56,085 research outputs found
Revisiting the Expected Cost of Solving uSVP and Applications to LWE
Abstract: Reducing the Learning with Errors problem (LWE) to the Unique-SVP problem and then applying lattice reduction is a commonly relied-upon strategy for estimating the cost of solving LWE-based constructions. In the literature, two different conditions are formulated under which this strategy is successful. One, widely used, going back to Gama & Nguyen\u27s work on predicting lattice reduction (Eurocrypt 2008) and the other recently outlined by Alkim et al. (USENIX 2016). Since these two estimates predict significantly different costs for solving LWE parameter sets from the literature, we revisit the Unique-SVP strategy. We present empirical evidence from lattice-reduction experiments exhibiting a behaviour in line with the latter estimate. However, we also observe that in some situations lattice-reduction behaves somewhat better than expected from Alkim et al.\u27s work and explain this behaviour under standard assumptions. Finally, we show that the security estimates of some LWE-based constructions from the literature need to be revised and give refined expected solving costs
Boundary induced non linearities at small Reynolds Numbers
We investigate the influence of boundary slip velocity in Newtonian fluids at
finite Reynolds numbers. Numerical simulations with Lattice Boltzmann method
(LBM) and Finite Differences method (FDM) are performed to quantify the effect
of heterogeneous boundary conditions on the integral and local properties of
the flow. Non linear effects are induced by the non homogeneity of the boundary
condition and change the symmetry properties of the flow inducing an overall
mean flow reduction. To explain the observed drag modification, reciprocal
relations for stationary ensembles are used, predicting a reduction of the mean
flow rate from the creeping flow to be proportional to the fourth power of the
friction Reynolds number. Both numerical schemes are then validated within the
theoretical predictions and reveal a pronounced numerical efficiency of the LBM
with respect to FDM.Comment: 29 pages, 10 figure
Informational Substitutes
We propose definitions of substitutes and complements for pieces of
information ("signals") in the context of a decision or optimization problem,
with game-theoretic and algorithmic applications. In a game-theoretic context,
substitutes capture diminishing marginal value of information to a rational
decision maker. We use the definitions to address the question of how and when
information is aggregated in prediction markets. Substitutes characterize
"best-possible" equilibria with immediate information aggregation, while
complements characterize "worst-possible", delayed aggregation. Game-theoretic
applications also include settings such as crowdsourcing contests and Q\&A
forums. In an algorithmic context, where substitutes capture diminishing
marginal improvement of information to an optimization problem, substitutes
imply efficient approximation algorithms for a very general class of (adaptive)
information acquisition problems.
In tandem with these broad applications, we examine the structure and design
of informational substitutes and complements. They have equivalent, intuitive
definitions from disparate perspectives: submodularity, geometry, and
information theory. We also consider the design of scoring rules or
optimization problems so as to encourage substitutability or complementarity,
with positive and negative results. Taken as a whole, the results give some
evidence that, in parallel with substitutable items, informational substitutes
play a natural conceptual and formal role in game theory and algorithms.Comment: Full version of FOCS 2016 paper. Single-column, 61 pages (48 main
text, 13 references and appendix
Critical region of the finite temperature chiral transition
We study a Yukawa theory with spontaneous chiral symmetry breaking and with a
large number N of fermions near the finite temperature phase transition.
Critical properties in such a system can be described by the mean field theory
very close to the transition point. We show that the width of the region where
non-trivial critical behavior sets in is suppressed by a certain power of 1/N.
Our Monte Carlo simulations confirm these analytical results. We discuss
implications for the chiral phase transition in QCD.Comment: 18 page
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