A New Operation on Sequences: the Boustrouphedon Transform

A generalization of the Seidel-Entringer-Arnold method for calculating the alternating permutation numbers (or secant-tangent numbers) leads to a new operation on integer sequences, the Boustrophedon transform.Comment: very minor change: corrected typo in author list. June 24 2002: correction to a proof; additional reference

Entropy in Image Analysis III

Image analysis can be applied to rich and assorted scenarios; therefore, the aim of this recent research field is not only to mimic the human vision system. Image analysis is the main methods that computers are using today, and there is body of knowledge that they will be able to manage in a totally unsupervised manner in future, thanks to their artificial intelligence. The articles published in the book clearly show such a future

An automatic marker for vector graphics drawing tasks

In recent years, the SVG file format has grown increasingly popular, largely due to its widespread adoption as the standard image format for vector graphics on the World Wide Web. However, vector graphics predate the modern Web, having served an important role in graphic and computer-aided design for decades prior to SVG's adoption as a web standard. Vector graphics are just as - if not more - relevant than ever today. As a result, training in vector graphics software, particularly in graphic and other creative design fields, forms an important part of the skills development necessary to enter the industry. This study explored the feasibility of a web application that can automatically mark/assess drawing tasks completed in popular vector graphics editors such as Adobe Illustrator, CorelDRAW, and Inkscape. This prototype has been developed using a collection of front-end and back-end web technologies, requiring that users need only a standards-compliant, modern web browser to submit tasks for assessment. Testing was carried out to assess how the application handled SVG markup produced by different users and vector graphics drawing software; and whether the assessment/scoring of submitted tasks was inline with that of a human marker. While some refinement is required, the application assessed six different tasks, submitted eleven times over by as many individuals, and for the greater part was successful in reporting scores in line with that of the researcher. As a prototype, serving as a proof of concept, the project proved the automatic marker a feasible concept. Exactly how marks should be assigned, for which criteria, and how much instruction should be provided are aspects for further study; along with support for curved path segments, and automatic task generation

The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems

We present a compendium of numerical simulation techniques, based on tensor network methods, aiming to address problems of many-body quantum mechanics on a classical computer. The core setting of this anthology are lattice problems in low spatial dimension at finite size, a physical scenario where tensor network methods, both Density Matrix Renormalization Group and beyond, have long proven to be winning strategies. Here we explore in detail the numerical frameworks and methods employed to deal with low-dimension physical setups, from a computational physics perspective. We focus on symmetries and closed-system simulations in arbitrary boundary conditions, while discussing the numerical data structures and linear algebra manipulation routines involved, which form the core libraries of any tensor network code. At a higher level, we put the spotlight on loop-free network geometries, discussing their advantages, and presenting in detail algorithms to simulate low-energy equilibrium states. Accompanied by discussions of data structures, numerical techniques and performance, this anthology serves as a programmer's companion, as well as a self-contained introduction and review of the basic and selected advanced concepts in tensor networks, including examples of their applications.Comment: 115 pages, 56 figure