791 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
Almost Optimal Streaming Algorithms for Coverage Problems
Maximum coverage and minimum set cover problems --collectively called
coverage problems-- have been studied extensively in streaming models. However,
previous research not only achieve sub-optimal approximation factors and space
complexities, but also study a restricted set arrival model which makes an
explicit or implicit assumption on oracle access to the sets, ignoring the
complexity of reading and storing the whole set at once. In this paper, we
address the above shortcomings, and present algorithms with improved
approximation factor and improved space complexity, and prove that our results
are almost tight. Moreover, unlike most of previous work, our results hold on a
more general edge arrival model. More specifically, we present (almost) optimal
approximation algorithms for maximum coverage and minimum set cover problems in
the streaming model with an (almost) optimal space complexity of
, i.e., the space is {\em independent of the size of the sets or
the size of the ground set of elements}. These results not only improve over
the best known algorithms for the set arrival model, but also are the first
such algorithms for the more powerful {\em edge arrival} model. In order to
achieve the above results, we introduce a new general sketching technique for
coverage functions: This sketching scheme can be applied to convert an
-approximation algorithm for a coverage problem to a
(1-\eps)\alpha-approximation algorithm for the same problem in streaming, or
RAM models. We show the significance of our sketching technique by ruling out
the possibility of solving coverage problems via accessing (as a black box) a
(1 \pm \eps)-approximate oracle (e.g., a sketch function) that estimates the
coverage function on any subfamily of the sets
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
Managing Risk of Bidding in Display Advertising
In this paper, we deal with the uncertainty of bidding for display
advertising. Similar to the financial market trading, real-time bidding (RTB)
based display advertising employs an auction mechanism to automate the
impression level media buying; and running a campaign is no different than an
investment of acquiring new customers in return for obtaining additional
converted sales. Thus, how to optimally bid on an ad impression to drive the
profit and return-on-investment becomes essential. However, the large
randomness of the user behaviors and the cost uncertainty caused by the auction
competition may result in a significant risk from the campaign performance
estimation. In this paper, we explicitly model the uncertainty of user
click-through rate estimation and auction competition to capture the risk. We
borrow an idea from finance and derive the value at risk for each ad display
opportunity. Our formulation results in two risk-aware bidding strategies that
penalize risky ad impressions and focus more on the ones with higher expected
return and lower risk. The empirical study on real-world data demonstrates the
effectiveness of our proposed risk-aware bidding strategies: yielding profit
gains of 15.4% in offline experiments and up to 17.5% in an online A/B test on
a commercial RTB platform over the widely applied bidding strategies
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
Spatially embedded random networks
Many real-world networks analyzed in modern network theory have a natural spatial element; e.g., the Internet, social networks, neural networks, etc. Yet, aside from a comparatively small number of somewhat specialized and domain-specific studies, the spatial element is mostly ignored and, in particular, its relation to network structure disregarded. In this paper we introduce a model framework to analyze the mediation of network structure by spatial embedding; specifically, we model connectivity as dependent on the distance between network nodes. Our spatially embedded random networks construction is not primarily intended as an accurate model of any specific class of real-world networks, but rather to gain intuition for the effects of spatial embedding on network structure; nevertheless we are able to demonstrate, in a quite general setting, some constraints of spatial embedding on connectivity such as the effects of spatial symmetry, conditions for scale free degree distributions and the existence of small-world spatial networks. We also derive some standard structural statistics for spatially embedded networks and illustrate the application of our model framework with concrete examples
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
Two major cuticular proteins are required for assembly of horizontal laminae and vertical pore canals in rigid cuticle of Tribolium castaneum
The insect exoskeleton is composed of cuticle primarily formed from structural cuticular proteins (CPs) and the polysaccharide chitin. Two CPs, TcCPR27 and TcCPR18, are major proteins present in the elytron (highly sclerotized and pigmented modified forewing) as well as the pronotum (dorsal sclerite of the prothorax) and ventral abdominal cuticle of the red flour beetle, Tribolium castaneum. Both CPs belong to the CPR family, which includes proteins that have an amino acid sequence motif known as the Rebers & Riddiford (R&R) consensus sequence. Injection of double-stranded RNA (dsRNA) for TcCPR27 and TcCPR18 resulted in insects with shorter, wrinkled, warped and less rigid elytra than those from control insects. To gain a more comprehensive understanding of the roles of CPs in cuticle assembly, we analyzed for the precise localization of TcCPR27 and the ultrastructural architecture of cuticle in TcCPR27- and TcCPR18-deficient elytra. Transmission electron microscopic analysis combined with immunodetection using goldlabeled secondary antibody revealed that TcCPR27 is present in dorsal elytral procuticle both in the horizontal laminae and in vertical pore canals. dsRNA-mediated RNA interference (RNAi) of TcCPR27 resulted in abnormal electron-lucent laminae and pore canals in elytra except for the boundary between these two structures in which electron-dense molecule(s) apparently accumulated. Insects subjected to RNAi for TcCPR18 also had disorganized laminae and pore canals in the procuticle of elytra. Similar ultrastructural defects were also observed in other body wall regions with rigid cuticle such as the thorax and legs of adult T. castaneum. TcCPR27 and TcCPR18 are required for proper formation of the horizontal chitinous laminae and vertical pore canals that are critical for formation and stabilization of rigid adult cuticle
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