2,257 research outputs found
Geometric Influences II: Correlation Inequalities and Noise Sensitivity
In a recent paper, we presented a new definition of influences in product
spaces of continuous distributions, and showed that analogues of the most
fundamental results on discrete influences, such as the KKL theorem, hold for
the new definition in Gaussian space. In this paper we prove Gaussian analogues
of two of the central applications of influences: Talagrand's lower bound on
the correlation of increasing subsets of the discrete cube, and the
Benjamini-Kalai-Schramm (BKS) noise sensitivity theorem. We then use the
Gaussian results to obtain analogues of Talagrand's bound for all discrete
probability spaces and to reestablish analogues of the BKS theorem for biased
two-point product spaces.Comment: 20 page
Geometric influences
We present a new definition of influences in product spaces of continuous
distributions. Our definition is geometric, and for monotone sets it is
identical with the measure of the boundary with respect to uniform enlargement.
We prove analogs of the Kahn-Kalai-Linial (KKL) and Talagrand's influence sum
bounds for the new definition. We further prove an analog of a result of
Friedgut showing that sets with small "influence sum" are essentially
determined by a small number of coordinates. In particular, we establish the
following tight analog of the KKL bound: for any set in of
Gaussian measure , there exists a coordinate such that the th
geometric influence of the set is at least , where
is a universal constant. This result is then used to obtain an isoperimetric
inequality for the Gaussian measure on and the class of sets
invariant under transitive permutation group of the coordinates.Comment: Published in at http://dx.doi.org/10.1214/11-AOP643 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Tachyon Condensation in Superstring Field Theory
It has been conjectured that at the stationary point of the tachyon potential
for the D-brane-anti-D-brane pair or for the non-BPS D-brane of superstring
theories, the negative energy density cancels the brane tensions. We study this
conjecture using a Wess-Zumino-Witten-like open superstring field theory free
of contact term divergences and recently shown to give 60% of the vacuum energy
by condensation of the tachyon field alone. While the action is non-polynomial,
the multiscalar tachyon potential to any fixed level involves only a finite
number of interactions. We compute this potential to level three, obtaining 85%
of the expected vacuum energy, a result consistent with convergence that can
also be viewed as a successful test of the string field theory. The resulting
effective tachyon potential is bounded below and has two degenerate global
minima. We calculate the energy density of the kink solution interpolating
between these minima finding good agreement with the tension of the D-brane of
one lower dimension.Comment: 41 pages, LaTeX, 1 figure. Added two reference
Manifest Electromagnetic Duality in Closed Superstring Field Theory
The free action for massless Ramond-Ramond fields is derived from closed
superstring field theory using the techniques of Siegel and Zwiebach. For the
uncompactified Type IIB superstring, this gives a manifestly Lorentz-covariant
action for a self-dual five-form field strength. Upon compactification to four
dimensions, the action depends on a U(1) field strength from 4D N=2
supergravity. However, unlike the standard Maxwell action, this action is
manifestly invariant under the electromagnetic duality transformation which
rotates into .Comment: Added three references and corrected one footnote. 15 pages harvma
IR Dynamics on Branes and Space-Time Geometry
We consider the type I theory compactified on . When the D5-brane wraps
the it yields a D2-brane in seven dimensions. In the leading
approximation the moduli space of vacua of the three dimensional field theory
on the brane is T^4/\ZZ_2. The dual M theory description of this theory is a
compactification on K3 and our 2-brane is the eleven dimensional 2-brane at a
point in K3. We use this fact to conclude that strong coupling IR effects in
the three dimensional theory on the brane turn its moduli space into a K3. This
interpretation allows us to solve various strongly coupled gauge theories in
three dimensions by identifying their Coulomb branch with a piece of a
(sometime singular) K3.Comment: 8 pages, uses harvmac, one reference adde
Project: Picturing Milwaukee: Thurston Woods Pilot Study
In the summer of 2012, students, scholars and affiliates of Buildings-Landscapes-Cultures, worked with residents and community organizations from the Thurston Woods neighborhood in Milwaukee, Wisconsin in order to explore, document and examine historic buildings and cultural landscapes of this area.https://dc.uwm.edu/sarup_facbooks/1002/thumbnail.jp
Characterization of Polymeric Materials by Thermal Analysis, Spectroscopy and Microscopic Techniques
Forecasting Chemical Abundance Precision for Extragalactic Stellar Archaeology
Increasingly powerful and multiplexed spectroscopic facilities promise
detailed chemical abundance patterns for millions of resolved stars in galaxies
beyond the Milky Way (MW). Here, we employ the Cram\'er-Rao Lower Bound (CRLB)
to forecast the precision to which stellar abundances for metal-poor, low-mass
stars outside the MW can be measured for 41 current (e.g., Keck, MMT, VLT,
DESI) and planned (e.g., MSE, JWST, ELTs) spectrograph configurations. We show
that moderate resolution () spectroscopy at blue-optical
wavelengths ( \AA) (i) enables the recovery of 2-4 times
as many elements as red-optical spectroscopy
( \AA) at similar or higher resolutions
() and (ii) can constrain the abundances of several neutron
capture elements to 0.3 dex. We further show that high-resolution
(), low S/N (10 pixel) spectra contain rich
abundance information when modeled with full spectral fitting techniques. We
demonstrate that JWST/NIRSpec and ELTs can recover (i) 10 and 30
elements, respectively, for metal-poor red giants throughout the Local Group
and (ii) [Fe/H] and [/Fe] for resolved stars in galaxies out to several
Mpc with modest integration times. We show that select literature abundances
are within a factor of 2 (or better) of our CRLBs. We suggest that, like
ETCs, CRLBs should be used when planning stellar spectroscopic observations. We
include an open source python package, \texttt{Chem-I-Calc}, that allows users
to compute CRLBs for spectrographs of their choosing.Comment: 60 pages, 24 figures, accepted for publication in ApJ
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