Search results for " Operator"
showing 10 items of 931 documents
Developing Domain-Knowledge Evolutionary Algorithms for Network-on-Chip Application Mapping
2013
This paper addresses the Network-on-Chip (NoC) application mapping problem. This is an NP-hard problem that deals with the optimal topological placement of Intellectual Property cores onto the NoC tiles. Network-on-Chip application mapping Evolutionary Algorithms are developed, evaluated and optimized for minimizing the NoC communication energy. Two crossover and one mutation operators are proposed. It is analyzed how each optimization algorithm performs with every genetic operator, in terms of solution quality and convergence speed. Our proposed operators are compared with state-of-the-art genetic operators for permutation problems. Finally, the problem is approached in a multi-objective w…
Edge Orientation and the Design of Problem-Specific Crossover Operators for the OCST Problem
2012
In the Euclidean optimal communication spanning tree problem, the edges in optimal trees not only have small weights but also point with high probability toward the center of the graph. These characteristics of optimal solutions can be used for the design of problem-specific evolutionary algorithms (EAs). Recombination operators of direct encodings like edge-set and NetDir can be extended such that they prefer not only edges with small distance weights but also edges that point toward the center of the graph. Experimental results show higher performance and robustness in comparison to EAs using existing crossover strategies.
Apparel sizing using trimmed PAM and OWA operators
2012
This paper is concerned with apparel sizing system design. One of the most important issues in the apparel development process is to define a sizing system that provides a good fit to the majority of the population. A sizing system classifies a specific population into homogeneous subgroups based on some key body dimensions. Standard sizing systems range linearly from very small to very large. However, anthropometric measures do not grow linearly with size, so they can not accommodate all body types. It is important to determine each class in the sizing system based on a real prototype that is as representative as possible of each class. In this paper we propose a methodology to develop an …
Atmospheric Turbulence Effects Removal on Infrared Sequences Degraded by Local Isoplanatism
2007
When observing an object horizontally at a long distance, degradations due to atmospheric turbulence often occur. Different methods have already been tested to get rid of this kind of degradation, especially on infrared sequences. It has been shown that the Wiener filter applied locally on each frame of a sequence allows to obtain good results in terms of edges, while the regularization by the Laplacian operator applied in the same way provides good results in terms of noise removal in uniform areas. In this article, we present hybrid methods which take advantages of both Wiener filter and Laplacian regularization.
Higher integrability and stability of (p,q)-quasiminimizers
2023
Using purely variational methods, we prove local and global higher integrability results for upper gradients of quasiminimizers of a $(p,q)$-Dirichlet integral with fixed boundary data, assuming it belongs to a slightly better Newtonian space. We also obtain a stability property with respect to the varying exponents $p$ and $q$. The setting is a doubling metric measure space supporting a Poincar\'e inequality.
X-ray Tomography of One-forms with Partial Data
2021
If the integrals of a one-form over all lines meeting a small open set vanish and the form is closed in this set, then the one-form is exact in the whole Euclidean space. We obtain a unique continuation result for the normal operator of the X-ray transform of one-forms, and this leads to one of our two proofs of the partial data result. Our proofs apply to compactly supported covector-valued distributions.
Local Gauge Conditions for Ellipticity in Conformal Geometry
2013
In this article we introduce local gauge conditions under which many curvature tensors appearing in conformal geometry, such as the Weyl, Cotton, Bach, and Fefferman-Graham obstruction tensors, become elliptic operators. The gauge conditions amount to fixing an $n$-harmonic coordinate system and normalizing the determinant of the metric. We also give corresponding elliptic regularity results and characterizations of local conformal flatness in low regularity settings.
Gradient regularity for elliptic equations in the Heisenberg group
2009
Abstract We give dimension-free regularity conditions for a class of possibly degenerate sub-elliptic equations in the Heisenberg group exhibiting super-quadratic growth in the horizontal gradient; this solves an issue raised in [J.J. Manfredi, G. Mingione, Regularity results for quasilinear elliptic equations in the Heisenberg group, Math. Ann. 339 (2007) 485–544], where only dimension dependent bounds for the growth exponent are given. We also obtain explicit a priori local regularity estimates, and cover the case of the horizontal p-Laplacean operator, extending some regularity proven in [A. Domokos, J.J. Manfredi, C 1 , α -regularity for p-harmonic functions in the Heisenberg group for …
Reilly's type inequality for the Laplacian associated to a density related with shrinkers for MCF
2015
Let $(\bar{M},,e^\psi)$ be a Riemannian manifold with a density, and let $M$ be a closed $n$-dimensional submanifold of $\bar{M}$ with the induced metric and density. We give an upper bound on the first eigenvalue $\lambda_1$ of the closed eigenvalue problem for $\Delta_\psi$ (the Laplacian on $M$ associated to the density) in terms of the average of the norm of the vector ${\vec{H}}_{{\psi}} + {\bar \nabla}$ with respect to the volume form induced by the density, where ${\vec{H}}_{{\psi}}$ is the mean curvature of $M$ associated to the density $e^\psi$. When $\bar{M}=\Bbb R^{n+k}$ or $\bar{M}=S^{n+k-1}$, the equality between $\lambda_1$ and its bound implies that $e^\psi$ is a Gaussian den…
Harnack estimates for degenerate parabolic equations modeled on the subelliptic $p-$Laplacian
2014
Abstract We establish a Harnack inequality for a class of quasi-linear PDE modeled on the prototype ∂ t u = − ∑ i = 1 m X i ⁎ ( | X u | p − 2 X i u ) where p ⩾ 2 , X = ( X 1 , … , X m ) is a system of Lipschitz vector fields defined on a smooth manifold M endowed with a Borel measure μ, and X i ⁎ denotes the adjoint of X i with respect to μ. Our estimates are derived assuming that (i) the control distance d generated by X induces the same topology on M ; (ii) a doubling condition for the μ-measure of d-metric balls; and (iii) the validity of a Poincare inequality involving X and μ. Our results extend the recent work in [16] , [36] , to a more general setting including the model cases of (1)…