Related papers: Tropical Geometric Tools for Machine Learning: the…

In the last few years there has been a growing interest towards methods for statistical inference and learning based on computational geometry and, notably, tropical geometry, that is, the study of algebraic varieties over the min-plus…

Topological Machine Learning (TML) is an emerging field that leverages techniques from algebraic topology to analyze complex data structures in ways that traditional machine learning methods may not capture. This tutorial provides a…

Robotic Template Library (RTL) is a set of tools for dealing with geometry and point cloud processing, especially in robotic applications. The software package covers basic objects such as vectors, line segments, quaternions, rigid…

Tropical geometry is a piecewise linear "shadow" of algebraic geometry. It allows for the computation of several cohomological invariants of an algebraic variety. In particular, its application to enumerative algebraic geometry led to…

This is a survey on tropical polytopes from the combinatorial point of view and with a focus on algorithms. Tropical convexity is interesting because it relates a number of combinatorial concepts including ordinary convexity, monomial…

Tropical Geometry and Mathematical Morphology share the same max-plus and min-plus semiring arithmetic and matrix algebra. In this chapter we summarize some of their main ideas and common (geometric and algebraic) structure, generalize and…

Support Vector Machines (SVMs) are one of the most popular supervised learning models to classify using a hyperplane in an Euclidean space. Similar to SVMs, tropical SVMs classify data points using a tropical hyperplane under the tropical…

We are on the verge of a revolutionary era in space exploration, thanks to advancements in telescopes such as the James Webb Space Telescope (\textit{JWST}). High-resolution, high signal-to-noise spectra from exoplanet and brown dwarf…

Designing polymers with high intrinsic thermal conductivity (TC) is critically important for the thermal management of organic electronics and photonics. However, this is a challenging task owing to the diversity of the chemical space and…

The package High-dimensional Metrics (\Rpackage{hdm}) is an evolving collection of statistical methods for estimation and quantification of uncertainty in high-dimensional approximately sparse models. It focuses on providing confidence…

We give an introduction to Tropical Geometry and prove some results in Tropical Intersection Theory. The first part of this paper is an introduction to tropical geometry aimed at researchers in Algebraic Geometry from the point of view of…

This is a survey article written for the Jahresberichte der DMV. Tropical geometry can be viewed as an efficient combinatorial tool to study degenerations in algebraic geometry. Abstract tropical curves are essentially metric graphs, and…

Tropical algebraic geometry is the geometry of the tropical semiring $(\mathbb{R},\min,+)$. Its objects are polyhedral cell complexes which behave like complex algebraic varieties. We give an introduction to this theory, with an emphasis on…

We develop a novel framework to construct and analyze finite valued, multidimensional mechanisms using tropical convex geometry. We geometrically characterize incentive compatibility using cells in the tropical convex hull of the type set.…

We describe the \proglang{R} package \pkg{glmmrBase} and an extension \pkg{glmmrOptim}. \pkg{glmmrBase} provides a flexible approach to specifying, fitting, and analysing generalised linear mixed models. We use an object-orientated class…

Distance metric learning (DML) aims to find an appropriate way to reveal the underlying data relationship. It is critical in many machine learning, pattern recognition and data mining algorithms, and usually require large amount of label…

Theory evaluation is a key problem in many areas: machine learning, scientific discovery, inverse engineering, decision making, software engineering, design, human sciences, etc. If we have a set of theories that are able to explain the…

In this article, we describe a {\tt R} package for sampling from an empirical likelihood-based posterior using a Hamiltonian Monte Carlo method. Empirical likelihood-based methodologies have been used in Bayesian modeling of many problems…

Polymers, integral to advancements in high-tech fields, necessitate the study of their thermal conductivity (TC) to enhance material attributes and energy efficiency. The TC of polymers obtained by molecular dynamics (MD) calculations and…

The R package trajmsm provides functions designed to simplify the estimation of the parameters of a model combining latent class growth analysis (LCGA), a trajectory analysis technique, and marginal structural models (MSMs) called LCGA-MSM.…