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

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

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

A discourse analysis of trainee teacher identity in online discussion forums

Teacher education involves an identity transformation for trainees from being a student to being a teacher. This discourse analysis examined the online discussion board communications of a cohort of trainee teachers to better understand the situated identities of the trainees and how they were presented online. Their discussion board posts were the primary method of communication during placement periods and, as such, provided insight into how the trainees situated their identities in terms of being a student or being a teacher. During the analysis, the community boundaries, language and culture were explored along with the tutor's power and role in the identity transformation process. This involved looking at the lexis used by the students, the use of pronouns to refer to themselves and others such as teachers and pupils, the types of messages allowed in the community and the effect of the tutor's messages on their communication. The research found that the trainees felt comfortable with teaching but did not feel like teachers during the course. Tutors and school teachers need to develop an awareness of the dual nature of trainees' identities and help promote the transition from student to teacher. In the beginning of the course, trainees should be familiarised with teacher vocabulary and practical concepts in addition to pedagogical theory. Towards the end of the course, trainee identity as teachers could be promoted through the use of authentic assessments that mirror real teacher tasks and requirements

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

Climate Injustice in Sri Lanka through the Lens of Flooding Events

Climate change is an issue of social justice as much as it is an issue of the environment. The impacts of climate change induced disasters are known to be felt disproportionately by those in the low socio-economic status. Against this backdrop, this paper investigates flood disasters in the light of climate injustice and the impacts on the socio-economic rights of affected communities in the Gampaha district. The present study used a cross-sectional study design with qualitative data from key informant interviews and quantitative data from secondary sources and primary data from a questionnaire-based survey in 200 households in the most affected Grama Niladhari Divisions of Wattala and Kelaniya Divisional Secretariat Divisions (DSDs). Receipt of Samurdhi relief was considered to represent the low socio-economic status. The study mobilized the disaster risk assessment factors and the findings revealed that those of low socio-economic status were of a significantly higher risk (Chi squared test, p<0.05) to flooding in terms of proximity to flooding source, structural vulnerability of housing, poor coping up ability, limited risk reduction measures and lack of opportunities to build resilience. Consequently, a significantly higher proportion (Chi squared test, p<0.05) of those of low socio-economic status were found to have faced difficulties in enjoying the aspects of the right to standard of living namely, right to health, water, food and adequate housing. In conclusion, floods have resulted in an injustice to those of low socio-economic status due to their disproportionately higher risk to flooding and the resultant impact on the full enjoyment of their socio-economic rights. Keywords: Climate change, Climate injustice, Floods, Socio-economic rights, Low socio-economic statu

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

Unlimited multistability in multisite phosphorylation systems

Reversible phosphorylation on serine, threonine and tyrosine is the most widely studied posttranslational modification of proteins (1, 2). The number of phosphorylated sites on a protein (n) shows a significant increase from prokaryotes, with n less than or equal to 7 sites, to eukaryotes, with examples having n greater than or equal to 150 sites (3). Multisite phosphorylation has many roles (4, 5) and site conservation indicates that increasing numbers of sites cannot be due merely to promiscuous phosphorylation. A substrate with n sites has an exponential number (2^n) of phospho-forms and individual phospho-forms may have distinct biological effects (6, 7). The distribution of these phospho-forms and how this distribution is regulated have remained unknown. Here we show that, when kinase and phosphatase act in opposition on a multisite substrate, the system can exhibit distinct stable phospho-form distributions at steady state and that the maximum number of such distributions increases with n. Whereas some stable distributions are focused on a single phospho-form, others are more diffuse, giving the phospho-proteome the potential to behave as a fluid regulatory network able to encode information and flexibly respond to varying demands. Such plasticity may underlie complex information processing in eukaryotic cells (8) and suggests a functional advantage in having many sites. Our results follow from the unusual geometry of the steady-state phospho-form concentrations, which we show to constitute a rational algebraic curve, irrespective of n. We thereby reduce the complexity of calculating steady states from simulating 3 times 2^n differential equations to solving two algebraic equations, while treating parameters symbolically. We anticipate that these methods can be extended to systems with multiple substrates and multiple enzymes catalysing different modifications, as found in posttranslational modification 'codes' (9) such as the histone code (10, 11). Whereas simulations struggle with exponentially increasing molecular complexity, mathematical methods of the kind developed here can provide a new language in which to articulate the principles of cellular information processing (12)

Perceived Causes and Effects of Project Delays: A Study of Government Building Construction Projects in the Central Province of Sri Lanka

The problem of delays in the construction industry is a global phenomenon, and Sri Lanka is no exception. The key objectives of this study are to identify and rank the factors that cause project delays in government construction projects and their effects as perceived by the three primary industry participants, namely the clients, consultants and contractors and assess the differences. A questionnaire survey was conducted to solicit the perceived causes and effects of project delays from clients, consultants and contractors responsible for government building construction projects in the Central province of Sri Lanka. Perceived delay factors of the said primary stakeholders were measured using a five-point Likert scale type statements. The causes and effects were ranked according to their Relative Importance Index (the product of Severity Index and Frequency Index). The Spearman Correlation method and Kruskal-Wallis tests were used to test the difference in the perception among the three primary stakeholders. Data were collected from 32 consultants, 49 contractors and 16 clients. This study identified improper project management by the contractor as the leading cause of project delay. The other main causes in the ranked order are shortage of labour, financial problems of the clients, improper day work planning by contractor, delay in payment process, scope changes, delays in drawings submission, delays in approvals, financial difficulties of the contractor and lack of communication. The highest level of agreement on causes of project delays was observed between clients and contractors whereas the lowest level of agreement was observed between clients and consultants. The main perceived effects of project delays are cost overrun, poor quality of the work, disputes, arbitration, litigation and total abandonment. In relation to the effects of project delays, a high level of agreement was observed among clients, consultants and contractors. Each party had a positive correlation for both causes and effects of project delays with the other two parties, while contractors and clients showed the highest agreement on delays causes. There was a very high correlation for ranked effects between any two parties. Keywords: Construction Projects, Delay Causes, Delay Effects, Clients, Contractors, Consultants, Correlational Analysi