1,420 research outputs found
Cassini Ring Seismology as a Probe of Saturn's Interior I: Rigid Rotation
Seismology of the gas giants holds the potential to resolve long-standing
questions about their internal structure and rotation state. We construct a
family of Saturn interior models constrained by the gravity field and compute
their adiabatic mode eigenfrequencies and corresponding Lindblad and vertical
resonances in Saturn's C ring, where more than twenty waves with pattern speeds
faster than the ring mean motion have been detected and characterized using
high-resolution Cassini Visual and Infrared Mapping Spectrometer (VIMS) stellar
occultation data. We present identifications of the fundamental modes of Saturn
that appear to be the origin of these observed ring waves, and use their
observed pattern speeds and azimuthal wavenumbers to estimate the bulk rotation
period of Saturn's interior to be (median and 5%/95% quantiles),
significantly faster than Voyager and Cassini measurements of periods in
Saturn's kilometric radiation, the traditional proxy for Saturn's bulk rotation
period. The global fit does not exhibit any clear systematics indicating strong
differential rotation in Saturn's outer envelope.Comment: 19 pages, 6 figures, 3 tables, accepted to ApJ; a bug fix improves
the fit, predicts faster bulk spin periods (Figure 4) and virtually
eliminates evidence for strong radial differential rotation (Figure 5
A new method for constructing small-bias spaces from Hermitian codes
We propose a new method for constructing small-bias spaces through a
combination of Hermitian codes. For a class of parameters our multisets are
much faster to construct than what can be achieved by use of the traditional
algebraic geometric code construction. So, if speed is important, our
construction is competitive with all other known constructions in that region.
And if speed is not a matter of interest the small-bias spaces of the present
paper still perform better than the ones related to norm-trace codes reported
in [12]
Nonlinear spectral calculus and super-expanders
Nonlinear spectral gaps with respect to uniformly convex normed spaces are
shown to satisfy a spectral calculus inequality that establishes their decay
along Cesaro averages. Nonlinear spectral gaps of graphs are also shown to
behave sub-multiplicatively under zigzag products. These results yield a
combinatorial construction of super-expanders, i.e., a sequence of 3-regular
graphs that does not admit a coarse embedding into any uniformly convex normed
space.Comment: Typos fixed based on referee comments. Some of the results of this
paper were announced in arXiv:0910.2041. The corresponding parts of
arXiv:0910.2041 are subsumed by the current pape
Pseudorandomness for Regular Branching Programs via Fourier Analysis
We present an explicit pseudorandom generator for oblivious, read-once,
permutation branching programs of constant width that can read their input bits
in any order. The seed length is , where is the length of the
branching program. The previous best seed length known for this model was
, which follows as a special case of a generator due to
Impagliazzo, Meka, and Zuckerman (FOCS 2012) (which gives a seed length of
for arbitrary branching programs of size ). Our techniques
also give seed length for general oblivious, read-once branching
programs of width , which is incomparable to the results of
Impagliazzo et al.Our pseudorandom generator is similar to the one used by
Gopalan et al. (FOCS 2012) for read-once CNFs, but the analysis is quite
different; ours is based on Fourier analysis of branching programs. In
particular, we show that an oblivious, read-once, regular branching program of
width has Fourier mass at most at level , independent of the
length of the program.Comment: RANDOM 201
Distributed Computing in the Asynchronous LOCAL model
The LOCAL model is among the main models for studying locality in the
framework of distributed network computing. This model is however subject to
pertinent criticisms, including the facts that all nodes wake up
simultaneously, perform in lock steps, and are failure-free. We show that
relaxing these hypotheses to some extent does not hurt local computing. In
particular, we show that, for any construction task associated to a locally
checkable labeling (LCL), if is solvable in rounds in the LOCAL model,
then remains solvable in rounds in the asynchronous LOCAL model.
This improves the result by Casta\~neda et al. [SSS 2016], which was restricted
to 3-coloring the rings. More generally, the main contribution of this paper is
to show that, perhaps surprisingly, asynchrony and failures in the computations
do not restrict the power of the LOCAL model, as long as the communications
remain synchronous and failure-free
Limitations to Frechet's Metric Embedding Method
Frechet's classical isometric embedding argument has evolved to become a
major tool in the study of metric spaces. An important example of a Frechet
embedding is Bourgain's embedding. The authors have recently shown that for
every e>0 any n-point metric space contains a subset of size at least n^(1-e)
which embeds into l_2 with distortion O(\log(2/e) /e). The embedding we used is
non-Frechet, and the purpose of this note is to show that this is not
coincidental. Specifically, for every e>0, we construct arbitrarily large
n-point metric spaces, such that the distortion of any Frechet embedding into
l_p on subsets of size at least n^{1/2 + e} is \Omega((\log n)^{1/p}).Comment: 10 pages, 1 figur
Spectral Sparsification and Regret Minimization Beyond Matrix Multiplicative Updates
In this paper, we provide a novel construction of the linear-sized spectral
sparsifiers of Batson, Spielman and Srivastava [BSS14]. While previous
constructions required running time [BSS14, Zou12], our
sparsification routine can be implemented in almost-quadratic running time
.
The fundamental conceptual novelty of our work is the leveraging of a strong
connection between sparsification and a regret minimization problem over
density matrices. This connection was known to provide an interpretation of the
randomized sparsifiers of Spielman and Srivastava [SS11] via the application of
matrix multiplicative weight updates (MWU) [CHS11, Vis14]. In this paper, we
explain how matrix MWU naturally arises as an instance of the
Follow-the-Regularized-Leader framework and generalize this approach to yield a
larger class of updates. This new class allows us to accelerate the
construction of linear-sized spectral sparsifiers, and give novel insights on
the motivation behind Batson, Spielman and Srivastava [BSS14]
Secret-Sharing for NP
A computational secret-sharing scheme is a method that enables a dealer, that
has a secret, to distribute this secret among a set of parties such that a
"qualified" subset of parties can efficiently reconstruct the secret while any
"unqualified" subset of parties cannot efficiently learn anything about the
secret. The collection of "qualified" subsets is defined by a Boolean function.
It has been a major open problem to understand which (monotone) functions can
be realized by a computational secret-sharing schemes. Yao suggested a method
for secret-sharing for any function that has a polynomial-size monotone circuit
(a class which is strictly smaller than the class of monotone functions in P).
Around 1990 Rudich raised the possibility of obtaining secret-sharing for all
monotone functions in NP: In order to reconstruct the secret a set of parties
must be "qualified" and provide a witness attesting to this fact.
Recently, Garg et al. (STOC 2013) put forward the concept of witness
encryption, where the goal is to encrypt a message relative to a statement "x
in L" for a language L in NP such that anyone holding a witness to the
statement can decrypt the message, however, if x is not in L, then it is
computationally hard to decrypt. Garg et al. showed how to construct several
cryptographic primitives from witness encryption and gave a candidate
construction.
One can show that computational secret-sharing implies witness encryption for
the same language. Our main result is the converse: we give a construction of a
computational secret-sharing scheme for any monotone function in NP assuming
witness encryption for NP and one-way functions. As a consequence we get a
completeness theorem for secret-sharing: computational secret-sharing scheme
for any single monotone NP-complete function implies a computational
secret-sharing scheme for every monotone function in NP
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