10,721 research outputs found
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
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
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
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
Fuzzy splicing systems
In this paper we introduce a new variant of splicing systems, called fuzzy splicing systems, and establish some basic properties of language families generated by this type of splicing systems. We study the “fuzzy effect” on splicing operations, and show that the “fuzzification” of splicing systems can increase and decrease the computational power of splicing systems with finite components with respect to fuzzy operations and cut-points chosen for threshold languages
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
Evaluating Matrix Circuits
The circuit evaluation problem (also known as the compressed word problem)
for finitely generated linear groups is studied. The best upper bound for this
problem is , which is shown by a reduction to polynomial
identity testing. Conversely, the compressed word problem for the linear group
is equivalent to polynomial identity testing. In
the paper, it is shown that the compressed word problem for every finitely
generated nilpotent group is in . Within
the larger class of polycyclic groups we find examples where the compressed
word problem is at least as hard as polynomial identity testing for skew
arithmetic circuits
LNCS
We present layered concurrent programs, a compact and expressive notation for specifying refinement proofs of concurrent programs. A layered concurrent program specifies a sequence of connected concurrent programs, from most concrete to most abstract, such that common parts of different programs are written exactly once. These programs are expressed in the ordinary syntax of imperative concurrent programs using gated atomic actions, sequencing, choice, and (recursive) procedure calls. Each concurrent program is automatically extracted from the layered program. We reduce refinement to the safety of a sequence of concurrent checker programs, one each to justify the connection between every two consecutive concurrent programs. These checker programs are also automatically extracted from the layered program. Layered concurrent programs have been implemented in the CIVL verifier which has been successfully used for the verification of several complex concurrent programs
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