Linear minimum mean square filter for discrete-time linear systems with Markov jumps and multiplicative noises

In this paper we obtain the linear minimum mean square estimator (LMMSE) for discrete-time linear systems subject to state and measurement multiplicative noises and Markov jumps on the parameters. It is assumed that the Markov chain is not available. By using geometric arguments we obtain a Kalman type filter conveniently implementable in a recurrence form. The stationary case is also studied and a proof for the convergence of the error covariance matrix of the LMMSE to a stationary value under the assumption of mean square stability of the system and ergodicity of the associated Markov chain is obtained. It is shown that there exists a unique positive semi-definite solution for the stationary Riccati-like filter equation and, moreover, this solution is the limit of the error covariance matrix of the LMMSE. The advantage of this scheme is that it is very easy to implement and all calculations can be performed offline. (c) 2011 Elsevier Ltd. All rights reserved.

Capillary coexistence and criticality in mesopores: Modification of the Kelvin theory

The classical model of capillary equilibrium in cylindrical pores is modified here by the introduction of molecular concepts and the solid fluid interaction potential. The new approach accurately predicts capillary coexistence and criticality, with results quantitatively matching those from density functional theory for nitrogen adsorption, while also predicting condensation pressures in agreement with reported experimental findings for MCM-41. The larger critical pore size for nitrogen adsorption in these materials, however, suggests a modification of the potential function parameters, evaluated here from data for hydroxylated silica.

Bounds on integrals of the Wigner function

The integral of the Wigner function over a subregion of the phase space of a quantum system may be less than zero or greater than one. It is shown that for systems with 1 degree of freedom, the problem of determining the best possible upper and lower bounds on such an integral, over an possible states, reduces to the problem of finding the greatest and least eigenvalues of a Hermitian operator corresponding to the subregion. The problem is solved exactly in the case of an arbitrary elliptical region. These bounds provide checks on experimentally measured quasiprobability distributions.

The pareto-stability concept is a natural solution concept for discrete matching markets with indifferences

In a decentralized setting the game-theoretical predictions are that only strong blockings are allowed to rupture the structure of a matching. This paper argues that, under indifferences, also weak blockings should be considered when these blockings come from the grand coalition. This solution concept requires stability plus Pareto optimality. A characterization of the set of Pareto-stable matchings for the roommate and the marriage models is provided in terms of individually rational matchings whose blocking pairs, if any, are formed with unmatched agents. These matchings always exist and give an economic intuition on how blocking can be done by non-trading agents, so that the transactions need not be undone as agents reach the set of stable matchings. Some properties of the Pareto-stable matchings shared by the Marriage and Roommate models are obtained.

Discrete and continuous models for dry masonry columns

The dynamic response of dry masonry columns can be approximated with finite-difference equations. Continuum models follow by replacing the difference quotients of the discrete model by corresponding differential expressions. The mathematically simplest of these models is a one-dimensional Cosserat theory. Within the presented homogenization context, the Cosserat theory is obtained by making ad hoc assumptions regarding the relative importance of certain terms in the differential expansions. The quality of approximation of the various theories is tested by comparison of the dispersion relations for bending waves with the dispersion relation of the discrete theory. All theories coincide with differences of less than 1% for wave-length-block-height (L/h) ratios bigger than 2 pi. The theory based on systematic differential approximation remains accurate up to L/h = 3 and then diverges rapidly. The Cosserat model becomes increasingly inaccurate for L/h < 2 pi. However, in contrast to the systematic approximation, the wave speed remains finite. In conclusion, considering its relative simplicity, the Cosserat model appears to be the natural starting point for the development of continuum models for blocky structures.

A Comparison of Bayesian and Sampling Theory Inferences in a Probit Model

HE PROBIT MODEL IS A POPULAR DEVICE for explaining binary choice decisions in econometrics. It has been used to describe choices such as labor force participation, travel mode, home ownership, and type of education. These and many more examples can be found in papers by Amemiya (1981) and Maddala (1983). Given the contribution of economics towards explaining such choices, and given the nature of data that are collected, prior information on the relationship between a choice probability and several explanatory variables frequently exists. Bayesian inference is a convenient vehicle for including such prior information. Given the increasing popularity of Bayesian inference it is useful to ask whether inferences from a probit model are sensitive to a choice between Bayesian and sampling theory techniques. Of interest is the sensitivity of inference on coefficients, probabilities, and elasticities. We consider these issues in a model designed to explain choice between fixed and variable interest rate mortgages. Two Bayesian priors are employed: a uniform prior on the coefficients, designed to be noninformative for the coefficients, and an inequality restricted prior on the signs of the coefficients. We often know, a priori, whether increasing the value of a particular explanatory variable will have a positive or negative effect on a choice probability. This knowledge can be captured by using a prior probability density function (pdf) that is truncated to be positive or negative. Thus, three sets of results are compared:those from maximum likelihood (ML) estimation, those from Bayesian estimation with an unrestricted uniform prior on the coefficients, and those from Bayesian estimation with a uniform prior truncated to accommodate inequality restrictions on the coefficients.

Derivation of the probability distribution function for the local density of states of a disordered quantum wire via the replica trick and supersymmetry

We consider the statistical properties of the local density of states of a one-dimensional Dirac equation in the presence of various types of disorder with Gaussian white-noise distribution. It is shown how either the replica trick or supersymmetry can be used to calculate exactly all the moments of the local density of states.' Careful attention is paid to how the results change if the local density of states is averaged over atomic length scales. For both the replica trick and supersymmetry the problem is reduced to finding the ground state of a zero-dimensional Hamiltonian which is written solely in terms of a pair of coupled spins which are elements of u(1, 1). This ground state is explicitly found for the particular case of the Dirac equation corresponding to an infinite metallic quantum wire with a single conduction channel. The calculated moments of the local density of states agree with those found previously by Al'tshuler and Prigodin [Sov. Phys. JETP 68 (1989) 198] using a technique based on recursion relations for Feynman diagrams. (C) 2001 Elsevier Science B.V. All rights reserved.

Non-Markovian quantum optical processes and pseudomodes

Non-Markovian behaviour in atomic systems coupled to a structured reservoir of quantum EM field modes, such as in high Q cavities, is treated using a quasimode description, and the pseudo mode theory for single quantum reservoir excitations is obtained via Fano diagonalisation. The atomic transitions are coupled to a discrete set of (cavity) quasimodes, which are also coupled to a continuum set of (external) quasimodes with slowly varying coupling constants. Each pseudomode corresponds to a cavity quasimode, and the original reservoir structure is obtained in expressions for the equivalent atom-true mode coupling constants. Cases of multiple excitation of the reservoir are now treatable via Markovian master equations for the atom-discrete quasimode system.

Saving, productivity and national income: a discrete-time geometric framework

This paper proposes an alternative geometric framework for analysing the inter-relationship between domestic saving, productivity and income determination in discrete time. The framework provides a means of understanding how low saving economies like the United States sustained high growth rates in the 1990s whereas high saving Japan did not. It also illustrates how the causality between saving and economic activity runs both ways and that discrete changes in national output and income depend on both current and previous accumulation behaviour. The open economy analogue reveals how international capital movements can create external account imbalances that enhance income growth for both borrower and lender economies. (C) 2002 Elsevier Science B.V. All rights reserved.

Modeling of phase equilibrium and vapor adsorption on carbon black based on a combination of a lattice theory and equation of state

A thermodynamic approach is developed in this paper to describe the behavior of a subcritical fluid in the neighborhood of vapor-liquid interface and close to a graphite surface. The fluid is modeled as a system of parallel molecular layers. The Helmholtz free energy of the fluid is expressed as the sum of the intrinsic Helmholtz free energies of separate layers and the potential energy of their mutual interactions calculated by the 10-4 potential. This Helmholtz free energy is described by an equation of state (such as the Bender or Peng-Robinson equation), which allows us a convenient means to obtain the intrinsic Helmholtz free energy of each molecular layer as a function of its two-dimensional density. All molecular layers of the bulk fluid are in mechanical equilibrium corresponding to the minimum of the total potential energy. In the case of adsorption the external potential exerted by the graphite layers is added to the free energy. The state of the interface zone between the liquid and the vapor phases or the state of the adsorbed phase is determined by the minimum of the grand potential. In the case of phase equilibrium the approach leads to the distribution of density and pressure over the transition zone. The interrelation between the collision diameter and the potential well depth was determined by the surface tension. It was shown that the distance between neighboring molecular layers substantially changes in the vapor-liquid transition zone and in the adsorbed phase with loading. The approach is considered in this paper for the case of adsorption of argon and nitrogen on carbon black. In both cases an excellent agreement with the experimental data was achieved without additional assumptions and fitting parameters, except for the fluid-solid potential well depth. The approach has far-reaching consequences and can be readily extended to the model of adsorption in slit pores of carbonaceous materials and to the analysis of multicomponent adsorption systems. (C) 2002 Elsevier Science (USA).

Analysis of adsorption data of graphitized thermal carbon black with a DFT-lattice gas theory

In this paper we analyzed the adsorption of gases and vapors on graphitised thermal carbon black by using a modified DFT-lattice theory, in which we assume that the behavior of the first layer in the adsorption film is different from those of second and higher layers. The effects of various parameters on the topology of the adsorption isotherm were first investigated, and the model was then applied in the analysis of adsorption data of numerous substances on carbon black. We have found that the first layer in the adsorption film behaves differently from the second and higher layers in such a way that the adsorbate-adsorbate interaction energy in the first layer is less than that of second and higher layers, and the same is observed for the partition function. Furthermore, the adsorbate-adsorbate and adsorbate-adsorbent interaction energies obtained from the fitting are consistently lower than the corresponding values obtained from the viscosity data and calculated from the Lorentz-Berthelot rule, respectively.

An augmented Lanczos algorithm for the efficient computation of a dot-product of a function of a large sparse symmetric matrix

The Lanczos algorithm is appreciated in many situations due to its speed. and economy of storage. However, the advantage that the Lanczos basis vectors need not be kept is lost when the algorithm is used to compute the action of a matrix function on a vector. Either the basis vectors need to be kept, or the Lanczos process needs to be applied twice. In this study we describe an augmented Lanczos algorithm to compute a dot product relative to a function of a large sparse symmetric matrix, without keeping the basis vectors.

Numerical study of hydrogenic effective mass theory for an impurity P donor in Si in the presence of an electric field and interfaces

In this paper we examine the effects of varying several experimental parameters in the Kane quantum computer architecture: A-gate voltage, the qubit depth below the silicon oxide barrier, and the back gate depth to explore how these variables affect the electron density of the donor electron. In particular, we calculate the resonance frequency of the donor nuclei as a function of these parameters. To do this we calculated the donor electron wave function variationally using an effective-mass Hamiltonian approach, using a basis of deformed hydrogenic orbitals. This approach was then extended to include the electric-field Hamiltonian and the silicon host geometry. We found that the phosphorous donor electron wave function was very sensitive to all the experimental variables studied in our work, and thus to optimize the operation of these devices it is necessary to control all parameters varied in this paper.

Contribution towards a reflection about methodological strategies in design education and the function of drawing in design

This work presents a reflection on Design education and specifically on the role of Drawing in this area. As a subject, Design has expanded its field of action expanding into new areas such as Experience Design or Service Design. It became necessary for the designer to have more than an education based on technological knowledge or know-how. Many authors like Meredith Davis, Don Norman or Jamie Hobson point out the urgency to review the curricula of Design courses because nowadays “… design is more than appearance, design is about interaction, about strategy and about services. Designers change social behavior” (Norman 2011). When shifting from a product-centered design to a person-centered design (in a structure, a service or in a relationship) what should the function of drawing in a design course be? What should its curriculum be? Our work methodology will be to confront today’s perspectives on design theory and practice in an attempt to add to the discussion on the methodological strategies in design teaching in the contemporary context.

Contribution towards a reflection about methodological strategies in Design Education and the function of Drawing in Design

This work presents a reflection on Design education and specifically on the role of Drawing in this area. As a subject, Design has expanded its field of action expanding into new areas such as Experience Design or Service Design. It became necessary for the designer to have more than an education based on technological knowledge or know-how. Many authors like Meredith Davis, Don Norman or Jamie Hobson point out the urgency to review the curricula of Design courses because nowadays “ … design is more than appearance, design is about interaction, about strategy and about services. Designers change social behavior” (Norman, 2011) When shifting from a product-centered design to a person-centered design (in a structure, a service or in a relationship) what should the function of drawing in a design course be? What should its curriculum be? Our work methodology will be to confront today’s perspectives on design theory and practice in an attempt to add to the discussion on the methodological strategies in design teaching in the contemporary context.