Related papers: Tropical Geometric Tools for Machine Learning: the…
As a new concept tropical halfspaces are introduced to the (linear algebraic) geometry of the tropical semiring (R,min,+). This yields exterior descriptions of the tropical polytopes that were recently studied by Develin and Sturmfels in a…
A supervised machine learning (ML) based computational methodology for the design of particulate multifunctional composite materials with desired thermal conductivity (TC) is presented. The design variables are physical descriptors of the…
Tropical Cyclones (TCs) are counted among the most destructive phenomena that can be found in nature. Every year, globally an average of 90 TCs occur over tropical waters, and global warming is making them stronger, larger and more…
Simulating from the multivariate truncated normal distribution (MTN) is required in various statistical applications yet remains challenging in high dimensions. Currently available algorithms and their implementations often fail when the…
Holistic linear regression extends the classical best subset selection problem by adding additional constraints designed to improve the model quality. These constraints include sparsity-inducing constraints, sign-coherence constraints and…
A programming tactic involving polyhedra is reported that has been widely applied in the polyhedral analysis of (constraint) logic programs. The method enables the computations of convex hulls that are required for polyhedral analysis to be…
R is a language and environment for statistical computing and graphics, which provides a wide variety of statistical tools (modeling, statistical testing, time series analysis, classification problems, machine learning, ...), together with…
This paper introduces the R package sgmcmc; which can be used for Bayesian inference on problems with large datasets using stochastic gradient Markov chain Monte Carlo (SGMCMC). Traditional Markov chain Monte Carlo (MCMC) methods, such as…
Algebraic methods have a long history in statistics. The most prominent manifestation of modern algebra in statistics can be seen in the field of algebraic statistics, which brings tools from commutative algebra and algebraic geometry to…
When performing an aggregate data meta-analysis of a continuous outcome, researchers often come across primary studies that report the sample median of the outcome. However, standard meta-analytic methods typically cannot be directly…
Linear discriminant analysis (LDA) is a powerful tool in building classifiers with easy computation and interpretation. Recent advancements in science technology have led to the popularity of datasets with high dimensions, high orders and…
We present the Macaulay2 package TropicalToric.m2 for toric intersection theory computations using tropical geometry.
Large language models (LLMs) are pretrained by minimizing the cross-entropy loss for next-token prediction. In this paper, we study whether this optimization strategy can induce geometric structure in the learned model weights and context…
Machine learning (ML) can facilitate efficient thermoelectric (TE) material discovery essential to address the environmental crisis. However, ML models often suffer from poor experimental generalizability despite high metrics. This study…
We consider a minimum enclosing and maximum inscribed tropical balls for any given tropical polytope over the tropical projective torus in terms of the tropical metric with the max-plus algebra. We show that we can obtain such tropical…
Tropical algebra is an emerging field with a number of applications in various areas of mathematics. In many of these applications appeal to tropical polynomials allows to study properties of mathematical objects such as algebraic varieties…
Because of the fast advance rate and the improved personnel safety, tunnel boring machines (TBMs) have been widely used in a variety of tunnel construction projects. The dynamic modeling of TBM load parameters (including torque, advance…
The family of stable distributions received extensive applications in many fields of studies since it incorporates both the skewness and heavy tails. In this paper, we introduce a package written in the R language called alphastable. The…
TopologicalNumbers.jl is an open-source Julia package designed to calculate topological invariants, mathematical quantities that characterize the properties of materials in condensed matter physics. These invariants, such as the Chern…
We present applications of tropical geometry to some integrable piecewise-linear maps, based on the lecture given by one of the authors (R. I.) at the workshop "Tropical Geometry and Integrable Systems" (University of Glasgow, July 2011),…