1,252 research outputs found
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
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
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 vertices is labeled
or independently and uniformly at random; each pair of vertices is
connected independently with probability if both of them have the same
label or 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 is and the average degree , 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
Structured networks and coarse-grained descriptions: a dynamical perspective
This chapter discusses the interplay between structure and dynamics in complex networks. Given a particular network with an endowed dynamics, our goal is to find partitions aligned with the dynamical process acting on top of the network. We thus aim to gain a reduced description of the system that takes into account both its structure and dynamics. In the first part, we introduce the general mathematical setup for the types of dynamics we consider throughout the chapter. We provide two guiding examples, namely consensus dynamics and diffusion processes (random walks), motivating their connection to social network analysis, and provide a brief discussion on the general dynamical framework and its possible extensions. In the second part, we focus on the influence of graph structure on the dynamics taking place on the network, focusing on three concepts that allow us to gain insight into this notion. First, we describe how time scale separation can appear in the dynamics on a network as a consequence of graph structure. Second, we discuss how the presence of particular symmetries in the network give rise to invariant dynamical subspaces that can be precisely described by graph partitions. Third, we show how this dynamical viewpoint can be extended to study dynamics on networks with signed edges, which allow us to discuss connections to concepts in social network analysis, such as structural balance. In the third part, we discuss how to use dynamical processes unfolding on the network to detect meaningful network substructures. We then show how such dynamical measures can be related to seemingly different algorithm for community detection and coarse-graining proposed in the literature. We conclude with a brief summary and highlight interesting open future directions
Avaliação de práticas de manejo da cultura do cajueiro comum.
Apesar de se reconhecer que e possivel obter significativos aumentos de producao na cultura, com a aplicacao de fertilizantes, esta e uma pratica muito pouco utilizada pelos produtores. O reduzido numero de resultados experimentais, os custos dos fertilizantes e o elevado numero de plantas improdutivas sao os principais fatores que concorrem para a nao adocao do uso de fertilizantes na cultura.bitstream/CNPAT-2010/1841/1/Pa-008.pd
Manejo do biótipo da espécie Conyza bonariensis resistente ao herbicida glyphosate no município de Campo Mourão.
Development of microsatellite markers in Annona crasiflora Mart., a brazilian cerrado fruit tree species
Características produtivas de cultivares de cebola sob dois métodos de manejo irrigação.
Suplemento. Edição dos Trabalhos do 50. Congresso Brasileiro de Olericultura, Guarapari, jul. 2010
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