Related papers: Maximum volume simplex method for automatic select…
Ultrashort time-domain spectroscopy and field-resolved spectroscopy of molecular fingerprints are gold standards for detecting samples' constituents and internal dynamics. However, they are hindered by the Nyquist criterion, leading to…
For a probability measure on a real separable Hilbert space, we are interested in "volume-based" approximations of the d-dimensional least squares error of it, i.e., least squares error with respect to a best fit d-dimensional affine…
Polyhedral-type approximations of convex-like domains in $\mathbb{C}^d$ have been considered recently by the second author. In particular, the decay rate of the error in optimal volume approximation as a function of the number of facets has…
Euclidean random matrices arise in a wide range of physical systems where interactions are determined by spatial configurations, including disordered media and cooperative phenomena in atomic ensembles. Unlike classical random matrix…
Molecular fingerprints are significant cheminformatics tools to map molecules into vectorial space according to their characteristics in diverse functional groups, atom sequences, and other topological structures. In this paper, we set out…
Fingerprinting techniques are widely used for localization because of their accuracy, especially in the presence of wireless channel noise. However, the fingerprinting techniques require significant storage and running time, which is a…
Most urban applications necessitate building footprints in the form of concise vector graphics with sharp boundaries rather than pixel-wise raster images. This need contrasts with the majority of existing methods, which typically generate…
Volume is a natural geometric measure for comparing polyhedral relaxations of non-convex sets. Speakman and Lee gave volume formulae for comparing relaxations of trilinear monomials, quantifying the strength of various natural relaxations.…
Current popular methods for Magnetic Resonance Fingerprint (MRF) recovery are bottlenecked by the heavy computations of a matched-filtering step due to the growing size and complexity of the fingerprint dictionaries in multi-parametric…
Acoustic velocity vectors are important for human's localization of sound at low frequencies. This paper proposes a sound field reproduction algorithm, which matches the acoustic velocity vectors in a circular listening area. In previous…
The 3D localisation of an object and the estimation of its properties, such as shape and dimensions, are challenging under varying degrees of transparency and lighting conditions. In this paper, we propose a method for jointly localising…
In simulation sciences, it is desirable to capture the real-world problem features as accurately as possible. Methods popular for scientific simulations such as the finite element method (FEM) and finite volume method (FVM) use piecewise…
As computers get faster, researchers -- not hardware or algorithms -- become the bottleneck in scientific discovery. Computational study of colloidal self-assembly is one area that is keenly affected: even after computers generate massive…
Several fundamental problems that arise in optimization and computer science can be cast as follows: Given vectors $v_1,\ldots,v_m \in \mathbb{R}^d$ and a constraint family ${\cal B}\subseteq 2^{[m]}$, find a set $S \in \cal{B}$ that…
Fingerprint, as one of the most popular and robust biometric traits, can be used in automatic identification and verification systems to identify individuals. Fingerprint matching is a vital and challenging issue in fingerprint recognition…
We consider how to directly extract a road map (also known as a topological representation) of an initially-unknown 2-dimensional environment via an online procedure that robustly computes a retraction of its boundaries. In this article, we…
In recent years, the dominant accuracy metric for vector search is the recall of a result list of fixed size (top-k retrieval), considering as ground truth the exact vector retrieval results. Although convenient to compute, this metric is…
Range-based set reconciliation is a simple approach to efficiently computing the union of two sets over a network, based on recursively partitioning the sets and comparing fingerprints of the partitions to probabilistically detect whether a…
We consider the computation of the volume of the union of high-dimensional geometric objects. While showing that this problem is #P-hard already for very simple bodies (i.e., axis-parallel boxes), we give a fast FPRAS for all objects where…
We construct a quasi-polynomial time deterministic approximation algorithm for computing the volume of an independent set polytope with restrictions. Randomized polynomial time approximation algorithms for computing the volume of a convex…