Number Of Random Points Research Articles

Factors determining roadkills in a mammal carnivore are road-type specific

Roads threaten the conservation of many wildlife species. Carnivores are one of the most susceptible groups due to their habitat requirements. We explored the roadkill patterns of European polecats (Mustela putorious) on motorways and roads to investigate if these patterns depend on road type, a research topic frequently neglected in the literature. We studied 85 roadkills on motorways and 73 on roads, and the corresponding number of random points with no roadkills in every road type. We characterized them with 7 habitat and 7 road-related variables. Roadkill sites were significantly associated with the abundance of rabbit burrows. However, this effect was stronger on motorways, as they provide more suitable habitat for the establishment of prey species on their wider rights-of-way, or on the road interchange islands, which provide wide unused spaces. In contrast, road interchange islands on conventional roads that are simple intersections and have narrower rights-of-way. Furthermore, roadkills occurred in areas with lower agricultural cover. Thus, natural habitats on roadsides could act as alternative foraging areas for this carnivore increasing their roadkill risk. Our results showed the need to consider the characteristics such as the availability of prey or the surrounding habitat, as well as intrinsic characteristics of the road type when studying wildlife roadkills as the road-type-mediated patterns demand-specific mitigation measures.

Improving the accuracy of estimators for the two-point correlation function

Aims. We show how to increase the accuracy of estimates of the two-point correlation function without sacrificing efficiency. Methods. We quantify the error of the pair-counts and of the Landy & Szalay estimator by comparing them with exact reference values. The standard method, using random point sets, is compared to geometrically motivated estimators and estimators using quasi-Monte Carlo integration. Results. In the standard method, the error scales proportionally to 1/√Nr, with Nr being the number of random points. In our improved methods, the error scales almost proportionally to 1/Nq, where Nq is the number of points from a low-discrepancy sequence. We study the run times of the new estimator in comparison to those of the standard estimator, keeping the same level of accuracy. For the considered case, we always see a speedup ranging from 50% up to a factor of several thousand. We also discuss how to apply these improved estimators to incompletely sampled galaxy catalogues.

Visualization of Coral Reef Cover with Photogrammetry Method at Coastal Waters of Lemon Island, Manokwari, Indonesia

Lemon Island waters are an island that has a diversity of coral reef ecosystems. The coastal areas of Lemon Island have different coral reef structures, so it is necessary to conduct research using underwater photogrammetry to visualize the condition of coral reefs. Photogrammetry is a process of obtaining information about an object through measurements made from photographs. The use of underwater photogrammetry in visualizing coral reefs can also be used to extract coral conditions such as size, condition, and percentage of coral colony cover. This study aims to determine the shape and condition of the visual life form of coral reefs in the waters of Lemon Island. The method used in this research is the photogrammetric method which is then analyzed using CPCe, using the number of random points used to analyze 30 photos for each frame. Based on the results obtained, it can be seen 6 forms of coral growth found in the waters of Lemon Island, namely, Acropora Branching, Acropora Submassive, Coral Branching, Coral Massive, Coral Submassive and Coral Mushroom. The total percentage of coral reef cover is 45.84%, so it is categorized in moderate condition.

Fast analytical calculation of the random pair counts for realistic survey geometry

Galaxy clustering is a standard cosmological probe that is commonly analysed through two-point statistics. In observations, the estimation of the two-point correlation function crucially relies on counting pairs in a random catalogue. The latter contains a large number of randomly distributed points, which accounts for the survey window function. Random pair counts can also be advantageously used for modelling the window function in the observed power spectrum. Since pair counting scales as 𝒪(N2), where N is the number of points, the computational time to measure random pair counts can be very expensive for large surveys. In this work, we present an alternative approach for estimating those counts that does not rely on the use of a random catalogue. We derived an analytical expression for the anisotropic random-random pair counts that accounts for the galaxy radial distance distribution, survey geometry, and possible galaxy weights. We show that a prerequisite is the estimation of the two-point correlation function of the angular selection function, which can be obtained efficiently using pixelated angular maps. Considering the cases of the VIPERS and SDSS-BOSS redshift surveys, we find that the analytical calculation is in excellent agreement with the pair counts obtained from random catalogues. The main advantage of this approach is that the primary calculation only takes a few minutes on a single CPU and it does not depend on the number of random points. Furthermore, it allows for an accuracy on the monopole equivalent to what we would otherwise obtain when using a random catalogue with about 1500 times more points than in the data at hand. We also describe and test an approximate expression for data-random pair counts that is less accurate than for random-random counts, but still provides subpercent accuracy on the monopole. The presented formalism should be very useful in accounting for the window function in next-generation surveys, which will necessitate accurate two-point window function estimates over huge observed cosmological volumes.

An Algorithm to Generate Random Points in Polygon Based on Triangulation

Random point generation plays an important role in assisting random sampling and is widely used in various disciplines. This paper proposes a new algorithm to generate random points in polygon based on Triangulation. Firstly, the polygons are triangulated, and then the number of random points in each triangle is allocated according to the triangle area. Finally, the given number of random points is generated inside the triangle. In the experiment, the results showed that the proposed algorithm is 20 times faster than the algorithm in QGIS software on average. And with the increase of the complexity of the polygon, the advantages of this algorithm are more obvious.

Degradation assessment of rolling bearing towards safety based on random matrix single ring machine learning

Aiming at problems of feature extraction of monitoring data may lose useful information and different feature extraction methods have great influence on the results in rolling bearing performance degradation assessment. A method which is based on random matrix theory to assess the degradation of rolling bearing is proposed to improve production safety. Firstly, the observation matrix was constructed by the raw data of rolling bearing health monitoring, and the random matrix model of rolling bearing operating states was established by the steps of normalization, singular matrix singular value decomposition and standardization. Then, three performance degradation indicators, the average spectral radius, the maximum eigenvalue, and the number of random points in the inner ring are proposed by constructing the linear eigenvalue statistic of the random matrix, combined with the single ring curve of the bearing operating states, to describe the fluctuation discipline of the random matrix elements and the variation law of the characteristic root distribution, thus characterize the statistical random characteristics of the operating states of the rolling bearing as a whole. Finally, the method was applied by the rolling bearing life test vibration data. And four different operation states of the bearing are selected to build the random matrix model and analysis. The analysis results are calculated by single ring curves and quantitative indicators of different states and proved that the method proposed in this paper can effectively identify different degradation states and realize safety states of rolling bearing, meanwhile, it can quantitatively assess the degree of performance degradation.

Lattice rules with random [formula omitted] achieve nearly the optimal [formula omitted] error independently of the dimension

We analyze a new random algorithm for numerical integration of d-variate functions over [0,1]d from a weighted Sobolev space with dominating mixed smoothness α≥0 and product weights 1≥γ1≥γ2≥⋯>0, where the functions are continuous and periodic when α>1∕2. The algorithm is based on rank-1 lattice rules with a random number of points n. For the case α>1∕2, we prove that the algorithm achieves almost the optimal order of convergence of O(n−α−1∕2), where the implied constant is independent of the dimension d if the weights satisfy ∑j=1∞γj1∕α<∞. The same rate of convergence holds for the more general case α>0 by adding a random shift to the lattice rule with random n. This shows, in particular, that the exponent of strong tractability in the randomized setting equals 1∕(α+1∕2), if the weights decay fast enough. We obtain a lower bound to indicate that our results are essentially optimal.This paper is a significant advancement over previous related works with respect to the potential for implementation and the independence of error bounds on the problem dimension. Other known algorithms which achieve the optimal error bounds, such as those based on Frolov’s method, are very difficult to implement especially in high dimensions. Here we adapt a lesser-known randomization technique introduced by Bakhvalov in 1961. This algorithm is based on rank-1 lattice rules which are very easy to implement given the integer generating vectors. A simple probabilistic approach can be used to obtain suitable generating vectors.

The effect of sample size on the accuracy of species distribution models: considering both presences and pseudo‐absences or background sites

Most high‐performing species distribution modelling techniques require both presences, and either absences or pseudo‐absences or background points. In this paper, we explore the effect of sample size, towards developing improved strategies for modelling. We generated 1800 virtual species with three levels of prevalence using ten modelling techniques, while varying the number of training presences (NTP) and the number of random points (NRP representing pseudo‐absences or background sites). For five of the ten modelling techniques we built two versions of models: one with an equal total weight (ETW) setting where the total weight for pseudo‐absence is equivalent to the total weight for presence, and another with an unequal total weight (UTW) setting where the total weight for pseudo‐absence is not required to be equal to the total weight for presence. We compared two strategies for NRP: a small multiplier strategy (i.e. setting NRP at a few times as large as NTP), and a large number strategy (i.e. using numerous random points). We produced ensemble models (by averaging the predictions from 30 models built with the same set of training presences and different sets of random points in equivalent numbers) for three NTP magnitudes and two NRP strategies. We found that model accuracy altered as NRP increased with four distinct patterns of performance: increasing, decreasing, arch‐shaped and horizontal. In most cases ETW improved model performance. Ensemble models had higher accuracy than the corresponding single models, and this improvement was pronounced when NTP was low. We conclude that a large NRP is not always an appropriate strategy. The best choice for NRP will depend on the modelling techniques used, species prevalence and NTP. We recommend building ensemble models instead of single models, using the small multiplier strategy for NRP with ETW, especially when only a small number of species presence records are available.

Computing and estimating the volume of the solution space of SMT(LA) constraints

The satisfiability modulo theories (SMT) problem is a decision problem, i.e., deciding the satisfiability of logical formulas with respect to combinations of background theories (like reals, integers, arrays, bit-vectors). In this paper, we study the counting version of SMT with respect to linear arithmetic – SMT(LA), which generalizes both model counting and volume computation of convex polytopes. We describe a method for estimating the volume of convex polytopes based on the Multiphase Monte-Carlo method. It employs a new technique to reutilize random points, so that the number of random points can be significantly reduced. We prove that the reutilization technique has no side-effect on the error. We also investigate a simplified version of hit-and-run method: the coordinate directions method. Based on volume estimation method for polytopes, we present an approach to estimating the volume of the solution space of SMT(LA) formulas. It employs a heuristic strategy to accelerate the volume estimation procedure. In addition, we devise some specific techniques for instances that arise from program analysis.

3D Model Retrieval Based on Distance Classification Histogram

This paper presents a new algorithm to retrieve 3D model on distance classification histogram. First, we select the certain number of random points on the model surface and compute the distance between two random points. Secondly, we sort the distance into two types which is based on the different geometry properties of these distance and construct the distance classification histogram. Finally, we measure the similarity of 3D models by comparing distance classification histogram. The experimental results on PSB show that our method has a good performance in precision and computational complication.

Adaptation of the CVT algorithm for catheter optimization in high dose rate brachytherapy

An innovative, simple, and fast method to optimize the number and position of catheters is presented for prostate and breast high dose rate (HDR) brachytherapy, both for arbitrary templates or template-free implants (such as robotic templates). Eight clinical cases were chosen randomly from a bank of patients, previously treated in our clinic to test our method. The 2D Centroidal Voronoi Tessellations (CVT) algorithm was adapted to distribute catheters uniformly in space, within the maximum external contour of the planning target volume. The catheters optimization procedure includes the inverse planning simulated annealing algorithm (IPSA). Complete treatment plans can then be generated from the algorithm for different number of catheters. The best plan is chosen from different dosimetry criteria and will automatically provide the number of catheters and their positions. After the CVT algorithm parameters were optimized for speed and dosimetric results, it was validated against prostate clinical cases, using clinically relevant dose parameters. The robustness to implantation error was also evaluated. Finally, the efficiency of the method was tested in breast interstitial HDR brachytherapy cases. The effect of the number and locations of the catheters on prostate cancer patients was studied. Treatment plans with a better or equivalent dose distributions could be obtained with fewer catheters. A better or equal prostate V100 was obtained down to 12 catheters. Plans with nine or less catheters would not be clinically acceptable in terms of prostate V100 and D90. Implantation errors up to 3 mm were acceptable since no statistical difference was found when compared to 0 mm error (p > 0.05). No significant difference in dosimetric indices was observed for the different combination of parameters within the CVT algorithm. A linear relation was found between the number of random points and the optimization time of the CVT algorithm. Because the computation time decrease with the number of points and that no effects were observed on the dosimetric indices when varying the number of sampling points and the number of iterations, they were respectively fixed to 2500 and to 100. The computation time to obtain ten complete treatments plans ranging from 9 to 18 catheters, with the corresponding dosimetric indices, was 90 s. However, 93% of the computation time is used by a research version of IPSA. For the breast, on average, the Radiation Therapy Oncology Group recommendations would be satisfied down to 12 catheters. Plans with nine or less catheters would not be clinically acceptable in terms of V100, dose homogeneity index, and D90. The authors have devised a simple, fast and efficient method to optimize the number and position of catheters in interstitial HDR brachytherapy. The method was shown to be robust for both prostate and breast HDR brachytherapy. More importantly, the computation time of the algorithm is acceptable for clinical use. Ultimately, this catheter optimization algorithm could be coupled with a 3D ultrasound system to allow real-time guidance and planning in HDR brachytherapy.

Mapping risk for nest predation on a barrier island

Barrier islands and coastal beach systems provide nesting habitat for marine and estuarine turtles. Densely settled coastal areas may subsidize nest predators. Our purpose was to inform conservation by providing a greater understanding of habitat-based risk factors for nest predation, for an estuarine turtle. We expected that habitat conditions at predated nests would differ from random locations at two spatial extents. We developed and validated an island-wide model for the distribution of predated Diamondback terrapin nests using locations of 198 predated nests collected during exhaustive searches at Fisherman Island National Wildlife Refuge, USA. We used aerial photographs to identify all areas of possible nesting habitat and searched each and surrounding environments for nests, collecting location and random-point microhabitat data. We built models for the probability of finding a predated nest using an equal number of random points and validated them with a reserve set (N = 67). Five variables in 9 a priori models were used and the best selected model (AIC weight 0.98) reflected positive associations with sand patches near marshes and roadways. Model validation had an average capture rate of predated nests of 84.14 % (26.17–97.38 %, Q1 77.53 %, median 88.07 %, Q3 95.08 %). Microhabitat selection results suggest that nests placed at the edges of sand patches adjacent to upland shrub/forest and marsh systems are vulnerable to predation. Forests and marshes provide cover and alternative resources for predators and roadways provide access; a suggestion is to focus nest protection efforts on the edges of dunes, near dense vegetation and roads.

Central limit theorems for random polytopes

Let K be a smooth convex set. The convex hull of independent random points in K is a random polytope. Central limit theorems for the volume and the number of i dimensional faces of random polytopes are proved as the number of random points tends to infinity. One essential step is to determine the precise asymptotic order of the occurring variances.

Random Vectors in the Isotropic Position

Letybe a random vector in Rn, satisfyingEy⊗y=id.LetMbe a natural number and lety1, …, yMbe independent copies ofy. We study the question of approximation of the identity operator by finite sums of the tensorsyi⊗yi. We prove that for some absolute constantCE1M∑i=1Myi⊗yi−id⩽C·lognM·(E‖y‖logM)1/logM,provided that the last expression is smaller than 1. We apply this estimate to improve a result of Bourgain concerning the number of random points needed to bring a convex body into a nearly isotropic position.

Paired Lévy–Mandelbrot Trajectory as a Homogeneous Fractal

This paper deals with the problem of using the Lévy–Mandelbrot (LM) trajectory for constructing a homogeneous random point fractal in three-dimensional space. For investigating stochastic properties of a random number of points M(R) within a radius R around an arbitrary occupied point, it is proposed to use a paired LM trajectory. It is found that for sufficiently large values of R the distribution of the random variable M(R)/&lt;M(R)&gt; does not depend on R and can be approximated by the gamma distribution with a unique parameter depending on the fractal dimension. This property is analogous to KNO scaling of multiplicity in hadron-hadron collisions.

Habitat Selection by Immature Spanish Imperial Eagles During the Dispersal Period

The Spanish imperial eagle Aquila adalberti is the most endangered bird of prey in Europe, with less than 150 pairs remaining alive, and it is one of the most endangered species in the world. The densest Spanish imperial eagle population is located in the Donana National Park, south-western Spain and is made up of 15-16 breeding pairs. Since 1973, a variety of management techniques have been implemented to increase productivity in the breeding population. Despite this, eagles have not colonized the surrounding area. Studies were carried out to provide a quantitative description of the habitats selected by immature Spanish imperial eagles during their dispersal period. The exact locations of the 23 temporary settling areas were determined by radio-tracking from the ground and periodic checks by light aircraft. To evaluate available but unused habitats, coordinates of the same number of random points were generated and compared to actual locations. The results indicated that young eagles select areas with pasture or cultivated farmland covered by scattered Quercus spp. trees (Oak savanna) and avoid irrigated fields and paved roads. The ecological data provided by this study can be used to predict those areas where changing land use would have the greatest, and least effects on dispersing eagles and, in consequence, on the stability of the breeding population. Management recommendations for those areas include modification of power lines to avoid electrocution during the dispersal phase, presumption against construction of new power lines or roads, presumption against any increase in tree plantations, and financial incentives to maintain existing management regimes in preferred areas, i.e. non-irrigated fields, pastures and cultivated farmland with a scattered distribution of Quercus spp. and Olea spp.

Global optimization with a limited solution time

In this paper the box constrained global optimization problem in presence of a limited solution time is considered. A method is studied based on a combination of multistart and singlestart which implies a decision sequence on the number of random points to be generated. Search strategies are numerically illustrated. Criteria are introduced to measure the performance of solution methods for the problem class. Moreover, the performance of search strategies, specifically the efficiency of generating random points is analyzed.

ORDERED APERTURE ANGLE OF POWER SPECTRA OF RANDOM ARRAY

The ratio of the power spectra of random array to whose unit is called the coherent factor. By analyzing the statistical data experiment of ours, we have studied the fine structures of the curves of coherent factor, introduced a new concept, namely the limited random walk; and found out the formula of the ordered aperture angle for which the values of coherent factor take from N2 to N. This formula has shown that the angle is inversely propertional to the dimension of random array, but is indeperdent of the total number of random points, and that the angle is several times as large as that of the power spectra of regular array in the same domain.

Matching and maximizing in a self-control paradigm using human subjects

Five experiments examined adult human females' sensitivity to variation in amount and delay of reinforcement, as well as their impulsiveness (preference for smaller, less delayed reinforcers over larger, more delayed reinforcers), self-control (the opposite of impulsiveness), and indifference (equal preference for larger, more delayed reinforcers and for smaller, less delayed reinforcers). Each experiment used four to five subjects, concurrent variable-interval schedules, reinforcers that consisted of opportunities to earn points exchangeable for money, and varied relative reinforcer amount and delay separately and/or together. Four experiments used a deduction procedure: a random number of points was repeatedly removed from the display counter at regular intervals, independently of the subjects' behavior. Three experiments used independent concurrent schedules; the other two used nonindependent concurrent schedules. One experiment allowed the subjects to play a radio during laboratory sessions. In all experiments the subjects' behavior was better predicted by a molar maximization model than by the generalized matching law. However, the indifference that occurred when the ratio was used did not closely approximate molar maximization. The deduction procedure appeared to have no effect on the subjects' choices. Use of the nonindependent concurrent schedules seemed to result in the subjects showing indifference and low sensitivity to changes in relative reinforcer amount and delay. Use of the radio also seemed to result in indifference. Unlike the behavior of pigeons, the behavior of adult human subjects within a self-control paradigm appears to be well described by molar maximization, but it may be possible to disrupt such behavior by environmental stimuli.

On the regular increase of the variance of the number of random points in euclidean space

On the regular increase of the variance of the number of random points in euclidean space