Arbitrary Distribution Research Articles

Ionisation Chemistry in the Inner Disc: A Combined Treatment of Ionic and Thermionic Emission and Arbitrary Grain Size Distributions

Ionisation Chemistry in the Inner Disc: A Combined Treatment of Ionic and Thermionic Emission and Arbitrary Grain Size Distributions

PICASSO: a universal brain phantom for positron emission tomography based on the activity painting technique

Objective. This study presents a universal phantom for positron emission tomography (PET) that allows arbitrary static and dynamic activity distributions of various complexities to be generated using a single PET acquisition.Approach. We collected a high-statistics dataset (with a total of 22.4 × 109prompt coincidences and an event density of 2.75 × 106events mm-3) by raster-scanning a single plane with a22Na point source mounted on a robotic arm in the field-of-view of the uEXPLORER PET/CT scanner. The source position was determined from the reconstructed dynamic frames. Uniquely, true coincidences were separated from scattered and random events based on the distance between their line-of-response and the known source location. Finally, we randomly sampled the dataset to generate the desired activity distributions modeling several different phantoms.Main results. Overall, the target and the reconstructed phantom images had good agreement. The analysis of a simple geometric distribution showed high quantitative accuracy of the phantom, with mean error of <-3.0% relative to the ground truth for activity concentrations ranging from 5.3 to 47.7 kBq ml-1. The model of a high-resolution18F-fluorodeoxyglucose distribution in the brain illustrates the usefulness of the technique in simulating realistic static neuroimaging studies. A dynamic18F-florbetaben study was modeled based on the time-activity curves of a human study and a segmented brain phantom with no coincidences repeating between frames. For all time points, the mean voxel-wise errors ranged from -4.4% to -0.7% in grey matter and from -3.9% to +2.8% in white matter.Significance. The proposed phantom technique is highly flexible and allows modeling of static and dynamic brain PET studies with high quantitative accuracy. It overcomes several key limitations of the existing phantoms and has many promising applications for the purposes of image reconstruction, data correction methods, and system performance evaluation, particularly for new high-performance dedicated brain PET scanners.

Dynamically variable intensity patterns projected using an optofluidic phase-shifter array

We present a concept for the dynamically variable definition of arbitrary intensity distributions using an array of optofluidic phase-shifters. These components consist of cylindrical fluidic surfaces whose interface may be controllably shaped using electrowetting-on-dielectrics actuation. Key to the generation of defined intensity distributions is the ability to calculate the required shape for this phase-shifting interface and to this end we present a novel procedure, to our knowledge, that combines a real-time optimization algorithm with an influence matrix approach to generate the required surface. We illustrate the effectiveness of this approach by reconstructing arbitrary surface profiles with one optofluidic phase-shifting component that is then used to project a desired two-dimensional intensity distribution. Using this approach, we further demonstrate the capability of a two-dimensional phase-shifter array to generate larger dynamically programmable intensity patterns by combining individual intensity distributions.

Statistical Modeling and Probable Calculation of the Strength of Materials with Random Distribution of Surface Defects

Based on the solutions of deterministic fracture mechanics and the methods of probability theory, the algorithm for calculating the probabilistic strength characteristics of plate elements of structures with an arbitrary stochastic distribution of surface defects is outlined. On the plate surface, there are uniformly distributed cracks that do not interact with each other, the plane of which is normal to the surface, and the depth is much less than its length on the surface. The cracks’ depth and angle of orientation are random values, and their joint distribution density is specified. Plates made of this material are under the influence of biaxial loading. The probability of failure, along with the mean value, the dispersion, and the variation coefficient of the plate’s strength, taking into account the surface defects under different types of stress, were determined. Their dependence on the type of loading, the size of the plate, and the surface structural heterogeneity of the material were studied graphically. Joint consideration of the influence of the interrelated properties of real materials, such as defectiveness and stochasticity, on strength and fracture, opens up new opportunities in creating a theory of strength and fracture of deformable solids.

Pricing of a Binary Option Under a Mixed Exponential Jump Diffusion Model

This paper focuses on the pricing problem of binary options under stochastic interest rates, stochastic volatility, and a mixed exponential jump diffusion model. Considering the negative interest rates in the market in recent years, this paper assumes that the stochastic interest rate follows the Hull–White (HW) model. In addition, we assume that the stochastic volatility follows the Heston volatility model, and the price of the underlying asset follows the jump diffusion model in which the jumps follow the mixed exponential jump model. Considering these factors comprehensively, the mixed exponential jump diffusion of the Heston–HW (abbreviated as MEJ-Heston–HW) model is established. Using the idea of measure transformation, the pricing formula of binary call options is derived by the martingale method, eigenfunction, and Fourier transform. Finally, the effects of the volatility term and the parameters of the mixed-exponential jump diffusion model on the option price in the O-U process are analyzed. In the numerical simulation, compared with the double exponential jump Heston–HW (abbreviated as DEJ-Heston–HW) model and the Heston–HW model, the mixed exponential jump model is an extension of the double exponential jump model, which can approximate any distribution in the sense of weak convergence, including arbitrary discrete distributions, normal distributions, and various thick-tailed distributions. Therefore, the MEJ-Heston–HW model adopted in this paper can better describe the price of the underlying asset.

A Pareto tail plot without moment restrictions

We propose a mean functional that exists for arbitrary probability distributions and characterizes the Pareto distribution within the set of distributions with finite left endpoint. This is in sharp contrast to the mean excess plot, which is meaningless for distributions without an existing mean and has non-standard behavior when the mean is finite, but the second moment does not exist. The construction of the plot is based on the principle of a single huge jump, which differentiates between distributions with moderately heavy and super heavy tails. We present an estimator of the tail function based on U-statistics and study its large sample properties. Several loss datasets illustrate the use of the new plot.

Branching random walks with regularly varying perturbations

We consider a modification of classical branching random walk, where we add i.i.d. perturbations to the positions of the particles in each generation. In this model, which was introduced and studied by Bandyopadhyay and Ghosh (2023), perturbations take the form 1/θ log X/E where θ is a positive parameter, X has an arbitrary distribution μ and E is exponential with parameter 1, independent of X. Working under finite mean assumption for μ, they proved almost sure convergence of the rightmost position to a constant limit, and identified the weak centered asymptotics when θ does not exceed certain critical parameter θ_0 . This paper complements their work by providing weak centered asymptotics for the case when θ &gt; θ_0 and presenting the results to μ with regularly varying tails. We prove almost sure convergence of the rightmost position and identify the appropriate centering for the weak convergence, which is of form αn + c log n, with constants α, c depending on the ratio of θ and θ_0. We describe the limiting distribution and provide explicitly the constants appearing in the centering.

Photovoltaic Charge Lithography on Passive Dielectric Substrates Using Fe:LiNbO3 Stamps

AbstractPhotovoltaic Fe:LiNbO3 is an outstanding material platform able to photo‐generate versatile charge patterns, useful for a broad variety of applications. However, in some cases, its photorefractive effect, light absorption, and active ferroelectric properties may interfere with the optimum operation of certain devices based on Fe:LiNbO3. Here, a novel optoelectronic method is proposed and demonstrated to transfer photovoltaic charge patterns from Fe:LiNbO3 to non‐photovoltaic passive substrates, thus removing these possible limitations. The method, denominated as photovoltaic charge lithography (PVCL), resembles the operation of a stamp and does not require external high‐voltage supplies or electron/ion beams. Upon contact between the active Fe:LiNbO3 stamp and a passive dielectric substrate, the light‐induced charge pattern can be faithfully mirrored on the passive substrate. The imprinted pattern is probed and characterized by dielectrophoretic and electrophoretic particle trapping. The results reveal that the charge builds up on the passive substrate during contact, allowing charge tunability. Moreover, arbitrary charge distributions can be flexibly tailored, using scanning laser beams or spatially structured light. Overall, PVCL opens the possibility of printing complex 1D/2D charge patterns of controlled polarity on different passive dielectric materials, enhancing the technological potential of Fe:LiNbO3 photovoltaic platforms.

Anchor Space Optimal Transport as a Fast Solution to Multiple Optimal Transport Problems.

In machine learning, optimal transport (OT) theory is extensively utilized to compare probability distributions across various applications, such as graph data represented by node distributions and image data represented by pixel distributions. In practical scenarios, it is often necessary to solve multiple OT problems. Traditionally, these problems are treated independently, with each OT problem being solved sequentially. However, the computational complexity required to solve a single OT problem is already substantial, making the resolution of multiple OT problems even more challenging. Although many applications of fast solutions to OT are based on the premise of a single OT problem with arbitrary distributions, few efforts handle such multiple OT problems with multiple distributions. Therefore, we propose the anchor space OT (ASOT) problem: an approximate OT problem designed for multiple OT problems. This proposal stems from our finding that in many tasks the mass transport tends to be concentrated in a reduced space from the original feature space. By restricting the mass transport to a learned anchor point space, ASOT avoids pairwise instantiations of cost matrices for multiple OT problems and simplifies the problems by canceling insignificant transports. This simplification greatly reduces its computational costs. We then prove the upper bounds of its 1 -Wasserstein distance error between the proposed ASOT and the original OT problem under different conditions. Building upon this accomplishment, we propose three methods to learn anchor spaces for reducing the approximation error. Furthermore, our proposed methods present great advantages for handling distributions of different sizes with GPU parallelization.

The immiscible to miscible transition and its consequences for 3-phase displacements in porous media of arbitrary wettability: Comparison of 3D pore network results with basic theory

The theory of the immiscible to miscible transition and its consequences for 3-phase displacements in a system of arbitrary wettability distribution has been studied in a previous paper using a “process based” model through the simplest case possible; a capillary bundle (CB) model. As expected, the CB model was not able to capture many realistic phenomena such as phase trapping, film and layer-flow, topological effects etc. However, it was recognized that it should be able to indicate certain expected qualitative trends in 3-phase displacements in real 3D connected networks.The current paper extends that earlier work by showing the consequences of changing the model of the porous medium to a 3D connected lattice pore network model (PNM) to capture phase trapping and rock connectivity. Initially a simple 3D regular cubic bond lattice is used for this initial work to make a clear comparison with the CB model. Two important characteristics of 3D network refer to (i) displacement phase accessibility, and (ii) defending phase trapping/escape. Three trapping/escape cases based on the probability of invading phase accessibility and defending phase escape have been defined in the 3D lattice network. Networks with different coordination numbers (z = 6 and 4) were studied in order to mimic different rock connectivity and study how and in which way the applied rules result in specific changes in 3-phase saturation paths, 3-phase pore occupancies and phase trapping. Again the focus is on the changes which are predicted to occur in all these quantities as the system moves from an immiscible (IFT σgo ∼ “large”) to a miscible (σgo → 0) case.In this paper, a weakly oil-wet (WOW) wettability distribution is considered and various phase invasions (gas, water, and oil) in the corresponding 2-phase systems are investigated. Both saturation paths and pore occupancy sequences of different phase invasions under different miscibility conditions are presented for both the CB and PNM models. It is found that having a well-connected network and considering a relaxed rule on defending and displacing phases, the results are quite similar to that of the CB model. Also, applying restricted trapping/escaping rules and less connected network mean deviation from the CB model, but the underlying physics of the immiscible to miscible transitions and the central physical parameter of 3-phase displacements in all cases are the same as those observed for the CB model.

Mathematical Modeling of Mating Probability and Fertile Egg Production in Helminth Parasites.

In this work, we obtained a general formulation for the mating probability and fertile egg production in helminth parasites, focusing on the reproductive behavior of polygamous parasites and its implications for transmission dynamics. By exploring various reproductive variables in parasites with density-dependent fecundity, such as helminth parasites, we departed from the traditional assumptions of Poisson and negative binomial distributions to adopt an arbitrary distribution model. Our analysis considered critical factors such as mating probability, fertile egg production, and the distribution of female and male parasites among hosts, whether they are distributed together or separately. We show that the distribution of parasites within hosts significantly influences transmission dynamics, with implications for parasite persistence and, therefore, with implications in parasite control. Using statistical models and empirical data from Monte Carlo simulations, we provide insights into the complex interplay of reproductive variables in helminth parasites, enhancing our understanding of parasite dynamics and the transmission of parasitic diseases.

An Efficient Algorithm for Gravity Forward Modeling (GFM) with Masses of Arbitrary Shapes and Density Distributions

Summary Currently, gravimetric forward modelling of mass density structures with arbitrary geometries and density distributions typically involves subdividing the mass body into individual geometric elements (such as rectangular prisms), calculating their gravitational contributions that are then summed up to obtain the gravitational attraction of the whole body. To achieve a more accurate approximation of the true geometric shape and density distribution, this rectangular prism model requires fine dividing, which significantly increases computational load and reduces numerical efficiency. To address this issue, we propose the algorithm for gravimetric forward modeling of arbitrary geometric shapes and density distributions in spectral domain that significantly improves numerical efficiency while preserves computational accuracy. The novelty of our proposed algorithm lies in dividing the masses into multiple layers of equal thickness in the vertical direction, providing constant upper and lower bounds. This allows to extended Parker's formulas and apply the Fast Fourier Transform (FFT) to increase numerical efficiency. The algorithm is tested using synthetic models and then used to compute gravitational effects of topography and sediments using real data from Tibet. Results show high accuracy and numerical efficiency than rectangular prism approach.

A note on generalized Floater–Hormann interpolation at arbitrary distributions of nodes

AbstractThe paper is concerned with a generalization of Floater–Hormann (briefly FH) rational interpolation recently introduced by the authors. Compared with the original FH interpolants, the generalized ones depend on an additional integer parameter $$\gamma &gt;1$$ γ &gt; 1 , that, in the limit case $$\gamma =1$$ γ = 1 returns the classical FH definition. Here we focus on the general case of an arbitrary distribution of nodes and, for any $$\gamma &gt;1$$ γ &gt; 1 , we estimate the sup norm of the error in terms of the maximum (h) and minimum ($$h^*$$ h ∗ ) distance between two consecutive nodes. In the special case of equidistant ($$h=h^*$$ h = h ∗ ) or quasi–equidistant ($$h\approx h^*$$ h ≈ h ∗ ) nodes, the new estimate improves previous results requiring some theoretical restrictions on $$\gamma $$ γ which are not needed as shown by the numerical tests carried out to validate the theory.

Reconstruction of ionospheric VTEC using empirical orthogonal function and its performance during extreme geomagnetic storm

This paper demonstrates that the spatial distribution of the ionospheric TEC over the Indian region can be reconstructed with appreciable accuracy using minimal numbers of empirical orthogonal functions as a basis. These basis functions were derived using the Singular Value Decomposition of a matrix composed of pragmatic vertical Total Electron Content (VTEC) values collected across varied ionospheric conditions and measured over the region of interest. The reconstruction was achieved by linearly combining the appropriately chosen significant bases with corresponding weight factors. The reconstruction accuracy of the algorithm was found to be better than 4 TECU (TECU = 1016 electrons/m2) for more than 99.9 % of the time when tested over the complete year of 2016 with only eight basis vectors. The containment factor, defined here, indicates the goodness of the chosen bases in representing the arbitrary VTEC distributions and is found to remain typically high, aiding in improved algorithm performance. The performance, however, was found to be sensitive to the seasons and geomagnetic conditions. Deteriorated performance was observed when tested for the St. Patrick's Day storm data. The deterioration was attributed to the structural alteration of the ionospheric plasma density and the presence of atypical modes during the storm. The results ascertain the prospect of a faithful representation of the spatial distribution of the ionospheric VTEC using limited parametric variables, which may find utility in navigation, radar, and various other applications.

Hybrid Overmodulation Strategy for Dual Two-Level Inverter With Arbitrary DC-Bus Voltage Distribution

Hybrid Overmodulation Strategy for Dual Two-Level Inverter With Arbitrary DC-Bus Voltage Distribution

On Reliability of Repairable Hot Double Redundant System with Arbitrarily Distributed Life- and Repair Times of Its Elements

The article introduces the concept of Marked Markov processes, which are used to study a repairable hot double redundant system with a single repair facility. It is assumed that components’ life- and repair times follow arbitrary distributions. The proposed approach allows for calculating the system’s reliability function, and its mean lifetime, as well as conducting the sensitivity analysis to the shape of input distributions. The new method was validated with numerical examples by comparing it with previously obtained analytical results and showed high accuracy.

Peridynamics-fueled convolutional neural network for predicting mechanical constitutive behaviors of fiber reinforced composites

Despite advancements in predicting the constitutive relationships of composite materials, characterizing the effects of microstructural randomness on their mechanical behaviors remains challenging. In this study, we propose a data-driven convolutional neural network (CNN) to efficiently predict the stress-strain curves containing three key material features (Tensile strength, modulus, and toughness) of fiber reinforced composites. Firstly, stress-strain curves for composites with arbitrary fiber distributions were generated using experimentally validated peridynamics (PD) model. Principal component analysis (PCA) was then employed to learn these curves in a lower-dimensional space, reducing computational costs. Subsequently, these reduced data, along with randomly distributed microstructural features, were used to train, validate, and evaluate the CNN models. The combined CNN and PCA model accurately predicted stress-strain curves with maximum errors of 2.5 % for tensile strength, 10% for modulus, and 20 % for toughness. Furthermore, data augmentation and Mean Squared Error (MSE) as a loss function significantly enhanced the model's prediction accuracy. Our findings indicated that DenseNet121 outperformed other CNN models in predicting the properties of fiber-reinforced materials, further demonstrating the effectiveness of the proposed model. This work successfully demonstrates the applicability of a data-driven CNN approach to predict stress-strain relations for engineering materials with intricate heterogeneous microstructures, paving the way for data-driven computational mechanics applied in composites.

On the Optimum Distribution of Multiple Helmholtz Resonators for Annular Combustors

Abstract The combustors of many modern land-based gas turbines and aero-engines are annular. This kind of combustors often suffer from thermoacoustic oscillations, with the occurrence of mostly the circumferential first-order, second-order and third-order oscillation modes in the annular combustion chamber. To solve this problem, passive control methods are widely used adding passive acoustic dampers such as Helmholtz resonators (HRs). Depending on the type and number of HRs, and the possible positions over the circumference to install them, there could easily have millions, or even billions, of possible arrangment patterns. Finding a good design is the key to solve this problem. In this paper, we perform a theoretical and numerical study of an annular combustor installed with multiple types of HRs over the circumference. Firstly, a simple annular duct with arbitrary distributions of these HRs is studied analytically by solving the nonlinear eigenvalue problem of a 1D network model. Based on the results of the analytical method, the impact of the HRs on the acoustic modes of the combustion chamber is studied and the optimum arrangement of multiple resonators is obtained. This arrangement usually gives a null (or small) mode splitting strength and a good damping effect. Finally, we apply the optimum arrangement to damp the thermoacoustic modes that have been captured by numerical simulation for a real annular combustor. We use numerical simulations based on solving the 3D Helmholtz equation in COMSOL to verify the feasibility of the optimum arrangement.

Signaling under double-crossing preferences: The case of discrete types

The class of double-crossing preferences, where signaling is cheaper for higher types than for lower types at low signaling levels and the opposite is true at high signaling levels, underlines the phenomenon of countersignaling, with intermediate types choosing higher actions than higher and lower types. We provide an algorithm to systematically construct an equilibrium and thus establish equilibrium existence for this general class of preferences with an arbitrary discrete-type distribution. Our analysis sheds light on the connection between discrete-type and continuous-type models and clarifies robust predictions of signaling under double-crossing preferences.

Optimal allocation of autonomous PV-powered fast charging stations for electrified transportation considering traffic dynamics

In response to the imperative to reduce greenhouse gas emissions, global efforts are focusing on electrifying transportation and adopting renewable energy sources. This necessitates establishing reliable fast-charging stations (FCSs) for the widespread integration of electric vehicles (EVs). Indeed, the arbitrary distribution of FCSs can detrimentally affect the efficiency of traffic movement. Thus, this paper presents a planning methodology aimed at optimizing the allocation of FCSs within large-scale transportation networks. The energy system proposed includes an autonomous photovoltaic (PV)-powered FCS based on a DC microgrid, supplemented by a stationary battery energy storage system for backup power. The behavior of EVs within the traffic flow is modeled using a realistic traffic simulation software called Dynamic Network Assignment Simulation for Advanced Road Telematics (DYNASMAT). The conflicting objectives of minimizing total annual costs and EV average waiting time at stations are addressed through multi-objective optimization. To solve this optimization problem, the GAMS software is employed. A transportation network with 92 nodes and 284 links is utilized to test the proposed approach. The proposed autonomous PV-powered FCS is compared with Natural Gas-fired Distributed Generators (NGDG)-powered FCS. The simulation results show that while the NGDG-powered FCS exhibits higher emissions, the autonomous PV-powered equivalent operates emission-free. However, the annual cost of the autonomous PV-powered FCS is higher than that of the NGDG-powered FCS.