Effect of basis set superposition error on the electron density of molecular complexes

The effect of basis set superposition error (BSSE) on molecular complexes is analyzed. The BSSE causes artificial delocalizations which modify the first order electron density. The mechanism of this effect is assessed for the hydrogen fluoride dimer with several basis sets. The BSSE-corrected first-order electron density is obtained using the chemical Hamiltonian approach versions of the Roothaan and Kohn-Sham equations. The corrected densities are compared to uncorrected densities based on the charge density critical points. Contour difference maps between BSSE-corrected and uncorrected densities on the molecular plane are also plotted to gain insight into the effects of BSSE correction on the electron density

High-SNR power offset in multiantenna communication

The analysis of the multiantenna capacity in the high-SNR regime has hitherto focused on the high-SNR slope (or maximum multiplexing gain), which quantifies the multiplicative increase as function of the number of antennas. This traditional characterization is unable to assess the impact of prominent channel features since, for a majority of channels, the slope equals the minimum of the number of transmit and receive antennas. Furthermore, a characterization based solely on the slope captures only the scaling but it has no notion of the power required for a certain capacity. This paper advocates a more refined characterization whereby, as function of SNRjdB, the high-SNR capacity is expanded as an affine function where the impact of channel features such as antenna correlation, unfaded components, etc, resides in the zero-order term or power offset. The power offset, for which we find insightful closed-form expressions, is shown to play a chief role for SNR levels of practical interest.

Automatic low baseline stereo in urban areas

In this work we propose a new automatic methodology for computing accurate digital elevation models (DEMs) in urban environments from low baseline stereo pairs that shall be available in the future from a new kind of earth observation satellite. This setting makes both views of the scene similarly, thus avoiding occlusions and illumination changes, which are the main disadvantages of the commonly accepted large-baseline configuration. There still remain two crucial technological challenges: (i) precisely estimating DEMs with strong discontinuities and (ii) providing a statistically proven result, automatically. The first one is solved here by a piecewise affine representation that is well adapted to man-made landscapes, whereas the application of computational Gestalt theory introduces reliability and automation. In fact this theory allows us to reduce the number of parameters to be adjusted, and tocontrol the number of false detections. This leads to the selection of a suitable segmentation into affine regions (whenever possible) by a novel and completely automatic perceptual grouping method. It also allows us to discriminate e.g. vegetation-dominated regions, where such an affine model does not apply anda more classical correlation technique should be preferred. In addition we propose here an extension of the classical ”quantized” Gestalt theory to continuous measurements, thus combining its reliability with the precision of variational robust estimation and fine interpolation methods that are necessary in the low baseline case. Such an extension is very general and will be useful for many other applications as well.

Speculation, risk premia and expectations in the yield curve

An affine asset pricing model in which traders have rational but heterogeneous expectations aboutfuture asset prices is developed. We use the framework to analyze the term structure of interestrates and to perform a novel three-way decomposition of bond yields into (i) average expectationsabout short rates (ii) common risk premia and (iii) a speculative component due to heterogeneousexpectations about the resale value of a bond. The speculative term is orthogonal to public informationin real time and therefore statistically distinct from common risk premia. Empirically wefind that the speculative component is quantitatively important accounting for up to a percentagepoint of yields, even in the low yield environment of the last decade. Furthermore, allowing for aspeculative component in bond yields results in estimates of historical risk premia that are morevolatile than suggested by standard Affine Gaussian term structure models which our frameworknests.

A new compact linear programming formulation for choice network revenue management

The choice network revenue management model incorporates customer purchase behavioras a function of the offered products, and is the appropriate model for airline and hotel networkrevenue management, dynamic sales of bundles, and dynamic assortment optimization.The optimization problem is a stochastic dynamic program and is intractable. A certainty-equivalencerelaxation of the dynamic program, called the choice deterministic linear program(CDLP) is usually used to generate dyamic controls. Recently, a compact linear programmingformulation of this linear program was given for the multi-segment multinomial-logit (MNL)model of customer choice with non-overlapping consideration sets. Our objective is to obtaina tighter bound than this formulation while retaining the appealing properties of a compactlinear programming representation. To this end, it is natural to consider the affine relaxationof the dynamic program. We first show that the affine relaxation is NP-complete even for asingle-segment MNL model. Nevertheless, by analyzing the affine relaxation we derive a newcompact linear program that approximates the dynamic programming value function betterthan CDLP, provably between the CDLP value and the affine relaxation, and often comingclose to the latter in our numerical experiments. When the segment consideration sets overlap,we show that some strong equalities called product cuts developed for the CDLP remain validfor our new formulation. Finally we perform extensive numerical comparisons on the variousbounds to evaluate their performance.

Driver scheduling problem modelling

The Drivers Scheduling Problem (DSP) consists of selecting a set of duties for vehicle drivers, for example buses, trains, plane or boat drivers or pilots, for the transportation of passengers or goods. This is a complex problem because it involves several constraints related to labour and company rules and can also present different evaluation criteria and objectives. Being able to develop an adequate model for this problem that can represent the real problem as close as possible is an important research area.The main objective of this research work is to present new mathematical models to the DSP problem that represent all the complexity of the drivers scheduling problem, and also demonstrate that the solutions of these models can be easily implemented in real situations. This issue has been recognized by several authors and as important problem in Public Transportation. The most well-known and general formulation for the DSP is a Set Partition/Set Covering Model (SPP/SCP). However, to a large extend these models simplify some of the specific business aspects and issues of real problems. This makes it difficult to use these models as automatic planning systems because the schedules obtained must be modified manually to be implemented in real situations. Based on extensive passenger transportation experience in bus companies in Portugal, we propose new alternative models to formulate the DSP problem. These models are also based on Set Partitioning/Covering Models; however, they take into account the bus operator issues and the perspective opinions and environment of the user.We follow the steps of the Operations Research Methodology which consist of: Identify the Problem; Understand the System; Formulate a Mathematical Model; Verify the Model; Select the Best Alternative; Present the Results of theAnalysis and Implement and Evaluate. All the processes are done with close participation and involvement of the final users from different transportation companies. The planner s opinion and main criticisms are used to improve the proposed model in a continuous enrichment process. The final objective is to have a model that can be incorporated into an information system to be used as an automatic tool to produce driver schedules. Therefore, the criteria for evaluating the models is the capacity to generate real and useful schedules that can be implemented without many manual adjustments or modifications. We have considered the following as measures of the quality of the model: simplicity, solution quality and applicability. We tested the alternative models with a set of real data obtained from several different transportation companies and analyzed the optimal schedules obtained with respect to the applicability of the solution to the real situation. To do this, the schedules were analyzed by the planners to determine their quality and applicability. The main result of this work is the proposition of new mathematical models for the DSP that better represent the realities of the passenger transportation operators and lead to better schedules that can be implemented directly in real situations.

Generic finiteness of equilibrium payoffs for bimatrix games

It is shown that in any affine space of payoff matrices the equilibriumpayoffs of bimatrix games are generically finite.

On bounds for network revenue management

The Network Revenue Management problem can be formulated as a stochastic dynamic programming problem (DP or the\optimal" solution V *) whose exact solution is computationally intractable. Consequently, a number of heuristics have been proposed in the literature, the most popular of which are the deterministic linear programming (DLP) model, and a simulation based method, the randomized linear programming (RLP) model. Both methods give upper bounds on the optimal solution value (DLP and PHLP respectively). These bounds are used to provide control values that can be used in practice to make accept/deny decisions for booking requests. Recently Adelman [1] and Topaloglu [18] have proposed alternate upper bounds, the affine relaxation (AR) bound and the Lagrangian relaxation (LR) bound respectively, and showed that their bounds are tighter than the DLP bound. Tight bounds are of great interest as it appears from empirical studies and practical experience that models that give tighter bounds also lead to better controls (better in the sense that they lead to more revenue). In this paper we give tightened versions of three bounds, calling themsAR (strong Affine Relaxation), sLR (strong Lagrangian Relaxation) and sPHLP (strong Perfect Hindsight LP), and show relations between them. Speciffically, we show that the sPHLP bound is tighter than sLR bound and sAR bound is tighter than the LR bound. The techniques for deriving the sLR and sPHLP bounds can potentially be applied to other instances of weakly-coupled dynamic programming.