When scientists analyze datasets in a search for underlying phenomena, patterns or causal factors, their first step is often an automatic or semi-automatic search for structures in the data. Of these feature-extraction methods, topological ones stand out due to their solid mathematical foundation. Topologically defined structures—as...

It compiles the key elements of...

Collaborative leadership is about delivering results across boundaries. The nature of that boundary is important, whether it's a formal contract or an informal agreement between two parties to work together for a common aim. And leaders need to be clear about where the boundary lies and how to use the different capabilities on either side...

Using the tools of complexity theory, Stephen Judd develops a formal description of associative learning in connectionist networks. He rigorously exposes the computational difficulties in training neural networks and explores how certain design principles will or will not make the problems easier.

Judd looks beyond the scope...

Finite-state devices, which include finite-state automata, graphs, and finite-state transducers, are in wide use in many areas of computer science. Recently, there has been a resurgence of the use of finite-state devices in all aspects of computational linguistics, including dictionary encoding, text processing, and speech processing. This...

Few branches of mathematics have been more influential in the social sciences than game theory. In recent years, it has become an essential tool for all social scientists studying the strategic behaviour of competing individuals, firms and countries. However, the mathematical complexity of game theory is often very intimidating for students...

Logic is sometimes called the foundation of mathematics: the logician studies the kinds of reasoning used in the individual steps of a proof. Alonzo Church was a pioneer in the field of mathematical logic, whose contributions to number theory and the theories of algorithms and computability laid the theoretical foundations of computer...

While compilers for high-level programming languages are large complex software systems, they have particular characteristics that differentiate them from other software systems. Their functionality is almost completely well-defined – ideally there exist complete precise descriptions of the source and target languages. Additional...