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.     

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.     

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.     

A multi-institutional, multinational study of programming concepts using card sort data

Abstract: This paper presents a case study of the use of a repeated single‐criterion card sort with an unusually large, diverse participant group. The study, whose goal was to elicit novice programmers' knowledge of programming concepts, involved over 20 researchers from four continents and 276 participants drawn from 20 different institutions. In this paper we present the design of the study and the unexpected result that there were few discernible systematic differences in the population. The study was one of the activities of the National Science Foundation funded Bootstrapping Research in Computer Science Education project (2003).     

MicroRNAs as Potential Biomarkers in the Differential Diagnosis of Lipomatous Tumors and Their Mimics

Adipocytic tumors are the most common subtype of soft tissue tumors. In current clinical practice, distinguishing benign lipomas from well-differentiated liposarcomas (WDLPS), as well as dedifferentiated liposarcomas (DDLPS) from their morphologic mimics, remains a significant diagnostic challenge. This is especially so when examining small biopsy samples and without the aid of additional ancillary tests. Recognizing the important role that microRNAs (miRNAs) play in tumorigenesis and their potential utility in tumor classification, we analyzed routine clinical tissue samples of benign and malignant lipomatous tumors, as well as other sarcoma mimics, to identify distinguishing miRNA-based signatures that can aid in the differential diagnosis of these entities. We discovered a 6-miRNA signature that separated lipomas from WDLPS with high confidence (AUC of 0.963), as well as a separate 6-miRNA signature that distinguished DDLPS from their more aggressive histologic mimics (AUC of 0.740). Functional enrichment analysis unveiled possible mechanistic involvement of these predictive miRNAs in adipocytic cancer-related biological processes and pathways such as PI3K/AKT/mTOR and MAPK signaling, further supporting the relevance of these miRNAs as biomarkers for adipocytic tumors. Our results demonstrate that miRNA expression profiling may potentially be used as an adjunctive tool for the diagnosis of benign and malignant adipocytic tumors. Further validation studies are warranted.     

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.