Analogies between linguistics and information theory

An analogy is established between the syntagm and paradigm from Saussurean linguistics and the message and messages for selection from the information theory initiated by Claude Shannon. The analogy is pursued both as an end itself and for its analytic value in understanding patterns of retrieval from full text systems. The multivalency of individual words when isolated from their syntagm is contrasted with the relative stability of meaning of multi-word sequences, when searching ordinary written discourse. The syntagm is understood as the linear sequence of oral and written language. Saussureâ??s understanding of the word, as a unit which compels recognition by the mind, is endorsed, although not regarded as final. The lesser multivalency of multi-word sequences is understood as the greater determination of signification by the extended syntagm. The paradigm is primarily understood as the network of associations a word acquires when considered apart from the syntagm. The restriction of information theory to expression or signals, and its focus on the combinatorial aspects of the message, is sustained. The message in the model of communication in information theory can include sequences of written language. Shannonâ??s understanding of the written word, as a cohesive group of letters, with strong internal statistical influences, is added to the Saussurean conception. Sequences of more than one word are regarded as weakly correlated concatenations of cohesive units.

Entanglement between collective operators in a linear harmonic chain

We investigate entanglement between collective operators of two blocks of oscillators in an infinite linear harmonic chain. These operators are defined as averages over local operators (individual oscillators) in the blocks. On the one hand, this approach of "physical blocks" meets realistic experimental conditions, where measurement apparatuses do not interact with single oscillators but rather with a whole bunch of them, i.e., where in contrast to usually studied "mathematical blocks" not every possible measurement is allowed. On the other, this formalism naturally allows the generalization to blocks which may consist of several noncontiguous regions. We quantify entanglement between the collective operators by a measure based on the Peres-Horodecki criterion and show how it can be extracted and transferred to two qubits. Entanglement between two blocks is found even in the case where none of the oscillators from one block is entangled with an oscillator from the other, showing genuine bipartite entanglement between collective operators. Allowing the blocks to consist of a periodic sequence of subblocks, we verify that entanglement scales at most with the total boundary region. We also apply the approach of collective operators to scalar quantum field theory.

Simplified theory of wideband spectra of liquid H2O and D2O (from 0 to 1000 cm(-1)) due to reorienting polar and vibrating H-bonded water molecules

A semi-phenomenological molecular model is presented, which is capable of describing with the use of analytical formulae, the wideband dielectric(1) and far-infrared spectra of ordinary and heavy water. In the model the vector of a dipole moment is presented as a sum of two components. The absolute value of the first one is constant; the second one changes harmonically with time. The key aspect of this work is consideration of FIR spectra due to the second component. In the context of the modified hybrid model presented in the work, reorientation of the dipoles in the rectangular potential well is considered, as a result of which the librational (near 700 cm (-1)) and translational (near 200 cm (-1)) absorption bands and the microwave Debye relaxation spectrum arise. It is shown that the time-dependent part of a dipole moment contributes most to the translational band, the relevant mechanism is taken to be stretching vibration of the H-bonded molecules. Previous linear-response molecular models were unsuccessful in describing this band (in heavy water) in terms of the complex dielectric permittivity. The spatial and time scales characteristic of water are estimated. (C) 2002 Elsevier Science B.V. All rights reserved.

Structure of spectra of linear operators in Banach spaces

Descriptive characterizations of the point, the continuous, and the residual spectra of operators in Banach spaces are put forward. In particular, necessary and sufficient conditions for three disjoint subsets of the complex plane to be the point spectrum, the continuous spectrum, and the residual spectrum of a linear continuous operator in a separable Banach space are obtained.

Model selection approaches for non-linear system identification: a review

The identification of non-linear systems using only observed finite datasets has become a mature research area over the last two decades. A class of linear-in-the-parameter models with universal approximation capabilities have been intensively studied and widely used due to the availability of many linear-learning algorithms and their inherent convergence conditions. This article presents a systematic overview of basic research on model selection approaches for linear-in-the-parameter models. One of the fundamental problems in non-linear system identification is to find the minimal model with the best model generalisation performance from observational data only. The important concepts in achieving good model generalisation used in various non-linear system-identification algorithms are first reviewed, including Bayesian parameter regularisation and models selective criteria based on the cross validation and experimental design. A significant advance in machine learning has been the development of the support vector machine as a means for identifying kernel models based on the structural risk minimisation principle. The developments on the convex optimisation-based model construction algorithms including the support vector regression algorithms are outlined. Input selection algorithms and on-line system identification algorithms are also included in this review. Finally, some industrial applications of non-linear models are discussed.

Fault reconstruction in linear dynamic systems using multivariate statistics

Treasure et al. (2004) recently proposed a new sub space-monitoring technique, based on the N4SID algorithm, within the multivariate statistical process control framework. This dynamic-monitoring method requires considerably fewer variables to be analysed when compared with dynamic principal component analysis (PCA). The contribution charts and variable reconstruction, traditionally employed for static PCA, are analysed in a dynamic context. The contribution charts and variable reconstruction may be affected by the ratio of the number of retained components to the total number of analysed variables. Particular problems arise if this ratio is large and a new reconstruction chart is introduced to overcome these. The utility of such a dynamic contribution chart and variable reconstruction is shown in a simulation and by application to industrial data from a distillation unit.

Insight into the solvent effect: A density functional theory study of cisplatin hydrolysis

The solvent effect on reactions in solutions is crucial for many systems. In this study, the reaction barrier with respect to the number of solvent molecules included in the system is systematically studied using density function theory calculations. Our results show that the barriers rapidly converge with respect to the number of solvent molecules. The solvent effect is investigated by calculating cisplatin hydrolysis in several types of solvents. The results are analyzed and a linear relationship between the reaction barrier and the interaction strength of solvent-reactants is found. Insight into the general solvent effect is obtained. (c) 2006 American Institute of Physics.

C-H bond activation over metal oxides: A new insight into the dissociation kinetics from density functional theory

The C-H activation on metal oxides is a fundamental process in chemistry. In this paper, we report a density functional theory study on the process of the C-H activation of CH4 on Pd(111), Pt(111), Ru(0001), Tc(0001), Cu(111), PdO(001), PdO(110), and PdO(100). A linear relationship between the C-H activation barrier and the chemisorption in the dissociation final state on the metal surfaces is obtained, which is consistent with the work in the literature. However, the relationship is poor on the metal oxide surfaces. Instead, a strong linear correlation between the barrier and the lattice O-H bond strength is found on the oxides. The new linear relationship is analyzed and the physical origin is identified. (c) 2008 American Institute of Physics.

Insight into association reactions on metal surfaces: Density-functional theory studies of hydrogenation reactions on Rh(111)

Hydrogenation reaction, as one of the simplest association reactions on surfaces, is of great importance both scientifically and technologically. They are essential steps in many industrial processes in heterogeneous catalysis, such as ammonia synthesis (N-2+3H(2)-->2NH(3)). Many issues in hydrogenation reactions remain largely elusive. In this work, the NHx (x=0,1,2) hydrogenation reactions (N+H-->NH, NH+H-->NH2 and NH2+H-->NH3) on Rh(111) are used as a model system to study the hydrogenation reactions on metal surfaces in general using density-functional theory. In addition, C and O hydrogenation (C+H-->CH and O+H-->OH) and several oxygenation reactions, i.e., C+O, N+O, O+O reactions, are also calculated in order to provide a further understanding of the barrier of association reactions. The reaction pathways and the barriers of all these reactions are determined and reported. For the C, N, NH, and O hydrogenation reactions, it is found that there is a linear relationship between the barrier and the valency of R (R=C, N, NH, and O). Detailed analyses are carried out to rationalize the barriers of the reactions, which shows that: (i) The interaction energy between two reactants in the transition state plays an important role in determining the trend in the barriers; (ii) there are two major components in the interaction energy: The bonding competition and the direct Pauli repulsion; and (iii) the Pauli repulsion effect is responsible for the linear valency-barrier trend in the C, N, NH, and O hydrogenation reactions. For the NH2+H reaction, which is different from other hydrogenation reactions studied, the energy cost of the NH2 activation from the IS to the TS is the main part of the barrier. The potential energy surface of the NH2 on metal surfaces is thus crucial to the barrier of NH2+H reaction. Three important factors that can affect the barrier of association reactions are generalized: (i) The bonding competition effect; (ii) the local charge densities of the reactants along the reaction direction; and (iii) the potential energy surface of the reactants on the surface. The lowest energy pathway for a surface association reaction should correspond to the one with the best compromise of these three factors. (C) 2003 American Institute of Physics.

Disturbance attenuation in linear systems via dynamical compensators: A parametric eigenstructure assignment approach

A simple approach is proposed for disturbance attenuation in multivariable linear systems via dynamical output compensators based on complete parametric eigenstructure assignment. The basic idea is to minimise the H-2 norm of the disturbance-output transfer function using the design freedom provided by eigenstructure assignment. For robustness, the closed-loop system is restricted to be nondefective. Besides the design parameters, the closed-loop eigenvalues are also optimised within desired regions on the left-half complex plane to ensure both closed-loop stability and dynamical performance. With the proposed approach, additional closed-loop specifications can be easily achieved. As a demonstration, robust pole assignment, in the sense that the closed-loop eigenvalues are as insensitive as possible to open-loop system parameter perturbations, is treated. Application of the proposed approach to robust control of a magnetic bearing with a pair of opposing electromagnets and a rigid rotor is discussed.

Linear and nonlinear properties of Rao-dust-Alfven waves in magnetized plasmas

The linear and nonlinear properties of the Rao-dust-magnetohydrodynamic (R-D-MHD) waves in a dusty magnetoplasma are studied. By employing the inertialess electron equation of motion, inertial ion equation of motion, Ampere's law, Faraday's law, and the continuity equation in a plasma with immobile charged dust grains, the linear and nonlinear propagation of two-dimensional R-D-MHD waves are investigated. In the linear regime, the existence of immobile dust grains produces the Rao cutoff frequency, which is proportional to the dust charge density and the ion gyrofrequency. On the other hand, the dynamics of amplitude modulated R-D-MHD waves is governed by the cubic nonlinear Schrodinger equation. The latter has been derived by using the reductive perturbation technique and the two-timescale analysis which accounts for the harmonic generation nonlinearity in plasmas. The stability of the modulated wave envelope against non-resonant perturbations is studied. Finally, the possibility of localized envelope excitations is discussed. (C) 2004 American Institute of Physics.

Exact theory for localized envelope modulated electrostatic wavepackets in space and dusty plasmas

Abundant evidence for the occurrence of modulated envelope plasma wave packets is provided by recent satellite missions. These excitations are characterized by a slowly varying localized envelope structure, embedding the fast carrier wave, which appears to be the result of strong modulation of the wave amplitude. This modulation may be due to parametric interactions between different modes or, simply, to the nonlinear (self-)interaction of the carrier wave. A generic exact theory is presented in this study, for the nonlinear self-modulation of known electrostatic plasma modes, by employing a collisionless fluid model. Both cold (zero-temperature) and warm fluid descriptions are discussed and the results are compared. The (moderately) nonlinear oscillation regime is investigated by applying a multiple scale technique. The calculation leads to a Nonlinear Schrodinger-type Equation (NLSE), which describes the evolution of the slowly varying wave amplitude in time and space. The NLSE admits localized envelope (solitary wave) solutions of bright(pulses) or dark- (holes, voids) type, whose characteristics (maximum amplitude, width) depend on intrinsic plasma parameters. Effects like amplitude perturbation obliqueness (with respect to the propagation direction), finite temperature and defect (dust) concentration are explicitly considered. Relevance with similar highly localized modulated wave structures observed during recent satellite missions is discussed.

Ground state of low-dimensional dipolar gases: Linear and zigzag chains

We study the ground-state phase diagram of ultracold dipolar gases in highly anisotropic traps. Starting from a one-dimensional geometry, by ramping down the transverse confinement along one direction, the gas reaches various planar distributions of dipoles. At large linear densities, when the dipolar gas exhibits a crystal-like phase, critical values of the transverse frequency exist below which the configuration exhibits transverse patterns. These critical values are found by means of a classical theory, and are in full agreement with classical Monte Carlo simulations. The study of the quantum system is performed numerically with Monte Carlo techniques and shows that the quantum fluctuations smoothen the transition and make it completely disappear in a gas phase. These predictions could be experimentally tested and would allow one to reveal the effect of zero-point motion on self-organized mesoscopic structures of matter waves, such as the transverse pattern of the zigzag chain.