Search results for "Applied Mathematics"
showing 10 items of 4379 documents
A third order partial differential equation for isotropic boundary based triangular Bézier surface generation
2011
Abstract We approach surface design by solving a linear third order Partial Differential Equation (PDE). We present an explicit polynomial solution method for triangular Bezier PDE surface generation characterized by a boundary configuration. The third order PDE comes from a symmetric operator defined here to overcome the anisotropy drawback of any operator over triangular Bezier surfaces.
Human T cells in silico: Modelling their electrophysiological behaviour in health and disease
2016
Although various types of ion channels are known to have an impact on human T cell effector functions, their exact mechanisms of influence are still poorly understood. The patch clamp technique is a well-established method for the investigation of ion channels in neurons and T cells. However, small cell sizes and limited selectivity of pharmacological blockers restrict the value of this experimental approach. Building a realistic T cell computer model therefore can help to overcome these kinds of limitations as well as reduce the overall experimental effort. The computer model introduced here was fed off ion channel parameters from literature and new experimental data. It is capable of simu…
Revisiting Bicausative Matrices: The Swiss Cheese of Chaos
2009
This paper returns to de Mesnard's paper of 2000, which has exposed the so-called method of bicausative matrices. This method was created to analyze the structural change between two matrices, as an improvement of the causative method of Jackson and al. (1990). In its 2000 paper, de Mesnard has shown that chaos affects the bicausative method: two solutions are found with a brutal switching between both. This new paper demonstrates that the chaos can be largely circumvented, is essentially localized in a small interval and is only a transitory effect between two non-chaotic "regimes", is not always observed, is limited to relatively small matrices.
FILTERING CHAOS: A TECHNIQUE TO ESTIMATE DYNAMICAL AND OBSERVATIONAL NOISE IN NONLINEAR SYSTEMS
2005
Nonlinear dynamical models are frequently used to approximate and predict observed physical, biological and economic systems. Such models will be subject to errors both in the model dynamics, and the observations of the underlying system. In order to improve models, it is necessary to understand the causes of error growth. A complication with chaotic models is that small errors may be amplified by the model dynamics. This paper proposes a technique for estimating levels of both dynamical and observational noise, based on the model drift. The method is demonstrated for a number of models, for cases with both stochastic and nonstochastic dynamical errors. The effect of smoothing or treating …
Attitude measurement by artificial vision
2005
The recent development of light and low-cost airborne platforms (microlight, drones, kites, balloons,...) has led to the need for simple and low-cost devices allowing attitude measurement with respect to a reference horizon of the platform itself or of an embedded setting. A theoretical study of the conditions for measuring attitude angles from artificial vision is proposed and an original practical algorithm allowing these measurements to be performed in real time is described. An implementation in a CMOS retina circuit is also presented. These points are illustrated by experiments confirming the feasibility of the device.
Noise-induced behavioral change driven by transient chaos
2022
We study behavioral change in the context of a stochastic, non-linear consumption model with preference adjusting, interdependent agents. Changes in long-run consumption behavior are modelled as noise induced transitions between coexisting attractors. A particular case of multistability is considered: two fixed points, whose immediate basins have smooth boundaries, coexist with a periodic attractor, with a fractal immediate basin boundary. If a trajectory leaves an immediate basin, it enters a set of complexly intertwined basins for which final state uncertainty prevails. The standard approach to predicting transition events rooted in the stochastic sensitivity function technique due to Mil…
Channel Assembling with Priority-Based Queues in Cognitive Radio Networks: Strategies and Performance Evaluation
2014
[EN] With the implementation of channel assembling (CA) techniques, higher data rate can be achieved for secondary users in multi-channel cognitive radio networks. Recent studies which are based on loss systems show that maximal capacity can be achieved using dynamic CA strategies. However the channel allocation schemes suffer from high blocking and forced termination when primary users become active. In this paper, we propose to introduce queues for secondary users so that those flows that would otherwise be blocked or forcibly terminated could be buffered and possibly served later. More specifically, in a multi-channel network with heterogeneous traffic, two queues are separately allocate…
Multivariate quality control studies applied to Ca(II) and Mg(II) determination by a portable method
1998
Made available in DSpace on 2022-04-28T19:53:14Z (GMT). No. of bitstreams: 0 Previous issue date: 1998-01-01 A portable or field test method for simultaneous spectrophotometric determination of calcium and magnesium in water using multivariate partial least squares (PLS) calibration methods is proposed. The method is based on the reaction between the analytes and methylthymol blue at pH 11. The spectral information was used as the X-block and the Ca(II) and Mg(II) concentrations obtained by a reference technique (ICP-AES) were used as the Y-block. Two series of analyses were performed, with a month's difference between them. The first series was used as the calibration set and the second on…
Exponential instability in the fractional Calder\'on problem
2017
In this note we prove the exponential instability of the fractional Calder\'on problem and thus prove the optimality of the logarithmic stability estimate from \cite{RS17}. In order to infer this result, we follow the strategy introduced by Mandache in \cite{M01} for the standard Calder\'on problem. Here we exploit a close relation between the fractional Calder\'on problem and the classical Poisson operator. Moreover, using the construction of a suitable orthonormal basis, we also prove (almost) optimality of the Runge approximation result for the fractional Laplacian, which was derived in \cite{RS17}. Finally, in one dimension, we show a close relation between the fractional Calder\'on pro…
Uniqueness and reconstruction for the fractional Calder\'on problem with a single measurement
2020
We show global uniqueness in the fractional Calder\'on problem with a single measurement and with data on arbitrary, possibly disjoint subsets of the exterior. The previous work \cite{GhoshSaloUhlmann} considered the case of infinitely many measurements. The method is again based on the strong uniqueness properties for the fractional equation, this time combined with a unique continuation principle from sets of measure zero. We also give a constructive procedure for determining an unknown potential from a single exterior measurement, based on constructive versions of the unique continuation result that involve different regularization schemes.