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Hypergraphs are instrumental in modeling complex relational systems that encompass a wide spectrum of high-order interactions among components. One prevalent analysis task is the properties estimation of large-scale hypergraphs, which involves selecting a subset of nodes and hyperedges while preserving the characteristics of the entire hypergraph. This paper aims to sample hypergraphs via random walks and is the first to perform unbiased random walks for sampling of nodes and hyperedges simultaneously in large-scale hypergraphs to the best of our knowledge. Initially, we analyze the stationary distributions of nodes and hyperedges for the simple random walk, and show that there is a high bias in both nodes and hyperedges. Subsequently, to eliminate the high bias of the simple random walk, we propose unbiased random walk strategies for nodes and hyperedges, respectively. Finally, a single joint walk schema is developed for sampling nodes and hyperedges simultaneously. To accelerate the convergence process, we employ delayed acceptance and history-aware techniques to assist our algorithm in achieving fast convergence. Extensive experimental results validate our theoretical findings, and the unbiased sampling algorithms for nodes and hyperedges have their complex hypergraph scenarios for which they are applicable. The joint random walk algorithm balanced the sampling applicable to both nodes and hyperedges. [ABSTRACT FROM AUTHOR]

Introduction: The visual signals evoked at the retinal ganglion cells are modified and modulated by various synaptic inputs that impinge on lateral geniculate nucleus cells before they are sent to the cortex. The selectivity of geniculate inputs for clustering or forming microcircuits on discrete dendritic segments of geniculate cell types may provide the structural basis for network properties of the geniculate circuitry and differential signal processing through the parallel pathways of vision. In our study, we aimed to reveal the patterns of input selectivity on morphologically discernable relay cell types and interneurons in the mouse lateral geniculate nucleus. Methods: We used two sets of Scanning Blockface Electron Microscopy (SBEM) image stacks and Reconstruct software to manually reconstruct of terminal boutons and dendrite segments. First, using an unbiased terminal sampling (UTS) approach and statistical modeling, we identified the criteria for volumebased sorting of geniculate boutons into their putative origins. Geniculate terminal boutons that were sorted in retinal and non-retinal categories based on previously described mitochondrial morphology, could further be sorted into multiple subpopulations based on their bouton volume distributions. Terminals deemed non-retinal based on the morphological criteria consisted of five distinct subpopulations, including small-sized putative corticothalamic and cholinergic boutons, two medium-sized putative GABAergic inputs, and a large-sized bouton type that contains dark mitochondria. Retinal terminals also consisted of four distinct subpopulations. The cutoff criteria for these subpopulations were then applied to datasets of terminals that synapse on reconstructed dendrite segments of relay cells or interneurons. Results: Using a network analysis approach, we found an almost complete segregation of retinal and cortical terminals on putative X-type cell dendrite segments characterized by grape-like appendages and triads. On these cells, interneuron appendages intermingle with retinal and other medium size terminals to form triads within glomeruli. In contrast, a second, presumed Y-type cell displayed dendrodendritic puncta adherentia and received all terminal types without a selectivity for synapse location; these were not engaged in triads. Furthermore, the contribution of retinal and cortical synapses received by X-, Yand interneuron dendrites differed such that over 60% of inputs to interneuron dendrites were from the retina, as opposed to 20% and 7% to X- and Y-type cells, respectively. Conclusion: The results underlie differences in network properties of synaptic inputs from distinct origins on geniculate cell types. [ABSTRACT FROM AUTHOR]

IntroductionThe visual signals evoked at the retinal ganglion cells are modified and modulated by various synaptic inputs that impinge on lateral geniculate nucleus cells before they are sent to the cortex. The selectivity of geniculate inputs for clustering or forming microcircuits on discrete dendritic segments of geniculate cell types may provide the structural basis for network properties of the geniculate circuitry and differential signal processing through the parallel pathways of vision. In our study, we aimed to reveal the patterns of input selectivity on morphologically discernable relay cell types and interneurons in the mouse lateral geniculate nucleus.MethodsWe used two sets of Scanning Blockface Electron Microscopy (SBEM) image stacks and Reconstruct software to manually reconstruct of terminal boutons and dendrite segments. First, using an unbiased terminal sampling (UTS) approach and statistical modeling, we identified the criteria for volume-based sorting of geniculate boutons into their putative origins. Geniculate terminal boutons that were sorted in retinal and non-retinal categories based on previously described mitochondrial morphology, could further be sorted into multiple subpopulations based on their bouton volume distributions. Terminals deemed non-retinal based on the morphological criteria consisted of five distinct subpopulations, including small-sized putative corticothalamic and cholinergic boutons, two medium-sized putative GABAergic inputs, and a large-sized bouton type that contains dark mitochondria. Retinal terminals also consisted of four distinct subpopulations. The cutoff criteria for these subpopulations were then applied to datasets of terminals that synapse on reconstructed dendrite segments of relay cells or interneurons.ResultsUsing a network analysis approach, we found an almost complete segregation of retinal and cortical terminals on putative X-type cell dendrite segments characterized by grape-like appendages and triads. On these cells, interneuron appendages intermingle with retinal and other medium size terminals to form triads within glomeruli. In contrast, a second, presumed Y-type cell displayed dendrodendritic puncta adherentia and received all terminal types without a selectivity for synapse location; these were not engaged in triads. Furthermore, the contribution of retinal and cortical synapses received by X-, Y- and interneuron dendrites differed such that over 60% of inputs to interneuron dendrites were from the retina, as opposed to 20% and 7% to X- and Y-type cells, respectively.ConclusionThe results underlie differences in network properties of synaptic inputs from distinct origins on geniculate cell types.

Day-fresh Great Cormorant pellets were collected at a huge single winter roost at Kreupel island in Lake IJsselmeer, The Netherlands. The roost is situated on a sandy island, 3 m above the water level and is regularly used by 1000–8000+ Cormorants. By examining pellets and thus reconstructing the previous day's meal of Cormorants gathering at the roost, we explored spatio-temporal differences in the diet of individual birds. We found that structural differences in pellets (size, colour and structure) are related to their content (fish species and fresh mass of a daily meal). Structurally larger and lighter coloured pellets contained larger and coarser fish and represented a higher total fish mass. Pellets of different size and structure were non-randomly distributed at the roost. Birds positioned centrally in the roost produced on average larger pellets than birds at the edges. Cormorants having few or no food remains in their pellets were more frequently recorded on the edge of the roost than in the centre and in particular, they were more likely to be located to the rear of the roost. The same was true for pellets showing a bloody signature which may be linked to either injury by sharp fin rays or to a parasite induced effect. Pellet data were corroborated by observations of differential distribution of faecal splashes of Cormorants, showing that individuals in the centre of the roost produced most guano. Clear diet differences existed within the roost between birds in the centre and elsewhere in the roost, whereas smaller differences existed between the front, edge and rear of the roost. Our data suggest a social hierarchy based on higher foraging success of birds returning earlier to the roost and settling in the centre, hereby forcing later arriving and less successful Cormorants towards the edge, rear and front position. We conclude that position at the roost is a reflection of previous foraging success, possibly caused by differences in dominance between Cormorants during the period of communal foraging. From a methodological point of view, our study demonstrates that, because of structural differences in pellets and spatial differences in occurrence, it is important to collect pellets randomly if one is to describe a proper diet sample by using pellets at any given site. Especially in marshlands and under trees and bush growth with a lot of litter, the likely collection of larger, more conspicuous pellets will cause a bias towards the larger fish species and sizes. Also sampling only at edge locations or specifically at the centre of a roost may give biased results, as this may result in an under- or overestimation in reconstructed fish uptake (e.g. fish size, mass, species) from the waterbody under study. [ABSTRACT FROM AUTHOR]

We present the first exact simulation method for multidimensional reflected Brownian motion (RBM). Exact simulation in this setting is challenging because of the presence of correlated local-time-like terms in the definition of RBM. We apply recently developed so-called ε-strong simulation techniques (also known as tolerance-enforced simulation) which allowus to provide a piecewise linear approximation to RBM with ε (deterministic) error in uniform norm. A novel conditional acceptance--rejection step is then used to eliminate the error. In particular, we condition on a suitably designed information structure so that a feasible proposal distribution can be applied. [ABSTRACT FROM AUTHOR]

The switching model is a well-known random network model that randomizes a network while keeping its degree sequence fixed. The idea behind the switching model is simple: a network is randomized by repeatedly rewiring pairs of edges. In this paper we demonstrate that despite its simple description, and in part due to it, much can go wrong when implementing the switching model. Specifically, we show that the model needs to be implemented carefully, to avoid biased sampling.We propose a precise definition of the switching model which guides its implementation. Furthermore, we argue that we should refer to the switching model with respect to a specific network class, and in fact define a family of switching models. This formalizes previous use of the switching model to randomize networks from numerous network classes. We show that the properties of these models depend on the network class, and in particular that their stationary distributions differ. Hence it is important to take into account which class of networks is being randomized. We derive conditions, and where possible adjust the models, such that sampling is unbiased for the switching model with respect to eight common network classes. These unbiased nullmodels are important, since common network analysis techniques such as motif finding and community detection rely on them. [ABSTRACT FROM AUTHOR]

The unbiasedness in feature space and geographical space is generally used for evaluating the samples' representation in measure region. Although auxiliary variables are often used for mapping soil variables, problems associated with categorical variables are rarely mentioned. In this paper, a method of unbiased sampling of soil which compromise ing between spreading in geographical space and feature space is presented for optimization of the sample pattern based on multidimensional categorical auxiliary variables. In this method, the feature space is constructed of categorical auxiliary variables; the optimization function which blends the uniform distributions of feature space and geographical space is minimized. The optimal pattern is obtained using simulated annealing. In addition, Feature Divation Index (FDI) is defined in the paper to measure the unbiasedness in feature space of samples. The method was tested through a case study on the soil heavy metal in farmland in Shunyi District, Beijing. As basis data of experiment, the spatial distribution data of samples in the study area were selected in 2007, 2008, 2009 years. The original sample size was 1139, from which the calculated optimal sampling number without considering spatial correlation was 450. Taking 100 as lower limit and 450 as upper limit, eight datasets of sampling number were set, which were 100, 150, 200, 250, 300, 350, 400, 450, respectively. According to scale transformation, the sampling scales were 0.225, 0.239, 0.255, 0.275, 0.302, 0.337, 0.389, 0.477, respectively. Two patterns were selected as the sampling layout to compare with the unbiased sampling: the patterns of uniform sampling in feature space (feature uniform sampling) and of uniform sampling in geographic space (geographical uniform sampling). Land type, soil texture and parent material as categorical auxiliary variables were used to represent the feature space of soil variables. The performances in the overall estimates, the uniformity in feature space and the mapping accuracy were compared between the 3 types of designs. It can be concluded that in the case of global estimation, based on relative error of mean, range, coefficient of skewness and kurtosis, the precision of geographical uniform sampling is worst; when the sampling scale is larger than 0.275, feature uniform sampling achieves best results; as the sampling scale becomes smaller, unbiased sampling can get better results. What's more, the sampling designs by geographical uniform sampling have the worst feature presentation. When the sampling scale is larger, the representative of samples by feature uniform sampling in feature space is the best; when sampling scale is less than 0.302, unbiased sampling is suggested as a prudent sampling strategy. Finally, in the case of forming geostatistical map, root mean square error (RMSE) between basis data and the Kriging predicted data is used. Unbiased sampling is shown to be competitive in reproducing area with high accuracy. In a word, among the methods of optimizing sampling based on auxiliary variable, the feature uniform sampling is suitable in the situation of large sampling scale or fewer sample points and can only be used in global estimation; the unbiased sampling is a good compromise between spreading in geographical space and feature space, and it can achieve better result in the case of small sampling scale or more sample points. [ABSTRACT FROM AUTHOR]

The applicability of a pump method for field surveys of hyporheos was investigated for taxon-specific collection bias by comparing a pump method with a core method in a shore area of the lower reach of Kizu River in Japan. A sampling bias index for the first 10 l of pump samples compared with 10 l hyporheic water (equivalent) core samples showed that the pump method underestimated the abundance of most taxa, except for the heliozoan Centrohelida. Animals were classified into three groups based on body size and sampling bias index; animals with small bodies and high sampling bias indices generally had flatness indices near 1.0. The animals were also classified into three groups based on patterns of reduction in serial fraction values in consecutive pumpings. Although Crustacea tended to be overrepresented in the pump samples, relative densities among them were comparable to those in the core samples, except for harpacticoid copepods. Animals with an intermediate reduction pattern had a similar relative abundance in the 50-l pump and 1,000-cm core samples, except for Crustacea and Centrohelida. The results suggest that by using an adequate taxon-dependent volume of water, the pump method is useful for examining the community composition of hyporheic fauna. [ABSTRACT FROM AUTHOR]

Highlights: [•] We used the ‘fractionator’ tree sampling method for yield estimation and to study apple quality variability. [•] A sample of 78 apples collected from a 17ha orchard in about 5hours produced a yield estimate with −4.8% error compared to packing records. [•] Starch and fruit mass had fairly high variability; SSC and flesh firmness had moderate variability. [•] Only fruit mass variations could be significantly related to position of fruit in the canopy. [ABSTRACT FROM AUTHOR]

Poisson disk sampling has excellent spatial and spectral properties, and plays an important role in a variety of visual computing. Although many promising algorithms have been proposed for multidimensional sampling in euclidean space, very few studies have been reported with regard to the problem of generating Poisson disks on surfaces due to the complicated nature of the surface. This paper presents an intrinsic algorithm for parallel Poisson disk sampling on arbitrary surfaces. In sharp contrast to the conventional parallel approaches, our method neither partitions the given surface into small patches nor uses any spatial data structure to maintain the voids in the sampling domain. Instead, our approach assigns each sample candidate a random and unique priority that is unbiased with regard to the distribution. Hence, multiple threads can process the candidates simultaneously and resolve conflicts by checking the given priority values. Our algorithm guarantees that the generated Poisson disks are uniformly and randomly distributed without bias. It is worth noting that our method is intrinsic and independent of the embedding space. This intrinsic feature allows us to generate Poisson disk patterns on arbitrary surfaces in (\\rlapI\kern 2.0pt\R^n). To our knowledge, this is the first intrinsic, parallel, and accurate algorithm for surface Poisson disk sampling. Furthermore, by manipulating the spatially varying density function, we can obtain adaptive sampling easily. [ABSTRACT FROM AUTHOR]

Abstract: A novel resampling algorithm (called Deterministic Resampling) is proposed, which avoids uncensored discarding of low weighted particles thereby avoiding sample impoverishment. The diversity of particles is maintained by deterministically sampling support particles to improve the residual resampling. A proof is given that our approach can be strictly unbiased and maintains the original state density distribution. Additionally, it is practically simple to implement in low dimensional state space applications. The core idea behind our approach is that it is important to (re)sample based on both the weight of particles and their state values, especially when the sample size is small. Our approach, verified by simulations, indicates that estimation accuracy is better than traditional methods with an affordable computation burden. [Copyright &y& Elsevier]

This paper focuses on sampling as a nexus of ethical dilemmas experienced by social workers and other applied empirical researchers. It is argued here that social workers and other applied researchers have an ethical obligation to construct the smallest representative samples possible. Although random sampling is considered by many researchers as the gold standard methodological procedure for maximizing external validity and optimizing sample size, in practice, random sampling often is difficult to implement. Recommendations include using (1) deliberate sampling to balance a sample's composition in terms of typicalness and diversity; (2) randomization tests; (3) a broader perspective on external validity; (4) one-sided hypotheses; (5) sequential sampling; and (6) planned missing data designs. [ABSTRACT FROM AUTHOR]

Background: Researchers have long been interested in counting the number of cells within the glomerulus. Investigators using different techniques have yielded conflicting results. The most direct method is to count the cells in serial sections from the entire glomerulus. This Exhaustive Count method is not usually practical. The disector/fractionator method counts the number of cells in a fraction of sections. The total is estimated from the product of the cell count and the reciprocal of the fraction. The Weibel-Gomez method determines the density of cells per glomerulus, then multiplies this density by glomerular volume to obtain cell number. In this study, we compared the disector/fractionator and Weibel-Gomez methods to identify a practical alternative for the time-consuming Exhaustive Count method. Methods: Glomeruli from a normal mouse kidney were completely sectioned and images obtained. Appropriate images were used to count glomerular cell number using each method. Results: The Exhaustive Count method yielded 213 ± 22 (mean ± SD) cells/glomerulus vs. the disector/fractionator average of 211 ± 29 cells/glomerulus (p = 0.82). The Weibel-Gomez method average of 235 ± 26 cells/glomerulus was statistically different from the Exhaustive Count method (p = 0.003). Conclusion: The Weibel-Gomez produced a 10% overestimation, whereas the disector/fractionator method was unbiased and thus a good substitute for the Exhaustive Count method. Copyright © 2006 S. Karger AG, Basel [ABSTRACT FROM AUTHOR]