Related papers: Polar Alignment and Atomic Decomposition
Combinatorics, like computer science, often has to deal with large objects of unspecified (or unusable) structure. One powerful way to deal with such an arbitrary object is to decompose it into more usable components. In particular, it has…
Different notions for order convergence have been considered by various authors. Associated to every notion of order convergence corresponds a topology, defined by taking as the closed sets those subsets of the poset satisfying that no net…
A reduced-order model algorithm, called ALP, is proposed to solve nonlinear evolution partial differential equations. It is based on approximations of generalized Lax pairs. Contrary to other reduced-order methods, like Proper Orthogonal…
Finite element simulations have been used to solve various partial differential equations (PDEs) that model physical, chemical, and biological phenomena. The resulting discretized solutions to PDEs often do not satisfy requisite physical…
For many applications, we need to use techniques to represent convex shapes and objects. In this work, we use level set method to represent shapes and find a necessary and sufficient condition on the level set function to guarantee the…
We consider the interaction of electromagnetic radiation of arbitrary polarization with multi-level atoms in a self-consistent manner, taking into account both spatial and temporal dependencies of local fields. This is done by numerically…
This material provides thorough tutorials on some optimization techniques frequently used in various engineering disciplines, including convex optimization, linearization techniques and mixed-integer linear programming, robust optimization,…
Motivated by a connection with the factorization of multivariate polynomials, we study integral convex polytopes and their integral decompositions in the sense of the Minkowski sum. We first show that deciding decomposability of integral…
We present a new optimization-based method for atomistic-to-continuum (AtC) coupling. The main idea is to cast the coupling of the atomistic and continuum models as a constrained optimization problem with virtual Dirichlet controls on the…
Scientific and commercial data is often incomplete. Recovery of the missing information is an important pre-processing step in data analysis. Real-world data can in many cases be represented as a superposition of two or more different types…
Using a simple picture of the constituent quark as a composite system of point-like partons, we construct the polarized parton distributions by a convolution between constituent quark momentum distributions and constituent quark structure…
In a recent paper, Amini et al. introduce a general framework to prove duality theorems between special decompositions and their dual combinatorial object. They thus unify all known ad-hoc proofs in one single theorem. While this…
In this paper we establish necessary and sufficient conditions for the existence of line segments (or flats) in the sphere of the nuclear norm via the notion of simultaneous polarization and a refined expression for the subdifferential of…
In this paper, we propose a novel partial order for binary discrete memoryless channels that we call the symmetric convex ordering. We show that Ar{\i}kan's polar transform preserves 'symmetric convex orders'. Furthermore, we show that…
We present a novel, general, and unifying point of view on sparse approaches to polynomial optimization. Solving polynomial optimization problems to global optimality is a ubiquitous challenge in many areas of science and engineering.…
We describe absolutely ordered $p$-normed spaces, for $1 \le p \le \infty$ which presents a model for "non-commutative" vector lattices and includes order theoretic orthogonality. To demonstrate its relevance, we introduce the notion of…
The full optimization of the design and operation of instruments whose functioning relies on the interaction of radiation with matter is a super-human task, given the large dimensionality of the space of possible choices for geometry,…
In this article, we present what we believe to be a simple way to motivate the use of Hilbert spaces in quantum mechanics. To achieve this, we study the way the notion of dimension can, at a very primitive level, be defined as the…
A polarity of a projective plane is a map, often assumed to be involutive, mapping a generic point to a generic line and reciprocally. The most classical polarity is the polarity with respect to a conic, but other exist: the harmonic…
Recent advancements in the synthesis of anisotropic macromolecules and nanoparticles have spurred an immense interest in theoretical and computational studies of self-assembly. The cornerstone of such studies is the role of shape in…