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Planning is an essential topic in the realm of automated driving. Besides planning algorithms that are widely covered in the literature, planning requires different software tools for its development, validation, and execution. This paper…

Robotics · Computer Science 2021-11-25 Kailin Tong , Zlatan Ajanovic , Georg Stettinger

This paper gives a key definition, for a new approach to dessins and algebraic numbers. The distant goal is to construct from each dessin $D$ an algebraic number $\eta_D$, in a systematic and useful way. The algebra of balanced dessins is…

Combinatorics · Mathematics 2018-02-14 Jonathan Fine

This paper introduces abstractions that are meaningful for computers and that can be built and used according to computers' own criteria, i.e., computable abstractions. It is analyzed how abstractions can be seen to serve as the building…

Artificial Intelligence · Computer Science 2015-03-31 Alejandro Sanchez Guinea

A personal and informal account of what a pure mathematician might expect when using tools from deep learning in their research.

Representation Theory · Mathematics 2023-05-29 Geordie Williamson

This article summarises a Web-book on "Complexity" that was developed to introduce undergraduate students to interesting complex systems in the biological, physical and social sciences, and the common tools, principles and concepts used for…

Physics Education · Physics 2007-05-23 Rajesh R. Parwani

Today, intelligent systems that offer artificial intelligence capabilities often rely on machine learning. Machine learning describes the capacity of systems to learn from problem-specific training data to automate the process of analytical…

Artificial Intelligence · Computer Science 2021-04-15 Christian Janiesch , Patrick Zschech , Kai Heinrich

Scrolling mechanism is used to display and edit large documents in a limited screen space or window. The scrolling mechanism may include a vertical scroll bar or a horizontal scroll bar or both to move the contents of the documents up and…

Human-Computer Interaction · Computer Science 2014-04-29 Umakant Mishra

Membrane computing is a well-established and successful research field which belongs to the more general area of molecular computing. Membrane computing aims at defining parallel and non-deterministic computing models, called membrane…

Distributed, Parallel, and Cluster Computing · Computer Science 2011-08-11 Bogdan Aman

Spin glasses are disordered magnetic systems that exhibit a variety of properties that are characteristic of complex systems. After a brief review of basic spin glass concepts, their use in areas such as computer science, biology, and other…

Statistical Mechanics · Physics 2012-05-16 D. L. Stein , C. M. Newman

Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a proper subset B which is embedded with a stronger structure S. By proper subset one understands a set included in A,…

General Mathematics · Mathematics 2007-05-23 W. B. Vasantha Kandasamy

We define recurrence matrices and study a few properties (links with automatic sequences, branch groups etc.) of them.

Rings and Algebras · Mathematics 2007-05-23 Roland Bacher

We review the concept of a graded bundle as a natural generalisation of a vector bundle. Such geometries are particularly nice examples of more general graded manifolds. With hindsight there are many examples of graded bundles that appear…

Differential Geometry · Mathematics 2016-05-12 Andrew J. Bruce , K. Grabowska , J. Grabowski

This paper addresses the challenge of geometric quality assurance in manufacturing, particularly when human assessment is required. It proposes using Blender, an open-source simulation tool, to create synthetic datasets for machine learning…

Computer Vision and Pattern Recognition · Computer Science 2024-12-19 Joel Sol , Amir M. Soufi Enayati , Homayoun Najjaran

The notion of wavelets is defined. It is briefly described {\it what} are wavelets, {\it how} to use them, {\it when} we do need them, {\it why} they are preferred and {\it where} they have been applied. Then one proceeds to the…

High Energy Physics - Phenomenology · Physics 2008-11-26 I. M. Dremin

In order to design strong paradigms for isolating lexical access and semantics, we need to know what a word is. Surprisingly few linguists and philosophers have a clear model of what a word is, even though words impact basically every…

Computation and Language · Computer Science 2024-02-21 Elliot Murphy

This paper deals with the arrow of complexification of engineering. We claim that the complexification of engineering consists in (a) that shift throughout which engineering becomes a science; thus it ceases to be a (mere) praxis or…

Adaptation and Self-Organizing Systems · Physics 2013-10-02 Carlos Eduardo Maldonado , Nelson Alfonso Gómez-Cruz

We define a type of biquandle which is a generalization of symplectic quandles. We use the extra structure of these bilinear biquandles to define new knot and link invariants and give some examples.

Quantum Algebra · Mathematics 2008-08-13 Sam Nelson , Jacquelyn L. Rische

Untangling is a process in which some vertices of a planar graph are moved to obtain a straight-line plane drawing. The aim is to move as few vertices as possible. We present an algorithm that untangles the cycle graph C_n while keeping at…

Computational Geometry · Computer Science 2011-02-07 Josef Cibulka

This tutorial review provides a guiding reference to researchers who want to have an overview of the large body of literature about graph spanners. It reviews the current literature covering various research streams about graph spanners,…

The purpose of this article is to review the achievements made in the last few years towards the understanding of the reasons behind the success and subtleties of neural network-based machine learning. In the tradition of good old applied…

Machine Learning · Computer Science 2020-12-09 Weinan E , Chao Ma , Stephan Wojtowytsch , Lei Wu