1,118 research outputs found
On the Number of ABC Solutions with Restricted Radical Sizes
We consider a variant of the ABC Conjecture, attempting to count the number
of solutions to , in relatively prime integers each of
absolute value less than with The ABC
Conjecture is equivalent to the statement that for , the number of
solutions is bounded independently of . If , it is conjectured
that the number of solutions is asymptotically We
prove this conjecture as long as $a+b+c \geq 2.
The Average Sensitivity of an Intersection of Half Spaces
We prove new bounds on the average sensitivity of the indicator function of
an intersection of halfspaces. In particular, we prove the optimal bound of
. This generalizes a result of Nazarov, who proved the
analogous result in the Gaussian case, and improves upon a result of Harsha,
Klivans and Meka. Furthermore, our result has implications for the runtime
required to learn intersections of halfspaces
A Polylogarithmic PRG for Degree Threshold Functions in the Gaussian Setting
We devise a new pseudorandom generator against degree 2 polynomial threshold
functions in the Gaussian setting. We manage to achieve error with
seed length polylogarithmic in and the dimension, and exponential
improvement over previous constructions
A Pseudorandom Generator for Polynomial Threshold Functions of Gaussian with Subpolynomial Seed Length
We develop a pseudorandom generator that fools degree- polynomial
threshold functions in variables with respect to the Gaussian distribution
and has seed length
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