Search results for "Polygon"

Modelling uncertainties in phase-space boundary integral models of ray propagation

2020

Abstract A recently proposed phase-space boundary integral model for the stochastic propagation of ray densities is presented and, for the first time, explicit connections between this model and parametric uncertainties arising in the underlying physical model are derived. In particular, an asymptotic analysis for a weak noise perturbation of the propagation speed is used to derive expressions for the probability distribution of the phase-space boundary coordinates after transport along uncertain, and in general curved, ray trajectories. Furthermore, models are presented for incorporating geometric uncertainties in terms of both the location of an edge within a polygonal domain, as well as …

Relaxation of periodic and nonstandard growth integrals by means of two-scale convergence

2019

An integral representation result is obtained for the variational limit of the family functionals $\int_{\Omega}f\left(\frac{x}{\varepsilon}, Du\right)dx$, as $\varepsilon \to 0$, when the integrand $f = f (x,v)$ is a Carath\'eodory function, periodic in $x$, convex in $v$ and with nonstandard growth.

On the convexity of Relativistic Hydrodynamics

2013

The relativistic hydrodynamic system of equations for a perfect fluid obeying a causal equation of state is hyperbolic (Anile 1989 {\it Relativistic Fluids and Magneto-Fluids} (Cambridge: Cambridge University Press)). In this report, we derive the conditions for this system to be convex in terms of the fundamental derivative of the equation of state (Menikoff and Plohr 1989 {\it Rev. Mod. Phys.} {\bf 61} 75). The classical limit is recovered.

A Fast and Very Accurate Approach to the Computation of Microlensing Magnification Patterns Based on Inverse Polygon Mapping

2006

A new method of calculating microlensing magnification patterns is proposed that is based on the properties of the backward gravitational lens mapping of a lattice of polygonal cells defined at the image plane. To a first-order approximation, the local linearity of the transformation allows us to compute the contribution of each image-plane cell to the magnification by apportioning the area of the inverse image of the cell (transformed cell) among the source-plane pixels covered by it. Numerical studies in the κ = 0.1-0.8 range of mass surface densities demonstrate that this method (provided with an exact algorithm for distributing the area of the transformed cells among the source-plane pi…

BUILDING AN ENTANGLEMENT MEASURE ON PHYSICAL GROUND

2008

We introduce on physical grounds a new measure of multipartite entanglement for pure states. The function we define is discriminant and monotone under LOCC and moreover can be expressed in terms of observables of the system.

Geometric efficiency for a parallel-surface source and detector system with at least one axisymmetric surface

2007

Abstract An exact and numerically friendly method is given to calculate the geometric efficiency G of a planar radiation source and cosine detector system. Either the source or the detector, but not necessarily both, must have axial symmetry. For two non-coaxial disks the results are in exact agreement with a recent generalization of Ruby's formula for G. Detailed formulas and sample numerical results are given for a disk combined with rectangles and triangles. A disk and a general polygon can be solved by dividing the polygon into triangles. The method can also be applied to electrical inductance calculations and a solution recently given for the inductance of circular and elliptic loops c…

2004

Analysis of extracts from two woad species (Isatis tinctoria and Isatis indigotica) and Polygonum tinctorium revealed that only one indigo precursor (indican) was present in Polygonum, but two precursors were found in Isatis spp. This was done using high performance liquid chromatography (HPLC), coupled to an evaporative light scattering detector (ELSD). In Isatis spp., the indigo precursors indican and a fraction representing isatan B were identified. The proportion of indican and isatan B was different between the two Isatis spp. tested. For the first time, it was possible to quantify the precursors in woad plant species, and the results were found to be in good agreement with those made …

Matroid optimization problems with monotone monomials in the objective

2022

Abstract In this paper we investigate non-linear matroid optimization problems with polynomial objective functions where the monomials satisfy certain monotonicity properties. Indeed, we study problems where the set of non-linear monomials consists of all non-linear monomials that can be built from a given subset of the variables. Linearizing all non-linear monomials we study the respective polytope. We present a complete description of this polytope. Apart from linearization constraints one needs appropriately strengthened rank inequalities. The separation problem for these inequalities reduces to a submodular function minimization problem. These polyhedral results give rise to a new hiera…

Distributed learning automata-based scheme for classification using novel pursuit scheme

2020

Learning Automata (LA) is a popular decision making mechanism to “determine the optimal action out of a set of allowable actions” (Agache and Oommen, IEEE Trans Syst Man Cybern-Part B Cybern 2002(6): 738–749, 2002). The distinguishing characteristic of automata-based learning is that the search for the optimising parameter vector is conducted in the space of probability distributions defined over the parameter space, rather than in the parameter space itself (Thathachar and Sastry, IEEE Trans Syst Man Cybern-Part B Cybern 32(6): 711–722, 2002). Recently, Goodwin and Yazidi pioneered the use of Ant Colony Optimisation (ACO) for solving classification problems (Goodwin and Yazidi 2016). In th…

Exact Voronoi diagram of smooth convex pseudo-circles: General predicates, and implementation for ellipses

2013

International audience; We examine the problem of computing exactly the Voronoi diagram (via the dual Delaunay graph) of a set of, possibly intersecting, smooth convex \pc in the Euclidean plane, given in parametric form. Pseudo-circles are (convex) sites, every pair of which has at most two intersecting points. The Voronoi diagram is constructed incrementally. Our first contribution is to propose robust and efficient algorithms, under the exact computation paradigm, for all required predicates, thus generalizing earlier algorithms for non-intersecting ellipses. Second, we focus on \kcn, which is the hardest predicate, and express it by a simple sparse $5\times 5$ polynomial system, which a…