10,815 research outputs found
Bond-Propagation Algorithm for Thermodynamic Functions in General 2D Ising Models
Recently, we developed and implemented the bond propagation algorithm for
calculating the partition function and correlation functions of random bond
Ising models in two dimensions. The algorithm is the fastest available for
calculating these quantities near the percolation threshold. In this paper, we
show how to extend the bond propagation algorithm to directly calculate
thermodynamic functions by applying the algorithm to derivatives of the
partition function, and we derive explicit expressions for this transformation.
We also discuss variations of the original bond propagation procedure within
the larger context of Y-Delta-Y-reducibility and discuss the relation of this
class of algorithm to other algorithms developed for Ising systems. We conclude
with a discussion on the outlook for applying similar algorithms to other
models.Comment: 12 pages, 10 figures; submitte
High rate locally-correctable and locally-testable codes with sub-polynomial query complexity
In this work, we construct the first locally-correctable codes (LCCs), and
locally-testable codes (LTCs) with constant rate, constant relative distance,
and sub-polynomial query complexity. Specifically, we show that there exist
binary LCCs and LTCs with block length , constant rate (which can even be
taken arbitrarily close to 1), constant relative distance, and query complexity
. Previously such codes were known to exist
only with query complexity (for constant ), and
there were several, quite different, constructions known.
Our codes are based on a general distance-amplification method of Alon and
Luby~\cite{AL96_codes}. We show that this method interacts well with local
correctors and testers, and obtain our main results by applying it to suitably
constructed LCCs and LTCs in the non-standard regime of \emph{sub-constant
relative distance}.
Along the way, we also construct LCCs and LTCs over large alphabets, with the
same query complexity , which additionally have
the property of approaching the Singleton bound: they have almost the
best-possible relationship between their rate and distance. This has the
surprising consequence that asking for a large alphabet error-correcting code
to further be an LCC or LTC with query
complexity does not require any sacrifice in terms of rate and distance! Such a
result was previously not known for any query complexity.
Our results on LCCs also immediately give locally-decodable codes (LDCs) with
the same parameters
Nuclear-spin relaxation of Pb in ferroelectric powders
Motivated by a recent proposal by O. P. Sushkov and co-workers to search for
a P,T-violating Schiff moment of the Pb nucleus in a ferroelectric
solid, we have carried out a high-field nuclear magnetic resonance study of the
longitudinal and transverse spin relaxation of the lead nuclei from room
temperature down to 10 K for powder samples of lead titanate (PT), lead
zirconium titanate (PZT), and a PT monocrystal. For all powder samples and
independently of temperature, transverse relaxation times were found to be
ms, while the longitudinal relaxation times exhibited a
temperature dependence, with of over an hour at the lowest temperatures,
decreasing to s at room temperature. At high temperatures, the
observed behavior is consistent with a two-phonon Raman process, while in the
low temperature limit, the relaxation appears to be dominated by a
single-phonon (direct) process involving magnetic impurities. This is the first
study of temperature-dependent nuclear-spin relaxation in PT and PZT
ferroelectrics at such low temperatures. We discuss the implications of the
results for the Schiff-moment search.Comment: 6 pages, 4 figure
Tunable Double Negative Band Structure from Non-Magnetic Coated Rods
A system of periodic poly-disperse coated nano-rods is considered. Both the
coated nano-rods and host material are non-magnetic. The exterior nano-coating
has a frequency dependent dielectric constant and the rod has a high dielectric
constant. A negative effective magnetic permeability is generated near the Mie
resonances of the rods while the coating generates a negative permittivity
through a field resonance controlled by the plasma frequency of the coating and
the geometry of the crystal. The explicit band structure for the system is
calculated in the sub-wavelength limit. Tunable pass bands exhibiting negative
group velocity are generated and correspond to simultaneously negative
effective dielectric permittivity and magnetic permeability. These can be
explicitly controlled by adjusting the distance between rods, the coating
thickness, and rod diameters
Maximum likelihood drift estimation for a threshold diffusion
We study the maximum likelihood estimator of the drift parameters of a
stochastic differential equation, with both drift and diffusion coefficients
constant on the positive and negative axis, yet discontinuous at zero. This
threshold diffusion is called drifted Oscillating Brownian motion.For this
continuously observed diffusion, the maximum likelihood estimator coincide with
a quasi-likelihood estimator with constant diffusion term. We show that this
estimator is the limit, as observations become dense in time, of the
(quasi)-maximum likelihood estimator based on discrete observations. In long
time, the asymptotic behaviors of the positive and negative occupation times
rule the ones of the estimators. Differently from most known results in the
literature, we do not restrict ourselves to the ergodic framework: indeed,
depending on the signs of the drift, the process may be ergodic, transient or
null recurrent. For each regime, we establish whether or not the estimators are
consistent; if they are, we prove the convergence in long time of the properly
rescaled difference of the estimators towards a normal or mixed normal
distribution. These theoretical results are backed by numerical simulations
Does Scientific Progress Consist in Increasing Knowledge or Understanding?
Bird argues that scientific progress consists in increasing knowledge. Dellsén objects that increasing knowledge is neither necessary nor sufficient for scientific progress, and argues that scientific progress rather consists in increasing understanding. Dellsén also contends that unlike Bird’s view, his view can account for the scientific practices of using idealizations and of choosing simple theories over complex ones. I argue that Dellsén’s criticisms against Bird’s view fail, and that increasing understanding cannot account for scientific progress, if acceptance, as opposed to belief, is required for scientific understanding
Modelling of impaired cerebral blood flow due to gaseous emboli
Bubbles introduced to the arterial circulation during invasive medical
procedures can have devastating consequences for brain function but their
effects are currently difficult to quantify. Here we present a Monte-Carlo
simulation investigating the impact of gas bubbles on cerebral blood flow. For
the first time, this model includes realistic adhesion forces, bubble
deformation, fluid dynamical considerations, and bubble dissolution. This
allows investigation of the effects of buoyancy, solubility, and blood pressure
on embolus clearance.
Our results illustrate that blockages depend on several factors, including
the number and size distribution of incident emboli, dissolution time and blood
pressure. We found it essential to model the deformation of bubbles to avoid
overestimation of arterial obstruction. Incorporation of buoyancy effects
within our model slightly reduced the overall level of obstruction but did not
decrease embolus clearance times. We found that higher blood pressures generate
lower levels of obstruction and improve embolus clearance. Finally, we
demonstrate the effects of gas solubility and discuss potential clinical
applications of the model
Linear-Space Approximate Distance Oracles for Planar, Bounded-Genus, and Minor-Free Graphs
A (1 + eps)-approximate distance oracle for a graph is a data structure that
supports approximate point-to-point shortest-path-distance queries. The most
relevant measures for a distance-oracle construction are: space, query time,
and preprocessing time. There are strong distance-oracle constructions known
for planar graphs (Thorup, JACM'04) and, subsequently, minor-excluded graphs
(Abraham and Gavoille, PODC'06). However, these require Omega(eps^{-1} n lg n)
space for n-node graphs. We argue that a very low space requirement is
essential. Since modern computer architectures involve hierarchical memory
(caches, primary memory, secondary memory), a high memory requirement in effect
may greatly increase the actual running time. Moreover, we would like data
structures that can be deployed on small mobile devices, such as handhelds,
which have relatively small primary memory. In this paper, for planar graphs,
bounded-genus graphs, and minor-excluded graphs we give distance-oracle
constructions that require only O(n) space. The big O hides only a fixed
constant, independent of \epsilon and independent of genus or size of an
excluded minor. The preprocessing times for our distance oracle are also faster
than those for the previously known constructions. For planar graphs, the
preprocessing time is O(n lg^2 n). However, our constructions have slower query
times. For planar graphs, the query time is O(eps^{-2} lg^2 n). For our
linear-space results, we can in fact ensure, for any delta > 0, that the space
required is only 1 + delta times the space required just to represent the graph
itself
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