal with extreme anisotropies is used to compute a SR-distance map as the solution of a corresponding eikonal equation. Subsequent backtracking on the distance map gives the geodesics. To validate the method, we consider the uniform cost case in which exact formulas for SR-geodesics are known and we show remarkable accuracy of the numerically computed SR-spheres. We also show a dramatic decrease in computational time with respect to a previous PDE-based iterative approach. Regarding image analysis applications, we show the potential of considering these data adaptive geodesics for a fully automated retinal vessel tree segmentation.Comment: CIARP 201

Análise Espacial da Estrutura Social da Região Metropolitana de Porto Alegre (RMPA) em 1991 e 2000

This paper discusses the spatial distribution of social structures in the Metropolitan Area of Porto Alegre in 1991 and 2000 (census years), using spatial statistical techniques with a geographic information system (GIS). These structures represent a social hierarchy of the metropolitan space from across the combination of labour variables. For this goal, I use a measure of spatial dispersion: the standard deviational ellipse which does show compactness and orientation of the distribution. The paper concludes with comments regarding the patterns and trends of the distributions

Os principais parques científicos e tecnológicos gaúchos: estrutura e características

In recent years, the development of science and/or technology parks has been one of the most used tools, even if it is controversial, of innovation policy in the world. This kind of experience can promote some fundamental elements for the innovation processes: the dynamics of learning and interaction and the use of local resources. In this context, this article aims to study the three main science and technology parks in the State of Rio Grande do Sul (Brazil) — Tecnopuc, Tecnosinos e Valetec —, looking at the parks’ firms. So, we analyse firms’ aspects such as areas of expertise, activities of cooperation for innovation, and the use of external financial resources. The results indicate the relative success of these parks in fostering innovation in the territory of Rio Grande do Sul

Análise espacial da centralidade e da dispersão da riqueza gaúcha de 1970 a 2000: notas preliminares

Developments in spatial methodsconcerned with location, spatial interaction, spatial structure and spatial processesare creating new possibilities for studies of the properties of socioeconomic systems. In this paper, we use spatial statistical techniques with a geographic information system (GIS) for describing the spatial distribution of economic data, such as the mean center, standard distance and standard deviational ellipse. Analyzing the reality of the State of Rio Grande do Sul (Brasil), we compare the distribution of GDP, monthly income and "per capita" income observed in the period 1970-2000 (census years). The paper concludeswith some brief reflections on the patterns and trends of these distributions

O papel das Instituições de Ensino Superior para o desenvolvimento territorial: Análise da comunidade de Pós-Graduação do Rio Grande do Sul e o caso das cidades de Pelotas e Rio Grande

Nowadays, the process of innovation has become an important agent to social and economic development of regions and countries. Thus, within the context of the “heterodox paradigm of economic geography”, the region-specific capacities are fundamental for such activities of development, which one has been more and more appraised: the knowledge from the higher education institutions (HEIs). This article analyses the role of HEIs in general and the situation in the State of Rio Grande do Sul (Brazil) in particular, in the period of 2000 through 2010, by means of the postgraduate structure. The paper ends with some considerations about a regional agenda of research to the municipalities of Pelotas and Rio Grande in the sense of their territorial development within the heterodox perspective. The results highlight the strength of postgraduate structure of the region and, consequently, higher education in general, also stressing the State potentialities for scientific, technological and of innovative progress

Os principais parques científicos e tecnológicos gaúchos: estrutura e características

In recent years, the development of science and/or technology parks has been one of the most used tools, even if it is controversial, of innovation policy in the world. This kind of experience can promote some fundamental elements for the innovation processes: the dynamics of learning and interaction and the use of local resources. In this context, this article aims to study the three main science and technology parks in the State of Rio Grande do Sul (Brazil) — Tecnopuc, Tecnosinos e Valetec —, looking at the parks’ firms. So, we analyse firms’ aspects such as areas of expertise, activities of cooperation for innovation, and the use of external financial resources. The results indicate the relative success of these parks in fostering innovation in the territory of Rio Grande do Sul