Minimal Steiner Trees for 2k×2kSquare Lattices

AbstractWe prove a conjecture of Chung, Graham, and Gardner (Math. Mag.62(1989), 83–96), giving the form of the minimal Steiner trees for the set of points comprising the vertices of a 2k×2ksquare lattice. Each full component of these minimal trees is the minimal Steiner tree for the four vertices of a square

Steiner Trees Over Generalized Checkerboards

To minimize the length of a planar network, we can build a Steiner minimal tree that is, a tree consisting of the original network points, as well as additional, strategically-placed (Steiner) points. Chung, Gardner and Graham [2] investigated building Steiner trees over grids of unit squares. We generalize their ideas to grids of rhombuses, and show that two near-optimal Steiner trees exist for each grid, one built from Steiner trees over rhombuses and one built from Steiner trees over isosceles triangles. Further, we conjecture that for grids with an odd number of layers, only the small angle of the rhombus drives which tree is shorter; for grids with an even number of layers, the small angle is the most important factor in determining which scheme to use

An analysis of market integration in the pig marketing system in Thailand : 1969-1979

This study describes the pig and pork marketing system in Thailand and attempts to choose an appropriate technique to analyse pig market integration for the period 1969-1979. Many economists who have studied agricultural markets in low income countries have concluded that the marketing systems in those countries are relatively inefficient, whereas anthropologists often conclude the opposite. This study attempts to show how the concept of market integration is useful and can be a proxy to indicate market efficiency especially in low income countries. Because of the unavailability and unreliability of data and the existence of parallel informal and illegal markets, correlation analysis using prices series data only is used in this analysis instead of regression/margins analysis which is normally used in high income countries. Regression analysis was at first used to investigate market integration but was rejected due to the need to specify the direction of causal relationship and because of multicollinearity problems. Absolute and first difference values of price data were then analysed using correlation analysis. Owing to biases caused by trend and seasonal influences in those values, this method was also rejected and the residual value from which the trend and seasonal influences have been removed was then used. Government intervention caused a structural change in the market during the study period. The 'unrestricted area' period and the 'restricted area' period were therefore analysed separately

A critical review of the current state of forensic science knowledge and its integration in legal systems

Forensic science has a significant historical and contemporary relationship with the criminal justice system. It is a relationship between two disciplines whose origins stem from different backgrounds. It is trite that effective communication assist in resolving underlying problems in any given context. However, a lack of communication continues to characterise the intersection between law and science. As recently as 2019, a six-part symposium on the use of forensic science in the criminal justice system again posed the question on how the justice system could ensure the reliability of forensic science evidence presented during trials. As the law demands finality, science is always evolving and can never be considered finite or final. Legal systems do not always adapt to the nature of scientific knowledge, and are not willing to abandon finality when that scientific knowledge shifts. Advocacy plays an important role in the promotion of forensic science, particularly advocacy to the broader scientific community for financial support, much needed research and more testing. However, despite its important function, advocacy should not be conflated with science. The foundation of advocacy is a cause; whereas the foundation of science is fact. The objective of this research was to conduct a qualitative literature review of the field of forensic science; to identify gaps in the knowledge of forensic science and its integration in the criminal justice system. The literature review will provide researchers within the field of forensic science with suggested research topics requiring further examination and research. To achieve its objective, the study critically analysed the historical development of, and evaluated the use of forensic science evidence in legal systems generally, including its role regarding the admissibility or inadmissibility of the evidence in the courtroom. In conclusion, it was determined that the breadth of forensic scientific knowledge is comprehensive but scattered. The foundational underpinning of the four disciplines, discussed in this dissertation, has been put to the legal test on countless occasions. Some gaps still remain that require further research in order to strengthen the foundation of the disciplines. Human influence will always be present in examinations and interpretations and will lean towards subjective decision making.JurisprudenceD. Phil

Integrative (Synchronisations-)Mechanismen der (Neuro-)Kognition vor dem Hintergrund des (Neo-)Konnektionismus, der Theorie der nichtlinearen dynamischen Systeme, der Informationstheorie und des Selbstorganisationsparadigmas

Der Gegenstand der vorliegenden Arbeit besteht darin, aufbauend auf dem (Haupt-)Thema, der Darlegung und Untersuchung der Lösung des Bindungsproblems anhand von temporalen integrativen (Synchronisations-)Mechanismen im Rahmen der kognitiven (Neuro-)Architekturen im (Neo-)Konnektionismus mit Bezug auf die Wahrnehmungs- und Sprachkognition, vor allem mit Bezug auf die dabei auftretende Kompositionalitäts- und Systematizitätsproblematik, die Konstruktion einer noch zu entwickelnden integrativen Theorie der (Neuro-)Kognition zu skizzie-ren, auf der Basis des Repräsentationsformats einer sog. „vektoriellen Form“, u.z. vor dem Hintergrund des (Neo-)Konnektionismus, der Theorie der nichtlinearen dynamischen Systeme, der Informationstheorie und des Selbstorganisations-Paradigmas

A simple proof of Graham and Pollak's theorem

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