1,721 research outputs found
Direct images of bundles under Frobenius morphisms
Let be a smooth projective variety of dimension over an algebraically
closed field with and be the relative
Frobenius morphism. For any vector bundle on , we prove that instability
of is bounded by instability of
()(Corollary \ref{cor3.8}). When is a smooth
projective curve of genus , it implies being stable whenever
is stable.Comment: the final version to appear in Invent. math. (2008
Verification in Staged Tile Self-Assembly
We prove the unique assembly and unique shape verification problems,
benchmark measures of self-assembly model power, are
-hard and contained in (and in
for staged systems with stages). En route,
we prove that unique shape verification problem in the 2HAM is
-complete.Comment: An abstract version will appear in the proceedings of UCNC 201
The Power of Duples (in Self-Assembly): It's Not So Hip To Be Square
In this paper we define the Dupled abstract Tile Assembly Model (DaTAM),
which is a slight extension to the abstract Tile Assembly Model (aTAM) that
allows for not only the standard square tiles, but also "duple" tiles which are
rectangles pre-formed by the joining of two square tiles. We show that the
addition of duples allows for powerful behaviors of self-assembling systems at
temperature 1, meaning systems which exclude the requirement of cooperative
binding by tiles (i.e., the requirement that a tile must be able to bind to at
least 2 tiles in an existing assembly if it is to attach). Cooperative binding
is conjectured to be required in the standard aTAM for Turing universal
computation and the efficient self-assembly of shapes, but we show that in the
DaTAM these behaviors can in fact be exhibited at temperature 1. We then show
that the DaTAM doesn't provide asymptotic improvements over the aTAM in its
ability to efficiently build thin rectangles. Finally, we present a series of
results which prove that the temperature-2 aTAM and temperature-1 DaTAM have
mutually exclusive powers. That is, each is able to self-assemble shapes that
the other can't, and each has systems which cannot be simulated by the other.
Beyond being of purely theoretical interest, these results have practical
motivation as duples have already proven to be useful in laboratory
implementations of DNA-based tiles
Scaling of the spin stiffness in random spin-1/2 chains : Crossover from pure-metallic behaviour to random singlet-localized regime
In this paper we study the localization transition induced by the disorder in
random antiferromagnetic spin-1/2 chains. The results of numerical large scale
computations are presented for the XX model using its free fermions
representation. The scaling behavior of the spin stiffness is investigated for
various disorder strengths. The disorder dependence of the localization length
is studied and a comparison between numerical results and bosonization
arguments is presented. A non trivial connection between localization effects
and the crossover from the pure XX fixed point to the infinite randomness fixed
point is pointed out.Comment: Published version, 7 pages, 6 figure
Self-Assembly of 4-sided Fractals in the Two-handed Tile Assembly Model
We consider the self-assembly of fractals in one of the most well-studied
models of tile based self-assembling systems known as the Two-handed Tile
Assembly Model (2HAM). In particular, we focus our attention on a class of
fractals called discrete self-similar fractals (a class of fractals that
includes the discrete Sierpi\'nski carpet). We present a 2HAM system that
finitely self-assembles the discrete Sierpi\'nski carpet with scale factor 1.
Moreover, the 2HAM system that we give lends itself to being generalized and we
describe how this system can be modified to obtain a 2HAM system that finitely
self-assembles one of any fractal from an infinite set of fractals which we
call 4-sided fractals. The 2HAM systems we give in this paper are the first
examples of systems that finitely self-assemble discrete self-similar fractals
at scale factor 1 in a purely growth model of self-assembly. Finally, we show
that there exists a 3-sided fractal (which is not a tree fractal) that cannot
be finitely self-assembled by any 2HAM system
Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
We examine the spin- quantum Heisenberg magnet with Gaussian-random,
infinite-range exchange interactions. The quantum-disordered phase is accessed
by generalizing to symmetry and studying the large limit. For large
the ground state is a spin-glass, while quantum fluctuations produce a
spin-fluid state for small . The spin-fluid phase is found to be generically
gapless - the average, zero temperature, local dynamic spin-susceptibility
obeys \bar{\chi} (\omega ) \sim \log(1/|\omega|) + i (\pi/2) \mbox{sgn}
(\omega) at low frequencies. This form is identical to the phenomenological
`marginal' spectrum proposed by Varma {\em et. al.\/} for the doped cuprates.Comment: 13 pages, REVTEX, 2 figures available by request from
[email protected]
Empirical approaches for the investigation of toxicant-induced loss of tolerance.
It has been hypothesized that sensitivity to low-level chemical exposures develops in two steps: initiation by an acute or chronic chemical exposure, followed by triggering of symptoms by low levels of previously tolerated chemical inhalants, foods, or drugs. The Working Group on Toxicant-induced Loss of Tolerance has formulated a series of research questions to test this hypothesis: Do some individuals experience sensitivity to chemicals at levels of exposure unexplained by classical toxicological thresholds and dose-response relationships, and outside normally expected variation in the population? Do chemically sensitive subjects exhibit masking that may interfere with the reproducibility of their responses to chemical challenges? Does chemical sensitivity develop because of acute, intermittent, or continuous exposure to certain substances? If so, what substances are most likely to initiate this process? An experimental approach for testing directly the relationship between patients' reported symptoms and specific exposures was outlined in response to the first question, which was felt to be a key question. Double-blind, placebo-controlled challenges performed in an environmentally controlled hospital facility (environmental medical unit) coupled with rigorous documentation of both objective and subjective responses are necessary to answer this question and to help elucidate the nature and origins of chemical sensitivity
Systems with Multiplicative Noise: Critical Behavior from KPZ Equation and Numerics
We show that certain critical exponents of systems with multiplicative noise
can be obtained from exponents of the KPZ equation. Numerical simulations in 1d
confirm this prediction, and yield other exponents of the multiplicative noise
problem. The numerics also verify an earlier prediction of the divergence of
the susceptibility over an entire range of control parameter values, and show
that the exponent governing the divergence in this range varies continuously
with control parameter.Comment: Four pages (In Revtex format) with 4 figures (in Postcript
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