Random inscribed polytopes in projective geometries

We establish central limit theorems for natural volumes of random inscribed polytopes in projective Riemannian or Finsler geometries. In addition, normal approximation of dual volumes and the mean width of random polyhedral sets are obtained. We deduce these results by proving a general central limit theorem for the weighted volume of the convex hull of random points chosen from the boundary of a smooth convex body according to a positive and continuous density in Euclidean space. In the background are geometric estimates for weighted surface bodies and a Berry–Esseen bound for functionals of independent random variables.

Understanding of spatiotemporal congestion patterns: A lattice model with predictive effect and density integral

To further enhance the adaptability of traffic model in actual traffic flow, this paper puts forward a lattice model with considering both the predictive effect and the continuous density of historical information. The critical stability condition is derived from linear stability analysis, and the phase diagram clearly shows that considering the predictive effect and the continuous historical density information is beneficial to reduce traffic congestion. Then, a mKdV equation is obtained by nonlinear analysis, which enable to depict the development process of blocked flow. Finally, the numerical simulation results are confirmed that the predictive effects and continuous historical density information have the ability to suppress traffic congestion.

Relative occurrence rates of terrestrial planets orbiting FGK stars

This paper aims to derive a map of relative planet occurrence rates that can provide constraints on the overall distribution of terrestrial planets around FGK stars. Based on the planet candidates in the Kepler DR25 data release, I first generate a continuous density map of planet distribution using a Gaussian kernel model and correct the geometric factor that the discovery space of a transit event decreases along with the increase of planetary orbital distance. Then I fit two exponential decay functions of detection efficiency along with the increase of planetary orbital distance and the decrease of planetary radius. Finally, the density map of planet distribution is compensated for the fitted exponential decay functions of detection efficiency to obtain a relative occurrence rate distribution of terrestrial planets. The result shows two regions with planet abundance: one corresponds to planets with radii between 0.5 and 1.5 R⊕ within 0.2 AU, the other corresponds to planets with radii between 1.5 and 3 R⊕ beyond 0.5 AU. It also confirms the features that may be caused by atmospheric evaporation: there is a vacancy of planets of sizes between 2.0 and 4.0 R⊕ inside of ∼ 0.5 AU, and a valley with relatively low occurrence rates between 0.2 and 0.5 AU for planets with radii between 1.5 and 3.0 R⊕.

Pancreatic Islet Purification from Large Mammals and Humans Using a COBE 2991 Cell Processor versus Large Plastic Bottles

The islet purification step in clinical islet isolation is important for minimizing the risks associated with intraportal infusion. Continuous density gradient with a COBE 2991 cell processor is commonly used for clinical islet purification. However, the high shear force involved in the purification method using the COBE 2991 cell processor causes mechanical damage to the islets. We and other groups have shown human/porcine islet purification using large cylindrical plastic bottles. Shear stress can be minimized or eliminated using large cylindrical plastic bottles because the bottles do not have a narrow segment and no centrifugation is required during tissue loading and the collection processes of islet purification. This review describes current advances in islet purification from large mammals and humans using a COBE 2991 cell processor versus large cylindrical plastic bottles.

The cosmic web through the lens of graph entropy

ABSTRACT We explore the information theory entropy of a graph as a scalar to quantify the cosmic web. We find entropy values in the range between 1.5 and 3.2 bits. We argue that this entropy can be used as a discrete analogue of scalars used to quantify the connectivity in continuous density fields. After showing that the entropy clearly distinguishes between clustred and random points, we use simulations to gauge the influence of survey geometry, cosmic variance, redshift space distortions, redshift evolution, cosmological parameters, and spatial number density. Cosmic variance shows the least important influence while changes from the survey geometry, redshift space distortions, cosmological parameters, and redshift evolution produce larger changes of the order of 10−2 bits. The largest influence on the graph entropy comes from changes in the number density of clustred points. As the number density decreases, and the cosmic web is less pronounced, the entropy can diminish up to 0.2 bits. The graph entropy is simple to compute and can be applied both to simulations and observational data from large galaxy redshift surveys; it is a new statistic that can be used in a complementary way to other kinds of topological or clustering measurements.

Sorting and cryopreservation of goat sperm with or without phenolic compounds

ABSTRACT The objectives of this study were to evaluate goat sperm sorting in continuous Percoll® density gradients and gamete freezability, in the presence or absence of phenolic antioxidants. For this, semen pools were sorted, frozen, and evaluated. The non-selected group (NSg) presented lower progressive motility (PM), linearity (LIN), straightness (STR), and wobble (WOB) than the selected groups, and straight line velocity (VSL) compared to those with catechin or resveratrol. The amplitude of lateral head displacement (ALH) was higher in NSg, and quercetin reduced the mitochondrial membrane potential (MMP). After thawing, the NSg presented lower PM than the selected groups, VSL and VAP (average path velocity) than the selected group with or without catechin, LIN and WOB than the selected with or without catechin or resveratrol, and STR than the selected with catechin. Moreover, NSg presented higher ALH and BCF than the samples selected with or without catechin. Plasma membrane integrity and intact and living cells were higher in the selected groups, and MMP was lower in the NSg and the selected group with quercetin. Thus, centrifugation in Percoll® continuous density gradients is a viable methodology to select goat sperm compatible with the freezing, especially in the presence of catechin or resveratrol.

Hybrid Continuous Density Hmm-Based Ensemble Neural Networks for Sensor Fault Detection and Classification in Wireless Sensor Network

Sensor devices in wireless sensor networks are vulnerable to faults during their operation in unmonitored and hazardous environments. Though various methods have been proposed by researchers to detect sensor faults, only very few research studies have reported on capturing the dynamics of the inherent states in sensor data during fault occurrence. The continuous density hidden Markov model (CDHMM) is proposed in this research to determine the dynamics of the state transitions due to fault occurrence, while neural networks are utilized to classify the faults based on the state transition probability density generated by the CDHMM. Therefore, this paper focuses on the fault detection and classification using the hybridization of CDHMM and various neural networks (NNs), namely the learning vector quantization, probabilistic neural network, adaptive probabilistic neural network, and radial basis function. The hybrid models of each NN are used for the classification of sensor faults, namely bias, drift, random, and spike. The proposed methods are evaluated using four performance metrics which includes detection accuracy, false positive rate, F1-score, and the Matthews correlation coefficient. The simulation results show that the learning vector quantization NN classifier outperforms the detection accuracy rate when compared to the other classifiers. In addition, an ensemble NN framework based on the hybrid CDHMM classifier is built with majority voting scheme for decision making and classification. The results of the hybrid CDHMM ensemble classifiers clearly indicates the efficacy of the proposed scheme in capturing the dynamics of change of statesm which is the vital aspect in determining rapidly-evolving instant faults that occur in wireless sensor networks.