Ken Thompson's 6-man Statistical Graphs

This note reviews Ken Thompson's statistics on 6-man White wins with Black to move and explains the way in which the statistics have been graphed logarithmically.

Global forecasting of thermal health hazards: the skill of probabilistic predictions of the Universal Thermal Climate Index (UTCI)

Although over a hundred thermal indices can be used for assessing thermal health hazards, many ignore the human heat budget, physiology and clothing. The Universal Thermal Climate Index (UTCI) addresses these shortcomings by using an advanced thermo-physiological model. This paper assesses the potential of using the UTCI for forecasting thermal health hazards. Traditionally, such hazard forecasting has had two further limitations: it has been narrowly focused on a particular region or nation and has relied on the use of single ‘deterministic’ forecasts. Here, the UTCI is computed on a global scale,which is essential for international health-hazard warnings and disaster preparedness, and it is provided as a probabilistic forecast. It is shown that probabilistic UTCI forecasts are superior in skill to deterministic forecasts and that despite global variations, the UTCI forecast is skilful for lead times up to 10 days. The paper also demonstrates the utility of probabilistic UTCI forecasts on the example of the 2010 heat wave in Russia.

Introducing "ecoputation": a universal systems design process

A universal systems design process is specified, tested in a case study and evaluated. It links English narratives to numbers using a categorical language framework with mathematical mappings taking the place of conjunctions and numbers. The framework is a ring of English narrative words between 1 (option) and 360 (capital); beyond 360 the ring cycles again to 1. English narratives are shown to correspond to the field of fractional numbers. The process can enable the development, presentation and communication of complex narrative policy information among communities of any scale, on a software implementation known as the "ecoputer". The information is more accessible and comprehensive than that in conventional decision support, because: (1) it is expressed in narrative language; and (2) the narratives are expressed as compounds of words within the framework. Hence option generation is made more effective than in conventional decision support processes including Multiple Criteria Decision Analysis, Life Cycle Assessment and Cost-Benefit Analysis.The case study is of a participatory workshop in UK bioenergy project objectives and criteria, at which attributes were elicited in environmental, economic and social systems. From the attributes, the framework was used to derive consequences at a range of levels of precision; these are compared with the project objectives and criteria as set out in the Case for Support. The design process is to be supported by a social information manipulation, storage and retrieval system for numeric and verbal narratives attached to the "ecoputer". The "ecoputer" will have an integrated verbal and numeric operating system. Novel design source code language will assist the development of narrative policy. The utility of the program, including in the transition to sustainable development and in applications at both community micro-scale and policy macro-scale, is discussed from public, stakeholder, corporate, Governmental and regulatory perspectives.

Climatic impacts of land-use change due to crop yield increases and a universal carbon tax from a scenario model*

Future land cover will have a significant impact on climate and is strongly influenced by the extent of agricultural land use. Differing assumptions of crop yield increase and carbon pricing mitigation strategies affect projected expansion of agricultural land in future scenarios. In the representative concentration pathway 4.5 (RCP4.5) from phase 5 of the Coupled Model Intercomparison Project (CMIP5), the carbon effects of these land cover changes are included, although the biogeophysical effects are not. The afforestation in RCP4.5 has important biogeophysical impacts on climate, in addition to the land carbon changes, which are directly related to the assumption of crop yield increase and the universal carbon tax. To investigate the biogeophysical climatic impact of combinations of agricultural crop yield increases and carbon pricing mitigation, five scenarios of land-use change based on RCP4.5 are used as inputs to an earth system model [Hadley Centre Global Environment Model, version 2-Earth System (HadGEM2-ES)]. In the scenario with the greatest increase in agricultural land (as a result of no increase in crop yield and no climate mitigation) there is a significant -0.49 K worldwide cooling by 2100 compared to a control scenario with no land-use change. Regional cooling is up to -2.2 K annually in northeastern Asia. Including carbon feedbacks from the land-use change gives a small global cooling of -0.067 K. This work shows that there are significant impacts from biogeophysical land-use changes caused by assumptions of crop yield and carbon mitigation, which mean that land carbon is not the whole story. It also elucidates the potential conflict between cooling from biogeophysical climate effects of land-use change and wider environmental aims.

Transreal proof of the existence of universal possible worlds

Transreal arithmetic is total, in the sense that the fundamental operations of addition, subtraction, multiplication and division can be applied to any transreal numbers with the result being a transreal number [1]. In particular division by zero is allowed. It is proved, in [3], that transreal arithmetic is consistent and contains real arithmetic. The entire set of transreal numbers is a total semantics that models all of the semantic values, that is truth values, commonly used in logics, such as the classical, dialetheaic, fuzzy and gap values [2]. By virtue of the totality of transreal arithmetic, these logics can be implemented using total, arithmetical functions, specifically operators, whose domain and counterdomain is the entire set of transreal numbers

On universal and periodic β-expansions, and the Hausdorff dimension of the set of all expansions

We study the topology of a set naturally arising from the study of β-expansions. After proving several elementary results for this set we study the case when our base is Pisot. In this case we give necessary and sufficient conditions for this set to be finite. This finiteness property will allow us to generalise a theorem due to Schmidt and will provide the motivation for sufficient conditions under which the growth rate and Hausdorff dimension of the set of β-expansions are equal and explicitly calculable.

On competitive bidding: scoring and position probability graphs

Iso-score curves graph (iSCG) and mathematical relationships between Scoring Parameters (SP) and Forecasting Parameters (FP) can be used in Economic Scoring Formulas (ESF) used in tendering to distribute the score among bidders in the economic part of a proposal. Each contracting authority must set an ESF when publishing tender specifications and the strategy of each bidder will differ depending on the ESF selected and the weight of the overall proposal scoring. The various mathematical relationships and density distributions that describe the main SPs and FPs, and the representation of tendering data by means of iSCGs, enable the generation of two new types of graphs that can be very useful for bidders who want to be more competitive: the scoring and position probability graphs.

The universal addressability of dumb things

Group exhibition curated by Mark Leckey.