Representation is integral to the functioning and legitimacy of modern government. Yet political theorists have often been reluctant to engage directly with questions of representation, and empirical political scientists have closed down such questions by making representation synonymous with congruence. Conceptually unproblematic and normatively inert for some, representation has been deemed impossible to pin down analytically and to defend normatively by others. But this is changing. Political theorists are now turning to political representation as a subject worthy of theoretical investigation in its own right. In their effort to rework the theory of political representation, they are also hoping to impact how representation is assessed and studied empirically. This volume gathers together chapters by key contributors to what amounts to a "representative turn" in political theory. Their approaches and emphases are diverse, but taken together they represent a compelling and original attempt at re-conceptualizing political representation and critically assessing the main theoretical and political implications following from this, namely for how we conceive and assess representative democracy. Each contributor is invited to look back and ahead on the transformations to democratic self-government introduced by the theory and practice of political representation. Representation and democracy: outright conflict, uneasy cohabitation, or reciprocal constitutiveness? For those who think democracy would be better without representation, this volume is a must-read: it will question their assumptions, while also exploring some of the reasons for their discomfort. Reclaiming Representation is essential reading for scholars and graduate researchers committed to staying on top of new developments in the field.

Representation and Understanding

In 1991-1993 our three-volume book "Representation of Lie Groups and Spe cial Functions" was published. When we started to write that book (in 1983), editors of "Kluwer Academic Publishers" expressed their wish for the book to be of encyclopaedic type on the subject. Interrelations between representations of Lie groups and special functions are very wide. This width can be explained by existence of different types of Lie groups and by richness of the theory of their rep resentations. This is why the book, mentioned above, spread to three big volumes. Influence of representations of Lie groups and Lie algebras upon the theory of special functions is lasting. This theory is developing further and methods of the representation theory are of great importance in this development. When the book "Representation of Lie Groups and Special Functions" ,vol. 1-3, was under preparation, new directions of the theory of special functions, connected with group representations, appeared. New important results were discovered in the traditional directions. This impelled us to write a continuation of our three-volume book on relationship between representations and special functions. The result of our further work is the present book. The three-volume book, published before, was devoted mainly to studying classical special functions and orthogonal polynomials by means of matrix elements, Clebsch-Gordan and Racah coefficients of group representations and to generaliza tions of classical special functions that were dictated by matrix elements of repre sentations.

This open access book provides an overview of the recent advances in representation learning theory, algorithms and applications for natural language processing (NLP). It is divided into three parts. Part I presents the representation learning techniques for multiple language entries, including words, phrases, sentences and documents. Part II then introduces the representation techniques for those objects that are closely related to NLP, including entity-based world knowledge, sememe-based linguistic knowledge, networks, and cross-modal entries. Lastly, Part III provides open resource tools for representation learning techniques, and discusses the remaining challenges and future research directions. The theories and algorithms of representation learning presented can also benefit other related domains such as machine learning, social network analysis, semantic Web, information retrieval, data mining and computational biology. This book is intended for advanced undergraduate and graduate students, post-doctoral fellows, researchers, lecturers, and industrial engineers, as well as anyone interested in representation learning and natural language processing.

Graph-structured data is ubiquitous throughout the natural and social sciences, from telecommunication networks to quantum chemistry. Building relational inductive biases into deep learning architectures is crucial for creating systems that can learn, reason, and generalize from this kind of data. Recent years have seen a surge in research on graph representation learning, including techniques for deep graph embeddings, generalizations of convolutional neural networks to graph-structured data, and neural message-passing approaches inspired by belief propagation. These advances in graph representation learning have led to new state-of-the-art results in numerous domains, including chemical synthesis, 3D vision, recommender systems, question answering, and social network analysis. This book provides a synthesis and overview of graph representation learning. It begins with a discussion of the goals of graph representation learning as well as key methodological foundations in graph theory and network analysis. Following this, the book introduces and reviews methods for learning node embeddings, including random-walk-based methods and applications to knowledge graphs. It then provides a technical synthesis and introduction to the highly successful graph neural network (GNN) formalism, which has become a dominant and fast-growing paradigm for deep learning with graph data. The book concludes with a synthesis of recent advancements in deep generative models for graphs—a nascent but quickly growing subset of graph representation learning.

Aims to collect papers on learning declarative knowledge and problem solving skills that involve multiple representations such as graphical and mathematical representations, knowledge at different levels of abstraction. This book covers approaches to this topic from different perspectives: educational, cognitive modelling and machine learning.

This two-volume set LNAI 14471-14472 constitutes the refereed proceedings of the 36th Australasian Joint Conference on Artificial Intelligence, AI 2023, held in Brisbane, QLD, Australia during November 28 – December 1, 2023. The 23 full papers presented together with 59 short papers were carefully reviewed and selected from 213 submissions. They are organized in the following topics: computer vision; deep learning; machine learning and data mining; optimization; medical AI; knowledge representation and NLP; explainable AI; reinforcement learning; and genetic algorithm.

In Art and Representation, John Willats presents a radically new theory of pictures. To do this, he has developed a precise vocabulary for describing the representational systems in pictures: the ways in which artists, engineers, photographers, mapmakers, and children represent objects. His approach is derived from recent research in visual perception and artificial intelligence, and Willats begins by clarifying the key distinction between the marks in a picture and the features of the scene that these marks represent. The methods he uses are thus closer to those of a modern structural linguist or psycholinguist than to those of an art historian. Using over 150 illustrations, Willats analyzes the representational systems in pictures by artists from a wide variety of periods and cultures. He then relates these systems to the mental processes of picture production, and, displaying an impressive grasp of more than one scholarly discipline, shows how the Greek vase painters, Chinese painters, Giotto, icon painters, Picasso, Paul Klee, and David Hockney have put these systems to work. But this book is not only about what systems artists use but also about why artists from different periods and cultures have used such different systems, and why drawings by young children look so different from those by adults. Willats argues that the representational systems can serve many different functions beyond that of merely providing a convincing illusion. These include the use of anomalous pictorial devices such as inverted perspective, which may be used for expressive reasons or to distance the viewer from the depicted scene by drawing attention to the picture as a painted surface. Willats concludes that art historical changes, and the developmental changes in children's drawings, are not merely arbitrary, nor are they driven by evolutionary forces. Rather, they are determined by the different functions that the representational systems in pictures can serve. Like readers of Ernst Gombrich's famous Art and Illusion (still available from Princeton University Press), on which Art and Representation makes important theoretical advances, or Rudolf Arnheim's Art and Visual Perception, Willats's readers will find that they will never again return to their old ways of looking at pictures.