15,911 research outputs found
An Alternative Conception of Tree-Adjoining Derivation
The precise formulation of derivation for tree-adjoining grammars has
important ramifications for a wide variety of uses of the formalism, from
syntactic analysis to semantic interpretation and statistical language
modeling. We argue that the definition of tree-adjoining derivation must be
reformulated in order to manifest the proper linguistic dependencies in
derivations. The particular proposal is both precisely characterizable through
a definition of TAG derivations as equivalence classes of ordered derivation
trees, and computationally operational, by virtue of a compilation to linear
indexed grammars together with an efficient algorithm for recognition and
parsing according to the compiled grammar.Comment: 33 page
Tight Bounds for Consensus Systems Convergence
We analyze the asymptotic convergence of all infinite products of matrices
taken in a given finite set, by looking only at finite or periodic products. It
is known that when the matrices of the set have a common nonincreasing
polyhedral norm, all infinite products converge to zero if and only if all
infinite periodic products with period smaller than a certain value converge to
zero, and bounds exist on that value.
We provide a stronger bound holding for both polyhedral norms and polyhedral
seminorms. In the latter case, the matrix products do not necessarily converge
to 0, but all trajectories of the associated system converge to a common
invariant space. We prove our bound to be tight, in the sense that for any
polyhedral seminorm, there is a set of matrices such that not all infinite
products converge, but every periodic product with period smaller than our
bound does converge.
Our technique is based on an analysis of the combinatorial structure of the
face lattice of the unit ball of the nonincreasing seminorm. The bound we
obtain is equal to half the size of the largest antichain in this lattice.
Explicitly evaluating this quantity may be challenging in some cases. We
therefore link our problem with the Sperner property: the property that, for
some graded posets, -- in this case the face lattice of the unit ball -- the
size of the largest antichain is equal to the size of the largest rank level.
We show that some sets of matrices with invariant polyhedral seminorms lead
to posets that do not have that Sperner property. However, this property holds
for the polyhedron obtained when treating sets of stochastic matrices, and our
bound can then be easily evaluated in that case. In particular, we show that
for the dimension of the space , our bound is smaller than the
previously known bound by a multiplicative factor of
Efficient Algorithms for the Consensus Decision Problem
We address the problem of determining if a discrete time switched consensus
system converges for any switching sequence and that of determining if it
converges for at least one switching sequence. For these two problems, we
provide necessary and sufficient conditions that can be checked in singly
exponential time. As a side result, we prove the existence of a polynomial time
algorithm for the first problem when the system switches between only two
subsystems whose corresponding graphs are undirected, a problem that had been
suggested to be NP-hard by Blondel and Olshevsky.Comment: Small modifications after comments from reviewer
Reachability of Consensus and Synchronizing Automata
We consider the problem of determining the existence of a sequence of
matrices driving a discrete-time consensus system to consensus. We transform
this problem into one of the existence of a product of the transition
(stochastic) matrices that has a positive column. We then generalize some
results from automata theory to sets of stochastic matrices. We obtain as a
main result a polynomial-time algorithm to decide the existence of a sequence
of matrices achieving consensus.Comment: Update after revie
Principles and Implementation of Deductive Parsing
We present a system for generating parsers based directly on the metaphor of
parsing as deduction. Parsing algorithms can be represented directly as
deduction systems, and a single deduction engine can interpret such deduction
systems so as to implement the corresponding parser. The method generalizes
easily to parsers for augmented phrase structure formalisms, such as
definite-clause grammars and other logic grammar formalisms, and has been used
for rapid prototyping of parsing algorithms for a variety of formalisms
including variants of tree-adjoining grammars, categorial grammars, and
lexicalized context-free grammars.Comment: 69 pages, includes full Prolog cod
Probabilistic Motion Estimation Based on Temporal Coherence
We develop a theory for the temporal integration of visual motion motivated
by psychophysical experiments. The theory proposes that input data are
temporally grouped and used to predict and estimate the motion flows in the
image sequence. This temporal grouping can be considered a generalization of
the data association techniques used by engineers to study motion sequences.
Our temporal-grouping theory is expressed in terms of the Bayesian
generalization of standard Kalman filtering. To implement the theory we derive
a parallel network which shares some properties of cortical networks. Computer
simulations of this network demonstrate that our theory qualitatively accounts
for psychophysical experiments on motion occlusion and motion outliers.Comment: 40 pages, 7 figure
Simulation of the elementary evolution operator with the motional states of an ion in an anharmonic trap
Following a recent proposal of L. Wang and D. Babikov, J. Chem. Phys. 137,
064301 (2012), we theoretically illustrate the possibility of using the
motional states of a ion trapped in a slightly anharmonic potential to
simulate the single-particle time-dependent Schr\"odinger equation. The
simulated wave packet is discretized on a spatial grid and the grid points are
mapped on the ion motional states which define the qubit network. The
localization probability at each grid point is obtained from the population in
the corresponding motional state. The quantum gate is the elementary evolution
operator corresponding to the time-dependent Schr\"odinger equation of the
simulated system. The corresponding matrix can be estimated by any numerical
algorithm. The radio-frequency field able to drive this unitary transformation
among the qubit states of the ion is obtained by multi-target optimal control
theory. The ion is assumed to be cooled in the ground motional state and the
preliminary step consists in initializing the qubits with the amplitudes of the
initial simulated wave packet. The time evolution of the localization
probability at the grids points is then obtained by successive applications of
the gate and reading out the motional state population. The gate field is
always identical for a given simulated potential, only the field preparing the
initial wave packet has to be optimized for different simulations. We check the
stability of the simulation against decoherence due to fluctuating electric
fields in the trap electrodes by applying dissipative Lindblad dynamics.Comment: 31 pages, 8 figures. Revised version. New title, new figure and new
reference
Antioxidant activities of polyphenols extracted from Perilla frutescens varieties
Various cultivars of Perilla frutescens (L.) (var. crispa and var. frutescens) Britt. were harvested in China and Japan. They were easily differentiated on the basis of their foliage color, that varied from red to green. Water extracts of dried plants were investigated for their antioxidant activity (AA) and their polyphenolic compounds compared. Among them, cinnamic acid derivatives (coumaroyl tartaric acid, caffeic acid and rosmarinic acid), flavonoids (apigenin 7-O-caffeoylglucoside, scutellarein 7-Odiglucuronide, luteolin 7-O-diglucuronide, apigenin 7-O-diglucuronide, luteolin 7-Oglucuronide, and scutellarein 7-O-glucuronide) and anthocyanins (mainly cis-shisonin, shisonin, malonylshisonin and cyanidin 3-O-(E)-caffeoylglucoside-5-O-malonylglucoside) were quantified. AA assays are based on the inhibition of the free radical 2,2-diphenyl-1- picrylhydrazyl (DPPH). The DPPH radical scavenging activity was calculated as Trolox® [(±)-6-hydroxy-2,5,7,8-tetramethylchromane-2-carboxylic acid] equivalent antioxidant capacity (TEAC). The mean amount of total phenolics of the water extracts (4-29 ?mol/100 mL) and the TEAC value calculated (23-167 ?mol TE/100 mL) confirmed the high antioxidant activity of these leaf water extracts. These results were highly correlated within some o-dihydroxylated polyphenolic compounds and AA. (Résumé d'auteur
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