Knowledge representation for mathematical discovery: Three experiments in graph theory

This paper describes the nature of mathematical discovery (including concept definition and exploration, example generation, and theorem conjecture and proof), and considers how such an intelligent process can be simulated by a machine. Although the material is drawn primarily from graph theory, the results are immediately relevant to research in mathematical discovery and learning.The thought experiment, a protocol paradigm for the empirical study of mathematical discovery, highlights behavioral objectives for machine simulation. This thought experiment provides an insightful account of the discovery process, motivates a framework for describing mathematical knowledge in terms of object classes, and is a rich source of advice on the design of a system to perform discovery in graph theory. The evaluation criteria for a discovery system, it is argued, must include both a set of behavior to display (behavioral objectives) and a target set of facts to be discovered (factual knowledge).Cues from the thought experiment are used to formulate two hierarchies of representational languages for graphy theory. The first hierarchy is based on the superficial terminology and knowledge of the thought experiment. Generated by formal grammars with set-theoretic semantics, this eminently reasonable approach ultimately fails to meet the factual knowledge criteria. The second hierarchy uses declarative expressions, each of which has a semantic interpretation as a stylized, recursive algorithm that defines a class by generating it correctly and completely. A simple version of one such representation is validated by a successful, implemented system called Graph Theorist (GT) for mathematical research in graph theory. GT generates correct examples, defines and explores new graph theory properties, and conjectures and proves theorems.Several themes run through this paper. The first is the dual goals, behavioral objectives and factural knowledge to be discovered, and the multiplicity of their demands on a discovery system. The second theme is the central role of object classes to knowledge representation. The third is the increased power and flexibility of a constructive (generator) definition over the more traditional predicate (tester) definition. The final theme is the importance of examples and recursion in mathematical knowledge. The results provide important guidance for further research in the simulation of mathematical discovery.     

On the geometrical material structure of anelasticity

Summary G-structures are the geometric backbone of the theory of material uniformity in continuum mechanics. Within this geometric framework, anelasticity is seen as a result of evolving distributions of inhomogeneity reflected as material nonintegrability. Constitutive principles governing thetime evolution of the G-structure underlying the finite-strain theory of anelasticity (e.g., plasticity) are proposed. The material Eshelby stress tensor is shown to be thedriving force behind this evolution. This should allow for a thermodynamically admissible formulation of anelasticity viewed as a G-structure evolution.     

The bone marrow stromal environment is a major factor in myeloma cell resistance to dexamethasone

The expression of several markers of epithelial cell proliferation was analyzed to establish baseline data for future chemoprevention studies of oral premalignant lesions. Punch biopsies (n = 60) from three different sites of oral mucosa (bucca, lateral tongue, and the floor of the mouth) were obtained from 20 normal donors of both sexes. After formaldehyde fixation and paraffin embedding, immunohistochemistry was used to detect the proliferation markers Mib-1, cyclin D1, and centromere-associated protein CENP-F. Analysis of sections stained for the three markers showed similar patterns, i.e., a low labeling index (LI) in the basal layer and a high LI in the parabasal layer at all three intraoral sites. No proliferative activity was seen above the parabasal layer (superficial layer). All sites showed similar Mib-1 LI values for the proliferative markers. The tongue epithelium exhibited higher parabasal LIs of cyclin D1 and CENP-F than did the other two sites. No significant differences were detected between smokers and nonsmokers. The data from normal mucosa were compared with those from low (n = 30)- and high (n = 17)-grade dysplastic leukoplakias. The Mib-1 LI showed a very significant change, with a 9-fold increase in the basal layer LI in dysplastic leukoplakias. Cyclin D1 and CENP-F showed similar trends with increments of up to 7-fold in the basal layer of high-grade dysplasia. Although the proliferative activity of the parabasal layer was similar in normal and leukoplakic epithelia, the superficial layer showed a significant increment in proliferative activity mainly in high-grade leukoplakia. These studies suggest that proliferation markers in the basal and superficial cells of premalignant lesions may serve as surrogate end point biomarkers for chemoprevention trials.     

On the modification of reprints.

Defends the practice of modifying reprints of journal articles to amend typographical and other errors that can affect meaning. A standard should be developed for dealing with such errors by hand writing corrections, including a list of errata, or issuing professionally corrected reprints with the notation that corrections have been made. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Nonsulfhydryl-reactive phenoxyacetic acids increase aqueous humor outflow facility

PURPOSE: The phenoxyacetic acid, ethacrynic acid (ECA), has potential use in glaucoma therapy because it acts to increase aqueous outflow in vivo and in vitro. In human trabecular meshwork (HTM) cell culture, ECA acts to change cell shape and attachment, effects that have been correlated with microtubule (MT) alterations and chemical sulfhydryl (SH) reactivity. To further explore these actions, we evaluated two non-SH reactive phenoxyacetic acids, inadcrinone and ticrynafen, and the MT-disrupting drug vinblastine. METHODS: Excised bovine and porcine eyes were perfused and outflow facility measured. Calf pulmonary artery endothelial and HTM cells were grown in culture and cytoskeletal effects evaluated after drug treatment. RESULTS: Indacrinone, ticrynafen, and vinblastine all caused an increase in outflow facility. In contrast with ECA, the outflow effects of indacrinone and ticrynafen were not blocked by excess cysteine. Although indacrinone and ticrynafen produced changes in cell shape in vitro, the beta-tubulin staining pattern of treated cells was not altered. Vinblastine caused cell shape change and the expected MT disruption. CONCLUSIONS: Phenoxyacetic acids can increase aqueous outflow facility and alter HTM cell shape and attachment in vitro by a non-SH, non-MT mechanism (which is probably shared also by ECA). These findings suggest the possibility of a broader class of glaucoma drugs that may be directed at the HTM. An understanding of the cellular target for these drugs has implications both for potential glaucoma therapy and for the cytoskeletal mechanisms involved in normal outflow function.     

Information Assurance Technology Forecast 2008

A virtual roundtable (featuring panelists Steven Bellovin, Terry Benzel, Bob Blakely, Dorothy Denning, Whitfield Diffie, Jeremy Epstein, and Paulo Verissimo) discussing the next 15 years in computer security.     

The Xcad-2 gene can provide a ventral signal independent of BMP-4

Patterning of the marginal zone in the Xenopus embryo has been attributed to interactions between dorsal genes expressed in the organizer and ventral-specific genes. In this antagonistic interplay of activities, BMP-4, a gene that is not expressed in the organizer, provides a strong ventralizing signal. The Xenopus caudal type homeobox gene, Xcad-2, which is expressed around the blastopore with a gap over the dorsal lip, was analyzed as part of the ventral signal. Xcad-2 was shown to efficiently repress during early gastrula stages the dorsal genes gsc, Xnot-2, Otx-2, XFKH1 and Xlim-1, while it positively regulates the ventral genes, Xvent-1 and Xvent-2, with Xpo exhibiting a strong positive response to Xcad-2 overexpression. Xcad-2 was also capable of inducing BMP-4 expression in the organizer region. Support for a ventralizing role for Xcad-2 was obtained from co-injection experiments with the dominant negative BMP receptor which was used to block BMP-4 signaling. Under lack-of-BMP-signaling conditions Xcad-2 could still regulate dorsal and ventral gene expression and restore normal development, suggesting that it can act downstream of BMP-4 signaling or independently of it. Xcad-2 could also inhibit secondary axis formation and dorsalization induced by the dominant negative BMP receptor. Xcad-2 was also shown to efficiently reverse the dorsalizing effects of LiCl. These results place Xcad-2 as part of the ventralizing gene program which acts during early gastrula stages and can execute its ventralizing function in the absence of BMP signaling.