Self-Similar Random Processes and Infinite-Dimensional Configuration Spaces

We discuss various infinite-dimensional configuration spaces that carry measures quasiinvariant under compactly-supported diffeomorphisms of a manifold M corresponding to a physical space. Such measures allow the construction of unitary representations of the diffeomorphism group, which are important to nonrelativistic quantum statistical physics and to the quantum theory of extended objects in d-dimensional Euclidean space. Special attention is given to measurable structure and topology underlying measures on generalized configuration spaces obtained from self-similar random processes (both for d = 1 and d > 1), which describe infinite point configurations having accumulation points

Some Variations on Maxwell's Equations

In the first sections of this article, we discuss two variations on Maxwell's equations that have been introduced in earlier work--a class of nonlinear Maxwell theories with well-defined Galilean limits (and correspondingly generalized Yang-Mills equations), and a linear modification motivated by the coupling of the electromagnetic potential with a certain nonlinear Schroedinger equation. In the final section, revisiting an old idea of Lorentz, we write Maxwell's equations for a theory in which the electrostatic force of repulsion between like charges differs fundamentally in magnitude from the electrostatic force of attraction between unlike charges. We elaborate on Lorentz' description by means of electric and magnetic field strengths, whose governing equations separate into two fully relativistic Maxwell systems--one describing ordinary electromagnetism, and the other describing a universally attractive or repulsive long-range force. If such a force cannot be ruled out {\it a priori} by known physical principles, its magnitude should be determined or bounded experimentally. Were it to exist, interesting possibilities go beyond Lorentz' early conjecture of a relation to (Newtonian) gravity.Comment: 26 pages, submitted to a volume in preparation to honor Gerard Emch v. 2: discussion revised, factors of 4\pi corrected in some equation

Manifolds associated with (Z2)n(Z_2)^n-colored regular graphs

In this article we describe a canonical way to expand a certain kind of $(\mathbb Z_2)^{n+1}$-colored regular graphs into closed $n$-manifolds by adding cells determined by the edge-colorings inductively. We show that every closed combinatorial $n$-manifold can be obtained in this way. When $n\leq 3$, we give simple equivalent conditions for a colored graph to admit an expansion. In addition, we show that if a $(\mathbb Z_2)^{n+1}$-colored regular graph admits an $n$-skeletal expansion, then it is realizable as the moment graph of an $(n+1)$-dimensional closed $(\mathbb Z_2)^{n+1}$-manifold.Comment: 20 pages with 9 figures, in AMS-LaTex, v4 added a new section on reconstructing a space with a $(Z_2)^n$-action for which its moment graph is a given colored grap

Energy Spectrum of Anyons in a Magnetic Field

For the many-anyon system in external magnetic field, we derive the energy spectrum as an exact solution of the quantum eigenvalue problem with particular topological constraints. Our results agree with the numerical spectra recently obtained for the 3- and the 4-anyon systems.Comment: 11 pages in Plain LaTeX (plus 4 figures available on request), DFPD 92/TH/4

Challenges and solutions for the eradication of sanitation backlogs in the policy context of Free Basic Sanitation

Despite the constitutional obligation for municipalities to provide Free Basic Sanitation (FBSan) services to all, many people living in informal settlements in South Africa are still lacking access to adequate sanitation facilities. This study used qualitative methods to examine challenges and identify solutions for the eradication of sanitation backlogs in informal settlement of South Africa in the policy context of the FBSan. Findings suggest that the disconnection between the policy and its application in practice has created a deep divide between the service providers and consumers as recipients of the services. Consumers’ perceptions and expectations are a major barrier to the acceptance of the sanitation services provided by municipalities, often resulting in violent protests. Service providers face challenges when addressing the disjuncture between what people aspire to and what is possible in providing sanitation services. These findings infer that consumers’ needs, sanitation practices and settlement conditions should be thoroughly examined prior to the selection and deployment of sanitation facilities in informal settlements. Consumers should be engaged and involved in the choice of sanitation technologies and facilities. Such engagement should evolve around various sanitation technologies and facilities applicable to the nature and context of informal settlements, so as to address negative perceptions, attitudes and behavior concerning services provided by municipalities. Addressing challenges related to the eradication of the sanitation backlogs in the policy context of FBSan services needs to be grounded in the clarification of sanitation policy, a deep understanding of consumers’ needs, challenges and practices as well as settlements conditions, coupled with meaningful consumers’ participation at various stages of the decision-making process and coordination amongst institutions involved. Municipalities need to engage all stakeholders (mainly consumers) in order to ensure that the selected infrastructure and service level deployed are consensual. Unless subjective clauses of the FBSan policy are clarified, monitoring, enforcement and accountability mechanisms established and implemented and, consumers are engaged in the decision making processes, the eradication of sanitation backlogs in informal settlements as currently planned may not materialize

The REVERE project:Experiments with the application of probabilistic NLP to systems engineering

Despite natural language’s well-documented shortcomings as a medium for precise technical description, its use in software-intensive systems engineering remains inescapable. This poses many problems for engineers who must derive problem understanding and synthesise precise solution descriptions from free text. This is true both for the largely unstructured textual descriptions from which system requirements are derived, and for more formal documents, such as standards, which impose requirements on system development processes. This paper describes experiments that we have carried out in the REVERE1 project to investigate the use of probabilistic natural language processing techniques to provide systems engineering support

Gesturing with an Injured Brain: How Gesture Helps Children with Early Brain Injury Learn Linguistic Constructions

Children with pre/perinatal unilateral brain lesions (PL) show remarkable plasticity for language development. Is this plasticity characterized by the same developmental trajectory that characterizes typically developing (TD) children, with gesture leading the way into speech ? We explored this question, comparing eleven children with PL – matched to thirty TD children on expressive vocabulary – in the second year of life. Children with PL showed similarities to TD children for simple but not complex sentence types. Children with PL produced simple sentences across gesture and speech several months before producing them entirely in speech, exhibiting parallel delays in both gesture+speech and speech-alone. However, unlike TD children, children with PL produced complex sentence types first in speech-alone. Overall, the gesture–speech system appears to be a robust feature of language learning for simple – but not complex – sentence constructions, acting as a harbinger of change in language development even when that language is developing in an injured brain