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.     

A bi-labeling based XPath processing system

We present BLAS, a Bi-LAbeling based XPath processing System. BLAS uses two labeling schemes to speed up query processing: P-labeling for processing consecutive child (or parent) axis traversals, and D-labeling for processing descendant (or ancestor) axis traversals. XML data are stored in labeled form and indexed. Algorithms are presented for translating XPath queries to SQL expressions. BLAS reduces the number of joins in the SQL query translated from a given XPath query and reduces the number of disk accesses required to execute the SQL query compared with the traditional XPath processing using D-labeling alone. We also propose an approximate P-labeling scheme and the corresponding query translation algorithm to handle XML data trees that contain a large number of distinct tag names, and/or are very deep. This extension captures a spectrum of XPath-to-SQL query translation schemes, ranging from existing schemes that do not use P-labels to the one that uses exact P-labels. Experimental results demonstrate the efficiency of the BLAS system.     

Optimizing disk storage to support statistical analysis operations

Data stored in spreadsheets and relational database tables can be viewed as “worksheets” consisting of rows and columns, with rows corresponding to records. Correspondingly, the typical practice is to store the data on disk in row major order. While this practice is reasonable in many cases, it is not necessarily the best practice when computation is dominated by column-based statistics. This short note discusses the performance tradeoffs between row major and column major storage of data in the context of statistical data analysis. A comparison of a software package utilizing column major storage and one using row major storage confirms our results.     

Transport of chemical and microbial compounds from known wastewater discharges: potential for use as indicators of human fecal contamination

The quality of drinking and recreational water is currently (2005) determined using indicator bacteria. However, the culture tests used to analyze forthese bacteria require a long time to complete and do not discriminate between human and animal fecal material sources. One complementary approach is to use chemicals found in human wastewater, which would have the advantages of (1) potentially shorter analysis times than the bacterial culture tests and (2) being selected for human-source specificity. At 10 locations, water samples were collected upstream and at two successive points downstream from a wastewaster treatment plant (WWTP); a treated effluent sample was also collected at each WWTP. This sampling plan was used to determine the persistence of a chemically diverse suite of emerging contaminants in streams. Samples were also collected at two reference locations assumed to have minimal human impacts. Of the 110 chemical analytes investigated in this project, 78 were detected at least once. The number of compounds in a given sample ranged from 3 at a reference location to 50 in a WWTP effluent sample. The total analyte load at each location varied from 0.018 microg/L at the reference location to 97.7 microg/L in a separate WWTP effluent sample. Although most of the compound concentrations were in the range of 0.01-1.0 microg/L, in some samples, individual concentrations were in the range of 5-38 microg/L. The concentrations of the majority of the chemicals present in the samples generally followed the expected trend: they were either nonexistent or at trace levels in the upstream samples, had their maximum concentrations in the WWTP effluent samples, and then declined in the two downstream samples. This research suggests that selected chemicals are useful as tracers of human wastewater discharge.     

Antioxidant properties of commercial, regular- and whole-wheat spaghetti

Whole grains contain more vitamins, minerals, natural antioxidants and dietary fibre than regular, refined grain products. Therefore, consumption of whole grain products is associated with beneficial health effects. The present investigation evaluated the antioxidant properties of 10 samples of regular- and whole-wheat spaghetti that are commercially available. The methods employed were total phenolic content (TPC), 2,2-diphenyl-1-picryhydrazyl (DPPH) free radical scavenging activity, oxygen radical absorbance capacity (ORAC) and ferulic acid content by HPLC analysis. The effects of cooking on the antioxidant properties of spaghetti were also studied. Whole wheat spaghetti exhibited significantly higher levels of total phenolic content (1389 μg/g) than regular wheat spaghetti (865 μg/g); however, TPC in both regular and whole wheat spaghetti was 48–78% of the original content after cooking. There were no significant differences in ORAC values (34.3–100.4 μmol Trolox equivalents/g) or DPPH scavenging activity (1.0–2.3 μmol Trolox equivalents) among whole wheat and regular spaghetti. Whole wheat spaghetti (234 μg/g) had significantly higher content of ferulic acid than regular spaghetti (p < 0.05). TPC and ferulic acid content were found to be good indicators of the antioxidant capacity of spaghetti with both indices demonstrating the superiority of whole wheat over regular pasta products. The current findings on spaghetti add to the mounting evidence on the potential health benefits to be derived from consuming whole grain products.     

Effects of simulated digestion in vitro on cell wall polysaccharides from kiwifruit (Actinidia spp.)

Cell wall polysaccharides are resistant to digestion and absorption in the human small intestine and are considered to be delivered to the colon in a chemically unaltered state. In this paper, pulp from green and gold kiwifruit was subjected to in vitro upper-intestinal tract digestion and the chemical and physical changes to cell wall polysaccharides (dietary fibre) were investigated. Yields of insoluble fibre decreased slightly with simulated digestion while soluble fibre yields increased. Constituent sugar and glycosyl linkage analysis of the soluble and insoluble fibre fractions revealed that the chemical composition and structure of the non-starch polysaccharides remained largely unchanged. However, the degree of methylesterification of galacturonic acid residues present in the pectin-rich soluble fibre fractions of both fruit decreased with treatment; size-exclusion chromatography detected changes in the molecular weight profiles of these fractions. These changes may affect the physicochemical properties and fermentability of kiwifruit dietary fibre in the large intestine.     

Poly(L‐lactic acid) with added α‐tocopherol and resveratrol: optical,physical, thermal and mechanical properties

Poly(L ‐lactic acid) (PLLA) films containing various concentrations of two natural antioxidants, α‐tocopherol and resveratrol, were fabricated by a melt compounding and compression molding process. The influence of the antioxidants on the optical properties such as color and UV‐visible light transmission was analyzed. The thermal, mechanical, rheological and physical properties of PLLA films with added antioxidants were assessed. PLLA films with added α‐tocopherol and resveratrol showed a yellowish brown color and the lightness was influenced by the presence of the antioxidants. The glass transition and melting temperatures were significantly reduced with the addition of antioxidants while enhanced thermal stability was observed, which could be a benefit and important for processing and production. PLLA films with added antioxidants were slightly more hydrophobic than neat PLLA. The combination effect of plasticizing and enhancement of the elastic modulus with differing concentrations of two antioxidants played a critical role in the mechanical and thermomechanical properties of PLLA films. The melt viscosity of the PLLA films with added antioxidants was substantially higher than that of neat PLLA. The higher melt viscosity and G′(ω) could be an indication of formation of entanglement between PLLA and the two antioxidants. Copyright © 2012 Society of Chemical Industry     

Analysis of Clinic Layouts and Patient-Centered Procedural Innovations Using Discrete-Event Simulation

Abstract

Given that healthcare costs in the U.S. continue to climb, engineering managers can help address this situation by identifying designs for cost savings. Using discrete-event simulation, the layout of four different healthcare clinic scenarios considered in a redesign program named Patient Aligned Care Teams were studied. Model 1 is an existing layout in many clinics and Model 2 is staff-centered, while Models 3 and 4 provide additional space including common hallway(s). Our main conclusion is that Model 4 reduces patient travel distances and average queueing waits, while also providing the best privacy in accordance with HIPAA and the most security for the staff.     

Extraction,optimisation and characterisation of phenolics from Thymus vulgaris L.: phenolic content and profiles in relation to antioxidant,antidiabetic and antihypertensive properties

The objectives of this study were to examine varying extraction conditions of Thymus vulgaris L. as related to phenolic content and profiles of the extracts and their antioxidant, antihypertensive and antidiabetic properties. Phenolics were extracted under various conditions pertaining to free and bound phenolics, solvent type and combination of extraction time and temperature, and these extracts were evaluated in terms of their antioxidant activities and inhibitory activities of angiotensin‐converting enzyme (ACE), α‐glucosidase and α‐amylase. The acetone–water solvent mixture (1:1; v/v) produced the extract with the greatest phenolic content, antioxidant activity and inhibitory activities of ACE and α‐glucosidase. The optimal extraction temperature for maximum phenolic content and antioxidant activity associated with methanol extraction was 60 °C, whereas a lower temperature at 40 °C was required to maximise inhibitory activities for ACE, α‐glucosidase and α‐amylase. An inverse relationship was seen between antioxidant and glucosidase inhibitory activities vs. the ACE and α‐amylase inhibitory activities, which suggests the need for extractions to be directed to specific bioactivities of thyme extracts. Generally, the results indicate major differences in phenolic profiles among the tested extraction conditions with thymol as the predominant phenolic seen in most extractions, while gallic acid, rosmarinic acid or diosmin also predominated in other extracts. Extracts with the same predominant phenolic compound and similar phenolic content showed major disparities in their ACE, glucosidase and α‐amylase inhibitory activities, indicating that the major phenolic profiles of thyme extracts may not be necessarily related to the degree of inhibition of ACE, glucosidase and α‐amylase enzymes.