Saving phase: Injectivity and stability for phase retrieval

Recent advances in convex optimization have led to new strides in the phase retrieval problem over finite-dimensional vector spaces. However, certain fundamental questions remain: What sorts of measurement vectors uniquely determine every signal up to a global phase factor, and how many are needed to do so? Furthermore, which measurement ensembles lend stability? This paper presents several results that address each of these questions. We begin by characterizing injectivity, and we identify that the complement property is indeed a necessary condition in the complex case. We then pose a conjecture that 4M-4 generic measurement vectors are both necessary and sufficient for injectivity in M dimensions, and we prove this conjecture in the special cases where M=2,3. Next, we shift our attention to stability, both in the worst and average cases. Here, we characterize worst-case stability in the real case by introducing a numerical version of the complement property. This new property bears some resemblance to the restricted isometry property of compressed sensing and can be used to derive a sharp lower Lipschitz bound on the intensity measurement mapping. Localized frames are shown to lack this property (suggesting instability), whereas Gaussian random measurements are shown to satisfy this property with high probability. We conclude by presenting results that use a stochastic noise model in both the real and complex cases, and we leverage Cramer-Rao lower bounds to identify stability with stronger versions of the injectivity characterizations.Comment: 22 page

Combating the Illicit Trade in Small Arms and Light Weapons: Strengthening Domestic Regulations

yesSmall arms and light weapons have become the weapons of choice in conflicts around the world and figure prominently in crime. Recently, considerable attention has been focused on the proliferation of SALW at the national, regional and international level. The recognition that m o s t illicit SALW began as legal weapons is, however, fundamental to efforts to reduce the proliferation and misuse of SALW and the diversion of civilian weapons is one source of supply. Indeed, it is estimated that there are as many SALW in the hands of civilians worldwide as there are in the possession of states, and that in many parts of the world diversion from civilian stocks is the principal source of the illicit supply. Consequently, strengthening domestic regulation, which reduces the diversion of legal weapons to illegal markets, is a critical part of any strategy to address illicit trafficking. It is also consistent with resolutions from the United Nations Security Council and other Commissions as well as regional initiatives. This briefing reviews the ways in which SALW are diverted from legal to illegal markets and the measures which can be used to reduce this diversion. In addressing illicit trafficking in all its aspects, it is imperative that the UN Conference not does neglect this significant problem

Solar Reector Design

The design of solar panels is investigated. Different aspects of this problem are presented. A formula averaging the solar energy received on a given location is derived rst. The energy received by the collecting solar panel is then calculated using a specially designed algorithm. The geometry of the device collecting the energy may then be optimised using different algorithms. The results show that for a given depth, devices of smaller width are more energy efficient than those of wider dimensions. This leads to a more economically efficient design

Durabilidade natural de madeiras amazônicas em contato com o solo.

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Carotid Artery Dissection

A dissecção da artéria carótida interna é uma causa de AVC isquémico, particularmente em doentes jovens, sem aparentes factores de risco cérebro-vasculares. Métodos: Os autores descrevem o quadro clínico e achados imagiológicos (TAC, RMN e angiografia de subtracção digital) de cinco doentes internados consecutivamente na Unidade Cérebro-Vascular do Hospital de S. José, num período de dois meses, com o diagnóstico de oclusão da artéria carótida interna por provável dissecção. Discussão: O conjunto de casos clínicos apresentados salienta a heterogeneidade de formas de apresentação desta patologia, quer do ponto de vista clínico, quer imagiológico

CASE STUDIES FROM DIFFERENT TYPES OF HEAT EXCHANGERS TO PLATE AND SHELL HEAT EXCHANGER: A REVIEW

A Plate and Shell Heat Exchanger (PSHE) is manufactured with round welded plates in its core. These plates are designed to withstand high pressures and temperatures. Failures in this kind of heat exchanger were registered in a short operating period. To obtain the failure modes present in this equipment and a theoretical framework concerning this field of study, a research methodology was proposed (Systematic Literature Review – SLR) and a theoretical survey was carried out focusing in the 316L stainless steel and titanium grade 1 for its use in the Brazilian offshore industry. Seeing that the whole PSHE structure is welded, it is necessary to account for the strain caused by severe expansion processes in heat exchanger joints. This regarding, the laser welding process was investigated because of its narrow melting zone. It is believed that it was possible to clarify which failure modes are related to corrosive processes or stress concentration highlighting the structural and mechanical characterization models employed. Considering that the research field is relatively new, it was feasible to establish a theoretical basis of solutions applicable to PSHE, such as the use of more recessive material, reduce the corrosiveness of the operating medium, and reduce external sources of tension. Also, new content was assembled to assess the future decision-making process, regarding the design or maintenance of welded plate exchangers

A Cheeger Inequality for the Graph Connection Laplacian

The O(d) Synchronization problem consists of estimating a set of unknown orthogonal transformations O_i from noisy measurements of a subset of the pairwise ratios O_iO_j^{-1}. We formulate and prove a Cheeger-type inequality that relates a measure of how well it is possible to solve the O(d) synchronization problem with the spectra of an operator, the graph Connection Laplacian. We also show how this inequality provides a worst case performance guarantee for a spectral method to solve this problem.Comment: To appear in the SIAM Journal on Matrix Analysis and Applications (SIMAX

Local Algorithms for Block Models with Side Information

There has been a recent interest in understanding the power of local algorithms for optimization and inference problems on sparse graphs. Gamarnik and Sudan (2014) showed that local algorithms are weaker than global algorithms for finding large independent sets in sparse random regular graphs. Montanari (2015) showed that local algorithms are suboptimal for finding a community with high connectivity in the sparse Erd\H{o}s-R\'enyi random graphs. For the symmetric planted partition problem (also named community detection for the block models) on sparse graphs, a simple observation is that local algorithms cannot have non-trivial performance. In this work we consider the effect of side information on local algorithms for community detection under the binary symmetric stochastic block model. In the block model with side information each of the $n$ vertices is labeled $+$ or $-$ independently and uniformly at random; each pair of vertices is connected independently with probability $a/n$ if both of them have the same label or $b/n$ otherwise. The goal is to estimate the underlying vertex labeling given 1) the graph structure and 2) side information in the form of a vertex labeling positively correlated with the true one. Assuming that the ratio between in and out degree $a/b$ is $\Theta(1)$ and the average degree $(a+b) / 2 = n^{o(1)}$, we characterize three different regimes under which a local algorithm, namely, belief propagation run on the local neighborhoods, maximizes the expected fraction of vertices labeled correctly. Thus, in contrast to the case of symmetric block models without side information, we show that local algorithms can achieve optimal performance for the block model with side information.Comment: Due to the limitation "The abstract field cannot be longer than 1,920 characters", the abstract here is shorter than that in the PDF fil

Alternativas tecnológicas para o controle de pragas do fruto da gravioleira.

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Estratégias para o controle de pragas do fruto da gravioleira.

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