相关论文: Geometric Aspects of Biological Sequence Compariso…

This paper investigates quasi-isometries between graphs with variable edge lengths. A quasi-isometry is a mapping between metric spaces that approximately preserves distances, allowing for a bounded amount of additive and multiplicative…

We analytically study proximity and distance properties of various kernels and similarity measures on graphs. This helps to understand the mathematical nature of such measures and can potentially be useful for recommending the adoption of…

The quasispecies model introduced by Eigen in 1971 has close connections with the isometry group of the space of binary sequences relative to the Hamming distance metric. Generalizing this observation we introduce an abstract quasispecies…

Motivated by the important problem of detecting association between genetic markers and binary traits in genome-wide association studies, we present a novel Bayesian model that establishes a hierarchy between markers and genes by defining…

Although random cell complexes occur throughout the physical sciences, there does not appear to be a standard way to quantify their statistical similarities and differences. The various proposals in the literature are usually motivated by…

We propose a series of methods to represent the evolution of a field of science at different levels: namely micro, meso and macro levels. We use a previously introduced asymmetric measure of paradigmatic proximity between terms that enables…

The concept of quasi-isometric embedding maps between $*$-algebras is introduced. We have obtained some basic results related to this notion and similar to quasi-isometric embedding maps on metric spaces, under some conditions, we give a…

We present a framework for discriminative sequence classification where the learner works directly in the high dimensional predictor space of all subsequences in the training set. This is possible by employing a new coordinate-descent…

We discuss aspects of global and gauged symmetries in quantum field theory and quantum gravity, focusing on discrete gauge symmetries. An effective Lagrangian description of $\Z_p$ gauge theories shows that they are associated with an…

We consider a Bayesian hierarchical version of the normal theory general linear model which is practically relevant in the sense that it is general enough to have many applications and it is not straightforward to sample directly from the…

In this work we reproduce the characterization of $\Gg^s$-sets from the euclidean setting [J. London Math. Soc. 49:267-280,1994] to more general metric spaces. These sets have Hausdorff dimension at least $s$ and are closed by countable…

Geodesic distance serves as a reliable means of measuring distance in nonlinear spaces, and such nonlinear manifolds are prevalent in the current multimodal learning. In these scenarios, some samples may exhibit high similarity, yet they…

The non-stationary evolution of observable quantities in complex systems can frequently be described as a juxtaposition of quasi-stationary spells. Given that standard theoretical and data analysis approaches usually rely on the assumption…

Researchers have recently suggested that models share common representations. In our work, we find numerous geometric similarities across the token embeddings of large language models. First, we find ``global'' similarities: token…

Optimal transport and its related problems, including optimal partial transport, have proven to be valuable tools in machine learning for computing meaningful distances between probability or positive measures. This success has led to a…

For a bounded metric space X, we define a metric on the set of all finite subsets of X. This generalizes the sequence-subset distance introduced by Wentu Song, Kui Cai and Kees A. Schouhamer Immink to study error correcting codes for DNA…

Metric learning has the aim to improve classification accuracy by learning a distance measure which brings data points from the same class closer together and pushes data points from different classes further apart. Recent research has…

We take a unifying and new approach toward polynomial and trigonometric approximation in an arbitrary number of variables, resulting in a precise and general ready-to-use tool that anyone can easily apply in new situations of interest. The…

Allometric scaling can reflect underlying mechanisms, dynamics and structures in complex systems; examples include typical scaling laws in biology, ecology and urban development. In this work, we study allometric scaling in scientific…

Discrete partially ordered sets can be turned into distance spaces in several ways. The distance functions may or may not satisfy the triangle inequality, and restriction of the distance to finite chains may or may not coincide with the…