Discrete Points In Space Research Articles

Differentiate data by higher-order structures

The comparison of two objects is a topic that exists widely in different research areas. In this study, the network distance is combined with the k-nearest neighbour network sequence to construct the topological structural distance (TSD). This indicator is used to quantitatively describe the difference between two sets of points in any metric structure. Several datasets were tested to demonstrate the effectiveness of this indicator. Calculations show that TSD can compare the intrinsic structure of low-dimensional and high-dimensional datasets and is not limited by dimension. In addition, TSD can also be used to characterize sets of points in discrete space, such as comparing the structure of different networks. The examples in this study show that TSD is a universal method for analyzing the intrinsic structure of data.

Trajectory generation based on power for urban air mobility

A method of generating trajectories based on power is proposed for Urban Air Taxis. The method is simpler and more direct than traditional methods because it does not require a detailed aircraft model or a flight control model. Instead, it allows the user to specify the route, the static longitudinal profile (altitude as a function of distance), and a power model to determine the progress in time along that profile. The power model can be determined from a recorded or simulated trajectory of the same aircraft type. This capability allows a trajectory to be generated or reshaped to avoid conflicts while preserving the basic performance characteristics. Net or excess power is defined as the rate of change of mechanical (kinetic and potential) energy, and it is modeled as a function of airspeed. The time steps between discrete points in space along the trajectory are used to yield a specified power as a function of airspeed, and they are determined by solving a cubic polynomial at each point. An elliptical profile is used to generate an example trajectory. The dependence of trip flight time on various parameters is analyzed and plotted.

Fast Context-Awareness Encoder for LiDAR Point Semantic Segmentation

A LiDAR sensor is a valuable tool for environmental perception as it can generate 3D point cloud data with reflectivity and position information by reflecting laser beams. However, it cannot provide the meaning of each point cloud cluster, so many studies focus on identifying semantic information about point clouds. This paper explores point cloud segmentation and presents a lightweight convolutional network called Fast Context-Awareness Encoder (FCAE), which can obtain semantic information about the point cloud cluster at different levels. The surrounding features of points are extracted as local features through the local context awareness network, then combined with global features, which are highly abstracted from the local features, to obtain more accurate semantic segmentation of the discrete points in space. The proposed algorithm has been compared and verified against other semantic KITTI data algorithms and has achieved state-of-the-art performance. Due to its ability to note fine-grained features on the z-axis in space, the algorithm shows higher prediction accuracy for certain types of objects. Moreover, the training and validation time is short, and the algorithm can meet high real-time requirements for 3D perception tasks.

A Motion Planning Method for Automated Vehicles in Dynamic Traffic Scenarios

We propose a motion planning method for automated vehicles (AVs) to complete driving tasks in dynamic traffic scenes. The proposed method aims to generate motion trajectories for an AV after obtaining the surrounding dynamic information and making a preliminary driving decision. The method generates a reference line by interpolating the original waypoints and generates optional trajectories with costs in a prediction interval containing three dimensions (lateral distance, time, and velocity) in the Frenet frame, and filters the optimal trajectory by a series of threshold checks. When calculating the feasibility of optional trajectories, the cost of all optional trajectories after removing obstacle interference shows obvious axisymmetric regularity concerning the reference line. Based on this regularity, we apply the constrained Simulated Annealing Algorithm (SAA) to improve the process of searching for the optimal trajectories. Experiments in three different simulated driving scenarios (speed maintaining, lane changing, and car following) show that the proposed method can efficiently generate safe and comfortable motion trajectories for AVs in dynamic environments. Compared with the method of traversing sampling points in discrete space, the improved motion planning method saves 70.23% of the computation time, and overcomes the limitation of the spatial sampling interval.

Sound field reconstruction in rooms: Inpainting meets super-resolution.

In this paper, a deep-learning-based method for sound field reconstruction is proposed. The possibility to reconstruct the magnitude of the sound pressure in the frequency band 30-300 Hz for an entire room by using a very low number of irregularly distributed microphones arbitrarily arranged is shown. Moreover, the approach is agnostic to the location of the measurements in the Euclidean space. In particular, the presented approach uses a limited number of arbitrary discrete measurements of the magnitude of the sound field pressure in order to extrapolate this field to a higher-resolution grid of discrete points in space with a low computational complexity. The method is based on a U-net-like neural network with partial convolutions trained solely on simulated data, which itself is constructed from numerical simulations of Green's function across thousands of common rectangular rooms. Although extensible to three dimensions and different room shapes, the method focuses on reconstructing the two-dimensional plane of a rectangular room from measurements of the three-dimensional sound field. Experiments using simulated data together with an experimental validation in a real listening room are shown. The results suggest a performance which may exceed conventional reconstruction techniques for a low number of microphones and computational requirements.

Fabrication and shape detection of a catheter using fiber Bragg grating

Considering the spatial position and shape detection properties of the fiber Bragg grating (FBG) curve sensor used in the human body, the positioning accuracy of the FBG curve sensor plays a major role in the pre-diagnosis and treatment of diseases. We present a new type of shape-sensing catheter (diameter of 2.0 mm and length of 810 mm) that is integrated with an array of four optical fibers, where each contains five nodes, to track the shape. Firstly, the distribution of the four orthogonal fiber gratings is wound around a nitinol wire using novel packaging technology, and the spatial curve shape is rebuilt based on the positioning of discrete points in space. An experimental platform is built, and then a reconstruction algorithm for coordinate point fitting of the Frenet frame is used to perform the reconstruction experiment on millimeter paper. The results show that, compared with those in previous studies, in 2D test, the maximum relative error for the end position is reduced to 2.74%, and in 3D reconstruction experiment, the maximum shape error is 3.43%, which verifies both the applicability of the sensor and the feasibility of the proposed method. The results reported here will provide an academic foundation and the key technologies required for navigation and positioning of non-invasive and minimally invasive surgical robots, intelligent structural health detection, and search and rescue operations in debris.

Morphological classification of odontogenic keratocysts using Bouligand–Minkowski fractal descriptors

The Odontogenic keratocyst (OKC) is a cystic lesion of the jaws, which has high growth and recurrence rates compared to other cysts of the jaws (for instance, radicular cyst, which is the most common jaw cyst type). For this reason OKCs are considered by some to be benign neoplasms. There exist two sub-types of OKCs (sporadic and syndromic) and the ability to discriminate between these sub-types, as well as other jaw cysts, is an important task in terms of disease diagnosis and prognosis. With the development of digital pathology, computational algorithms have become central to addressing this type of problem. Considering that only basic feature-based methods have been investigated in this problem before, we propose to use a different approach (the Bouligand–Minkowski descriptors) to assess the success rates achieved on the classification of a database of histological images of the epithelial lining of these cysts. This does not require the level of abstraction necessary to extract histologically-relevant features and therefore has the potential of being more robust than previous approaches. The descriptors were obtained by mapping pixel intensities into a three dimensional cloud of points in discrete space and applying morphological dilations with spheres of increasing radii. The descriptors were computed from the volume of the dilated set and submitted to a machine learning algorithm to classify the samples into diagnostic groups. This approach was capable of discriminating between OKCs and radicular cysts in 98% of images (100% of cases) and between the two sub-types of OKCs in 68% of images (71% of cases). These results improve over previously reported classification rates reported elsewhere and suggest that Bouligand–Minkowski descriptors are useful features to be used in histopathological images of these cysts.

Combined arrival-time imaging and time reversal for scatterer identification

The computational inverse problem of identifying a scatterer in a time-dependent wave field is considered. The wave speed of the background medium and the wave source are assumed to be known. Wave measurements, possibly noisy, are given at chosen discrete points in space (sensor locations) and time. The goal is to find scatterer parameters such as location, size and shape. The computational solution procedure consists of two steps. In the first step, a standard fast Arrival-Time Imaging (ATI) algorithm is employed. This results in a rough image which provides possible regions for the location of the scatterer. In the second step an optimization scheme based on Time Reversal (TR) is used to determine the location, size and shape of the scatterer. The preliminary ATI step has the effect of reducing considerably the search space for the TR optimization. Also, proposed here is an improved definition of the objective function used for the optimization, which tends to eliminate spurious solutions. Numerical experiments, based on a finite element discretization in space and an explicit Newmark time-stepping, show the identification capability of the proposed scheme, for a model problem involving the linear scalar wave equation in a bounded domain. Two types of scatterers are considered: a crack with a known orientation, whose location and size are sought, and a rectangular scatterer whose location, aspect ratio and size are sought. The performance of the scheme in the presence of measurement noise is also demonstrated.

Accurate non-adiabatic quantum dynamics from pseudospectral sampling of time-dependent Gaussian basis sets

Quantum molecular dynamics requires an accurate representation of the molecular potential energy surface from a minimal number of electronic structure calculations, particularly for nonadiabatic dynamics where excited states are required. In this paper, we employ pseudospectral sampling of time-dependent Gaussian basis functions for the simulation of non-adiabatic dynamics. Unlike other methods, the pseudospectral Gaussian molecular dynamics tests the Schrödinger equation with N Dirac delta functions located at the centers of the Gaussian functions reducing the scaling of potential energy evaluations from O(N2) to O(N). By projecting the Gaussian basis onto discrete points in space, the method is capable of efficiently and quantitatively describing the nonadiabatic population transfer and intra-surface quantum coherence. We investigate three model systems: the photodissociation of three coupled Morse oscillators, the bound state dynamics of two coupled Morse oscillators, and a two-dimensional model for collinear triatomic vibrational dynamics. In all cases, the pseudospectral Gaussian method is in quantitative agreement with numerically exact calculations. The results are promising for nonadiabatic molecular dynamics in molecular systems where strongly correlated ground or excited states require expensive electronic structure calculations.

A method for estimating soil water diffusivity from moisture profiles and its application across an experimental catchment

Summary Despite the well-accepted value of soil hydraulic properties for describing and modeling matter and energy fluxes in the unsaturated zone, their accurate measurement across scales is still a daunting task. The increasing availability of continuous soil water content measurements at discrete points in space, as provided by sensor networks, offers still unexplored possibilities for evaluating soil physical properties across landscapes. In this study, we propose a new method, based on the Bruce and Klute equation, to estimate effective soil water diffusivity from soil water profile data observed during continuous desiccation periods. An analytical expression is proposed for the diffusion-soil water relationship, assuming an exponential relationship between soil water content and the Boltzmann variable. The method has been evaluated using soil water profile data observed at inter-row and under canopy locations across a rainfed olive orchard in SW Spain. The spatial variability of the effective soil water diffusivity across the orchard was estimated. Different soil conditions under the tree canopies as compared to inter-row areas resulted in significantly different effective diffusivity relationships, reflecting the effect of trees on soil physical properties and water dynamics across olive orchards. The proposed method offers a suitable alternative to traditional laboratory methods and can be easily extended to estimate soil hydraulic conductivity and water retention curves.

Real-time information processing of environmental sensor network data using bayesian gaussian processes

In this article, we consider the problem faced by a sensor network operator who must infer, in real time, the value of some environmental parameter that is being monitored at discrete points in space and time by a sensor network. We describe a powerful and generic approach built upon an efficient multi-output Gaussian process that facilitates this information acquisition and processing. Our algorithm allows effective inference even with minimal domain knowledge, and we further introduce a formulation of Bayesian Monte Carlo to permit the principled management of the hyperparameters introduced by our flexible models. We demonstrate how our methods can be applied in cases where the data is delayed, intermittently missing, censored, and/or correlated. We validate our approach using data collected from three networks of weather sensors and show that it yields better inference performance than both conventional independent Gaussian processes and the Kalman filter. Finally, we show that our formalism efficiently reuses previous computations by following an online update procedure as new data sequentially arrives, and that this results in a four-fold increase in computational speed in the largest cases considered.

Spatial and temporal corroboration of a fire‐scar‐based fire history in a frequently burned ponderosa pine forest

Fire scars are used widely to reconstruct historical fire regime parameters in forests around the world. Because fire scars provide incomplete records of past fire occurrence at discrete points in space, inferences must be made to reconstruct fire frequency and extent across landscapes using spatial networks of fire-scar samples. Assessing the relative accuracy of fire-scar fire history reconstructions has been hampered due to a lack of empirical comparisons with independent fire history data sources. We carried out such a comparison in a 2780-ha ponderosa pine forest on Mica Mountain in southern Arizona (USA) for the time period 1937-2000. Using documentary records of fire perimeter maps and ignition locations, we compared reconstructions of key spatial and temporal fire regime parameters developed from documentary fire maps and independently collected fire-scar data (n = 60 plots). We found that fire-scar data provided spatially representative and complete inventories of all major fire years (> 100 ha) in the study area but failed to detect most small fires. There was a strong linear relationship between the percentage of samples recording fire scars in a given year (i.e., fire-scar synchrony) and total area burned for that year (y = 0.0003x + 0.0087, r2 = 0.96). There was also strong spatial coherence between cumulative fire frequency maps interpolated from fire-scar data and ground-mapped fire perimeters. Widely reported fire frequency summary statistics varied little between fire history data sets: fire-scar natural fire rotations (NFR) differed by < 3 yr from documentary records (29.6 yr); mean fire return intervals (MFI) for large-fire years (i.e., > or = 25% of study area burned) were identical between data sets (25.5 yr); fire-scar MFIs for all fire years differed by 1.2 yr from documentary records. The known seasonal timing of past fires based on documentary records was furthermore reconstructed accurately by observing intra-annual ring position of fire scars and using knowledge of tree-ring growth phenology in the Southwest. Our results demonstrate clearly that representative landscape-scale fire histories can be reconstructed accurately from spatially distributed fire-scar samples.

Convex hull method of acoustic field interpolation.

Empirical knowledge of the local acoustic field typically comes in the form of time samples at discrete points in space corresponding to the locations of, say, omnidirectional microphones or hydrophones on an underwater array. To determine the acoustic field at an arbitrary point in space requires either propagation modeling, signal interpolation, or some combination of the two. In this paper, a method of field interpolation is presented which estimates the acoustic field at any point within the convex hull of all sample points. This method is compared against more traditional inverse beamforming methods using both simulated and measured data.

Effect of Passive Surface Water Flux Meter Design on Water and Solute Mass Flux Estimates

Standard methods for determining pollutant loads in streams typically require the collection of separate instantaneous measurements of water velocities and solute concentrations at discrete points in space and time. A recently developed device, the passive surface water flux meter (PSFM), has been introduced as an alternate method for the measurement of time-integrated surface water flux (velocity) and solute mass flux. This paper extends PSFM development by evaluating and comparing two PSFM designs in laboratory flumes, as well as reporting on initial steady-state field testing. The shape of the PSFM body determines the velocity with which water passes through the device, and different designs may thus be preferred for different applications. Experiments compared the accuracy of flux measurement by the previously introduced hydrofoil-shaped PSFM and nitrate-sorbing cartridge with that of a newly designed cylindrical-shaped PSFM and phosphate-sorbing cartridges. Testing was performed in a laboratory flume...

The representativeness problem of a station net applied to the verification of a precipitation forecast based on areas

AbstractThe results and conclusions obtained in a verification process can be strongly influenced by its methodology, especially when some assumptions are made in order to avoid the limitations of the observational data (i.e., the lack of representativeness of the data or poor area coverage). Several aspects of the verification process must be studied if reliable conclusions are to be obtained.This paper discusses the problems related to the development of a verification method for a precipitation forecast defined over continuous areas using observational data from discrete points in space (meteorological stations). To tackle this asymmetry, the concept of the station net quality is first introduced.The verification approach is based on deterministic categorical scores. The effects of the number of stations, the spatial distribution of the station net and the precipitation thresholds used in the verification process are shown. Using different sets of precipitation stations, the scores show a strong sensitivity to the station net quality. The suitability of the scores used in this study is also analysed and the verification process is finally adapted to compensate for undesired effects. Copyright © 2007 Royal Meteorological Society

Hybrid approaches to the solutions of the “Lighthill–Whitham–Richards” model

This paper presents a hybrid “Lighthill–Whitham–Richards” (LWR) model combining both macroscopic and microscopic traffic descriptions. Simple interfaces are defined to translate the boundary conditions when changing the traffic description. They are located in discrete points in space and are based on a generalisation of demand and supply concepts. Simulation results show that the proposed interfaces ensure an accurate wave propagation along two links differently described. Furthermore, the demand and supply formulation of the hybrid model makes it fully compatible with major LWR extensions developed over the past few years (intersections modeling, multi-lanes representation, etc.). Finally, we prove that Newell’s optimal velocity car-following model can be derived from the Godunov scheme applied to the LWR model in Lagrangian coordinates. This proposes a microscopic resolution of the LWR model that is fully compatible with the usual macroscopic representation. This microscopic resolution is included in the hybrid model.

Extinction Criteria in Stage‐Structured Population Models with Impulsive Culling

We propose stage-structured population models for species whose adult members are subject to culling, with a view to understanding the culling regimes that are likely to result in eradication of the species. A purely time-dependent model is proposed in which culling occurs at particular discrete times, not necessarily equally spaced. Then a reaction-diffusion model is proposed for a situation in which the adults can diffuse; in this model the culling is continuous in time but occurs only at particular discrete points in space. Such a model might be appropriate for pheromone trapping of insects. For both models conditions are obtained that are sufficient for species eradication.

On Efficient Computation of the Optimization Problem Arising in the Inverse Modeling of Non-Stationary Multiphase Multicomponent Flow Through Porous Media

In this paper we discuss a method of solving inverse problems in non-isothermal multiphase multicomponent flow through porous media. The conceptual model is described by a system of non-linear partial differential equations which involve unknown parameters. These parameters are to be determined using a set of observations at discrete points in space and time by an optimization method. It is based on a reduced Gauss-Newton iteration in combination with an efficient gradient computation which takes advantage of a recently developed efficient numerical simulation technique. A sensitivity analysis is carried out for the optimum parameter set. Numerical experiments are performed for a one dimensional column experiment carried out at the VEGAS, University of Stuttgart, Germany.

Inexpensive Electronic Water Level Recorders for Hydrologic Studies

AbstractHydrologic investigations typically involve the collection of water level measurements at discrete points in space and time. The high cost of commercial electronic recorders can be a burden. We have developed an inexpensive (∼$200) electronic water level recorder consisting of a Motorola microcontroller, a clock, memory, pressure transducers, and associated circuitry. The instrument is powered by a 6‐V battery. These devices, each capable of monitoring up to eight channels of analog input, are presently providing continuous monitoring of nested piezometers, tide gauges, and rain gauges in hydrologic studies at the Savannah River site and the North Inlet (South Carolina) Long‐Term Ecological Research (LTER) site. The instruments can be custom tailored to record water levels at any specified time interval, or whenever the water level changes by a specified amount, and can store up to 32,000 water level observations. These instruments have been used to conduct slug tests and can be configured to monitor observation wells for pumping tests. Simplicity of construction and availability of components offer hydrologists an inexpensive but reliable method of water level recording. Several examples of the use of this instrumentation in diverse hydrologic settings are described.

Optimal active pointwise control of thin plates via state-control parametrization

A direct method to solve an optimal control problem by parametrizing both state and open-loop control variables is developed. This technique is designed to suppress the undesirable vibrations of a rectangular plate by open-closed loop control applied at discrete points in space. The closed-loop mechanism is assumed to be proportional to displacement. The measure of performance of the structure is taken as a combination of its total energy and the penalty terms describing the expenditure of the open-closed loop forces used in the control process. Using modal expansion and an appropriate transformation, the optimal control of a distributed parameter system is reduced to the optimal control of a linear time-varying lumped parameter system. Next, a computationally efficient formulation to evaluate the optimal control and trajectory of the structure, based on shifted Legendre polynomial approximations of the state variable and each open-loop control variable, is developed. This converts the linear quadratic problem into a mathematical programming problem, where a necessary condition for optimality is derived as a system of linear algebraic equations. A minimization algorithm is then used to determine numerically the feedback parameters of the closed-loop control. A numerical example involving a simply supported plate is provided to substantiate the theoretical results by demonstrating the effectiveness of the proposed method. The results of computer simulation studies compare favourably to optimal solutions obtained by the variational method (Blanton and Sadek 1992), indicating that the suggested approach provides better control of the vibrating plate