566 research outputs found
Implementation of higher-order absorbing boundary conditions for the Einstein equations
We present an implementation of absorbing boundary conditions for the
Einstein equations based on the recent work of Buchman and Sarbach. In this
paper, we assume that spacetime may be linearized about Minkowski space close
to the outer boundary, which is taken to be a coordinate sphere. We reformulate
the boundary conditions as conditions on the gauge-invariant
Regge-Wheeler-Zerilli scalars. Higher-order radial derivatives are eliminated
by rewriting the boundary conditions as a system of ODEs for a set of auxiliary
variables intrinsic to the boundary. From these we construct boundary data for
a set of well-posed constraint-preserving boundary conditions for the Einstein
equations in a first-order generalized harmonic formulation. This construction
has direct applications to outer boundary conditions in simulations of isolated
systems (e.g., binary black holes) as well as to the problem of
Cauchy-perturbative matching. As a test problem for our numerical
implementation, we consider linearized multipolar gravitational waves in TT
gauge, with angular momentum numbers l=2 (Teukolsky waves), 3 and 4. We
demonstrate that the perfectly absorbing boundary condition B_L of order L=l
yields no spurious reflections to linear order in perturbation theory. This is
in contrast to the lower-order absorbing boundary conditions B_L with L<l,
which include the widely used freezing-Psi_0 boundary condition that imposes
the vanishing of the Newman-Penrose scalar Psi_0.Comment: 25 pages, 9 figures. Minor clarifications. Final version to appear in
Class. Quantum Grav
Quantum Weakly Nondeterministic Communication Complexity
We study the weakest model of quantum nondeterminism in which a classical
proof has to be checked with probability one by a quantum protocol. We show the
first separation between classical nondeterministic communication complexity
and this model of quantum nondeterministic communication complexity for a total
function. This separation is quadratic.Comment: 12 pages. v3: minor correction
Quantum Interactive Proofs with Competing Provers
This paper studies quantum refereed games, which are quantum interactive
proof systems with two competing provers: one that tries to convince the
verifier to accept and the other that tries to convince the verifier to reject.
We prove that every language having an ordinary quantum interactive proof
system also has a quantum refereed game in which the verifier exchanges just
one round of messages with each prover. A key part of our proof is the fact
that there exists a single quantum measurement that reliably distinguishes
between mixed states chosen arbitrarily from disjoint convex sets having large
minimal trace distance from one another. We also show how to reduce the
probability of error for some classes of quantum refereed games.Comment: 13 pages, to appear in STACS 200
Testing Linear-Invariant Non-Linear Properties
We consider the task of testing properties of Boolean functions that are
invariant under linear transformations of the Boolean cube. Previous work in
property testing, including the linearity test and the test for Reed-Muller
codes, has mostly focused on such tasks for linear properties. The one
exception is a test due to Green for "triangle freeness": a function
f:\cube^{n}\to\cube satisfies this property if do not all
equal 1, for any pair x,y\in\cube^{n}.
Here we extend this test to a more systematic study of testing for
linear-invariant non-linear properties. We consider properties that are
described by a single forbidden pattern (and its linear transformations), i.e.,
a property is given by points v_{1},...,v_{k}\in\cube^{k} and
f:\cube^{n}\to\cube satisfies the property that if for all linear maps
L:\cube^{k}\to\cube^{n} it is the case that do
not all equal 1. We show that this property is testable if the underlying
matroid specified by is a graphic matroid. This extends
Green's result to an infinite class of new properties.
Our techniques extend those of Green and in particular we establish a link
between the notion of "1-complexity linear systems" of Green and Tao, and
graphic matroids, to derive the results.Comment: This is the full version; conference version appeared in the
proceedings of STACS 200
Making Classical Ground State Spin Computing Fault-Tolerant
We examine a model of classical deterministic computing in which the ground
state of the classical system is a spatial history of the computation. This
model is relevant to quantum dot cellular automata as well as to recent
universal adiabatic quantum computing constructions. In its most primitive
form, systems constructed in this model cannot compute in an error free manner
when working at non-zero temperature. However, by exploiting a mapping between
the partition function for this model and probabilistic classical circuits we
are able to show that it is possible to make this model effectively error free.
We achieve this by using techniques in fault-tolerant classical computing and
the result is that the system can compute effectively error free if the
temperature is below a critical temperature. We further link this model to
computational complexity and show that a certain problem concerning finite
temperature classical spin systems is complete for the complexity class
Merlin-Arthur. This provides an interesting connection between the physical
behavior of certain many-body spin systems and computational complexity.Comment: 24 pages, 1 figur
Isolation and characterization of bacterial agents associated of wetwood disease on elm trees in Iran
Elm trees (Ulmus spp.) are one of the most widespread landscape plants, widely used as ornamental trees to embellish parks and streets of different countries including Iran. Elm trees cultivation is seriously limited by biotic factors such as bacterial pathogens. Recently, bacterial wetwood has been identified as a common disease on elm trees in Northwest Iran. In present study, in order to identify bacterial pathogens associated with elm trees, wetwood infected samples were collected from elm trees showing wetwood symptom across Tabriz city and immediately transferred to the lab. After isolation and purification of isolates, hypersensitive reaction (HR), pathogenicity, biochemical and molecular tests were used to characterize the isolates. In total of 92 isolates obtained, 32 and 10 isolates were able to induce HR and wetwood symptoms on tobacco leaves and young branches of elm, respectively. Based on biochemical and molecular tests, the identity of the isolates studied were determined as Brevundimonas bullata, Paracoccus alcaliphilus, P. marcusii and Luteimonas aestuarii. To the best of our knowledge, this study shows that these four bacterial species here reported are responsible for the causal agent-complex of wetwood disease on elm trees for the first time in the world
On analog quantum algorithms for the mixing of Markov chains
The problem of sampling from the stationary distribution of a Markov chain
finds widespread applications in a variety of fields. The time required for a
Markov chain to converge to its stationary distribution is known as the
classical mixing time. In this article, we deal with analog quantum algorithms
for mixing. First, we provide an analog quantum algorithm that given a Markov
chain, allows us to sample from its stationary distribution in a time that
scales as the sum of the square root of the classical mixing time and the
square root of the classical hitting time. Our algorithm makes use of the
framework of interpolated quantum walks and relies on Hamiltonian evolution in
conjunction with von Neumann measurements.
There also exists a different notion for quantum mixing: the problem of
sampling from the limiting distribution of quantum walks, defined in a
time-averaged sense. In this scenario, the quantum mixing time is defined as
the time required to sample from a distribution that is close to this limiting
distribution. Recently we provided an upper bound on the quantum mixing time
for Erd\"os-Renyi random graphs [Phys. Rev. Lett. 124, 050501 (2020)]. Here, we
also extend and expand upon our findings therein. Namely, we provide an
intuitive understanding of the state-of-the-art random matrix theory tools used
to derive our results. In particular, for our analysis we require information
about macroscopic, mesoscopic and microscopic statistics of eigenvalues of
random matrices which we highlight here. Furthermore, we provide numerical
simulations that corroborate our analytical findings and extend this notion of
mixing from simple graphs to any ergodic, reversible, Markov chain.Comment: The section concerning time-averaged mixing (Sec VIII) has been
updated: Now contains numerical plots and an intuitive discussion on the
random matrix theory results used to derive the results of arXiv:2001.0630
trans-Dibromidobis(1-ethyl-3-methylimidazol-2-ylidene)palladium(II)
The title compound, trans-[PdBr2(C6H10N2)2], was synthesized ionothermally in the ionic liquid solvent 1-ethyl-3-methylimidazolium bromide. In the crystal, the PdII atoms are square-planarly coordinated to two Br atoms and two neutral (C6H10N2) ligands. The PdII atom is located on an inversion centre
Improved Approximation Algorithms for Projection Games
The projection games (aka Label-Cover) problem is of great importance to the field of approximation algorithms, since most of the NP-hardness of approximation results we know today are reductions from Label-Cover. In this paper we design several approximation algorithms for projection games:
1. A polynomial-time approximation algorithm that improves on the previous best approximation by Charikar, Hajiaghayi and Karloff [7].
2. A sub-exponential time algorithm with much tighter approximation for the case of smooth projection games.
3. A PTAS for planar graphs.National Science Foundation (U.S.) (Grant 1218547
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