The horofunction boundary of the Hilbert geometry

We investigate the horofunction boundary of the Hilbert geometry defined on an arbitrary finite-dimensional bounded convex domain D. We determine its set of Busemann points, which are those points that are the limits of `almost-geodesics'. In addition, we show that any sequence of points converging to a point in the horofunction boundary also converges in the usual sense to a point in the Euclidean boundary of D. We prove that all horofunctions are Busemann points if and only if the set of extreme sets of the polar of D is closed in the Painleve-Kuratowski topology.Comment: 24 pages, 2 figures; minor changes, examples adde

Malaria and land use: a spatial and temporal risk analysis in Southern Sri Lanka

Malaria / Waterborne diseases / Disease vectors / Land use / Water use / GIS / Statistical analysis / Risks / Mapping / Public health / Sri Lanka / Uda Walawe / Thanamalvila / Embilipitiya

Trace Spaces: an Efficient New Technique for State-Space Reduction

State-space reduction techniques, used primarily in model-checkers, all rely on the idea that some actions are independent, hence could be taken in any (respective) order while put in parallel, without changing the semantics. It is thus not necessary to consider all execution paths in the interleaving semantics of a concurrent program, but rather some equivalence classes. The purpose of this paper is to describe a new algorithm to compute such equivalence classes, and a representative per class, which is based on ideas originating in algebraic topology. We introduce a geometric semantics of concurrent languages, where programs are interpreted as directed topological spaces, and study its properties in order to devise an algorithm for computing dihomotopy classes of execution paths. In particular, our algorithm is able to compute a control-flow graph for concurrent programs, possibly containing loops, which is "as reduced as possible" in the sense that it generates traces modulo equivalence. A preliminary implementation was achieved, showing promising results towards efficient methods to analyze concurrent programs, with very promising results compared to partial-order reduction techniques

The Dynamics of Zeroth-Order Ultrasensitivity: A Critical Phenomenon in Cell Biology

It is well known since the pioneering work of Goldbeter and Koshland [Proc. Natl. Acad. Sci. USA, vol. 78, pp. 6840-6844 (1981)] that cellular phosphorylation- dephosphorylation cycle (PdPC), catalyzed by kinase and phosphatase under saturated condition with zeroth order enzyme kinetics, exhibits ultrasensitivity, sharp transition. We analyse the dynamics aspects of the zeroth order PdPC kinetics and show a critical slowdown akin to the phase transition in condensed matter physics. We demonstrate that an extremely simple, though somewhat mathematically "singular" model is a faithful representation of the ultrasentivity phenomenon. The simplified mathematical model will be valuable, as a component, in developing complex cellular signaling network theory as well as having a pedagogic value.Comment: 8 pages, 3 figure

Geometric Path Integrals. A Language for Multiscale Biology and Systems Robustness

In this paper we suggest that, under suitable conditions, supervised learning can provide the basis to formulate at the microscopic level quantitative questions on the phenotype structure of multicellular organisms. The problem of explaining the robustness of the phenotype structure is rephrased as a real geometrical problem on a fixed domain. We further suggest a generalization of path integrals that reduces the problem of deciding whether a given molecular network can generate specific phenotypes to a numerical property of a robustness function with complex output, for which we give heuristic justification. Finally, we use our formalism to interpret a pointedly quantitative developmental biology problem on the allowed number of pairs of legs in centipedes

Singularly Perturbed Monotone Systems and an Application to Double Phosphorylation Cycles

The theory of monotone dynamical systems has been found very useful in the modeling of some gene, protein, and signaling networks. In monotone systems, every net feedback loop is positive. On the other hand, negative feedback loops are important features of many systems, since they are required for adaptation and precision. This paper shows that, provided that these negative loops act at a comparatively fast time scale, the main dynamical property of (strongly) monotone systems, convergence to steady states, is still valid. An application is worked out to a double-phosphorylation ``futile cycle'' motif which plays a central role in eukaryotic cell signaling.Comment: 21 pages, 3 figures, corrected typos, references remove

DEVELOPMENT OF AN ECO~BUSINESS DIRECTORY: APPROACHES AND CHALLENGES

Eco-business is the provision of products and services that are environmentally friendly.When the preferences of the society are heading towards environmental safety, ,manufacturers need to adjust their production and marketing strategies to respond to thischange in consumer preferences. Eco-business aims at exploiting the market mechanismto provide the market with more environmentally responsible products. This studypresents the approaches used and challenges faced in the development of an eeo businessdirectory for Sri LankaThe building of the preliminary model for an eco business directory was done with thehelp of five types of surveys. Firstly, an island-wide industrial survey has been carried outwhich included major industries, hotel industry and minor industries. Secondly, an expertopinion survey was carried out to review the existing situation on a sectoral basisregarding eco-friendly products/services and to explore the possibilities and recentdevelopments of new products and services. Thirdly, a survey of existing literature wasdone in order to understand experiences regarding eco-friendly products in differentcontexts. In addition, NGO activities related environment has been collected in order toidentify gaps in public participation. In addition, available financial mechanisms for ecoindustries have also been listed.The main challenges faced in the preparation was the limited response from the relevantparties for the surveys. The lack of awareness on the 'eco friendly' products and serviceswas another issue which need further theoretical and practical definitionsIf eco ousinesses are to be establisued as a complete business s.rategy, environmentalclaims had to be accurate and independently substantiated. It is not likely that marketplace would resolve these problems on its own. The paper elaborates on the need ofguidelines and specifications on eco friendly products and services.

Self-Regulation in a Web-Based Course: A Case Study

Little is known about how successful students in Web-based courses self-regulate their learning. This descriptive case study used a social cognitive model of self-regulated learning (SRL) to investigate how six graduate students used and adapted traditional SRL strategies to complete tasks and cope with challenges in a Web-based technology course; it also explored motivational and environmental influences on strategy use. Primary data sources were three transcribed interviews with each of the students over the course of the semester, a transcribed interview with the course instructor, and the students’ reflective journals. Archived course documents, including transcripts of threaded discussions and student Web pages, were secondary data sources. Content analysis of the data indicated that these students used many traditional SRL strategies, but they also adapted planning, organization, environmental structuring, help seeking, monitoring, record keeping, and self-reflection strategies in ways that were unique to the Web-based learning environment. The data also suggested that important motivational influences on SRL strategy use—self-efficacy, goal orientation, interest, and attributions—were shaped largely by student successes in managing the technical and social environment of the course. Important environmental influences on SRL strategy use included instructor support, peer support, and course design. Implications for online course instructors and designers, and suggestions for future research are offered

Reversible acetylation regulates acetate and propionate metabolism in Mycobacterium smegmatis

Carbon metabolic pathways are important to the pathogenesis of Mycobacterium tuberculosis, the causative agent of tuberculosis. However, extremely little is known about metabolic regulation in mycobacteria. There is growing evidence for lysine acetylation being a mechanism of regulating bacterial metabolism. Lysine acetylation is a post-translational modification in which an acetyl group is covalently attached to the side chain of a lysine residue. This modification is mediated by acetyltransferases, which add acetyl groups, and deacetylases, which remove the acetyl groups. Here we set out to test whether lysine acetylation and deacetylation impact acetate metabolism in the model mycobacteria Mycobacterium smegmatis, which possesses 25 candidate acetyltransferases and 3 putative lysine deacetylases. Using mutants lacking predicted acetyltransferases and deacetylases we showed that acetate metabolism in M. smegmatis is regulated by reversible acetylation of acetyl-CoA synthetase (Ms-Acs) through the action of a single pair of enzymes: the acetyltransferase Ms-PatA and the sirtuin deacetylase Ms-SrtN. We also confirmed that the role of Ms-PatA in regulating Ms-Acs regulation depends on cAMP binding. We additionally demonstrated a role for Ms-Acs, Ms-PatA and Ms-SrtN in regulating the metabolism of propionate in M. smegmatis. Finally, along with Ms-Acs, we identified a candidate propionyl-CoA synthetase, Ms5404, as acetylated in whole-cell lysates. This work lays the foundation for studying the regulatory circuit of acetylation and deacetylation in the cellular context of mycobacteria

Designing electronic collaborative learning environments

Electronic collaborative learning environments for learning and working are in vogue. Designers design them according to their own constructivist interpretations of what collaborative learning is and what it should achieve. Educators employ them with different educational approaches and in diverse situations to achieve different ends. Students use them, sometimes very enthusiastically, but often in a perfunctory way. Finally, researchers study them and—as is usually the case when apples and oranges are compared—find no conclusive evidence as to whether or not they work, where they do or do not work, when they do or do not work and, most importantly, why, they do or do not work. This contribution presents an affordance framework for such collaborative learning environments; an interaction design procedure for designing, developing, and implementing them; and an educational affordance approach to the use of tasks in those environments. It also presents the results of three projects dealing with these three issues