66,066 research outputs found
Better Pseudorandom Generators from Milder Pseudorandom Restrictions
We present an iterative approach to constructing pseudorandom generators,
based on the repeated application of mild pseudorandom restrictions. We use
this template to construct pseudorandom generators for combinatorial rectangles
and read-once CNFs and a hitting set generator for width-3 branching programs,
all of which achieve near-optimal seed-length even in the low-error regime: We
get seed-length O(log (n/epsilon)) for error epsilon. Previously, only
constructions with seed-length O(\log^{3/2} n) or O(\log^2 n) were known for
these classes with polynomially small error.
The (pseudo)random restrictions we use are milder than those typically used
for proving circuit lower bounds in that we only set a constant fraction of the
bits at a time. While such restrictions do not simplify the functions
drastically, we show that they can be derandomized using small-bias spaces.Comment: To appear in FOCS 201
Inter edge Tunneling in Quantum Hall Line Junctions
We propose a scenario to understand the puzzling features of the recent
experiment by Kang and coworkers on tunneling between laterally coupled quantum
Hall liquids by modeling the system as a pair of coupled chiral Luttinger
liquid with a point contact tunneling center. We show that for filling factors
the effects of the Coulomb interactions move the system deep into
strong tunneling regime, by reducing the magnitude of the Luttinger parameter
, leading to the appearance of a zero-bias differential conductance peak of
magnitude at zero temperature. The abrupt appearance of the zero
bias peak as the filling factor is increased past a value ,
and its gradual disappearance thereafter can be understood as a crossover
controlled by the main energy scales of this system: the bias voltage , the
crossover scale , and the temperature . The low height of the zero bias
peak observed in the experiment, and its broad finite width,
can be understood naturally within this picture. Also, the abrupt reappearance
of the zero-bias peak for can be explained as an effect caused
by spin reversed electrons, \textit{i. e.} if the 2DEG is assumed to have a
small polarization near . We also predict that as the temperature is
lowered should decrease, and the width of zero-bias peak should become
wider. This picture also predicts the existence of similar zero bias peak in
the spin tunneling conductance near for .Comment: 17 pages, 8 figure
Using Localised ‘Gossip’ to Structure Distributed Learning
The idea of a “memetic” spread of solutions through a human culture in parallel to their development is applied as a distributed approach to learning. Local parts of a problem are associated with a set of overlappingt localities in a space and solutions are then evolved in those localites. Good solutions are not only crossed with others to search for better solutions but also they propogate across the areas of the problem space where they are relatively successful. Thus the whole population co-evolves solutions with the domains in which they are found to work. This approach is compared to the equivalent global evolutionary computation approach with respect to predicting the occcurence of heart disease in the Cleveland data set. It greatly outperforms the global approach, but the space of attributes within which this evolutionary process occurs can effect its efficiency
Adiabatically switched-on electrical bias in continuous systems, and the Landauer-Buttiker formula
Consider a three dimensional system which looks like a cross-connected pipe
system, i.e. a small sample coupled to a finite number of leads. We investigate
the current running through this system, in the linear response regime, when we
adiabatically turn on an electrical bias between leads. The main technical tool
is the use of a finite volume regularization, which allows us to define the
current coming out of a lead as the time derivative of its charge. We finally
prove that in virtually all physically interesting situations, the conductivity
tensor is given by a Landauer-B{\"u}ttiker type formula.Comment: 20 pages, submitte
On Regularization Parameter Estimation under Covariate Shift
This paper identifies a problem with the usual procedure for
L2-regularization parameter estimation in a domain adaptation setting. In such
a setting, there are differences between the distributions generating the
training data (source domain) and the test data (target domain). The usual
cross-validation procedure requires validation data, which can not be obtained
from the unlabeled target data. The problem is that if one decides to use
source validation data, the regularization parameter is underestimated. One
possible solution is to scale the source validation data through importance
weighting, but we show that this correction is not sufficient. We conclude the
paper with an empirical analysis of the effect of several importance weight
estimators on the estimation of the regularization parameter.Comment: 6 pages, 2 figures, 2 tables. Accepted to ICPR 201
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