The Traveling Salesman Problem Under Squared Euclidean Distances

Let $P$ be a set of points in $\mathbb{R}^d$, and let $\alpha \ge 1$ be a real number. We define the distance between two points $p,q\in P$ as $|pq|^{\alpha}$, where $|pq|$ denotes the standard Euclidean distance between $p$ and $q$. We denote the traveling salesman problem under this distance function by TSP($d,\alpha$). We design a 5-approximation algorithm for TSP(2,2) and generalize this result to obtain an approximation factor of $3^{\alpha-1}+\sqrt{6}^{\alpha}/3$ for $d=2$ and all $\alpha\ge2$. We also study the variant Rev-TSP of the problem where the traveling salesman is allowed to revisit points. We present a polynomial-time approximation scheme for Rev-TSP$(2,\alpha)$ with $\alpha\ge2$, and we show that Rev-TSP$(d, \alpha)$ is APX-hard if $d\ge3$ and $\alpha>1$. The APX-hardness proof carries over to TSP$(d, \alpha)$ for the same parameter ranges.Comment: 12 pages, 4 figures. (v2) Minor linguistic change

Non-Destructive Testing Techniques for Corrosion Assessment in Reinforced Concrete Structures in Kenya

Deterioration of concrete structures is inevitable due to the fact that it is subjected to deterring environmental factors. Therefore, inspection and maintenance of these structures should be done to ensure their serviceability. Many concrete structures have been constructed in Kenya. A survey of some of the existing multi-storey buildings shows that even some of the old ones are in good condition; examples are the Norfork Hotel, Sarova Stanley Hotel and the railway bridges built in early 1900s. Yet, ageing structures require periodic monitoring to check their serviceability. Currently, inspection of most structures is done solely by simple visual means which is not always adequate. In order to enhance reliable assessment of structures, the present research introduces non-destructive testing (NDT) techniques for corrosion damage diagnosis in Kenyan concrete structures. Visual inspection is followed by half-cell potential measurements, carbonation tests and chloride tests. Laboratory analysis as well as field testing shows that NDT techniques provide safe, fast and reliable tools for the assessment of structural integrity. Keywords: Reinforced Concrete, Deterioration, Inspection, Non-destructive testin

Do reptile responses to habitat structure and time since fire depend on landscape structure?

Land use changes, such as the development of agriculture and plantation forestry, and altered fire regimes, are major drivers of biodiversity loss worldwide, influencing the availability of suitable habitat for species. Reptiles are sensitive to both these processes as they are influenced by native vegetation extent and habitat structure. While much is known about the independent effects of fire and land use change on species distributions, few studies have investigated potential interactive effects" specifically, whether the influence of site-scale variables on reptiles depends on the properties of the surrounding landscape. We sampled reptiles at 107 sites in fire-prone heathy woodland, interspersed with plantation forestry and agriculture in south-west Victoria, Australia. We investigated the responses of seven reptile species to both site-scale variables (time since fire and several measures of habitat structure) and landscape-scale variables (extent of native vegetation and plantations and the presence of pasture within a 3.14 square km area) to 1) identify whether species' responses to fire and habitat depended on landscape structure, and 2) examine the relative influence of time since fire, habitat structure and landscape structure on reptile abundance. We predicted that responses to site-scale variables would vary with a key landscape structure variable: the amount of native vegetation cover. Further, we predicted that site-scale variables would be stronger predictors of species abundance than landscape-scale variables. Generalised linear models, accounting for imperfect detection, were used to estimate species responses to site and landscape-scale predictors. For two species (Amphibolurus muricatus and Liopholis whitii) there was evidence that their responses to site-scale variables depended on landscape structure. However, contrary to our first prediction, native vegetation cover was not the only landscape structure variable that influenced species' responses to site-scale variables. Three species (Acritoscincus duperreyi, A. muricatus, and Lerista bougainvillii) responded to both habitat structure and landscape structure variables, though the relative influence of the variables at the different scales was varied among the species. One species (Lampropholis guichenoti) responded to fire and habitat structure variables at the site-scale but did not respond to landscape structure. One species (Aprasia striolata) responded to landscape structure variables but not to site-scale variables. Our second prediction, that site-scale variables would be the strongest predictors of abundance, was true for two species, but overall, our results were varied, with species responding at both scales. Examining species' responses to drivers at multiple spatial scales is essential for conservation management, as even species with low dispersal capacity such as reptiles can respond to processes occurring at large spatial scales

Scheduling divisible loads with time and cost constraints

In distributed computing, divisible load theory provides an important system model for allocation of data-intensive computations to processing units working in parallel. The main task is to define how a computation job should be split into parts, to which processors those parts should be allocated and in which sequence. The model is characterized by multiple parameters describing processor availability in time, transfer times of job parts to processors, their computation times and processor usage costs. The main criteria are usually the schedule length and cost minimization. In this paper, we provide the generalized formulation of the problem, combining key features of divisible load models studied in the literature, and prove its NP-hardness even for unrestricted processor availability windows. We formulate a linear program for the version of the problem with a fixed number of processors. For the case with an arbitrary number of processors, we close the gaps in the study of special cases, developing efficient algorithms for single criterion and bicriteria versions of the problem, when transfer times are negligible

Nutrient availability controls the impact of mammalian herbivores on soil carbon and nitrogen pools in grasslands

Grasslands are subject to considerable alteration due to human activities globally, including widespread changes in populations and composition of large mammalian herbivores and elevated supply of nutrients. Grassland soils remain important reservoirs of carbon (C) and nitrogen (N). Herbivores may affect both C and N pools and these changes likely interact with increases in soil nutrient availability. Given the scale of grassland soil fluxes, such changes can have striking consequences for atmospheric C concentrations and the climate. Here, we use the Nutrient Network experiment to examine the responses of soil C and N pools to mammalian herbivore exclusion across 22 grasslands, under ambient and elevated nutrient availabilities (fertilized with NPK + micronutrients). We show that the impact of herbivore exclusion on soil C and N pools depends on fertilization. Under ambient nutrient conditions, we observed no effect of herbivore exclusion, but under elevated nutrient supply, pools are smaller upon herbivore exclusion. The highest mean soil C and N pools were found in grazed and fertilized plots. The decrease in soil C and N upon herbivore exclusion in combination with fertilization correlated with a decrease in aboveground plant biomass and microbial activity, indicating a reduced storage of organic matter and microbial residues as soil C and N. The response of soil C and N pools to herbivore exclusion was contingent on temperature – herbivores likely cause losses of C and N in colder sites and increases in warmer sites. Additionally, grasslands that contain mammalian herbivores have the potential to sequester more N under increased temperature variability and nutrient enrichment than ungrazed grasslands. Our study highlights the importance of conserving mammalian herbivore populations in grasslands worldwide. We need to incorporate local-scale herbivory, and its interaction with nutrient enrichment and climate, within global-scale models to better predict land–atmosphere interactions under future climate change.National Science Foundation Research Coordination Network, Long Term Ecological Research, Institute on the Environment, Strategic Resources of the Netherlands Institute of Ecology, Research Foundation Flanders, VENI grant, NWO-RUBICON grant, NWO-VENI grant, German Centre for Integrative Biodiversity Research, German Research Foundation (FZT 118).http://wileyonlinelibrary.com/journal/gcbpm2021Mammal Research InstituteZoology and Entomolog