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 $n \geq 8$, our bound is smaller than the previously known bound by a multiplicative factor of $\frac{3}{2 \sqrt{\pi n}}$

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 $Cd^+$ 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