Related papers: Distance preserving mappings from ternary vectors …
Determinantal point processes (DPPs) are elegant probabilistic models of repulsion that arise in quantum physics and random matrix theory. In contrast to traditional structured models like Markov random fields, which become intractable and…
Maximum distance profile codes are characterized by the property that two trajectories which start at the same state and proceed to a different state will have the maximum possible distance from each other relative to any other…
Developing autonomous robots capable of learning and reproducing complex motions from demonstrations remains a fundamental challenge in robotics. On the one hand, movement primitives (MPs) provide a compact and modular representation of…
This article introduces the novel notion of dimension preserving approximation for continuous functions defined on $[0,1]$ and initiates the study of it. Restrictions and extensions of continuous functions in regards to fractal dimensions…
Dynamic mode decomposition (DMD) has become a powerful data-driven method for analyzing the spatiotemporal dynamics of complex, high-dimensional systems. However, conventional DMD methods are limited to matrix-based formulations, which…
Motivated by the problem of constructing bijective maps with low differential uniformity, we introduce the notion of permutation resemblance of a function, which looks to measure the distance a given map is from being a permutation. We…
The dynamic time warping (dtw) distance fails to satisfy the triangle inequality and the identity of indiscernibles. As a consequence, the dtw-distance is not warping-invariant, which in turn results in peculiarities in data mining…
Distance transformation is an image processing technique used for many different applications. Related to a binary image, the general idea is to determine the distance of all background points to the nearest object point (or vice versa). In…
Diffusion models are distinguished by their exceptional generative performance, particularly in producing high-quality samples through iterative denoising. While current theory suggests that the number of denoising steps required for…
In this paper we present a topological framework for studying signed permutations and their reversal distance. As a result we can give an alternative approach and interpretation of the Hannenhalli-Pevzner formula for the reversal distance…
Using the concept of dynamical mappings, two symmetry conserving nonperturbative approaches are presented. The first is based on the 1/N-expansion and sorted out using Holstein-Primakoff mapping. The second consists of dynamically mapping…
Traditional numerical techniques for solving time-dependent partial-differential-equation (PDE) initial-value problems (IVPs) store a truncated representation of the function values and some number of their time derivatives at each time…
In this work, we consider the problem of pattern matching under the dynamic time warping (DTW) distance motivated by potential applications in the analysis of biological data produced by the third generation sequencing. To measure the DTW…
Diffusion maps (DM) constitute a classic dimension reduction technique, for data lying on or close to a (relatively) low-dimensional manifold embedded in a much larger dimensional space. The DM procedure consists in constructing a spectral…
Prior work inspired by compression algorithms has described how the Burrows Wheeler Transform can be used to create a distance measure for bioinformatics problems. We describe issues with this approach that were not widely known, and…
We propose reducible algebraic curves as a mechanism to construct Partial MDS (PMDS) codes geometrically. We obtain new general existence results, new explicit constructions and improved estimates on the smallest field sizes over which such…
Accurately predicting the geographic ranges of species is crucial for assisting conservation efforts. Traditionally, range maps were manually created by experts. However, species distribution models (SDMs) and, more recently, deep…
Diffusion probabilistic models (DPMs) have emerged as a promising technique in generative modeling. The success of DPMs relies on two ingredients: time reversal of diffusion processes and score matching. In view of possibly unguaranteed…
Learning-based motion planning can quickly generate near-optimal trajectories. However, it often requires either large training datasets or costly collection of human demonstrations. This work proposes an alternative approach that quickly…
Let $M(n,d)$ be the maximum size of a permutation array on $n$ symbols with pairwise Hamming distance at least $d$. Some permutation arrays can be constructed using blocks of certain type [2] called product blocks in this paper. We study…