2,644 research outputs found
Solving Quadratic Equations via PhaseLift when There Are About As Many Equations As Unknowns
This note shows that we can recover a complex vector x in C^n exactly from on
the order of n quadratic equations of the form ||^2 = b_i, i = 1, ...,
m, by using a semidefinite program known as PhaseLift. This improves upon
earlier bounds in [3], which required the number of equations to be at least on
the order of n log n. We also demonstrate optimal recovery results from noisy
quadratic measurements; these results are much sharper than previously known
results.Comment: 6 page
Impact of Ethanol Production on U.S. and Regional Gasoline Prices and On the Profitability of U.S. Oil Refinery Industry
Using pooled regional time-series data and panel data estimation, we quantify the impact of monthly ethanol production on monthly retail regular gasoline prices. This analysis suggests that the growth in ethanol production has caused retail gasoline prices to be 0.40 per gallon lower than would otherwise have been the case. The analysis shows that the negative impact of ethanol on gasoline prices varies considerably across regions. The Midwest region has the biggest impact, at 0.17/gallon. The results also indicate that ethanol production has significantly reduced the profit margin of the oil refinery industry. The results are robust with respect to alternative model specifications.crack spread, crude oil prices, ethanol, gasoline prices, Resource /Energy Economics and Policy,
Robust Principal Component Analysis?
This paper is about a curious phenomenon. Suppose we have a data matrix,
which is the superposition of a low-rank component and a sparse component. Can
we recover each component individually? We prove that under some suitable
assumptions, it is possible to recover both the low-rank and the sparse
components exactly by solving a very convenient convex program called Principal
Component Pursuit; among all feasible decompositions, simply minimize a
weighted combination of the nuclear norm and of the L1 norm. This suggests the
possibility of a principled approach to robust principal component analysis
since our methodology and results assert that one can recover the principal
components of a data matrix even though a positive fraction of its entries are
arbitrarily corrupted. This extends to the situation where a fraction of the
entries are missing as well. We discuss an algorithm for solving this
optimization problem, and present applications in the area of video
surveillance, where our methodology allows for the detection of objects in a
cluttered background, and in the area of face recognition, where it offers a
principled way of removing shadows and specularities in images of faces
Speculation and Volatility Spillover in the Crude Oil and Agricultural Commodity Markets: A Bayesian Analysis
This paper assesses the roles of various factors influencing the volatility of crude oil prices and the possible linkage between this volatility and agricultural commodity markets. Stochastic volatility models are applied to weekly crude oil, corn and wheat futures prices from November 1998 to January 2009. Model parameters are estimated using Bayesian Markov chain Monte Carlo methods. The main results are as follows. Speculation, scalping, and petroleum inventories are found to be important in explaining oil price variation. Several properties of crude oil price dynamics are established including mean-reversion, a negative correlation between price and volatility, volatility clustering, and infrequent compound Poisson jumps. We find evidence of volatility spillover among crude oil, corn and wheat markets after the fall of 2006. This could be largely explained by tightened interdependence between these markets induced by ethanol production.Gibbs sampling, Merton jump, leverage effect, stochastic volatility, Demand and Price Analysis, Financial Economics, Resource /Energy Economics and Policy, G13, Q4,
Stability vs. optimality in selfish ring routing
We study the asymmetric atomic selfish routing in ring networks, which has diverse practical applications in network design and analysis. We are concerned with minimizing the maximum latency of source-destination node-pairs over links with linear latencies. We obtain the first constant upper bound on the price of anarchy and significantly improve the existing upper bounds on the price of stability. Moreover, we show that any optimal solution is a good approximate Nash equilibrium. Finally, we present better performance analysis and fast implementation of pseudo-polynomial algorithms for computing approximate Nash equilibria
Nanoindentation of the a and c domains in a tetragonal BaTiO3 single crystal
Nanoindentation in conjunction with piezoresponse force microscopy was used to study domain switching and to measure the mechanical properties of individual ferroelectric domains in a tetragonal BaTiO3 single crystal. It was found that nanoindentation has induced local domain switching; the a and c domains of BaTiO3 have different elastic moduli but similar hardness. Nanoindentation modulus mapping on the a and c domains further confirmed such difference in elasticity. Finite element modeling was used to simulate the von Mises stress and plastic strain profiles of the indentations on both a and c domains, which introduces a much higher stress level than the critical value for domain nucleation
Dense Error Correction for Low-Rank Matrices via Principal Component Pursuit
We consider the problem of recovering a low-rank matrix when some of its
entries, whose locations are not known a priori, are corrupted by errors of
arbitrarily large magnitude. It has recently been shown that this problem can
be solved efficiently and effectively by a convex program named Principal
Component Pursuit (PCP), provided that the fraction of corrupted entries and
the rank of the matrix are both sufficiently small. In this paper, we extend
that result to show that the same convex program, with a slightly improved
weighting parameter, exactly recovers the low-rank matrix even if "almost all"
of its entries are arbitrarily corrupted, provided the signs of the errors are
random. We corroborate our result with simulations on randomly generated
matrices and errors.Comment: Submitted to ISIT 201
Fast initialization of the spin state of an electron in a quantum dot in the Voigt configuration
We consider the initialization of the spin-state of a single electron trapped
in a self-assembled quantum dot via optical pumping of a trion level. We show
that with a magnetic field applied perpendicular to the growth direction of the
dot, a near-unity fidelity can be obtained in a time equal to a few times the
inverse of the spin-conserving trion relaxation rate. This method is several
orders-of-magnitude faster than with the field aligned parallel, since this
configuration must rely on a slow hole spin-flip mechanism. This increase in
speed does result in a limit on the maximum obtainable fidelity, but we show
that for InAs dots, the error is very small.Comment: 4 pages, 4 figure
Plasmonic Brownian ratchet
Here we present a Brownian ratchet based on plasmonic interactions. By
periodically turning on and off a laser beam that illuminates a periodic array
of plasmonic nanostructures with broken spatial symmetry, the random thermal
motion of a subwavelength dielectric bead is rectified into one direction. By
means of the Molecular Dynamics technique we show a statistical directed drift
in particle flow
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