Related papers: An Efficient Algorithm for Vertex Enumeration of T…
Two-dimensional patterns are used in many research areas in computer science, ranging from image processing to specification and verification of complex software systems (via scenarios). The contribution of this paper is twofold. First, we…
An efficient computer algorithm is described for the perspective drawing of a wide class of surfaces. The class includes surfaces corresponding lo single-valued, continuous functions which are defined over rectangular domains. The algorithm…
In this note we compute some enumerative invariants of real and complex projective spaces by means of some enriched graphs called floor diagrams.
We propose a fast and scalable algorithm to project a given density on a set of structured measures defined over a compact 2D domain. The measures can be discrete or supported on curves for instance. The proposed principle and algorithm are…
Random projection has been widely used in data classification. It maps high-dimensional data into a low-dimensional subspace in order to reduce the computational cost in solving the related optimization problem. While previous studies are…
This paper presents an efficient gradient projection-based method for structural topological optimization problems characterized by a nonlinear objective function which is minimized over a feasible region defined by bilateral bounds and a…
Some methods based on simple regularizing geometric element transformations have heuristically been shown to give runtime efficient and quality effective smoothing algorithms for meshes. We describe the mathematical framework and a…
This paper presents enhancements to the projection pursuit tree classifier and visual diagnostic methods for assessing their impact in high dimensions. The original algorithm uses linear combinations of variables in a tree structure where…
We produce algorithms to detect whether a complex affine variety computed and presented numerically by the machinery of numerical algebraic geometry corresponds to an associated component of a polynomial ideal.
Calculations of the Fourier transform of a constant quantity over an area or volume defined by polygons (connected vertices) are often useful in modeling wave scattering, or in fourier-space filtering of real-space vector-based volumes and…
In the burgeoning field of medical imaging, precise computation of 3D volume holds a significant importance for subsequent qualitative analysis of 3D reconstructed objects. Combining multivariate calculus, marching cube algorithm, and…
Modeling of microlensing events poses computational challenges for the resolution of the lens equation and the high dimensionality of the parameter space. In particular, numerical noise represents a severe limitation to fast and efficient…
We review results of papers written on the topic of polynomial amoebas with an emphasis on computational aspects of the topic. The polynomial amoebas have a lot of applications in various domains of science. Computation of the amoeba for a…
Every polyhedral cone can be described either by its facets or by its extreme rays. Computation of one description from the other is a problem that can be very complex, i.e. one encounter the combinatorial explosion. We present here several…
Hypervolume indicator is a commonly accepted quality measure for comparing Pareto approximation set generated by multi-objective optimizers. The best known algorithm to calculate it for $n$ points in $d$-dimensional space has a run time of…
We consider problems with multiple linear objectives and linear constraints and use Adjustable Robust Optimization and Polynomial Optimization as tools to approximate the Pareto set with polynomials of arbitrarily large degree. The main…
Random Projection is a foundational research topic that connects a bunch of machine learning algorithms under a similar mathematical basis. It is used to reduce the dimensionality of the dataset by projecting the data points efficiently to…
In this work, we address the unsupervised classification issue by exploiting the general idea of Random Projection Ensemble. Specifically, we propose to generate a set of low dimensional independent random projections and to perform…
We investigate the performance of entropy estimation methods, based either on block entropies or compression approaches, in the case of bidimensional sequences. We introduce a validation dataset made of images produced by a large number of…
Enumerating all 3-manifold triangulations of a given size is a difficult but increasingly important problem in computational topology. A key difficulty for enumeration algorithms is that most combinatorial triangulations must be discarded…