Differentially Private Release and Learning of Threshold Functions
April 28, 2015
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Computer Science
Cryptography and Security
Machine Learning
Cryptography and Security
Machine Learning
We prove new upper and lower bounds on the sample complexity of (ϵ,δ) differentially private algorithms for releasing approximate answers to
threshold functions. A threshold function cx over a totally ordered domain
X ev...
Relative Error Bound Analysis for Nuclear Norm Regularized Matrix
Completion
April 26, 2015
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Computer Science
Statistics
Machine Learning
Machine Learning
In this paper, we develop a relative error bound for nuclear norm regularized
matrix completion, with the focus on the completion of full-rank matrices.
Under the assumption that the top eigenspaces of the target matrix are
incoherent, we d...
Decoding quantum information via the Petz recovery map
April 17, 2015
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Physics
Computer Science
Mathematics
Quantum Physics
Information Theory
Information Theory
Quantum Physics
Information Theory
Information Theory
We obtain a lower bound on the maximum number of qubits, Qn,ϵ(N), which can be transmitted over n uses of a quantum
channel N, for a given non-zero error threshold ϵ. To
obtain our result, we fi...
Can Almost Everybody be Almost Happy? PCP for PPAD and the
Inapproximability of Nash
April 9, 2015
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Computer Science
Computational Complexity
Computer Science and Game Theory
Computational Complexity
Computer Science and Game Theory
We conjecture that PPAD has a PCP-like complete problem, seeking a near
equilibrium in which all but very few players have very little incentive to
deviate. We show that, if one assumes that this problem requires exponential
time, several o...
A Non-classification Result for Wild Knots
April 9, 2015
Mathematics
General Topology
Geometric Topology
Using methods of descriptive theory it is shown that the classification
problem for wild knots is strictly harder than that for countable structures....
An information-theoretic proof of a hypercontractive inequality
April 7, 2015
Mathematics
Probability
Combinatorics
In this note I give an information-theoretic proof of the
Bonami-Beckner-Gross hypercontractive inequality....
A new non-extensive equation of state for the fluid phases of argon
including the metastable states, from the melting line to 2300 K and 50 GPa
March 31, 2015
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Physics
Statistical Mechanics
Materials Science
Soft Condensed Matter
A new equation of state for argon has been developed in view to extend the
range of validity of the equation of state previously proposed by Tegeler et
al. (Ref. 4) and to obtain a better physical description of the experimental
thermodynam...
One-dimensional F-definable sets in F((t))
March 19, 2015
Mathematics
Logic
In this note we study one-dimensional definable sets in power series fields
with perfect residue fields. Using the description of automorphisms given by
Schilling, in \cite{S44}, we show that such sets are unions of existentially
definable ...
Continuous warped time-frequency representations - Coorbit spaces and
discretization
March 18, 2015
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Mathematics
Functional Analysis
We present a novel family of continuous, linear time-frequency transforms
adaptable to a multitude of (nonlinear) frequency scales. Similar to classical
time-frequency or time-scale representations, the representation coefficients
are obtai...
An Isodiametric Problem with Additional Constraints in Euclidean space
R^3
March 11, 2015
Mathematics
Dynamical Systems
Let Cθ be a circular cone in Euclidean space R3,which
apex is the origin and apex angle of the cone is θ∈(π/3,π). Let Mθ be the class of compact convex domains in Euclidean
space $\m...