In this article we review some generalizations of classical theories of measurement for concatenation (e.g., mass or length) and conjoint structures (e.g., momentum of mass-velocity pairs or loudness of intensity-frequency pairs). The earlier results on additive representations are briefly surveyed. Generalizations to nonadditive structures are outlined, and their more complex uniqueness result...

In the last lecture, we studied codes based on univarite polynomials, also known as Reed-Solomon codes, and on multivariate polynomials, also known as Reed-Muller codes. The Reed-Solomon codes had rate R = 1 − δ, which is optimal (given by the Singleton bound), but required alphabets of large size (|Σ| ≥ n). Multivariate polynomials in a constant number of variables, however, gave codes of posi...

It has been known that quantum error correction via concatenated codes can be done with exponentially small failure rate if the error rate for physical qubits is below a certain accuracy threshold. Other, unconcatenated codes with their own attractive features—improved accuracy threshold, local operations—have also been studied. By iteratively distilling a certain two-qubit entangled state it i...

Genome-scale sequencing has been of great benefit in recovering species trees but has not provided final answers. Despite the rapid accumulation of molecular sequences, resolving short and deep branches of the tree of life has remained a challenge and has prompted the development of new strategies that can make the best use of available data. One such strategy-the concatenation of gene alignmen...

Recently two ways of concatenating pushdowns have be investigated and it has been argued that the resulting storage types might be useful for the description of natural languages. In this paper I will consider concatenations of oneeturn pushdowns. I will give characterizations of the languages accepted by automata using these storage types in terms of linear grammars with controlled derivations...

String concatenation via the “+” operator is one of the most convenient things to do in Java, and also one of the most expensive, in terms of memory and performance. In this paper, we present a comprehensive approach to reduce the overhead of consuming string concatenation operations by implicitly transforming the Java bytecode. The transformation is based on the results of the liveness analysi...

We settle in the negative the following Problem 51 (Comon{Dauchet, RTA'93 3], RTA'95 4]). Given an arbitrary nite term rewriting system R, is the rst-order theory of one-step rewriting (!R) decidable? Decidability would imply the decid-ability of the rst-order theory of encompassment (that is, being an instance of a subterm) 1], as well as several known decidability results in rewriting. (It is...

We present a class of O(n log n) heuristics for the Steiner tree problem in the Euclidean plane. These heuristics identify a small number of subsets with few, geometrically close, terminals using minimum spanning trees and other well-known structures from computational geometry: De-launay triangulations, Gabriel graphs, relative neighbourhood graphs, and higher-order Voronoi diagrams. Full Stei...