1,990 research outputs found
Strong noise sensitivity and random graphs
The noise sensitivity of a Boolean function describes its likelihood to flip
under small perturbations of its input. Introduced in the seminal work of
Benjamini, Kalai and Schramm [Inst. Hautes \'{E}tudes Sci. Publ. Math. 90
(1999) 5-43], it was there shown to be governed by the first level of Fourier
coefficients in the central case of monotone functions at a constant critical
probability . Here we study noise sensitivity and a natural stronger
version of it, addressing the effect of noise given a specific witness in the
original input. Our main context is the Erd\H{o}s-R\'{e}nyi random graph, where
already the property of containing a given graph is sufficiently rich to
separate these notions. In particular, our analysis implies (strong) noise
sensitivity in settings where the BKS criterion involving the first Fourier
level does not apply, for example, when polynomially fast in the
number of variables.Comment: Published at http://dx.doi.org/10.1214/14-AOP959 in the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Class invariants for quartic CM fields
One can define class invariants for a quartic primitive CM field K as special
values of certain Siegel (or Hilbert) modular functions at CM points
corresponding to K. We provide explicit bounds on the primes appearing in the
denominators of these algebraic numbers. This allows us, in particular, to
construct S-units in certain abelian extensions of K, where S is effectively
determined by K. It also yields class polynomials for primitive quartic CM
fields whose coefficients are S-integers.Comment: 14 page
Ultrasmall volume Plasmons - yet with complete retardation effects
Nano particle-plasmons are attributed to quasi-static oscillation with no
wave propagation due to their subwavelength size. However, when located within
a band-gap medium (even in air if the particle is small enough), the particle
interfaces are acting as wave-mirrors, incurring small negative retardation.
The latter when compensated by a respective (short) propagation within the
particle substantiates a full-fledged resonator based on constructive
interference. This unusual wave interference in the deep subwavelength regime
(modal-volume<0.001lambda^3) significantly enhances the Q-factor, e.g. 50
compared to the quasi-static limit of 5.5.Comment: 16 pages, 6 figure
Decomposing and re-composing lightweight compression schemes - and why it matters
We argue for a richer view of the space of lightweight compression schemes for columnar DBMSes: We demonstrate how even simple simple schemes used in DBMSes decompose into constituent schemes through a columnar perspective on their decompression. With our concrete examples, we touch briefly on what follows from these and other decompositions: Composition of alternative compression schemes as well as other practical and analytical implications
A STRINGENT CONSTRAINT ON ALTERNATIVES TO A MASSIVE BLACK HOLE AT THE CENTER OF NGC 4258
There is now dynamical evidence for massive dark objects at the center of
several galaxies, but suggestions that these are supermassive black holes are
based only on indirect astrophysical arguments. The recent unprecedented
measurement of the rotation curve of maser emission sources at the center of
NGC 4258, and the remarkable discovery that it is Keplerian to high precision,
provides us a unique opportunity for testing alternatives to a BH (e.g., a
massive cluster of stellar remnants, brown dwarfs, low-mass stars, or halo dark
matter).
We use a conservative upper limit on the systematic deviation from a
Keplerian rotation curve to constrain the mass distribution at the galaxy
center. Based on evaporation and physical collision time-scale arguments, we
show that a central cluster is ruled out, *unless* the cluster consists of
*extremely* dense objects with mass less than about 0.05 solar masses (e.g.,
low mass BHs or elementary particles). Since both of these dynamically-allowed
systems are very improbable for other astrophysical reasons, we conclude that a
central dense cluster at the center of NGC 4258 is *very* improbable, thus
leaving the alternative possibility of a massive BH. We also show that the mass
of the BH must be at least 98% of the mass enclosed within the inner edge of
the masering disk (3.6*10^7 solar masses). A substantial contribution to that
mass from a density cusp in the background mass distribution is excluded.Comment: Submitted to ApJ (Letters) on March 15, 1995. 11 pages including 1
figure; uuencoded, compressed postscript
BCC vs. HCP - The Effect of Crystal Symmetry on the High Temperature Mobility of Solid He
We report results of torsional oscillator (TO) experiments on solid He at
temperatures above 1K. We have previously found that single crystals, once
disordered, show some mobility (decoupled mass) even at these rather high
temperatures. The decoupled mass fraction with single crystals is typically 20-
30%. In the present work we performed similar measurements on polycrystalline
solid samples. The decoupled mass with polycrystals is much smaller, 1%,
similar to what is observed by other groups. In particular, we compared the
properties of samples grown with the TO's rotation axis at different
orientations with respect to gravity. We found that the decoupled mass fraction
of bcc samples is independent of the angle between the rotation axis and
gravity. In contrast, hcp samples showed a significant difference in the
fraction of decoupled mass as the angle between the rotation axis and gravity
was varied between zero and 85 degrees. Dislocation dynamics in the solid
offers one possible explanation of this anisotropy.Comment: 10 pages, 5 figures, to appear in Journal of Low Temperature Physics
- special issue on Supersolidit
A Gross-Zagier formula for quaternion algebras over totally real fields
We prove a higher dimensional generalization of Gross and Zagier's theorem on
the factorization of differences of singular moduli. Their result is proved by
giving a counting formula for the number of isomorphisms between elliptic
curves with complex multiplication by two different imaginary quadratic fields
and , when the curves are reduced modulo a supersingular prime
and its powers. Equivalently, the Gross-Zagier formula counts optimal
embeddings of the ring of integers of an imaginary quadratic field into
particular maximal orders in , the definite quaternion algebra
over \QQ ramified only at and infinity. Our work gives an analogous
counting formula for the number of simultaneous embeddings of the rings of
integers of primitive CM fields into superspecial orders in definite quaternion
algebras over totally real fields of strict class number 1. Our results can
also be viewed as a counting formula for the number of isomorphisms modulo
between abelian varieties with CM by different fields. Our
counting formula can also be used to determine which superspecial primes appear
in the factorizations of differences of values of Siegel modular functions at
CM points associated to two different CM fields, and to give a bound on those
supersingular primes which can appear. In the special case of Jacobians of
genus 2 curves, this provides information about the factorizations of
numerators of Igusa invariants, and so is also relevant to the problem of
constructing genus 2 curves for use in cryptography.Comment: 32 page
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