The field of computational learning theory arose out of the desire to for mally understand the process of learning. As potential applications to artificial intelligence became apparent, the new field grew rapidly. The learning of geo metric objects became a natural area of study. The possibility of using learning techniques to compensate for unsolvability provided an attraction for individ uals with an immediate need to solve such difficult problems. Researchers at the Center for Night Vision were interested in solving the problem of interpreting data produced by a variety of sensors. Current vision techniques, which have a strong geometric component, can be used to extract features. However, these techniques fall short of useful recognition of the sensed objects. One potential solution is to incorporate learning techniques into the geometric manipulation of sensor data. As a first step toward realizing such a solution, the Systems Research Center at the University of Maryland, in conjunction with the Center for Night Vision, hosted a Workshop on Learning and Geometry in January of 1991. Scholars in both fields came together to learn about each others' field and to look for common ground, with the ultimate goal of providing a new model of learning from geometrical examples that would be useful in computer vision. The papers in the volume are a partial record of that meeting.

This book covers different, current research directions in the context of variational methods for non-linear geometric data. Each chapter is authored by leading experts in the respective discipline and provides an introduction, an overview and a description of the current state of the art. Non-linear geometric data arises in various applications in science and engineering. Examples of nonlinear data spaces are diverse and include, for instance, nonlinear spaces of matrices, spaces of curves, shapes as well as manifolds of probability measures. Applications can be found in biology, medicine, product engineering, geography and computer vision for instance. Variational methods on the other hand have evolved to being amongst the most powerful tools for applied mathematics. They involve techniques from various branches of mathematics such as statistics, modeling, optimization, numerical mathematics and analysis. The vast majority of research on variational methods, however, is focused on data in linear spaces. Variational methods for non-linear data is currently an emerging research topic. As a result, and since such methods involve various branches of mathematics, there is a plethora of different, recent approaches dealing with different aspects of variational methods for nonlinear geometric data. Research results are rather scattered and appear in journals of different mathematical communities. The main purpose of the book is to account for that by providing, for the first time, a comprehensive collection of different research directions and existing approaches in this context. It is organized in a way that leading researchers from the different fields provide an introductory overview of recent research directions in their respective discipline. As such, the book is a unique reference work for both newcomers in the field of variational methods for non-linear geometric data, as well as for established experts that aim at to exploit new research directions or collaborations. Chapter 9 of this book is available open access under a CC BY 4.0 license at link.springer.com.

This book constitutes the thoroughly refereed post-proceedings of the 11th International Workshop on Theoretical Foundations of Computer Vision, held in Dagstuhl Castle, Germany in April 2002. The 27 revised full papers presented went through two rounds of reviewing and improvement and assess the state of the art in geometry, morphology, and computational imaging. The papers are organized in sections on geometry - models and algorithms; property measurement in the grid and on finite samples; features, shape, and morphology; and computer vision and scene analysis.

This volume in the Springer Lecture Notes in Computer Science (LNCS) series contains 98 papers presented at the S+SSPR 2008 workshops. S+SSPR 2008 was the sixth time that the SPR and SSPR workshops organized by Technical Committees, TC1 and TC2, of the International Association for Pattern Rec- nition (IAPR) wereheld as joint workshops. S+SSPR 2008was held in Orlando, Florida, the family entertainment capital of the world, on the beautiful campus of the University of Central Florida, one of the up and coming metropolitan universities in the USA. S+SSPR 2008 was held during December 4–6, 2008 only a few days before the 19th International Conference on Pattern Recog- tion(ICPR2008),whichwasheldin Tampa,onlytwo hoursawayfromOrlando, thus giving the opportunity of both conferences to attendees to enjoy the many attractions o?ered by two neighboring cities in the state of Florida. SPR 2008 and SSPR 2008 received a total of 175 paper submissions from many di?erent countries around the world, thus giving the workshop an int- national clout, as was the case for past workshops. This volume contains 98 accepted papers: 56 for oral presentations and 42 for poster presentations. In addition to parallel oral sessions for SPR and SSPR, there was also one joint oral session with papers of interest to both the SPR and SSPR communities. A recent trend that has emerged in the pattern recognition and machine lea- ing research communities is the study of graph-based methods that integrate statistical andstructural approaches.

This volume offers a well-structured overview of existent computational approaches to Riemann surfaces and those currently in development. The authors of the contributions represent the groups providing publically available numerical codes in this field. Thus this volume illustrates which software tools are available and how they can be used in practice. In addition examples for solutions to partial differential equations and in surface theory are presented. The intended audience of this book is twofold. It can be used as a textbook for a graduate course in numerics of Riemann surfaces, in which case the standard undergraduate background, i.e., calculus and linear algebra, is required. In particular, no knowledge of the theory of Riemann surfaces is expected; the necessary background in this theory is contained in the Introduction chapter. At the same time, this book is also intended for specialists in geometry and mathematical physics applying the theory of Riemann surfaces in their research. It is the first book on numerics of Riemann surfaces that reflects the progress made in this field during the last decade, and it contains original results. There are a growing number of applications that involve the evaluation of concrete characteristics of models analytically described in terms of Riemann surfaces. Many problem settings and computations in this volume are motivated by such concrete applications in geometry and mathematical physics.

The three-dimensional structure and function of molecules present many challenges and opportunities for developing an understanding of biological systems. With the increasing availability of molecular structures and the advancing accuracy of structure predictions and molecular simulations, the space for algorithmic advancement on many analytical and predictive problems is both broad and deep. To support this field, a rich set of methods and algorithms are available, addressing a variety of important problems such as protein-protein interactions, the effect of mutations on protein structure and function, and protein structure determination. Despite recent advancements in the field, in particular in protein folding with the development of AlphaFold, many problems still remain unsolved. In this book we focus on a number of topics in Structural Bioinformatics: Cryo-EM structural detection, protein conformational exploration, elucidation of molecular binding surface using geometry, the effect of mutations, insertions and deletions on protein structural stability, and protein-ligand binding.

Additive manufacturing (AM) methods have great potential for promoting transformative research in many fields across the vast spectrum of engineering and materials science. AM is one of the leading forms of advanced manufacturing which enables direct computer-aided design (CAD) to part production without part-specific tooling. In October 2015 the National Academies of Sciences, Engineering, and Medicine convened a workshop of experts from diverse communities to examine predictive theoretical and computational approaches for various AM technologies. While experimental workshops in AM have been held in the past, this workshop uniquely focused on theoretical and computational approaches and involved areas such as simulation-based engineering and science, integrated computational materials engineering, mechanics, materials science, manufacturing processes, and other specialized areas. This publication summarizes the presentations and discussions from the workshop.