Calmness of the Feasible Set Mapping for Linear Inequality Systems

In this paper we deal with parameterized linear inequality systems in the n-dimensional Euclidean space, whose coefficients depend continuosly on an index ranging in a compact Hausdorff space. The paper is developed in two different parametric settings: the one of only right-hand-side perturbations of the linear system, and that in which both sides of the system can be perturbed. Appealing to the backgrounds on the calmness property, and exploiting the specifics of the current linear structure, we derive different characterizations of the calmness of the feasible set mapping, and provide an operative expresion for the calmness modulus when confined to finite systems. In the paper, the role played by the Abadie constraint qualification in relation to calmness is clarified, and illustrated by different examples. We point out that this approach has the virtue of tackling the calmness property exclusively in terms of the system’s data.

Robust solutions to multi-objective linear programs with uncertain data

In this paper we examine multi-objective linear programming problems in the face of data uncertainty both in the objective function and the constraints. First, we derive a formula for the radius of robust feasibility guaranteeing constraint feasibility for all possible scenarios within a specified uncertainty set under affine data parametrization. We then present numerically tractable optimality conditions for minmax robust weakly efficient solutions, i.e., the weakly efficient solutions of the robust counterpart. We also consider highly robust weakly efficient solutions, i.e., robust feasible solutions which are weakly efficient for any possible instance of the objective matrix within a specified uncertainty set, providing lower bounds for the radius of highly robust efficiency guaranteeing the existence of this type of solutions under affine and rank-1 objective data uncertainty. Finally, we provide numerically tractable optimality conditions for highly robust weakly efficient solutions.

Game theory and programming; National Science Foundation summer mathematics institute notes.

Bibliography: leaves [87]-[88]

Adaptive phase measurements in linear optical quantum computation

Photon counting induces an effective non-linear optical phase shift in certain states derived by linear optics from single photons. Although this non-linearity is non-deterministic, it is sufficient in principle to allow scalable linear optics quantum computation (LOQC). The most obvious way to encode a qubit optically is as a superposition of the vacuum and a single photon in one mode-so-called 'single-rail' logic. Until now this approach was thought to be prohibitively expensive (in resources) compared to 'dual-rail' logic where a qubit is stored by a photon across two modes. Here we attack this problem with real-time feedback control, which can realize a quantum-limited phase measurement on a single mode, as has been recently demonstrated experimentally. We show that with this added measurement resource, the resource requirements for single-rail LOQC are not substantially different from those of dual-rail LOQC. In particular, with adaptive phase measurements an arbitrary qubit state a alpha/0 > + beta/1 > can be prepared deterministically.

Analytical solutions of linear finite- and small-strain one-dimensional consolidation

Analytical solutions are presented for linear finite-strain one-dimensional consolidation of initially unconsolidated soil layers with surcharge loading for both one- and two-way drainage. These solutions complement earlier solutions for initially unconsolidated soil layers without surcharge and initially normally consolidated soil layers with surcharge. Small-strain solutions for the consolidation of initially unconsolidated soil layers with surcharge loading are also presented, and the relationship between the earlier solutions for initially unconsolidated soil without surcharge and the corresponding small-strain solutions, which was not addressed in the earlier work, is clarified. The new solutions for initially unconsolidated soil with surcharge loading can be applied to the analysis of low stress consolidation tests and to the partial validation of numerical solutions of non-linear finite-strain consolidation. They also clarify a formerly perplexing aspect of finite-strain solution charts first noted in numerical solutions. Copyright (C) 2004 John Wiley Sons, Ltd.

Bifurcations in the non-dissipative dynamics of ultra cold atoms

We present the first experimental observation of several bifurcations in a controllable non-linear Hamiltonian system. Dynamics of cold atoms are used to test predictions of non-linear, non-dissipative Hamiltonian dynamics.

A comparison of linear forecasting models and neural networks:an application to Euro inflation and Euro Divisia

Linear models reach their limitations in applications with nonlinearities in the data. In this paper new empirical evidence is provided on the relative Euro inflation forecasting performance of linear and non-linear models. The well established and widely used univariate ARIMA and multivariate VAR models are used as linear forecasting models whereas neural networks (NN) are used as non-linear forecasting models. It is endeavoured to keep the level of subjectivity in the NN building process to a minimum in an attempt to exploit the full potentials of the NN. It is also investigated whether the historically poor performance of the theoretically superior measure of the monetary services flow, Divisia, relative to the traditional Simple Sum measure could be attributed to a certain extent to the evaluation of these indices within a linear framework. Results obtained suggest that non-linear models provide better within-sample and out-of-sample forecasts and linear models are simply a subset of them. The Divisia index also outperforms the Simple Sum index when evaluated in a non-linear framework. © 2005 Taylor & Francis Group Ltd.

A performance assessment method for hospitals:the case of municipal hospitals in Angola

Over 60% of the recurrent budget of the Ministry of Health (MoH) in Angola is spent on the operations of the fixed health care facilities (health centres plus hospitals). However, to date, no study has been attempted to investigate how efficiently those resources are used to produce health services. Therefore the objectives of this study were to assess the technical efficiency of public municipal hospitals in Angola; assess changes in productivity over time with a view to analyzing changes in efficiency and technology; and demonstrate how the results can be used in the pursuit of the public health objective of promoting efficiency in the use of health resources. The analysis was based on a 3-year panel data from all the 28 public municipal hospitals in Angola. Data Envelopment Analysis (DEA), a non-parametric linear programming approach, was employed to assess the technical and scale efficiency and productivity change over time using Malmquist index.The results show that on average, productivity of municipal hospitals in Angola increased by 4.5% over the period 2000-2002; that growth was due to improvements in efficiency rather than innovation. © 2008 Springer Science+Business Media, LLC.

Technical efficiency:efficiency, change, technical progress and productivity growth in the national health systems of continental African countries

In May 2006, the Ministers of Health of all the countries on the African continent, at a special session of the African Union, undertook to institutionalise efficiency monitoring within their respective national health information management systems. The specific objectives of this study were: (i) to assess the technical efficiency of National Health Systems (NHSs) of African countries for measuring male and female life expectancies, and (ii) to assess changes in health productivity over time with a view to analysing changes in efficiency and changes in technology. The analysis was based on a five-year panel data (1999-2003) from all the 53 countries of continental Africa. Data Envelopment Analysis (DEA) - a non-parametric linear programming approach - was employed to assess the technical efficiency. Malmquist Total Factor Productivity (MTFP) was used to analyse efficiency and productivity change over time among the 53 countries' national health systems. The data consisted of two outputs (male and female life expectancies) and two inputs (per capital total health expenditure and adult literacy). The DEA revealed that 49 (92.5%) countries' NHSs were run inefficiently in 1999 and 2000; 50 (94.3%), 48 (90.6%) and 47 (88.7%) operated inefficiently in 2001, 2002, and 2003 respectively. All the 53 countries' national health systems registered improvements in total factor productivity attributable mainly to technical progress. Fifty-two countries did not experience any change in scale efficiency, while thirty (56.6%) countries' national health systems had a Pure Efficiency Change (PEFFCH) index of less than one, signifying that those countries' NHSs pure efficiency contributed negatively to productivity change. All the 53 countries' national health systems registered improvements in total factor productivity, attributable mainly to technical progress. Over half of the countries' national health systems had a pure efficiency index of less than one, signifying that those countries' NHSs pure efficiency contributed negatively to productivity change. African countries may need to critically evaluate the utility of institutionalising Malmquist TFP type of analyses to monitor changes in health systems economic efficiency and productivity over time. African national health systems, per capita total health expenditure, technical efficiency, scale efficiency, Malmquist indices of productivity change, DEA

A note on DEA models in technology selection:an improvement of Karsak and Ahiska's approach

This paper introduces a compact form for the maximum value of the non-Archimedean in Data Envelopment Analysis (DEA) models applied for the technology selection, without the need to solve a linear programming (LP). Using this method the computational performance the common weight multi-criteria decision-making (MCDM) DEA model proposed by Karsak and Ahiska (International Journal of Production Research, 2005, 43(8), 1537-1554) is improved. This improvement is significant when computational issues and complexity analysis are a concern.

Measurement efficiency and productivity in SAS/OR

This paper explores the use of the optimisation procedures in SAS/OR software with application to the measurement of efficiency and productivity of decision-making units (DMUs) using data envelopment analysis (DEA) techniques. DEA was originally introduced by Charnes et al. [J. Oper. Res. 2 (1978) 429] is a linear programming method for assessing the efficiency and productivity of DMUs. Over the last two decades, DEA has gained considerable attention as a managerial tool for measuring performance of organisations and it has widely been used for assessing the efficiency of public and private sectors such as banks, airlines, hospitals, universities and manufactures. As a result, new applications with more variables and more complicated models are being introduced. Further to successive development of DEA a non-parametric productivity measure, Malmquist index, has been introduced by Fare et al. [J. Prod. Anal. 3 (1992) 85]. Employing Malmquist index, productivity growth can be decomposed into technical change and efficiency change. On the other hand, the SAS is a powerful software and it is capable of running various optimisation problems such as linear programming with all types of constraints. To facilitate the use of DEA and Malmquist index by SAS users, a SAS/MALM code was implemented in the SAS programming language. The SAS macro developed in this paper selects the chosen variables from a SAS data file and constructs sets of linear-programming models based on the selected DEA. An example is given to illustrate how one could use the code to measure the efficiency and productivity of organisations.

Motion sharpening and contrast:Gain control precedes compressive non-linearity?

Blurred edges appear sharper in motion than when they are stationary. We (Vision Research 38 (1998) 2108) have previously shown how such distortions in perceived edge blur may be accounted for by a model which assumes that luminance contrast is encoded by a local contrast transducer whose response becomes progressively more compressive as speed increases. If the form of the transducer is fixed (independent of contrast) for a given speed, then a strong prediction of the model is that motion sharpening should increase with increasing contrast. We measured the sharpening of periodic patterns over a large range of contrasts, blur widths and speeds. The results indicate that whilst sharpening increases with speed it is practically invariant with contrast. The contrast invariance of motion sharpening is not explained by an early, static compressive non-linearity alone. However, several alternative explanations are also inconsistent with these results. We show that if a dynamic contrast gain control precedes the static non-linear transducer then motion sharpening, its speed dependence, and its invariance with contrast, can be predicted with reasonable accuracy. © 2003 Elsevier Science Ltd. All rights reserved.

A type system with usage aspects

Linear typing schemes can be used to guarantee non-interference and so the soundness of in-place update with respect to a functional semantics. But linear schemes are restrictive in practice, and more restrictive than necessary to guarantee soundness of in-place update. This limitation has prompted research into static analysis and more sophisticated typing disciplines to determine when in-place update may be safely used, or to combine linear and non-linear schemes. Here we contribute to this direction by defining a new typing scheme that better approximates the semantic property of soundness of in-place update for a functional semantics. We begin from the observation that some data are used only in a read-only context, after which it may be safely re-used before being destroyed. Formalising the in-place update interpretation in a machine model semantics allows us to refine this observation, motivating three usage aspects apparent from the semantics that are used to annotate function argument types. The aspects are (1) used destructively, (2), used read-only but shared with result, and (3) used read-only and not shared with the result. The main novelty is aspect (2), which allows a linear value to be safely read and even aliased with a result of a function without being consumed. This novelty makes our type system more expressive than previous systems for functional languages in the literature. The system remains simple and intuitive, but it enjoys a strong soundness property whose proof is non-trivial. Moreover, our analysis features principal types and feasible type reconstruction, as shown in M. Konen'y (In TYPES 2002 workshop, Nijmegen, Proceedings, Springer-Verlag, 2003).

A study of magnetic non-linearity and finite length effects in solid iron subjected to a travelling MMF wave

This thesis describes an experimental and analytic study of the effects of magnetic non-linearity and finite length on the loss and field distribution in solid iron due to a travelling mmf wave. In the first half of the thesis, a two-dimensional solution is developed which accounts for the effects of both magnetic non-linearity and eddy-current reaction; this solution is extended, in the second half, to a three-dimensional model. In the two-dimensional solution, new equations for loss and flux/pole are given; these equations contain the primary excitation, the machine parameters and factors describing the shape of the normal B-H curve. The solution applies to machines of any air-gap length. The conditions for maximum loss are defined, and generalised torque/frequency curves are obtained. A relationship between the peripheral component of magnetic field on the surface of the iron and the primary excitation is given. The effects of magnetic non-linearity and finite length are combined analytically by introducing an equivalent constant permeability into a linear three-dimensional analysis. The equivalent constant permeability is defined from the non-linear solution for the two-dimensional magnetic field at the axial centre of the machine to avoid iterative solutions. In the linear three-dimensional analysis, the primary excitation in the passive end-regions of the machine is set equal to zero and the secondary end faces are developed onto the air-gap surface. The analyses, and the assumptions on which they are based, were verified on an experimental machine which consists of a three-phase rotor and alternative solid iron stators, one with copper end rings, and one without copper end rings j the main dimensions of the two stators are identical. Measurements of torque, flux /pole, surface current density and radial power flow were obtained for both stators over a range of frequencies and excitations. Comparison of the measurements on the two stators enabled the individual effects of finite length and saturation to be identified, and the definition of constant equivalent permeability to be verified. The penetration of the peripheral flux into the stator with copper end rings was measured and compared with theoretical penetration curves. Agreement between measured and theoretical results was generally good.

The spatial patterns of beta-amyloid (Abeta) deposits in elderly non-demented patients and patients with Alzheimer’s disease

The spatial patterns of diffuse, primitive, classic and compact beta-amyloid (Abeta) deposits were studied in the medial temporal lobe in 14 elderly, non-demented patients (ND) and in nine patients with Alzheimer’s disease (AD). In both patient groups, Abeta deposits were clustered and in a number of tissues, a regular periodicity of Abeta deposit clusters was observed parallel to the tissue boundary. The primitive deposit clusters were significantly larger in the AD cases but there were no differences in the sizes of the diffuse and classic deposit clusters between patient groups. In AD, the relationship between Abeta deposit cluster size and density in the tissue was non-linear. This suggested that cluster size increased with increasing Abeta deposit density in some tissues while in others, Abeta deposit density was high but contained within smaller clusters. It was concluded that the formation of large clusters of primitive deposits could be a factor in the development of AD.