1,513 research outputs found
Dynamic sampling schemes for optimal noise learning under multiple nonsmooth constraints
We consider the bilevel optimisation approach proposed by De Los Reyes,
Sch\"onlieb (2013) for learning the optimal parameters in a Total Variation
(TV) denoising model featuring for multiple noise distributions. In
applications, the use of databases (dictionaries) allows an accurate estimation
of the parameters, but reflects in high computational costs due to the size of
the databases and to the nonsmooth nature of the PDE constraints. To overcome
this computational barrier we propose an optimisation algorithm that by
sampling dynamically from the set of constraints and using a quasi-Newton
method, solves the problem accurately and in an efficient way
Social welfare and profit maximization from revealed preferences
Consider the seller's problem of finding optimal prices for her
(divisible) goods when faced with a set of consumers, given that she can
only observe their purchased bundles at posted prices, i.e., revealed
preferences. We study both social welfare and profit maximization with revealed
preferences. Although social welfare maximization is a seemingly non-convex
optimization problem in prices, we show that (i) it can be reduced to a dual
convex optimization problem in prices, and (ii) the revealed preferences can be
interpreted as supergradients of the concave conjugate of valuation, with which
subgradients of the dual function can be computed. We thereby obtain a simple
subgradient-based algorithm for strongly concave valuations and convex cost,
with query complexity , where is the additive
difference between the social welfare induced by our algorithm and the optimum
social welfare. We also study social welfare maximization under the online
setting, specifically the random permutation model, where consumers arrive
one-by-one in a random order. For the case where consumer valuations can be
arbitrary continuous functions, we propose a price posting mechanism that
achieves an expected social welfare up to an additive factor of
from the maximum social welfare. Finally, for profit maximization (which may be
non-convex in simple cases), we give nearly matching upper and lower bounds on
the query complexity for separable valuations and cost (i.e., each good can be
treated independently)
Improved algorithm for quantum separability and entanglement detection
Determining whether a quantum state is separable or entangled is a problem of
fundamental importance in quantum information science. It has recently been
shown that this problem is NP-hard. There is a highly inefficient `basic
algorithm' for solving the quantum separability problem which follows from the
definition of a separable state. By exploiting specific properties of the set
of separable states, we introduce a new classical algorithm that solves the
problem significantly faster than the `basic algorithm', allowing a feasible
separability test where none previously existed e.g. in 3-by-3-dimensional
systems. Our algorithm also provides a novel tool in the experimental detection
of entanglement.Comment: 4 pages, revtex4, no figure
A Nearly Linear-Time PTAS for Explicit Fractional Packing and Covering Linear Programs
We give an approximation algorithm for packing and covering linear programs
(linear programs with non-negative coefficients). Given a constraint matrix
with n non-zeros, r rows, and c columns, the algorithm computes feasible primal
and dual solutions whose costs are within a factor of 1+eps of the optimal cost
in time O((r+c)log(n)/eps^2 + n).Comment: corrected version of FOCS 2007 paper: 10.1109/FOCS.2007.62. Accepted
to Algorithmica, 201
Gain switching of an external cavity grating-coupled surface emitting laser with wide tunability
The gain-switched, single frequency operation of an external cavity grating-coupled surface emitting laser with a wavelength tuning range of 100 nm was presented. The light in the grating section was coupled out of the laser at a specific angle to the surface of the device. Analysis showed that within the driving current range, lasing in the device only occurred when the external cavity was properly aligned
Algebraic Model for scattering of three-s-cluster systems. II. Resonances in the three-cluster continuum of 6He and 6Be
The resonance states embedded in the three-cluster continuum of 6He and 6Be
are obtained in the Algebraic Version of the Resonating Group Method. The model
accounts for a correct treatment of the Pauli principle. It also provides the
correct three-cluster continuum boundary conditions by using a Hyperspherical
Harmonics basis. The model reproduces the observed resonances well and achieves
good agreement with other models. A better understanding for the process of
formation and decay of the resonance states in six-nucleon systems is obtained.Comment: 8 pages, 10 postscript figures, submitted to Phys. Rev.
Adaptive Stochastic Primal-Dual Coordinate Descent for Separable Saddle Point Problems
We consider a generic convex-concave saddle point problem with separable
structure, a form that covers a wide-ranged machine learning applications.
Under this problem structure, we follow the framework of primal-dual updates
for saddle point problems, and incorporate stochastic block coordinate descent
with adaptive stepsize into this framework. We theoretically show that our
proposal of adaptive stepsize potentially achieves a sharper linear convergence
rate compared with the existing methods. Additionally, since we can select
"mini-batch" of block coordinates to update, our method is also amenable to
parallel processing for large-scale data. We apply the proposed method to
regularized empirical risk minimization and show that it performs comparably
or, more often, better than state-of-the-art methods on both synthetic and
real-world data sets.Comment: Accepted by ECML/PKDD201
Precision Tests of the Standard Model
30 páginas, 11 figuras, 11 tablas.-- Comunicación presentada al 25º Winter Meeting on Fundamental Physics celebrado del 3 al 8 de MArzo de 1997 en Formigal (España).Precision measurements of electroweak observables provide stringent tests of the Standard Model structure and an accurate determination of its parameters. An overview of the present experimental status is presented.This work has been supported in part
by CICYT (Spain) under grant No. AEN-96-1718.Peer reviewe
Coupling of Linearized Gravity to Nonrelativistic Test Particles: Dynamics in the General Laboratory Frame
The coupling of gravity to matter is explored in the linearized gravity
limit. The usual derivation of gravity-matter couplings within the
quantum-field-theoretic framework is reviewed. A number of inconsistencies
between this derivation of the couplings, and the known results of tidal
effects on test particles according to classical general relativity are pointed
out. As a step towards resolving these inconsistencies, a General Laboratory
Frame fixed on the worldline of an observer is constructed. In this frame, the
dynamics of nonrelativistic test particles in the linearized gravity limit is
studied, and their Hamiltonian dynamics is derived. It is shown that for
stationary metrics this Hamiltonian reduces to the usual Hamiltonian for
nonrelativistic particles undergoing geodesic motion. For nonstationary metrics
with long-wavelength gravitational waves (GWs) present, it reduces to the
Hamiltonian for a nonrelativistic particle undergoing geodesic
\textit{deviation} motion. Arbitrary-wavelength GWs couple to the test particle
through a vector-potential-like field , the net result of the tidal forces
that the GW induces in the system, namely, a local velocity field on the system
induced by tidal effects as seen by an observer in the general laboratory
frame. Effective electric and magnetic fields, which are related to the
electric and magnetic parts of the Weyl tensor, are constructed from that
obey equations of the same form as Maxwell's equations . A gedankin
gravitational Aharonov-Bohm-type experiment using to measure the
interference of quantum test particles is presented.Comment: 38 pages, 7 figures, written in ReVTeX. To appear in Physical Review
D. Galley proofs corrections adde
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