The use of optimization in a simulation based design environment has become a common trend in industry today. Computer simulation tools are common place in many engineering disciplines, providing the designers with tools to evaluate a design’s performance without building a physical prototype. This has triggered the development of optimization techniques suitable for dealing with such simulatio...

Drawing on recent machine learning work in dimensionality reduction, novel techniques for approximate conformal parameterization of point-set surfaces are introduced. An improved approximation of local tangent-spaces leads to a new method for computing Laplacian weights on point set neighbourhoods. These weights allow for linear minimization of the Dirichlet energy, and a robust one-parameter m...

Memory becomes a limiting factor in contemporary applications, such as analyses of the Webgraph and molecular sequences, when many objects need to be counted simultaneously. Robert Morris [Communications of the ACM, 21:840–842, 1978] proposed a probabilistic technique for approximate counting that is extremely space-efficient. The basic idea is to increment a counter containing the value X with...

Determinantal point processes (DPPs) are random point processes well-suited for modeling repulsion. In machine learning, the focus of DPP-based models has been on diverse subset selection from a discrete and finite base set. This discrete setting admits an efficient sampling algorithm based on the eigendecomposition of the defining kernel matrix. Recently, there has been growing interest in usi...

Given a set A ={a1, . . . ,an} of n image points and a set B ={b1, . . . ,bn} of n model points,the problem is to find a transformation matching (a one-to-one mapping) each point a ∈ A tosome point b ∈ B such that the length of the longest edge in the matching is minimized (so-calledbottleneck distance). The geometric transformations we allow are translation, rot...

In the present paper, Radial Basis Function interpolations are applied to approximate a fuzzy function $tilde{f}:Rrightarrow mathcal{F}(R)$, on a discrete point set $X={x_1,x_2,ldots,x_n}$, by a fuzzy-valued function $tilde{S}$. RBFs are based on linear combinations of terms which include a single univariate function. Applying RBF to approximate a fuzzy function, a linear system wil...

Let $varphi(z)=z^m, z in mathbb{U}$, for some positive integer $m$, and $C_varphi$ be the composition operator on the Bergman space $mathcal{A}^2$ induced by $varphi$. In this article, we completely determine the point spectrum, spectrum, essential spectrum, and essential norm of the operators $C^*_varphi C_varphi, C_varphi C^*_varphi$ as well as self-commutator and anti-self-commutators of $C_...

We show how to obtain the probability density function for the amplitude of the curvature perturbation, R, produced during an epoch of slow-roll, single-field inflation, working directly from n-point correlation functions of R. These n-point functions are the usual output of quantum field theory calculations, and as a result we bypass approximate statistical arguments based on the central limit...