Energy-Efficient Algorithms

We initiate the systematic study of the energy complexity of algorithms (in addition to time and space complexity) based on Landauer's Principle in physics, which gives a lower bound on the amount of energy a system must dissipate if it destroys information. We propose energy-aware variations of three standard models of computation: circuit RAM, word RAM, and transdichotomous RAM. On top of these models, we build familiar high-level primitives such as control logic, memory allocation, and garbage collection with zero energy complexity and only constant-factor overheads in space and time complexity, enabling simple expression of energy-efficient algorithms. We analyze several classic algorithms in our models and develop low-energy variations: comparison sort, insertion sort, counting sort, breadth-first search, Bellman-Ford, Floyd-Warshall, matrix all-pairs shortest paths, AVL trees, binary heaps, and dynamic arrays. We explore the time/space/energy trade-off and develop several general techniques for analyzing algorithms and reducing their energy complexity. These results lay a theoretical foundation for a new field of semi-reversible computing and provide a new framework for the investigation of algorithms.Comment: 40 pages, 8 pdf figures, full version of work published in ITCS 201

Distinguishing schemes and tasks in children's development of multiplicative reasoning

We present a synthesis of findings from constructivist teaching experiments regarding six schemes children construct for reasoning multiplicatively and tasks to promote them. We provide a task-generating platform game, depictions of each scheme, and supporting tasks. Tasks must be distinguished from children’s thinking, and learning situations must be organized to (a) build on children’s available schemes, (b) promote the next scheme in the sequence, and (c) link to intended mathematical concepts

Buzz monitoring in word space

This paper discusses the task of tracking mentions of some topically interesting textual entity from a continuously and dynamically changing flow of text, such as a news feed, the output from an Internet crawler or a similar text source - a task sometimes referred to as buzz monitoring. Standard approaches from the field of information access for identifying salient textual entities are reviewed, and it is argued that the dynamics of buzz monitoring calls for more accomplished analysis mechanisms than the typical text analysis tools provide today. The notion of word space is introduced, and it is argued that word spaces can be used to select the most salient markers for topicality, find associations those observations engender, and that they constitute an attractive foundation for building a representation well suited for the tracking and monitoring of mentions of the entity under consideration

Neural Mechanisms for Information Compression by Multiple Alignment, Unification and Search

This article describes how an abstract framework for perception and cognition may be realised in terms of neural mechanisms and neural processing. This framework — called information compression by multiple alignment, unification and search (ICMAUS) — has been developed in previous research as a generalized model of any system for processing information, either natural or artificial. It has a range of applications including the analysis and production of natural language, unsupervised inductive learning, recognition of objects and patterns, probabilistic reasoning, and others. The proposals in this article may be seen as an extension and development of Hebb’s (1949) concept of a ‘cell assembly’. The article describes how the concept of ‘pattern’ in the ICMAUS framework may be mapped onto a version of the cell assembly concept and the way in which neural mechanisms may achieve the effect of ‘multiple alignment’ in the ICMAUS framework. By contrast with the Hebbian concept of a cell assembly, it is proposed here that any one neuron can belong in one assembly and only one assembly. A key feature of present proposals, which is not part of the Hebbian concept, is that any cell assembly may contain ‘references’ or ‘codes’ that serve to identify one or more other cell assemblies. This mechanism allows information to be stored in a compressed form, it provides a robust mechanism by which assemblies may be connected to form hierarchies and other kinds of structure, it means that assemblies can express abstract concepts, and it provides solutions to some of the other problems associated with cell assemblies. Drawing on insights derived from the ICMAUS framework, the article also describes how learning may be achieved with neural mechanisms. This concept of learning is significantly different from the Hebbian concept and appears to provide a better account of what we know about human learning

Common Place Names

Articles about American placenames in Word Ways have generally reflected their great diversity. But what about their commonality? There\u27s lots of duplication among the names of American places. Isn\u27t it time that we had an article appreciating that fact