Geometry and combinatorics of the cutting angle method

Lower approximation of Lipschitz functions plays an important role in deterministic global optimization. This article examines in detail the lower piecewise linear approximation which arises in the cutting angle method. All its local minima can be explicitly enumerated, and a special data structure was designed to process them very efficiently, improving previous results by several orders of magnitude. Further, some geometrical properties of the lower approximation have been studied, and regions on which this function is linear have been identified explicitly. Connection to a special distance function and Voronoi diagrams was established. An application of these results is a black-box multivariate random number generator, based on acceptance-rejection approach.

Cutting angle method - a tool for constrained global optimization

Cutting angle method (CAM) is a deterministic global optimization technique applicable to Lipschitz functions f: Rn → R. The method builds a sequence of piecewise linear lower approximations to the objective function f. The sequence of solutions to these relaxed problems converges to the global minimum of f. This article adapts CAM to the case of linear constraints on the feasible domain. We show how the relaxed problems are modified, and how the numerical efficiency of solving these problems can be preserved. A number of numerical experiments confirms the improved numerical efficiency.

Capping the SRO's sweet tooth

The consequences of the State Revenue Office's (SRO) liking for fixtures and its liberal interpretation of the definition of chattels have been coming before the Supreme Court regularly.

Regional-scale models for relating land cover to basin surface-water quality using remotely sensed data in a GIS

Plant-based management systems implementing deep-rooted, perennial vegetation have been identified as important in mitigating the spread of secondary dryland salinity due to its capacity to influence water table depth. The Glenelg Hopkins catchment is a highly modified watershed in the southwest region of Victoria, where dryland salinity management has been identified as a priority. Empirical relationships between the proportion of native vegetation and in-stream salinity were examined in the Glenelg Hopkins catchment using a linear regression approach. Whilst investigations of these relationships are not unique, this is the first comprehensive attempt to establish a link between land use and in-stream salinity in the study area. The results indicate that higher percentage land cover with native vegetation was negatively correlated with elevated in-stream salinity. This inverse correlation was consistent across the 3 years examined (1980, 1995, and 2002). Recognising the potential for erroneously inferring causal relationships, the methodology outlined here was both a time and cost-effective tool to inform management strategies at a regional scale, particularly in areas where processes may be operating at scales not easily addressed with on-site studies.

Appraisal of random and systematic land cover transitions for regional water balance and revegetation strategies

This study describes the use of landscape transition analysis as a means for effective basin management. Land cover transitions from 1995 to 2002 were analyzed using a cross-tabulation matrix for an important economic zone in south-west Victoria, Australia. Specifically, the matrix was used to determine whether the transitions were random or systematic. Random landscape transitions occur when a land cover replaces other land covers in proportion to their availability. Systematic landscape transitions occur when there are deviations from random patterns, and land use types ‘target’ other land use types for replacement. The analysis was conducted with 11 land cover categories and showed that dryland pastures have been systematically losing area to dryland crops and blue gum (Eucalyptus globulus) plantations. Dryland crops have systematically expanded in the north-east of the catchment, an area where increasing in-stream salinization has occurred concurrently with this transition. The systematic expansion of the blue gum plantations has been predominantly in the south-west of the catchment and has the potential to reduce stream flows and groundwater recharge in an already water-stressed region, as blue gums use more water than the dryland pastures they are replacing. All other transitions were largely random. These findings have implications for land use planning in the study area for regional water balance and revegetation strategies. Landscape transition analysis is a cost-effective means of contributing to the management of water resources at a regional scale, and is highly recommended for future basin planning.

Association of reduced riparian vegetation cover in agricultural landscapes with coarse detritus dynamics in lowland streams

Studies were conducted on streams flowing through agricultural floodplains in south-eastern Australia to quantify whether reductions in riparian canopy cover were associated with alterations to the input and benthic standing stocks of coarse allochthonous detritus. Comparisons were made among three farmland reaches and three reaches within reserves with intact cover of remnant overstorey trees. Detritus inputs to these reaches were measured monthly over 2 years using litter traps. Direct inputs to streams within the reserves were relatively high (550–617 g ash free dry weight (AFDW) m^–2 year^–1), but were lower at farmland reaches with the lowest canopy covers (83–117 gAFDW m^–2 year^–1). Only a minor fraction of the total allochthonous input (<10%) entered any of the study reaches laterally. The mean amounts of benthic detritus were lowest in the most open farmland reaches. Standing stocks of benthic detritus were found to be highly patchy across a large number of agricultural streams, but were consistently very low where the streamside canopy cover was below ~35%. Canopy cover should be restored along cleared agricultural streams because allochthonous detritus is a major source of food and habitat for aquatic ecosystems. Given the absence of pristine lowland streams in south-eastern Australia, those reaches with the most intact remnant overstorey canopies should be used to guide restoration.

'The witness who saw, /He left little doubt' : a comparative consideration of expert testimony in mental disability law cases in common and civil law systems

The question of how courts assess expert evidence - especially when mental disability is an issue - raises the corollary question of whether courts adequately evaluate the content of the expert testimony or whether judicial decision making may be influenced by teleology (cherry picking evidence), pretextuality (accepting experts who distort evidence to achieve socially desirable aims), and/or sanism (allowing prejudicial and stereotyped evidence). Such threats occur despite professional standards in forensic psychology and other mental health disciplines that require ethical expert testimony. The result is expert testimony that, in many instances, is at best incompetent and at worst biased. The paper details threats to competent expert testimony in a comparative law context - in both the common law (involuntary civil commitment laws and risk assessment criminal laws) and, more briefly, civil law. We conclude that teleology, pretextuality, and sanism have an impact upon judicial decision making in both the common law and civil law. Finally, we speculate as to whether the new United Nations Convention on the Rights of Persons with Disabilities is likely to have any impact on practices in this area. Copyright © 2009 John Wiley & Sons, Ltd.

Saw palmetto supplement use and prostate cancer risk

Saw palmetto is an herb used to treat the symptoms of benign prostatic hyperplasia. In vitro studies have found that saw palmetto inhibits growth of prostatic cancer cells and may induce apoptosis. To evaluate whether saw palmetto supplements are associated with a reduced risk of prostate cancer, we conducted a prospective cohort study of 35,171 men aged 50-76 yr in western Washington state. Subjects completed questionnaires between 2000 and 2002 on frequency of use of saw palmetto supplements and saw palmetto-containing multivitamins over the previous 10 yr in addition to other information on supplement intake, medical history, and demographics. Men were followed through December 2003 (mean of 2.3 yr of follow-up) via the western Washington Surveillance, Epidemiology, and End Results cancer registry, during which time 580 developed prostate cancer. Ten percent of the cohort used saw palmetto at least once per week for a year in the 10 yr before baseline. No association was found between this level of use of saw palmetto and risk of prostate cancer development [hazard ratio (HR) = 0.95; 95% confidence interval = 0.74-1.23] or with increasing frequency or duration of use. In this free-living population, use of commercial saw palmetto, which varies widely in dose and constituent ratios, was not associated with prostate cancer risk.

Influence of land cover on water resources

The influence of land cover on water quality and quantity was examined using a multidisciplinary approach that integrated land use maps, historical databases, and statistical modelling. Systematic changes in the Glenelg Hopkins landscape were identified, in addition to a relationship between greater proportions of vegetation and better water quality.

Effects of snow cover on the timing and success of reproduction in high-Arctic pink-footed geese Anser brachyrhynchus

During four breeding seasons, 2003–2006, we studied the relationship between snow cover and nesting performance in pink-footed geese (Anser brachyrhynchus) in a key breeding site on Svalbard. Snow cover in late May, i.e., at the time of egg laying of geese, was derived from MODIS satellite images. Snow cover had a profound cascading effect on reproductive output via the number of nesting pairs and timing of nesting, which affected nest success, while there was only a tendency for a negative effect on clutch size. Hence, we estimated a five-fold difference in the number of young produced (to post-hatching) between years with little snow and years with high snow cover. The results from the study area correlated with whole-population productivity estimates recorded in autumn. Thus, snow cover derived from MODIS satellite images appears to provide a useful indicator of the breeding conditions in the Arctic.

Assessment of spatiotemporal varying relationships between rainfall, land cover and surface water area using geographically weighted regression

Traditional regression techniques such as ordinary least squares (OLS) are often unable to accurately model spatially varying data and may ignore or hide local variations in model coefficients. A relatively new technique, geographically weighted regression (GWR) has been shown to greatly improve model performance compared to OLS in terms of higher R 2 and lower corrected Akaike information criterion (AICC). GWR models have the potential to improve reliabilities of the identified relationships by reducing spatial autocorrelations and by accounting for local variations and spatial non-stationarity between dependent and independent variables. In this study, GWR was used to examine the relationship between land cover, rainfall and surface water habitat in 149 sub-catchments in a predominately agricultural region covering 2.6 million ha in southeast Australia. The application of the GWR models revealed that the relationships between land cover, rainfall and surface water habitat display significant spatial non-stationarity. GWR showed improvements over analogous OLS models in terms of higher R 2 and lower AICC. The increased explanatory power of GWR was confirmed by the results of an approximate likelihood ratio test, which showed statistically significant improvements over analogous OLS models. The models suggest that the amount of surface water area in the landscape is related to anthropogenic drainage practices enhancing runoff to facilitate intensive agriculture and increased plantation forestry. However, with some key variables not present in our analysis, the strength of this relationship could not be qualified. GWR techniques have the potential to serve as a useful tool for environmental research and management across a broad range of scales for the investigation of spatially varying relationships.