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This is a survey article on real algebra and geometry, and in particular on its recent applications in optimization and convexity. We first introduce basic notions and results from the classical theory. We then explain how these relate to…

Algebraic Geometry · Mathematics 2016-06-24 Tim Netzer

In-context learning is a popular inference strategy where large language models solve a task using only a few labeled demonstrations without needing any parameter updates. Although there have been extensive studies on English in-context…

Computation and Language · Computer Science 2024-06-10 Miaoran Zhang , Vagrant Gautam , Mingyang Wang , Jesujoba O. Alabi , Xiaoyu Shen , Dietrich Klakow , Marius Mosbach

Causal discovery aims to automatically uncover causal relationships from data, a capability with significant potential across many scientific disciplines. However, its real-world applications remain limited. Current methods often rely on…

One of the elements that have popularized and facilitated the use of geographical information on a variety of computational applications has been the use of Web maps; this has opened new research challenges on different subjects, from…

Computers and Society · Computer Science 2009-11-05 Rafael Ponce-Medellin , Gabriel Gonzalez-Serna , Rocio Vargas , Lirio Ruiz

In this article, we reflect upon our positive experiences incorporating or working on extra credit projects in algebra-based introductory physics that asked students to connect physics with humanities, social sciences, and everyday life. We…

Physics Education · Physics 2025-09-19 Brooke Rouret , Jaya Shivangani Kashyap , Jeremy Levy , Chandralekha Singh

We discuss certain ternary algebraic structures appearing more or less naturally in various domains of theoretical and mathematical physics. Far from being exhaustive, this article is intended above all to draw attention to these algebras,…

Mathematical Physics · Physics 2007-05-23 Richard Kerner

In distributed classification, each learner observes its environment and deduces a classifier. As a learner has only a local view of its environment, classifiers can be exchanged among the learners and integrated, or merged, to improve…

Discrete Mathematics · Computer Science 2015-01-23 Philippe J. Giabbanelli , Joseph G. Peters

In this note we report on an implementation of discovery-oriented problems in courses on Real Analysis and Differential Equations. We explain a type of task-design that gives students the opportunity to conjecture, refute and prove. What is…

History and Overview · Mathematics 2020-05-26 Thomas Pawlaschyk , Sven-Ake Wegner

The article reveals the experience of organizing blended learning for geography students using Google Classroom, and discloses its potential uses in the study of geography. For the last three years, the authors have tested such inclass and…

Computers and Society · Computer Science 2019-09-12 Olha Bondarenko , Svitlana Mantulenko , Andrey Pikilnyak

The multi-layered nature of societal developments poses a challenge in the teaching and learning of history of mathematics. As an attempt to tackle this challenge we experimented with the use of Knowledge-Maps. The focus of our interest…

History and Overview · Mathematics 2019-12-18 Nicola Oswald , Sarah Khellaf , Jana Peters

In this paper we make some considerations about using a dynamic geometry software for teaching history of mathematica at university level. After a short introduction to the software GeoGebra, we discuss four activities. The first is an…

History and Overview · Mathematics 2020-12-11 Aldo Brigaglia , Maria Anna Raspanti , Enrico Rogora

The authors have been using a largely algebraic form of ``computational discovery'' in various undergraduate classes at their respective institutions for some decades now to teach pure mathematics, applied mathematics, and computational…

History and Overview · Mathematics 2024-07-31 Neil J. Calkin , Eunice Y. S. Chan , Robert M. Corless

Google Earth is a huge source of interesting illustrations of various natural phenomena. It can represent a valuable tool for science education, not only for teaching geography and geology, but also physics. Here we suggest that Google…

Physics Education · Physics 2015-06-03 Fabrizio Logiurato

We develop a random model for relation algebras. We prove some preliminary results and pose questions that lay out a new direction of research.

Combinatorics · Mathematics 2018-02-20 Jeremy F. Alm

Knowledge Graphs (KG) and associated Knowledge Graph Embedding (KGE) models have recently begun to be explored in the context of drug discovery and have the potential to assist in key challenges such as target identification. In the drug…

Biomolecules · Quantitative Biology 2022-06-01 Stephen Bonner , Ian P Barrett , Cheng Ye , Rowan Swiers , Ola Engkvist , Charles Tapley Hoyt , William L Hamilton

Modern cameras are equipped with a wide array of sensors that enable recording the geospatial context of an image. Taking advantage of this, we explore depth estimation under the assumption that the camera is geocalibrated, a problem we…

Computer Vision and Pattern Recognition · Computer Science 2021-09-22 Scott Workman , Hunter Blanton

In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…

Rings and Algebras · Mathematics 2008-11-07 Douglas Lundholm

The amount and complexity of data delivered by modern galaxy surveys has been steadily increasing over the past years. Extracting coherent scientific information from these large and multi-modal data sets remains an open issue and data…

Instrumentation and Methods for Astrophysics · Physics 2023-01-18 Marc Huertas-Company , François Lanusse

Search systems are increasingly used for gaining knowledge through accessing relevant resources from a vast volume of content. However, search systems provide only limited support to users in knowledge acquisition contexts. Specifically,…

Information Retrieval · Computer Science 2022-04-26 Yasin Ghafourian

The outcomes of elections, product sales, and the structure of social connections are all determined by the choices individuals make when presented with a set of options, so understanding the factors that contribute to choice is crucial. Of…

Machine Learning · Computer Science 2020-11-09 Kiran Tomlinson , Austin R. Benson