456 research outputs found
Improved sparse approximation over quasi-incoherent dictionaries
This paper discusses a new greedy algorithm for solving the sparse approximation problem over quasi-incoherent dictionaries. These dictionaries consist of waveforms that are uncorrelated "on average," and they provide a natural generalization of incoherent dictionaries. The algorithm provides strong guarantees on the quality of the approximations it produces, unlike most other methods for sparse approximation. Moreover, very efficient implementations are possible via approximate nearest-neighbor data structure
Entanglement of internal and external angular momenta of a single atom
We consider the exchange of spin and orbital angular momenta between a
circularly polarized Laguerre-Gaussian beam of light and a single atom trapped
in a two-dimensional harmonic potential. The radiation field is treated
classically but the atomic center-of-mass motion is quantized. The spin and
orbital angular momenta of the field are individually conserved upon
absorption, and this results in the entanglement of the internal and external
degrees of freedom of the atom. We suggest applications of this entanglement in
quantum information processing.Comment: 4 pages, 2 figure
Stochastic Budget Optimization in Internet Advertising
Internet advertising is a sophisticated game in which the many advertisers
"play" to optimize their return on investment. There are many "targets" for the
advertisements, and each "target" has a collection of games with a potentially
different set of players involved. In this paper, we study the problem of how
advertisers allocate their budget across these "targets". In particular, we
focus on formulating their best response strategy as an optimization problem.
Advertisers have a set of keywords ("targets") and some stochastic information
about the future, namely a probability distribution over scenarios of cost vs
click combinations. This summarizes the potential states of the world assuming
that the strategies of other players are fixed. Then, the best response can be
abstracted as stochastic budget optimization problems to figure out how to
spread a given budget across these keywords to maximize the expected number of
clicks.
We present the first known non-trivial poly-logarithmic approximation for
these problems as well as the first known hardness results of getting better
than logarithmic approximation ratios in the various parameters involved. We
also identify several special cases of these problems of practical interest,
such as with fixed number of scenarios or with polynomial-sized parameters
related to cost, which are solvable either in polynomial time or with improved
approximation ratios. Stochastic budget optimization with scenarios has
sophisticated technical structure. Our approximation and hardness results come
from relating these problems to a special type of (0/1, bipartite) quadratic
programs inherent in them. Our research answers some open problems raised by
the authors in (Stochastic Models for Budget Optimization in Search-Based
Advertising, Algorithmica, 58 (4), 1022-1044, 2010).Comment: FINAL versio
The Furman University River Basins Research Initiative: A Multidisciplinary Examination of Urban Influences on Piedmont Streams
2008 S.C. Water Resources Conference - Addressing Water Challenges Facing the State and Regio
Multi-valued Logic Gates for Quantum Computation
We develop a multi-valued logic for quantum computing for use in multi-level
quantum systems, and discuss the practical advantages of this approach for
scaling up a quantum computer. Generalizing the methods of binary quantum
logic, we establish that arbitrary unitary operations on any number of d-level
systems (d > 2) can be decomposed into logic gates that operate on only two
systems at a time. We show that such multi-valued logic gates are
experimentally feasible in the context of the linear ion trap scheme for
quantum computing. By using d levels in each ion in this scheme, we reduce the
number of ions needed for a computation by a factor of log d.Comment: Revised version; 8 pages, 3 figures; to appear in Physical Review
Testable bounded degree graph properties are random order streamable
We study which property testing and sublinear time algorithms can be transformed into graph streaming algorithms for random order streams. Our main result is that for bounded degree graphs, any property that is constant-query testable in the adjacency list model can be tested with constant space in a single-pass in random order streams. Our result is obtained by estimating the distribution of local neighborhoods of the vertices on a random order graph stream using constant space. We then show that our approach can also be applied to constant time approximation algorithms for bounded degree graphs in the adjacency list model: As an example, we obtain a constant-space single-pass random order streaming algorithms for approximating the size of a maximum matching with additive error epsilon n (n is the number of nodes). Our result establishes for the first time that a large class of sublinear algorithms can be simulated in random order streams, while Omega(n) space is needed for many graph streaming problems for adversarial orders
On Exchange of Orbital Angular Momentum Between Twisted Photons and Atomic Electrons
We obtain an expression for the matrix element for a twisted
(Laguerre-Gaussian profile) photon scattering from a hydrogen atom. We consider
photons incoming with an orbital angular momentum (OAM) of ,
carried by a factor of not present in a plane-wave or pure
Gaussian profile beam. The nature of the transfer of units of OAM from
the photon to the azimuthal atomic quantum number of the atom is investigated.
We obtain simple formulae for these OAM flip transitions for elastic forward
scattering of twisted photons when the photon wavelength is large
compared with the atomic target size , and small compared the Rayleigh range
, which characterizes the collimation length of the twisted photon beam.Comment: 16 page
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