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Mathematical Tools (mathematical + tool)
Selected AbstractsPotentialities of quantile regression to predict ozone concentrationsENVIRONMETRICS, Issue 2 2009S. I. V. Sousa Abstract This paper aims: (i) to analyse the influence of ozone precursors (both meteorological variables and pollutant concentrations) on ozone concentrations at different ozone levels; and (ii) to predict next day hourly ozone concentrations using a new approach based on quantile regression (QR). The performance of this model was compared with multiple linear regressions (MLR) for the three following periods: daylight, night time and all day. QR as proven to be an useful mathematical tool to evidence the heterogeneity of ozone predictor influences at different ozone levels. Such heterogeneity is generally hidden when an ordinary least square regression model is applied. The influence of previous concentrations of ozone and nitrogen monoxide on next day ozone concentrations was higher for lower quantiles. When QR was applied, the wind direction (WD) was found to be significant in the medium quantiles and the relative humidity (RH) in the higher quantiles. On the contrary, using the MLR models, both variables were not statistically significant. Moreover, QR allowed more efficient previsions of extreme values which are very useful once the forecasting of higher concentrations is fundamental to develop strategies for protecting the public health. Copyright © 2008 John Wiley & Sons, Ltd. [source] A spatial queuing approach to optimize coordinated signal settings to obviate gridlock in adjacent work zonesJOURNAL OF ADVANCED TRANSPORTATION, Issue 4 2010C.K. Wong Abstract Gridlock is defined when traffic comes to a complete halt inducing huge delays. If a work zone on a two-lane two-way highway is set up, in which one of the traffic lanes is closed for maintenance road works, the remaining lane has to be controlled to serve the two-way traffic alternatively. The study objective is to optimize the traffic signal controls across two closely spaced work zones to prevent a gridlock, which can occur easily if upstream and downstream signals are not well coordinated. When vehicle queues build up in the middle sections between two work zones and further expand to occupy the single available lanes in both directions, the two-way traffic is then blocked and no vehicle can leave from the queues generating a gridlock. To address this problem, spatial queues are important parameters that must be explicitly analyzed. The cell transmission model, which is known to be a robust mathematical tool for the modeling of queue dynamics, is adopted in this study. A signal cell is used to represent each traffic signal control, the exit flow capacity of which is defined in accordance with the signal plan. A set of linear constraints is established to relate all of the model parameters and variables. The objective function is taken as the total number of vehicles in the critical section between the two work zones. The minimization of this objective function can effectively obviate the occurrence of a gridlock. The optimization problem is formulated as a Binary-Mixed-Integer-Linear-Program that can be solved by the standard branch-and-bound technique. Numerical examples are given to demonstrate the effectiveness of the proposed methodology. Copyright © 2010 John Wiley & Sons, Ltd. [source] Adaptive dynamics as a mathematical tool for studying the ecology of speciation processesJOURNAL OF EVOLUTIONARY BIOLOGY, Issue 5 2005M. DOEBELI First page of article [source] Scaling and correlation analysis of galactic imagesMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 4 2001P. Frick Different scaling and autocorrelation characteristics and their application to astronomical images are discussed: the structure function, the autocorrelation function, Fourier spectra and wavelet spectra. The choice of the mathematical tool is of great importance for the scaling analysis of images. The structure function, for example, cannot resolve scales that are close to the dominating large-scale structures, and can lead to the wrong interpretation that a continuous range of scales with a power law exists. The traditional Fourier technique, applied to real data, gives very spiky spectra, in which the separation of real maxima and high harmonics can be difficult. We recommend as the optimal tool the wavelet spectrum with a suitable choice of the analysing wavelet. We introduce the wavelet cross-correlation function, which enables us to study the correlation between images as a function of scale. The cross-correlation coefficient strongly depends on the scale. The classical cross-correlation coefficient can be misleading if a bright, extended central region or an extended disc exists in the galactic images. An analysis of the scaling and cross-correlation characteristics of nine optical and radio maps of the nearby spiral galaxy NGC 6946 is presented. The wavelet spectra allow us to separate structures on different scales like spiral arms and diffuse extended emission. Only the images of thermal radio emission and H, emission give indications of three-dimensional Kolmogorov-type turbulence on the smallest resolved scales . The cross-correlations between the images of NGC 6946 show strong similarities between the images of total radio emission, red light and mid-infrared dust emission on all scales. The best correlation is found between total radio emission and dust emission. Thermal radio continuum and H, emission are best correlated on a scale of about , the typical width of a spiral arm. On a similar scale, the images of polarized radio and H, emission are anticorrelated, a fact that remains undetected with classical cross-correlation analysis. [source] Introductory quantum physics courses using a LabVIEW multimedia moduleCOMPUTER APPLICATIONS IN ENGINEERING EDUCATION, Issue 2 2007Ismael Orquín Abstract We present the development of a LabVIEW multimedia module for introductory Quantum Physics courses and our experience in the use of this application as an educational tool in learning methodologies. The program solves the time-dependent Schrödinger equation (TDSE) for arbitrary potentials. We describe the numerical method used for solving this equation, as well as some mathematical tools employed to reduce the calculation time and to obtain more accurate results. As an illustration, we present the evolution of a wave packet for three different potentials: the repulsive barrier potential, the repulsive step potential, and the harmonic oscillator. This application has been successfully integrated in the learning strategies of the course Quantum Physics for Engineering at the Polytechnic University of Valencia, Spain. © 2007 Wiley Periodicals, Inc. Comput Appl Eng Educ. 15: 124,133, 2007; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/cae.20100 [source] Semi-analytic Approaches to Collateralized Debt Obligation ModellingECONOMIC NOTES, Issue 2 2004Christian Bluhm Collateralized debt obligations (CDOs) constitute an important class of asset-backed securities. Most major banks use CDOs as portfolio management tools for achieving regulatory capital relief, economic risk transfer and funding. On the other side, banks and other financial institutions invest in CDO tranches with a risk/return profile matching their risk appetite and investment policies. For both sides (risk selling and risk buying) of a CDO transaction, sound mathematical tools are required for an evaluation of the deal. In this paper, we investigate some techniques for CDO modelling, paying special attention to approaches based on semi-analytic approximations. [source] Meta-analysis of functional imaging data using replicator dynamicsHUMAN BRAIN MAPPING, Issue 1 2005Jane Neumann Abstract Despite the rapidly growing number of meta-analyses in functional neuroimaging, the field lacks formal mathematical tools for the quantitative and qualitative evaluation of meta-analytic data. We propose to use replicator dynamics in the meta-analysis of functional imaging data to address an important aspect of neuroimaging research, the search for functional networks of cortical areas that underlie a specific cognitive task. The replicator process requires as input only a list of activation locations, and it results in a network of locations that jointly show significant activation in most studies included in the meta-analysis. These locations are likely to play a critical role in solving the investigated cognitive task. Our method was applied to a meta-analysis of the Stroop interference task using data provided by the publicly accessible database BrainMap DBJ. Hum Brain Mapp 25:165,173, 2005. © 2005 Wiley-Liss, Inc. [source] Solution of axisymmetric Maxwell equationsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 10 2003Franck Assous Abstract In this article, we study the static and time-dependent Maxwell equations in axisymmetric geometry. Using the mathematical tools introduced in (Math. Meth. Appl. Sci. 2002; 25: 49), we investigate the decoupled problems induced in a meridian half-plane, and the splitting of the solution in a regular part and a singular part, the former being in the Sobolev space H1 component-wise. It is proven that the singular parts are related to singularities of Laplace-like or wave-like operators. We infer from these characterizations: (i) the finite dimension of the space of singular fields; (ii) global space and space,time regularity results for the electromagnetic field. This paper is the continuation of (Modél. Math. Anal. Numér. 1998; 32: 359, Math. Meth. Appl. Sci. 2002; 25: 49). Copyright © 2003 John Wiley & Sons, Ltd. [source] Theoretical tools to solve the axisymmetric Maxwell equationsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 1 2002F. Assous Abstract In this paper, the mathematical tools, which are required to solve the axisymmetric Maxwell equations, are presented. An in-depth study of the problems posed in the meridian half-plane, numerical algorithms, as well as numerical experiments, based on the implementation of the theory described hereafter, shall be presented in forthcoming papers. In the present paper, the attention is focused on the (orthogonal) splitting of the electromagnetic field in a regular part and a singular part, the former being in the Sobolev space H1 component-wise. It is proven that the singular fields are related to singularities of Laplace-like operators, and, as a consequence, that the space of singular fields is finite dimensional. This paper can be viewed as the continuation of References (J. Comput. Phys. 2000; 161: 218,249, Modél. Math. Anal. Numér, 1998; 32: 359,389) Copyright © 2002 John Wiley & Sons, Ltd. [source] A general approach for determining the diffraction contrast factor of straight-line dislocationsACTA CRYSTALLOGRAPHICA SECTION A, Issue 2 2009Jorge Martinez-Garcia Dislocations alter perfect crystalline order and produce anisotropic broadening of the X-ray diffraction profiles, which is described by the dislocation contrast factor. Owing to the lack of suitable mathematical tools to deal with dislocations in crystals of any symmetry, contrast factors are so far only known for a few slip systems in high-symmetry phases and little detail is given in the literature on the calculation procedure. In the present paper a general approach is presented for the calculation of contrast factors for any dislocation configuration and any lattice symmetry. The new procedure is illustrated with practical examples of hexagonal metals and some low-symmetry mineral phases. [source] Applications of Markov Chains in Particulate Process Engineering: A ReviewTHE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 6 2004Henri Berthiaux Abstract Processes involving particles, are known to exhibit extremely unpredictable behaviour, mainly due to the mesoscopic nature of granular media. Understanding particulate processes, not only for intellectual satisfaction, but also for process design and operation, basically requires a systems approach in modelling. Because they combine simplicity and flexibility, the stochastic models based on the Markov chain theory are very valuable mathematical tools to this respect. However, they are still largely ignored by the whole core of chemical engineering researchers. This motivates the existence of this review paper, in which we examine the three traditional issues: mixing and transport, separation and transformation. Les procédés faisant intervenir des particules sont connus pour avoir un comportement extrêmement non prévisible, principalement à cause de la nature mésoscopique des milieux granulaires. Comprendre les procédés particulaires, non seulement pour la satisfaction intellectuelle, mais aussi pour la conception et le fonctionnement des procédés, nécessite en fait une approche des systèmes dans la modélisation. Parce qu'ils allient simplicité et flexibilité, les modèles stochastiques basés sur la théorie des chaînes de Markov sont des outils mathématiques à cet égard très valables. Cependant, ceux-ci sont encore largement ignorés par une majorité de chercheurs en génie chimique. Cette lacune motive le présent article, dans lequel nous examinons les trois thèmes traditionnels : mélange et transport, séparation, transformation. [source] Mechanics with variable-order differential operatorsANNALEN DER PHYSIK, Issue 11-12 2003C.F.M. Coimbra Abstract This work presents the novel concept of Variable-Order (VO) Calculus through the description of a simple problem in Mechanics. A mathematical definition for the VO-differential operator that is suitable to mechanical modelling is proposed, and an example concerning the effect of nonuniform viscoelastic frictional forces is described. A numerical method for the solution of Variable Order Differential Equations (VODEs) is proposed. The physical model under study requires mathematical tools that lie beyond the traditional methods of Constant-Order (CO) differential equations. The VO-Calculus formulation is compared to a CO-Calculus model in order to show the limitations of the latter in resolving the transition between the relevant dynamic regimes. [source] BML revisited: Statistical physics, computer simulation, and probability,COMPLEXITY, Issue 2 2006Raissa M. D'Souza Abstract Statistical physics, computer simulation, and discrete mathematics are intimately related through the study of shared lattice models. These models lie at the foundation of all three fields, are studied extensively, and can be highly influential. Yet new computational and mathematical tools may challenge even well-established beliefs. Consider the BML model, which is a paradigm for modeling self-organized patterns of traffic flow and first-order jamming transitions. Recent findings, on the existence of intermediate states, bring into question the standard understanding of the jamming transition. We review the results and show that the onset of full-jamming can be considerably delayed based on the geometry of the system. We also introduce an asynchronous version of BML, which lacks the self-organizing properties of BML, has none of the puzzling intermediate states, but has a sharp, discontinuous, transition to full jamming. We believe this asynchronous version will be more amenable to rigorous mathematical analysis than standard BML. We discuss additional models, such as bootstrap percolation, the honey-comb dimer model and the rotor-router, all of which exemplify the interplay between the three fields, while also providing cautionary tales. Finally, we synthesize implications for how results from one field may relate to the other, and also implications specific to computer implementations. © 2006 Wiley Periodicals, Inc. Complexity, 12, 30,39, 2006 [source] | ||||||||||||||||||||||