Two-dimensional Probability Distribution Research Articles

The short-term intermittency evaluation of distributed photovoltaic power

Uncertainty of distributed photovoltaic(PV) power brings great challenges to the safe and stable operation of power system, in which the intermittency problem is more challenging than the fluctuation. This paper focuses on the intermittency problem of distributed PV power, firstly, an intermittency evaluation method based on generalized extreme value(GEV) theory is proposed to solve the problem of the lack of "small-sample big-gap" events. Secondly, focusing on high risk events such as high-frequency and warning mutation events, probabilistic evaluation indexes were established, including T-hour-period mutation intensity and T-hour-period mutation frequency. Finally, a two-dimensional joint probability distribution of intermittency elements is established, and the concepts of return period and return level are introduced into the photovoltaic field to provide data support for the configuration of energy storage capacity and duration, and to provide auxiliary decision-making for the execution time and development cycle of interactive projects. The proposed method provides a solution for intermittency evaluation in small sample status quo with strong data compatibility and engineering replicability.

Combining Savage and Laplace: a new approach to ambiguity

AbstractThis paper presents a new representation of preference orderings for the study of ambiguity-related decision-making. The central feature is a preference-based decomposition of subjective probabilities that provides information about inherent ambiguity. The probability decomposition is combined with a utility function reflecting the decision-maker’s attitude toward ambiguity. The proposed theory generalizes Savage’s SEU and allows for a straightforward measurement of ambiguity and ambiguity aversion while keeping concepts for measuring risk and risk attitudes unaffected. For the measurement of ambiguity, concepts of probability theory can be used since decision acts can be interpreted as two-dimensional probability distributions. The proposed measure of ambiguity aversion exploits the properties of the utility function in the same way as the Arrow/Pratt measure of risk aversion.

Nonparametric assessment of two-dimensional density of nonlinear location signal distribution for object recognition despite background noise

Problem statement Searching for objects in shelter environments is a challenge associated with the difficulty of obtaining and interpreting search results. Currently, within the statistical theory of detection and recognition, no models and methods have been developed that allow automatically identifying the detected object. This is due to the difficulty of describing signal and noise models in the form of known statistical distributions. The variety of signals leads to the inability to describe them by any universal law of distribution. Therefore, traditional detection and recognition criteria do not provide high reliability of object search and identification. The purpose of the study. To develop and test the method for nonparametric estimation of nonlinear location signals, assess the potential possibilities of applying the developed method for automatic (automated) signal detection (recognition) systems. Results. The model for recognizing nonlinear location signals based on nonparametric approximation of two-dimensional probability distribution densities is presented. The potential possibility of improving the efficiency of nonlinear locators is shown. Practical significance. For nonlinear location systems a toolkit for estimating the probability of the detected object belonging to a given class of objects is proposed.

Two-dimensional probability distribution of the solution to the random Burgers–Riemann problem

We investigate Burgers’ partial differential equation with random Riemann initial states and random-field solution. Previous works obtained the generalized probability density function in the one-dimensional case, by using different methods. We explore a technique that has not been employed in this context before, which fully develops the potential of the Dirac delta function. We start with the one-dimensional scenario and afterward extend to two dimensions. The generalized probability density function is derived in those cases, both for non-independent and independent initial conditions, and general statistics are obtained as a consequence.

Stochastic Analysis of Molecular Dynamics Reveals the Rotation Dynamics Distribution of Water around Lysozyme.

Water dynamics is essential to biochemical processes by mediating all such reactions, including biomolecular degeneration in solutions. To disentangle the molecular-scale distribution of water dynamics around a solute biomolecule, we investigated here the rotational dynamics of water around lysozyme by combining molecular dynamics (MD) simulations and broadband dielectric spectroscopy (BDS). A statistical analysis using the relaxation times and trajectories of every single water molecule was proposed, and the two-dimensional probability distribution of water at a distance from the lysozyme surface with a rotational relaxation time was given. For the observed lysozyme solutions of 34-284 mg/mL, we discovered that the dielectric relaxation time obtained from this distribution agrees well with the measured γ relaxation time, which suggests that rotational self-correlation of water molecules underlies the gigahertz domain of the dielectric spectra. Regardless of protein concentration, water rotational relaxation time versus the distance from the lysozyme surface revealed that the water rotation is severely retarded within 3 Å from the lysozyme surface and is nearly comparable to pure water when farther than 10 Å. The dimension of the first hydration layer was subsequently identified in terms of the relationship between the acceleration of water rotation and the distance from the protein surface.

Assessing the benefits of Imaging Infrared Radiometer observations for the CALIOP version 4 cloud and aerosol discrimination algorithm

Abstract. The features detected in monolayer atmospheric columns sounded by the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) and classified as cloud or aerosol layers by the CALIOP version 4 (V4) cloud and aerosol discrimination (CAD) algorithm are reassessed using perfectly collocated brightness temperatures measured by the Imaging Infrared Radiometer (IIR) aboard the same satellite. Using the IIR's three wavelength measurements of layers that are confidently classified by the CALIOP CAD algorithm, we calculate two-dimensional (2-D) probability distribution functions (PDFs) of IIR brightness temperature differences (BTDs) for different cloud and aerosol types. We then compare these PDFs with 1-D radiative transfer simulations for ice and water clouds and dust and marine aerosols. Using these IIR 2-D BTD signature PDFs, we develop and deploy a new IIR-based CAD algorithm and compare the classifications obtained to the results reported by the CALIOP-only V4 CAD algorithm. IIR observations are shown to be able to identify clouds with a good accuracy. The IIR cloud identifications agree very well with layers classified as confident clouds by the V4 CAD algorithm (88 %). More importantly, simultaneous use of IIR information reduces the ambiguity in a notable fraction of “not confident” V4 cloud classifications. 28 % and 14 % of the ambiguous V4 cloud classifications are reclassified more appropriately as confident cloud layers through the use of the IIR observations in the tropics and in the midlatitudes, respectively. IIR observations are of relatively little help in deriving high-confidence classifications for most aerosols, as the low altitudes and small optical depths of aerosol layers yield IIR signatures that are similar to those of clear skies. However, misclassifications of aerosol layers, such as dense dust or elevated smoke layers, by the V4 CAD algorithm can be corrected to cloud layer classification by including IIR information. 10 %, 16 %, and 6 % of the ambiguous V4 dust, polluted dust, and tropospheric elevated smoke, respectively, are found to be misclassified cloud layers by the IIR measurements.

Assessment of failure probabilities and the allowable size of defects in structural elements using the criteria of fracture mechanics

The possibility of assessing the safe size of the defects of metal continuity using risk criteria are considered. Such defects occur at all stages of the life cycle of structures. Assessment of their hazard and determination of their allowable size becomes important when the defects can lead to brittle or quasi-brittle fracture. In this case, models of linear and nonlinear fracture mechanics are used. In these models, defects are considered as internal elliptical or surface semi-elliptical cracks. The stochastic variety of shapes, sizes, locations, and orientations of defects has a significant effect on the destruction mechanisms. In this regard, the relevant probabilistic problem of assessing the permissible size of defects according to the criteria of the risk of destruction comes to the fore. We consider a general approach to assessing hazard of defects by risk criteria. Two settings of the probabilistic problem of risk assessment based on of one- and two-parameter fracture criteria are presented. The risk function in the form of the probability of fracture according to a given criterion is used as the main calculated characteristic. The expression of the risk function based on one-parameter criteria of fracture mechanics is presented. The main attention is paid to the probabilistic model based on the two-parameter fracture criterion by E. M. Morozov. This criterion provides ample opportunities for analyzing fracture mechanisms with a change in the size of defects. An expression for the risk function based on the family of two-dimensional probability distributions of Lu – Bhattacharya of the Weibull type is obtained. It is shown that the correlations of the fracture mechanisms can significantly affect the values of the fracture probabilities, and, consequently, the allowable size of defects.

Dark Energy Survey Year 3 Results: Galaxy mock catalogs for BAO analysis

The calibration and validation of scientific analysis in simulations is a fundamental tool to ensure unbiased and robust results in observational cosmology. In particular, mock galaxy catalogs are a crucial resource to achieve these goals in the measurement of baryon acoustic oscillation (BAO) in the clustering of galaxies. Here we present a set of 1952 galaxy mock catalogs designed to mimic the Dark Energy Survey Year 3 BAO sample over its full photometric redshift range 0.6 < zphoto < 1.1. The mocks are based upon 488 ICE-COLA fastN-body simulations of full-sky light cones and were created by populating halos with galaxies, using a hybrid halo occupation distribution – halo abundance matching model. This model has ten free parameters, which were determined, for the first time, using an automatic likelihood minimization procedure. We also introduced a novel technique to assign photometric redshift for simulated galaxies, following a two-dimensional probability distribution with VIMOS Public Extragalactic Redshift Survey data. The calibration was designed to match the observed abundance of galaxies as a function of photometric redshift, the distribution of photometric redshift errors, and the clustering amplitude on scales smaller than those used for BAO measurements. An exhaustive analysis was done to ensure that the mocks reproduce the input properties. Finally, mocks were tested by comparing the angular correlation functionw(θ), angular power spectrumCℓ, and projected clusteringξp(r⊥) to theoretical predictions and data. The impact of volume replication in the estimate of the covariance is also investigated. The success in accurately reproducing the photometric redshift uncertainties and the galaxy clustering as a function of redshift render this mock creation pipeline as a benchmark for future analyses of photometric galaxy surveys.

Using Infinite-server Resource Queue with Splitting of Requests for Modeling Two-channel Data Transmission

New Radio Access Technology 3GPP New Radio has become the fundamental wireless technology in the fifth-generation networks, which allows us to achieve high data rates due to the ability to work in the millimeter-wave band. But the key feature and the main problem of 5G New Radio networks is that people themselves, cars, buildings, etc. are signal blockers, while the base stations of the fourth generation networks have widescreen broadcasting and such small obstacles do not cause loss of connection. Service providers and mobile operators are already testing the proposed technology. In this connection, the scientific community has the task of analyzing the performance of these systems and increasing it in the future. Currently, there are known studies of “basic” mathematical models of such networks. By this term, we mean models built in the simplest possible assumptions. However, due to the justified necessity of introducing new technology into the daily lives of subscribers, service providers pose the scientific community with the task of analyzing the effectiveness of the most appropriate mathematical models. For example, a technology of splitting transmitted data into two streams using as 5G and both 4G transmission technologies is considered now by 3GPP Project Coordination Group. The paper is devoted to such a problem. We consider a mathematical model of the message transmitting with the implementation of the splitting function in the communication networks of New Radio technology in the form of a resource queueing system with a renewal arrival process and non-exponential service. For this problem, an approximation of a stationary two-dimensional probability distribution of the number of occupied resources in parallel service units is obtained. It is shown that this approximation coincides with the Gaussian distribution, and its area of applicability is shown.

A force model of high-speed dry milling CF/PEEK considering fiber distribution characteristics

Carbon fiber reinforced polyetheretherketone (CF/PEEK) is an emerging material that is widely used in the automotive and aviation industry due to its high shock resistance, thermostability, and recyclability. However, its dry-machining requirement with an unclear dynamic material removal process limits the machining efficiency and surface quality. To this end, we firstly established a two-dimensional joint probability distribution model of cutting carbon fibers based on the microstructure of CF/PEEK. Compared with previous brittle models, the plastic model is verified to be more consistent with experimental results. A high-speed dry (HSD) milling force model considering carbon fiber distribution is then developed and is proofed with a high prediction accuracy of about 92.6%. With the proposed model, the milling force can be separated into forces of cutting carbon fibers and PEEK matrix, by which the influences of high-speed dry milling process on carbon fibers and PEEK matrix can be analyzed. The results show that carbon fiber distribution exhibits a significant impact on milling force and is more easily affected by milling parameters compared with the PEEK matrix. It is also verified feasible to HSD milling CF/PEEK, and the work gives the guidance of breaking the low-speed machining limits by improving the machining process.

Some applications of the GRAN1 to analyze two-dimensional continuous probability distributions

The article considers the use of GRAN1 software in the analysis of two-dimensional continuous probability distributions. The learning process can be provided by freely distributable software, through the use of cloud technologies, in particular software from the GRAN package. However, the use of any technology in the educational process, including modern information and communication technologies, as well as the content of education, must be pedagogically balanced, which will avoid any negative consequences for the formation of the future member of society, his mental and physical development. Attention is drawn to the fact that children are increasingly looking for entertainment, using mobile devices, sharing new products with their peers and spending time together, playing a variety of online games, and parents cannot control this process. At the same time, teachers conduct lessons using mobile devices to draw attention to the subject, they are teaching. In the process of using computer technology, students can form a special type of thinking, the so-called “clip consciousness”, which leads to fragmentary thinking and the irreversibility of changes in consciousness. Therefore, the problem of excessive use of mobile devices by children requires constant analysis and coverage. The article discusses some examples of using the GRAN1 software to solve problems in probability theory. Examples of approximate calculation of the value of the double integral are given. Tables of values of the corresponding integrals are described. The use of modern information and communication technologies during mathematics lessons is considered.

Prediction and evaluation of fatigue life under random load based on low load strengthening characteristic

To improve the shortcomings of peak over threshold (POT) extrapolation method and reflect the diversity and dynamics of road conditions, an improved POT extrapolation method to reconstruct the load sequence in the middle of threshold is proposed. Based on the improved extrapolated load, the distribution characteristics of mean and amplitude are analyzed and the two-dimensional joint probability distribution is established. To discuss the influence of low load strengthening characteristics on fatigue life under random load, based on the two-dimensional joint probability distribution, the theory of low load strengthening is introduced in compiling load spectrum. The fatigue life predicted by 8-level load spectrum and 10-level strengthened load spectrum are compared with the test results, respectively. Which verifies the effectiveness and accuracy of life prediction based on improved POT extrapolation and low load strengthening under random load.

Multidimensional Approaches to Calculation of Design Floods at Confluences—PROIL Model and Copulas

In confluence areas, where river flow slowdowns can be substantial, the selection of design flows for the purpose of designing a flood control system directly depends on flood waves at the mainstem and its tributaries. The aim of this paper is twofold: to elaborate a procedure that will define the flood exceedance probability in the analyzed area within a multidimensional probability space and to develop a methodology for defining flood coincidence in the mainstem reach with its main tributaries and thus determine design flows in order to design the flood control system in the confluence area. Mathematical models are based on (1) two-dimensional probability distribution (PROIL model) and (2) the copula function (Archimedean class of copulas), and fitted to a practical application in a two-dimensional probability distribution space. In case of random variables, simultaneous quantitative characteristics of flood wave (water flow) hydrographs for the mainstem and a tributary are considered. The paper discusses the specific reach of the Danube, from the Hungarian-Serbian border to the city of Smederevo, which encompasses three significant tributaries—the Drava, the Tisa, and the Sava.

The Pattern of Tongue's Motion: A Free-Exploration Study.

The human tongue is involved in many essential daily activities and is comprised of eight muscles. To date tools for quantifications of the tongue's intrinsic motions are limited. In this study we explored the tongue's motion during a free-exploration paradigm, using a discreet wireless intra-oral wearable device. Six healthy subjects were instructed to freely move the tip of their tongue on the wearable device while attempting to cover the entire surface of the hard palate. The goal of this study is to compose a two-dimensional probability distribution model of the tongue's motion. We conclude that 90-seconds of non-continuous data collection was sufficient for visualizing the two-dimensional probability distribution of the free-exploration paradigm. The results suggest that the subjects concentrate the majority of the motion in the central portion of the palate.

Comparative stochastic analysis of the anomalous dynamics of machines under the action of operational defects

The possibility of increasing the confidence of vibroacoustic diagnostics of the technical condition of rotor-type machinery is being investigated. The search for additional sensitive and reliable features is based on the analysis of two-dimensional probability distribution densities of vibration amplitudes. This approach allows to assess the degree and character of the nonlinearity of the machine dynamic model as an oscillatory system. An example of diagnosing the technical condition of a compressor installation is given, showing the possibility of an indirect operational assessment of the accomplished repair. Keywords vibroacoustic diagnostics, nonlinear oscillations, stochastic connection, sliding bearing, defects. fbalitsky@gmail.com

Metaheuristics-Based Approximation of Two-Dimensional Probability Distributions for Stochastic Systems Control

This paper is concerned with approximation of probability distributions behind discrete-time systems with stochastic dynamics. The aim is to facilitate advances in studies for control of such stochastic systems. An approach to approximating two-dimensional probability distributions using metaheuristics is suggested. Then, its effectiveness is demonstrated with a numerical example of stabilization synthesis.

Quantifying the Relationship between Drought and Water Scarcity Using Copulas: Case Study of Beijing–Tianjin–Hebei Metropolitan Areas in China

Making the distinction between drought and water scarcity is not trivial, because they often occur simultaneously. In this study, we used Copulas to quantify the relationship between drought and water scarcity. Beijing–Tianjin–Hebei Metropolitan Areas (BTHMA) was chosen as the study area. Standard Precipitation and Evapotranspiration Index (SPEI) and water exploitation index plus (WEI+) was chosen to represent metrological drought and water scarcity. Inverse Distance Weighted method was used for spatial analysis of SPEI and WEI+, and Archimedean Copula was used to establish two-dimensional joint probability distribution of SPEI and WEI+. The results are as follows: (1) The southern part of the study area was wetter. The middle part was drier, with moderate drought happened for most times. (2) WEI+ of Beijing and Tianjin showed significant decreasing trends from 2000 to 2015, while WEI+ of Hebei Province did not, which indicated that Hebei Province is facing much severer water scarcity situation than Beijing and Tianjin. (3) Gumbel copula was the best-fitting model to establish the joint probability distribution of SPEI and WEI+. The condition probability provided a probability distribution of water scarcity under different drought conditions, which can provide technical support for government managers during policy making.

Two-dimensional translation-invariant probability distributions: approximations, characterizations and no-go theorems

We study the properties of the set of marginal distributions of infinite translation-invariant systems in the two-dimensional square lattice. In cases where the local variables can only take a small number d of possible values, we completely solve the marginal or membership problem for nearest-neighbours distributions (d = 2, 3) and nearest and next-to-nearest neighbours distributions (d = 2). Remarkably, all these sets form convex polytopes in probability space. This allows us to devise an algorithm to compute the minimum energy per site of any TI Hamiltonian in these scenarios exactly. We also devise a simple algorithm to approximate the minimum energy per site up to arbitrary accuracy for the cases not covered above. For variables of a higher (but finite) dimensionality, we prove two no-go results. To begin, the exact computation of the energy per site of arbitrary TI Hamiltonians with only nearest-neighbour interactions is an undecidable problem. In addition, in scenarios with d≥2947, the boundary of the set of nearest-neighbour marginal distributions contains both flat and smoothly curved surfaces and the set itself is not semi-algebraic. This implies, in particular, that it cannot be characterized via semidefinite programming, even if we allow the input of the programme to include polynomials of nearest-neighbour probabilities.

The quantitative assessment of epicardial fat distribution on human hearts: Implications for epicardial electrophysiology.

Epicardial electrophysiological procedures rely on dependable interfacing with the myocardial tissue. For example, epicardial pacing systems must generate sustainable chronic pacing capture, while epicardial ablations must effectively deliver energy to the target hyper-excitable myocytes. The human heart has a significant adipose layer which may impede epicardial procedures. The objective of this study was to quantitatively assess the relative location of epicardial adipose on the human heart, to define locations where epicardial therapies might be performed successfully. We studied perfusion-fixed human hearts (n = 105) in multiple isolated planes including: left ventricular margin, diaphragmatic surface, and anterior right ventricle. Relative adipose distribution was quantitatively assessed via planar images, using a custom-generated image analysis algorithm. In these specimens, 76.7 ± 13.8% of the left ventricular margin, 72.7 ± 11.3% of the diaphragmatic surface, and 92.1 ± 8.7% of the anterior right margin were covered with superficial epicardial adipose layers. Percent adipose coverage significantly increased with age (P < 0.001) and history of coronary artery disease (P < 0.05). No significant relationships were identified between relative percent adipose coverage and gender, body weight or height, BMI, history of hypertension, and/or history of congestive heart failure. Additionally, we describe two-dimensional probability distributions of epicardial adipose coverage for each of the three analysis planes. In this study, we detail the quantitative assessment and probabilistic mapping of the distribution of superficial epicardial adipose on the adult human heart. These findings have implications relative to performing epicardial procedures and/or designing procedures or tools to successfully perform such treatments. Clin. Anat. 31:661-666, 2018. © 2018 Wiley Periodicals, Inc.

USING ACCUMULATION AND SIMPLE VOTING METHOD FOR RECOGNIZING CLASSES OF TARGETS BASED ON JOINT DISTRIBUTION OF PAIRS OF ECHO SIGNALS AMPLITUDES

With the development of the defense industry and aviation, there is an increasing number of different air targets. In this regard, the detection and identification of the type of target is currently a actual problem. The algorithm for recognizing object classes based on a two-dimensional probability distribution density of the correlating amplitudes is known from the recently written works. In this paper the methods of increasing the probability of correct radar target classes recognition are considered. The methods are applied with regard to recognition algorithm, which makes a decision based on two attributes (effective radar cross-section and correlation coefficient of the received echo amplitudes samples).The averaging and the simple voting methods were used for increasing the recognition reliability. In this paper is considered evaluation of efficiency of proposed methods. The results of numerical simulation showed that both methods provide the significant gain.