Probability Distribution Of Location Research Articles

Probability of He+ Ion at Quantum Number 3 ≤ n ≤ 4 in Momentum Space

Ions resulting from the ionization of helium atoms are known as helium ions. Atom of Helium The probability distribution of the particle locations and velocities inside a helium atom is referred to as probability. Using theoretical study methods, the goal of this research is to find the probability of an electron's position in a helium atom at the quantum number 3 ≤ n ≤ 4. This type of research is non-experimental research by developing previously existing theories. This type of research is non-experimental research by transforming the radial wave function of hydrogenic atoms in position space into a radial wave function in momentum space using the Fourier transformation, then including a number of Gegenbauer functions and using the probability equation of finding an electron in a Helium ion in momentum space. The results of this research provide information regarding the position and probability of the existence of electrons in the helium atom. The probability value for the Helium ion is obtained using the equation P(p) = which is used to indicate the probability of finding an electron in a helium atom is directly proportional to the principal quantum number (n) and the value of the electron's momentum. The larger the electron momentum interval, the greater the probability.

Location-and-Preference Joint Prediction for Task Assignment in Spatial Crowdsourcing

With the rapid development of mobile networks and the ubiquity of mobile devices, spatial crowdsourcing (SC), which refers to assigning spatial–temporal tasks to moving workers, has drawn increasing attention. Thus, many researchers aim at various task assignment methods in SC. However, existing works generally consider workers’ location and preference categories separately. Ignorance of the correlation between them can often lead to poor assignment results. In this article, we propose a location-and-preference joint prediction model (JPM) to predict workers’ locations and preference categories jointly at each sample timestamp. Based on the predictive location probability distribution and preference probability distribution, we elaborately design a greedy multiattribute joint task assignment algorithm (MAJA) to maximize the average number of completed tasks under constraints. Then, an overall procedure incorporating the JPM and MAJA, called the location-and-preference joint prediction-based task assignment (LPJTA), is implemented to focus on assigning tasks to workers who are near the task location and willing to perform the task based on predicting locations and preference categories. We theoretically analyze the time complexity and approximation ratio of the proposed methods and construct extensive experiments on three real datasets to empirically verify their effectiveness, comparing with the state-of-the-art baselines.

Indoor mm-Wave Coverage Enhancement: Reconfigurable Intelligent Surface Deployment Strategy Based on Human Mobility Model

Reconfigurable intelligent surface (RIS) is regarded as a promising technology to assist indoor millimeter wave (mm-Wave) communication due to its ability to manipulate electromagnetic waves directionally. Due to the complexity of indoor environment, different RIS deployment strategies significantly affect the system performance. However, the existing work investigating RIS indoor deployment ignored the influence of human mobility to indoor signal coverage, therefore a practical indoor deployment strategy remains unknown. In this letter, based on the consideration of human blockage to mm-Wave signal and probability distribution of human location, we propose an indoor RIS deployment strategy with human mobility model to minimize the outage probability, which is more applicable to the realistic indoor environment. An algorithm is presented to minimize the outage probability at a subspace scale of the room geometry and calculate the corresponding RIS location for single RIS deployment and multiple RISs cooperative deployment. Numerical results are provided to display how our deployment strategy works, which indicate that deploying RIS correctly can decrease the indoor communication outage probability significantly.

A tribo-dynamic based pitting evolution model of planetary gear sets: A topographical updating approach

Considering the coupling effects of the tribology and dynamics, a dynamic pitting evolution model of planetary gear sets is developed. A fast dynamic load distribution algorithm is proposed to obtain the dynamic contact load considering complex pitting topography. Then the mixed elastohydrodynamic lubrication theory is adopted to acquire the tribological parameters. Combing the dynamic load and Zaretsky's fatigue criterion, a contact fatigue model is developed to predict the pitting topography during the degradation process. An iterative algorithm framework is developed to realize the topographical updating in the dynamic pitting prediction. The effectiveness of the proposed model is demonstrated using two experimental examples. The probability distribution of the pitting location is investigated using the proposed model. It is revealed that the gamma distribution is more consistent with the pitting distribution along the involute direction than the normal distribution. Owing to the “competition mechanism” of the pitting and surface wear, the pitting center approaches the pitch point with the increase of the surface roughness. The proposed model is capable of evaluating tribo-dynamic behaviors of planetary gear sets during the life-cycle degradation process of pitting failure. Moreover, it can provide theoretical guidance for the pitting fault mechanism and model-based fault diagnosis.

Diagnosis of internal cracks in concrete using vibro-acoustic modulation and machine learning

This paper investigates the utility of physics-informed machine learning models for vibro-acoustic modulation (VAM)–based damage localization in concrete structures. Vibro-acoustic modulation is a nonlinear dynamics-based non-destructive testing method, which was initially developed to perform damage detection and later extended to accomplish damage localization. The VAM-based damage (hidden crack) diagnosis is performed by analyzing the damage index pattern on the surface of the component to arrive at the size and location of the hidden damage. Past investigations have employed heuristically selected damage index thresholds as well as computationally expensive Bayesian estimation methods for VAM-based damage localization in two (surface) dimensions. Compared to these studies, the proposed methodology automates the threshold selection (algorithmic instead of heuristic), increases the speed of the probabilistic damage diagnosis process, and enables the estimation of damage depth. We generate training data (damage index) for the machine learning models using the pertinent nonlinear dynamics (finite element) models using different combinations of test parameters. The (supervised) machine learning models are thus informed by computational physics models. These include two types of artificial neural network (ANN) models: classification models that identify whether a sensor location is damaged or not and regression models that enable Bayesian estimation to obtain the posterior probability distribution of damage location and size. The accuracy of machine learning-based diagnosis is evaluated using both numerical and laboratory experiments. The proposed physics-informed machine learning models for VAM-based damage diagnosis are able to achieve an accuracy of about 60–64% in the validation experiments, indicating the potential of these methods for internal crack detection. The results show that for complex (nonlinear dynamics-driven) diagnostic methods, damage index patterns learned from physics models could be successfully used for damage detection as well as localization.

Accelerating Bayesian microseismic event location with deep learning

Abstract. We present a series of new open-source deep-learning algorithms to accelerate Bayesian full-waveform point source inversion of microseismic events. Inferring the joint posterior probability distribution of moment tensor components and source location is key for rigorous uncertainty quantification. However, the inference process requires forward modelling of microseismic traces for each set of parameters explored by the sampling algorithm, which makes the inference very computationally intensive. In this paper we focus on accelerating this process by training deep-learning models to learn the mapping between source location and seismic traces for a given 3D heterogeneous velocity model and a fixed isotropic moment tensor for the sources. These trained emulators replace the expensive solution of the elastic wave equation in the inference process. We compare our results with a previous study that used emulators based on Gaussian processes to invert microseismic events. For fairness of comparison, we train our emulators on the same microseismic traces and using the same geophysical setting. We show that all of our models provide more accurate predictions, ∼ 100 times faster predictions than the method based on Gaussian processes, and a 𝒪(105) speed-up factor over a pseudo-spectral method for waveform generation. For example, a 2 s long synthetic trace can be generated in ∼ 10 ms on a common laptop processor, instead of ∼ 1 h using a pseudo-spectral method on a high-profile graphics processing unit card. We also show that our inference results are in excellent agreement with those obtained from traditional location methods based on travel time estimates. The speed, accuracy, and scalability of our open-source deep-learning models pave the way for extensions of these emulators to generic source mechanisms and application to joint Bayesian inversion of moment tensor components and source location using full waveforms.

Bayesian Multiple Emitter Fitting using Reversible Jump Markov Chain Monte Carlo

In single molecule localization-based super-resolution imaging, high labeling density or the desire for greater data collection speed can lead to clusters of overlapping emitter images in the raw super-resolution image data. We describe a Bayesian inference approach to multiple-emitter fitting that uses Reversible Jump Markov Chain Monte Carlo to identify and localize the emitters in dense regions of data. This formalism can take advantage of any prior information, such as emitter intensity and density. The output is both a posterior probability distribution of emitter locations that includes uncertainty in the number of emitters and the background structure, and a set of coordinates and uncertainties from the most probable model.

Gaussian-product subdivision surfaces

Probabilistic distribution models like Gaussian mixtures have shown great potential for improving both the quality and speed of several geometric operators. This is largely due to their ability to model large fuzzy data using only a reduced set of atomic distributions, allowing for large compression rates at minimal information loss. We introduce a new surface model that utilizes these qualities of Gaussian mixtures for the definition and control of a parametric smooth surface. Our approach is based on an enriched mesh data structure, which describes the probability distribution of spatial surface locations around each vertex via a Gaussian covariance matrix. By incorporating this additional covariance information, we show how to define a smooth surface via a nonlinear probabilistic subdivision operator based on products of Gaussians, which is able to capture rich details at fixed control mesh resolution. This entails new applications in surface reconstruction, modeling, and geometric compression.

Simulation-based analysis method for damage survivability of passenger ships

ABSTRACTA new approach for analysing the level of survivability for a passenger ship in the event of a collision damage is presented. Monte Carlo simulation is used for generating a large number of damage cases. The probability distributions for damage extent and location are based on the current SOLAS regulation. Each case is calculated with time-domain flooding simulation, assuming quasi-static motions and calm sea, thus enabling evaluation of the righting lever curve during the flooding process. The ship survivability is analysed based on requirements for a sufficient reserve stability. The proposed method is demonstrated with a large passenger ship design. Based on the detailed investigation of the results, the effects of various design changes are studied. Furthermore, the impact of waves on the flooding process is studied. The presented method for survivability assessment is robust and especially suitable for comparing design variations, or ships with similar main dimensions.

Evolutionary Planning of Multi-UAV Search for Missing Tourists

In recent years, there have been increasing reports of missing tourists around the world. The use of unmanned aerial vehicles (UAVs) can significantly improve the performance of search and rescue operations. However, planning the search paths of UAVs can be a highly complex optimization problem, and one of the most challenging tasks in the problem formulation is the estimation of target location probability distribution over time. This paper presents a problem of scheduling multiple UAVs to search for missing tourists and proposes a method for estimating tourist location probabilities which change with topographic features, weather conditions, and time. To solve the problem efficiently, we propose a hybrid evolutionary algorithm which consists of the main algorithm and a sub-algorithm. The main algorithm uses specific migration and mutation operators to evolve a population of main solutions, and the sub-algorithm combines a problem-specific heuristic and tabu search method to optimize each UAV path. The experimental results on a wide variety of test instances (including five real-world instances) demonstrate the performance advantages of the proposed method.

A new Monte Carlo mobile node localization algorithm based on Newton interpolation

There are some deficiencies in the Monte Carlo localization algorithm based on rangefinder, which like location probability distribution of the k moment in the prediction phase only related to the localization of the k − 1 moment and the maximum and minimum velocity. And the influences of the motion condition on the movement of the mobile node at k moment are also not considered before the k − 1 moment. What is more is the process of selecting the effective particles is slow in the algorithm. Considering the situations above, this paper presented a Monte Carlo mobile node localization algorithm based on Newton interpolation, which uses the inheritedness of Newton interpolation, inheriting the historical trajectory prediction mechanism of the moving node to estimate the current moment’s movement speed and movement direction of the moving node, and optimized the moving node motion model, and used particle filter that is optimized by weight of importance to prevent particle collection depletion. The inference and simulation results show that the algorithm has improved the accuracy of the forecast using Newton interpolation. And this algorithm has effectively avoided the degradation of particles and improved the localization accuracy.

Comparison of Heuristic Algorithms in Discrete Search and Surveillance Tasks Using Aerial Swarms

The search of a given area is one of the most studied tasks in swarm robotics. Different heuristic methods have been studied in the past taking into account the peculiarities of these systems (number of robots, limited communications and sensing and computational capacities). In this work, we introduce a behavioral network made up of different well-known behaviors that act together to achieve a good performance, while adapting to different scenarios. The algorithm is compared with six strategies based on movement patterns in terms of three performance models. For the comparison, four scenario types are considered: plain, with obstacles, with the target location probability distribution and a combination of obstacles and the target location probability distribution. For each scenario type, different variations are considered, such as the number of agents and area size. Results show that although simplistic solutions may be convenient for the simplest scenario type, for the more complex ones, the proposed algorithm achieves better results.

Dimension-dependent stimulated radiative interaction of a single electron quantum wavepacket

In the foundation of quantum mechanics, the spatial dimensions of electron wavepacket are understood only in terms of an expectation value – the probability distribution of the particle location. One can still inquire how the quantum electron wavepacket size affects a physical process. Here we address the fundamental physics problem of particle–wave duality and the measurability of a free electron quantum wavepacket. Our analysis of stimulated radiative interaction of an electron wavepacket, accompanied by numerical computations, reveals two limits. In the quantum regime of long wavepacket size relative to radiation wavelength, one obtains only quantum-recoil multiphoton sidebands in the electron energy spectrum. In the opposite regime, the wavepacket interaction approaches the limit of classical point-particle acceleration. The wavepacket features can be revealed in experiments carried out in the intermediate regime of wavepacket size commensurate with the radiation wavelength.

Dissociating location-based and object-based cue validity effects in object-based attention

Encoding predictive information and allocating visual attention according to the probability distribution is one of the marvelous achievements of our visual system. Unlike previous studies on object-based attention in which the validity of location-based cues and that of object-based cues covaried, we differentiate the two and examine whether our visual system can calculate the usefulness of the cue based on, separately and independently, the probability distribution of location on one hand and object that contains multiple locations on the other. We adopted the cueing paradigm with the double-rectangle display (Egly, Driver, & Rafal, 1994) and manipulated cue validity with respect to a particular location or the object as a whole. Results showed a spatial-cueing effect when location-based cues were informative and a same-object advantage when object-based cues were informative. We thus demonstrate here that different kinds of cue validity (location-based vs. object-based) determine different attention effects respectively (spatial-cueing effect vs. object-based advantage).

Multiple searchers searching for a randomly distributed immobile target on a unit network

The authors study an optimal searcher path problem of the following type. A team of searchers tries to find an immobile target on a unit network (in a unit network, all edges are of unit length). The target is located at some point on this network, and its location probability distribution is known to the searcher team. Searchers move along the edges on the network at a constant speed. When one searcher passes the target location, detection happens and the search ends. The objective is to find paths for this team of searchers to minimize the expected search time. A linear binary programming model is built to find the optimal search strategy. Computational experiments are conducted to test the capability of this model, and to analyze how searcher team size and target distribution might affect the search time. Analytical results are given for a special problem scenario: one searcher searching for a uniformly distributed target on a tree. We prove that, any depth‐first search path is optimal for a given searcher start point, and the best start point is one of the leaf nodes.

A probabilistic approach to compute strategies for players of a search game in a bounded space

In this article, we present a unique search game model to search/hide an immobile object by/from a mobile sensor in a two-dimensional bounded space. In the proposed model, the mobile sensor is a searcher, the immobile object is a target and the search space is a square/rectangular region. The proposed model is suitable for the case where the searcher has no prior knowledge about the probability distribution of the target location in the region. The game model helps the players (searcher and target) to choose their best response strategies considering all possible strategies of their respective opponents and computes the expected payoffs and Nash Equilibrium of the game. The novelty of the proposed model is to guide both the players to choose their best response strategies. The proposed model is set up as follows: Initially, the search space which is a square/rectangular region is divided into square blocks of equal size to represent it as a grid and the distance is measured from the starting block of the searcher to all other blocks using shortest path followed by which the transition probabilities of each block is determined. Once the payoff matrix is obtained, we use lrslib tool to compute the mixed strategies, Nash equilibria and expected payoffs. The proposed model is applicable in real-time scenarios which involve large square/rectangular grids where the number of blocks is large.

Exit location distribution in the stochastic exit problem by the generalized cell mapping method

The exit location distribution (ELD) in the stochastic exit problem is studied by the generalized cell mapping (GCM) method. According to the global properties of the underlying noise-free system, a proper bounded region is chosen in state space and divided into small cells. The one-step transient probability matrix that governs the global transient short-time solutions of the stochastic system is computed with the consideration of the absorbing boundary condition in exit problem. Based on it, the probability distribution of exit location on domain boundary can be obtained by sufficient evolution of system response starting from the attractor. Two typical examples are given to illustrate the application of the proposed GCM method. It shows that the results obtained by the GCM method agree well with either the results from direct numerical integration or the theoretical predictions.

Estimation of linear target-layer trajectories using cluttered point cloud data

The problem of estimating a target-layer trajectory, modeled by a straight line, in 2D point clouds that contain target locations and overwhelming clutter is studied. These point clouds are generated by an image-based pre-processing tool, termed ATR, operating on SONAR image data that results in: (1) point locations and (2) an ATR score: a measure of the “target-likeness” for each point. The model of choice assumes that the observed point cloud is a superposition of two spatial processes: (1) a 1D Poisson process along the target-layer line, corrupted by 2D Gaussian noise, denoting target locations and (2) a 2D Poisson process denoting clutter. It is further assumed that the target-likeness measure follows known probability distributions for both target locations and clutter. The line is parameterized by distance from the origin and the angle with respect to a horizontal axis, and the likelihood of these parameters for observed data is derived. Using a maximum-likelihood approach, a gradient-based estimate for line parameters and other nuisance parameters is developed. A formal procedure that tests for the presence of a target-layer trajectory in the point cloud data is additionally developed. The success of this method in both simulated and real datasets collected by NSWC PCD is demonstrated.

A Robust Image Tampering Detection Method Based on Maximum Entropy Criteria

This paper proposes a novel image watermarking method based on local energy and maximum entropy aiming to improve the robustness. First, the image feature distribution is extracted by employing the local energy model and then it is transformed as a digital watermark by employing a Discrete Cosine Transform (DCT). An offset image is thus obtained according to the difference between the extracted digital watermarking and the feature distribution of the watermarked image. The entropy of the pixel value distribution is computed first. The Lorenz curve is used to measure the polarization degree of the pixel value distribution. In the pixel location distribution flow, the maximum entropy criteria is applied in segmenting the offset image into potentially tampered regions and unchanged regions. All-connected graph and 2-D Gaussian probability are utilized to obtain the probability distribution of the pixel location. Finally, the factitious tampering probability value of a pending detected image is computed through combining the weighting factors of pixel value and pixel location distribution. Experimental results show that the proposed method is more robust against the commonly used image processing operations, such as Gaussian noise, impulse noise, etc. Simultaneously, the proposed method achieves high sensitivity against factitious tampering.

Estimation of microwave pollution

The aim of this work is to investigate the strength of microwave signals in microwave polluted environment. In this paper the signal strength is estimated by assuming a statistical model of microwave sources. The location of the source around the observer is assumed to be random. The source emits band limited stochastic signals which are radiated as electromagnetic waves with random polarization and phase. The expression for mean square values of power density at observation point are derived using two different source location probability distribution models. The model is applied to estimate total incident power on human body area in the presence of specific number of sources.