distribution function
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2022 ◽  
pp. 108128652110728
Ping Yang ◽  
Xu Wang ◽  
Peter Schiavone

The method of continuously distributed dislocations is used to study the distribution of screw dislocations in a linear array piled up near the interface of a two-phase isotropic elastic thin film with equal thickness in each phase. The resulting singular integral equation is solved numerically using the Gauss–Chebyshev integration formula to arrive at the dislocation distribution function and the number of dislocations in the pileup.

2022 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Huthaifa Alqaralleh

Purpose This paper aims to contribute to the clarification of whether the dependence and causality between oil and the macrofundamentals change across different quantiles of the distribution function. Design/methodology/approach Within the context of an asymmetric quantile approach, we drop the assumption that variables operate at the upper tails of the distribution in the way that they operate at the mean. Findings Our innovative approach indicates that the response of oil prices not only differs according to the underlying source of the variables shock but also differs across the quantiles. Originality/value Although a number of recent studies are closely related to our present research, our novel findings offer some important insights that foreshadow the empirical results. The current research addresses to answer the following questions, in sequence: (i) Is there any extreme value dependence between the crude oil and macroeconomic variables? If yes, (ii) is the dependence symmetric or asymmetric? Finally, (iii) can this dependence be driven by the phases of the economic cycle?

Alexey Bufetov ◽  
Peter Nejjar

AbstractThis paper studies the mixing behavior of the Asymmetric Simple Exclusion Process (ASEP) on a segment of length N. Our main result is that for particle densities in (0, 1),  the total-variation cutoff window of ASEP is $$N^{1/3}$$ N 1 / 3 and the cutoff profile is $$1-F_{\mathrm {GUE}},$$ 1 - F GUE , where $$F_{\mathrm {GUE}}$$ F GUE is the Tracy-Widom distribution function. This also gives a new proof of the cutoff itself, shown earlier by Labbé and Lacoin. Our proof combines coupling arguments, the result of Tracy–Widom about fluctuations of ASEP started from the step initial condition, and exact algebraic identities coming from interpreting the multi-species ASEP as a random walk on a Hecke algebra.

2022 ◽  
Emre Brookes ◽  
Mattia Rocco

Abstract Recent spectacular advances by AI programs in 3D structure predictions from protein sequences have revolutionized the field in terms of accuracy and speed. The resulting "folding frenzy" has already produced predicted protein structure databases for the entire human and other organisms' proteomes. However, rapidly ascertaining a predicted structure's reliability based on measured properties in solution should be considered. Shape-sensitive hydrodynamic parameters such as the diffusion and sedimentation coefficients (D0t(20,w),s0(20,w)) and the intrinsic viscosity ([η]) can provide a rapid assessment of the overall structure likeliness, and SAXS would yield the structure-related pair-wise distance distribution function p(r) vs. r. Using the extensively validated UltraScan SOlution MOdeler (US-SOMO) suite we have calculated from the AlphaFold structures the corresponding D0t(20,w), s0(20,w), [η], p(r) vs. r, and other parameters. Circular dichroism spectra were also computed. The resulting US-SOMO-AF database should aid in rapidly evaluating the consistency in solution of AlphaFold predicted protein structures.

2022 ◽  
Rocío García-Cuevas ◽  
Javier F. Jiménez-Alonso ◽  
Carlos Renedo M.C. ◽  
Francisco Martinez

<p>The evaluation of the vibration performance of footbridges due to walking pedestrians is an issue of increasing importance in current footbridge design practice. The growing trend of slender footbridges with long spans and light materials has led to serviceability problems in lateral vibrations, which occur when the number of pedestrians reaches a “critical number”. Considering the mode of vibration in which the lateral instability is more likely to develop, the structural response depends on the modal characteristics of the footbridge; in particular, the natural frequency and the damping ratio. These modal parameters are stochastic variables, as it is not possible to determine them without a level of uncertainty. Thus, the purpose of this paper is to obtain the value of the lateral dynamic response of slender footbridges with a certain confidence level under uncertainty conditions. The uncertainties of those modal parameters are considered using a probabilistic approach. Both the natural frequency and the damping ratio are modelled as uncorrelated random variables that follow a predetermined probabilistic distribution function. Consequently, the structural response will also be described by a probabilistic distribution function, which can be estimated through Monte Carlo numerical simulations. As a result, the study allows the footbridge lateral response and the critical number of pedestrians to be calculated for different confidence levels and load scenarios, especially for crowd densities above the “critical number”.</p>

Nicola Esposito ◽  
Agostino Mele ◽  
Bruno Castanier ◽  
Massimiliano Giorgio

In this paper, a new gamma-based degradation process with random effect is proposed that allows to account for the presence of measurement error that depends in stochastic sense on the measured degradation level. This new model extends a perturbed gamma model recently suggested in the literature, by allowing for the presence of a unit to unit variability. As the original one, the extended model is not mathematically tractable. The main features of the proposed model are illustrated. Maximum likelihood estimation of its parameters from perturbed degradation measurements is addressed. The likelihood function is formulated. Hence, a new maximization procedure that combines a particle filter and an expectation-maximization algorithm is suggested that allows to overcome the numerical issues posed by its direct maximization. Moreover, a simple algorithm based on the same particle filter method is also described that allows to compute the cumulative distribution function of the remaining useful life and the conditional probability density function of the hidden degradation level, given the past noisy measurements. Finally, two numerical applications are developed where the model parameters are estimated from two sets of perturbed degradation measurements of carbon-film resistors and fuel cell membranes. In the first example the presence of random effect is statistically significant while in the second example it is not significant. In the applications, the presence of random effect is checked via appropriate statistical procedures. In both the examples, the influence of accounting for the presence of random effect on the estimates of the cumulative distribution function of the remaining useful life of the considered units is also discussed. Obtained results demonstrate the affordability of the proposed approach and the usefulness of the proposed model.

2022 ◽  
Vol 15 (1) ◽  
pp. 22
Roman V. Ivanov

The paper discusses an extension of the variance-gamma process with stochastic linear drift coefficient. It is assumed that the linear drift coefficient may switch to a different value at the exponentially distributed time. The size of the drift jump is supposed to have a multinomial distribution. We have obtained the distribution function, the probability density function and the lower partial expectation for the considered process in closed forms. The results are applied to the calculation of the value at risk and the expected shortfall of the investment portfolio in the related multivariate stochastic model.

Water ◽  
2022 ◽  
Vol 14 (2) ◽  
pp. 143
Marwan Kheimi ◽  
Shokry M. Abdelaziz

A new daily water balance model is developed and tested in this paper. The new model has a similar model structure to the existing probability distributed rainfall runoff models (PDM), such as HyMOD. However, the model utilizes a new distribution function for soil water storage capacity, which leads to the SCS (Soil Conservation Service) curve number (CN) method when the initial soil water storage is set to zero. Therefore, the developed model is a unification of the PDM and CN methods and is called the PDM–CN model in this paper. Besides runoff modeling, the calculation of daily evaporation in the model is also dependent on the distribution function, since the spatial variability of soil water storage affects the catchment-scale evaporation. The generated runoff is partitioned into direct runoff and groundwater recharge, which are then routed through quick and slow storage tanks, respectively. Total discharge is the summation of quick flow from the quick storage tank and base flow from the slow storage tank. The new model with 5 parameters is applied to 92 catchments for simulating daily streamflow and evaporation and compared with AWMB, SACRAMENTO, and SIMHYD models. The performance of the model is slightly better than HyMOD but is not better compared with the 14-parameter model (SACRAMENTO) in the calibration, and does not perform as well in the validation period as the 7-parameter model (SIMHYD) in some areas, based on the NSE values. The linkage between the PDM–CN model and long-term water balance model is also presented, and a two-parameter mean annual water balance equation is derived from the proposed PDM–CN model.

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