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Seawater intrusion (SI) poses a substantial threat to water security in coastal regions, where numerical models play a pivotal role in supporting groundwater management and protection. However, the inherent heterogeneity of coastal aquifers introduces significant uncertainties into SI predictions, potentially diminishing their effectiveness in management decisions. Data assimilation (DA) offers a solution by integrating various types of observational data with the model to characterize heterogeneous coastal aquifers. Traditional DA techniques, like ensemble smoother using the Kalman formula (ESK) and Markov chain Monte Carlo, face challenges when confronted with the non‐linearity, non‐Gaussianity, and high‐dimensionality issues commonly encountered in aquifer characterization. In this study, we introduce a novel DA approach rooted in deep learning (DL), referred to as ESDL, aimed at effectively characterizing coastal aquifers with varying levels of heterogeneity. We systematically investigate a range of factors that impact the performance of ESDL, including the number and types of observations, the degree of aquifer heterogeneity, the structure and training options of the DL models. Our findings reveal that ESDL excels in characterizing heterogeneous aquifers under non‐linear and non‐Gaussian conditions. Comparison between ESDL and ESK under different experimentation settings underscores the robustness of ESDL. Conversely, in certain scenarios, ESK displays noticeable biases in the characterization results, especially when measurement data from non‐linear and discontinuous processes are used. To optimize the efficacy of ESDL, attention must be given to the design of the DL model and the selection of observational data, which are crucial to ensure the universal applicability of this DA method. Key Points Non‐linearity and non‐Gaussianity in coastal aquifer characterization problems pose challenges to traditional data assimilation (DA) methods We propose to address these issues with a deep learning‐based DA method called ESDL Various factors influencing the performance of ESDL are systematically investigated

In this paper, statistical-model generalizations of independent low-rank matrix analysis (ILRMA) are proposed for achieving high-quality blind source separation (BSS). BSS is a crucial problem in realizing many audio applications, where the audio sources must be separated using only the observed mixture signal. Many algorithms for solving BSS have been proposed, especially in the history of independent component analysis and nonnegative matrix factorization. In particular, ILRMA can achieve the highest separation performance for music or speech mixtures, where ILRMA assumes both independence between sources and the low-rankness of time-frequency structure in each source. In this paper, we propose two extensions of the source distribution assumed in ILRMA. We introduce a heavy-tailed property by replacing the conventional Gaussian source distribution with a generalized Gaussian or Student’s t distribution. Convergence-guaranteed efficient algorithms are derived for the proposed methods, and the relationship between the generalized Gaussian and Student’s t distributions in the source model estimation is revealed. By experimental evaluation, the validity of the heavy-tailed generalizations of ILRMA is confirmed.

The magnitude and distribution of observation innovations, which have an important impact on the analyzed accuracy, are critical variables in data assimilation. Variational quality control (VarQC) based on the contaminated Gaussian distribution (CGD) of observation innovations is now widely used in data assimilation, owing to the more reasonable representation of the probability density function of innovations that can sufficiently absorb observations by assigning different weights iteratively. However, the inaccurate parameters prevent VarQC from showing the advantages it should have in the GRAPES (Global/Regional Assimilation and PrEdiction System) m3DVAR system. Consequently, the parameter optimization methods are considerable critical studies to improve VarQC. In this paper, we describe two probable CGDs to include the non-Gaussian distribution of actual observation errors, Gaussian plus flat distribution and Huber norm distribution. The potential optimization methods of the parameters are introduced in detail for different VarQCs. With different parameter configurations, the optimization analysis shows that the Gaussian plus flat distribution and the Huber norm distribution are more consistent with the long-tail distribution of actual innovations compared to the Gaussian distribution. The VarQC’s cost and gradient functions with Huber norm distribution are more reasonable, while the VarQC’s cost function with Gaussian plus flat distribution may converge on different minimums due to its non-concave properties. The weight functions of two VarQCs gradually decrease with the increase of innovation but show different shapes, and the VarQC with Huber norm distribution shows more elasticity to assimilate the observations with a high contamination rate. Moreover, we reveal a general derivation relationship between the CGDs and VarQCs. A novel schematic interpretation that classifies the assimilated data into three categories in VarQC is presented. They are conducive to the development of a new VarQC method in the future.

This paper deals with estimating the underlying parameter of a length-biased inverse Gaussian distribution, when the observations are prone to length-biased sampling. Length-biased sampling occurs when the observations of smaller lengths or dimensions are neglected from the sample. We focus on a particular type of sequential fixed-accuracy confidence interval for estimation purposes. This method proves to be both time and cost efficient as one is able to perform the estimation using an optimal number of observations according to some set criteria. We discuss the applicability of our proposed method with regards to estimating the cluster size of the \"Eastern Tropical Pacific Dolphins\", which are often vulnerable to length biasedness.

A linear structural equation model relates random variables of interest and corresponding Gaussian noise terms via a linear equation system. Each such model can be represented by a mixed graph in which directed edges encode the linear equations and bidirected edges indicate possible correlations among noise terms. We study parameter identifiability in these models, that is, we ask for conditions that ensure that the edge coefficients and correlations appearing in a linear structural equation model can be uniquely recovered from the covariance matrix of the associated distribution. We treat the case of generic identifiability, where unique recovery is possible for almost every choice of parameters. We give a new graphical condition that is sufficient for generic identifiability and can be verified in time that is polynomial in the size of the graph. It improves criteria from prior work and does not require the directed part of the graph to be acyclic. We also develop a related necessary condition and examine the \"gap\" between sufficient and necessary conditions through simulations on graphs with 25 or 50 nodes, as well as exhaustive algebraic computations for graphs with up to five nodes.

Current-conduction/transport mechanisms (CCMs or CTMs) through barrier and barrier height (BH) formation in the Al/(CdZnO)/p-Si/Al diodes, which were prepared by the sol–gel method, were examined in the range of 110–380 K. The decrease of zero-bias BH (ΦBo) and increase of ideality factor (n) with decreasing temperature were observed. The classic Richardson plot indicated two distinct linear regions that correspond to low and high temperature range (LTR and HTR), respectively. Contrary to this, the acquired Richardson constant value (A*) was much lower than its theoretical value (32 A cm−2 K−2). Such abnormal behavior of the ΦBo, n and A* was attributed to the evidence of the barrier inhomogeneities, especially at low temperature. Therefore, the ΦBo−n, ΦBo and (n−1 − n) versus q/2kT plots were sketched to acquire significant clues for the Gaussian distribution (GD) of the BHs at rectifier contact area with the mean BH (\\[ \\bar{\\Phi }_{\\rm{Bo}} \\]) and standard deviation (σso), which also have two linear parts with distinct slopes. \\[ \\bar{\\Phi } \\] and σso were calculated from the slope and intercept of ΦBo versus q/2kT plot as 0.802 eV and 0.066 V for LTR, 1.043 eV and 0.106 V for HTR, respectively. The \\[ \\bar{\\Phi }_{\\rm{Bo}} \\] and A* were acquired by utilizing the σso values and using the Richardson plot as 0.626 eV and 14.26 A cm−2 K−2 for LTR and 1.021 eV and 32.53 A cm−2 K−2 for HTR, respectively. Thus, the I–V–T characteristics of the Al/(CdZnO)/p-Si/Al diodes at forward biases were successfully elucidated by the double-GD of BHs with mean BHs of 0.626 eV and 1.021 eV, respectively.

The 27 November 2019 Mw 6.0 earthquake that occurred in the southwestern part of the Hellenic Arc near Crete Island provided evidence of the high potential for strong earthquakes and active seismicity in the Hellenic Arc. In addition, tsunamis have been reported to occur for the region after major earthquakes in the historical past, so the seismic hazard of the Hellenic Arc should be evaluated in detail. The aim of this study is to evaluate the seismic hazard of the Hellenic Arc more reliably and accurately by estimating the conditional probabilities of a strong earthquake based on Weibull, gamma, log-normal, exponential, Rayleigh, and inverse Gaussian distribution models for the inter-event time of Mw ≥ 6.0 earthquakes that occurred between 1900 and 2019 in the study area. The fit between each model and the data was tested using four different test criteria, namely the log-likelihood value, Akaike information criterion, Bayesian information criteria, and Kolmogorov–Smirnov test. According to the results, the inverse Gaussian distribution was selected as the best, the log-normal distribution as the second best, the Weibull and gamma distributions as intermediate, and the Rayleigh and exponential distribution as the poorest and second poorest model, respectively. The conditional probability of an earthquake with magnitude Mw ≥ 6.0 is estimated to be higher than 0.70 according to all of the models used in this study for the base year te = 0 (te = 2015) and t > 5 years (t > 2020). Moreover, the results obtained based on the inverse Gaussian, exponential, log-normal, and Weibull distribution models are close to each other and are higher than 0.60 for te = 0 and t ≥ 3 years (t ≥ 2018). The outcomes of this study when using the different distribution models will contribute to assessments of the seismic as well as tsunami hazards for the region.

Cavitation damage on a mercury target vessel for a pulsed spallation neutron source is induced by a proton beam injection in mercury. Cavitation damage is one of factors affecting the allowable beam power and the life time of a mercury target vessel. The prediction method of the cavitation damage using Monte Carlo simulations was proposed taking into account the uncertainties of the core position of cavitation bubbles and impact pressure distributions. The distribution of impact pressure attributed to individual cavitation bubble collapsing was assumed to be Gaussian distribution and the probability distribution of the maximum value of impact pressures was assumed to be three kinds of distributions: the delta function and Gaussian and Weibull distributions. Two parameters in equations describing the distribution of impact pressure were estimated using Bayesian optimization by comparing the distribution of the cavitation damage obtained from the experiment with the distribution of the accumulated plastic strain obtained from the simulation. Regardless of the distribution type, the estimated maximum impact pressure was 1.2–2.9 GPa and existed in the range of values predicted by the ratio of the diameter and depth of the pit. The estimated dispersion of the impact pressure distribution was 1.0–1.7 μm and corresponded to the diameter of major pits. In the distribution of the pits described by the accumulated plastic strain, which was assumed in three cases, the delta function and Gaussian and Weibull distributions, the Weibull distribution agreed well with the experimental results, particularly including relatively large pit size. Furthermore, the Weibull distribution reproduced the depth profile, i.e., pit shape, better than that using the delta function or Gaussian distribution. It can be said that the cavitation erosion phenomenon is predictable by adopting the Weibull distribution. This prediction method is expected to be applied to predict the cavitation damage in fluid equipment such as pumps and fluid parts.

Au/PVA/n-GaAs (MPS) type Schottky diodes (SDs) were fabricated and investigated in a temperature range of 80–360 K to explain their possible conduction mechanisms (CMs). Three distinct linear regions with different slopes were observed in ln(I)–V plots. The first region (R1), is within the range of 0.22–0.60 V, the second region (R2), is within the range of 0.64–0.90 V, and the third region (R3), is within the range of 1.1–1.5 V. It was shown that both ideality factor (n) and zero-bias barrier height (ΦBo) are strong functions of temperature for all three regions. It was noticed that n values decreased and ΦBo values increased with increasing temperature. In order to ascertain the possible CMs, ΦBo − n, − ΦBo − q/2kT, and (n−1 − 1) − q/2kT plots were also examined. In each of these plots, two linear regions were obtained within each of the three regions. The region from 80–180 K is called the low-temperature range (LTR), and the region from 200–360 K is called the high-temperature range (HTR). It has been revealed that the reason for the deviation from the classical thermionic emission (TE) theory cannot be explained only by the existence of the interface layer, interface states (NSS) or quantum mechanical tunneling mechanisms, which can be also explained by the double Gaussian distribution (DGD) due to barrier inhomogeneity. Finally, the experimental Richardson constants (A*) were calculated from the interception point of the modified Richardson curve in LTR and HTR for all three regions. It was calculated as 6.22 and 8.13 A/cm2K2 for RI, 7.77 and 8.14 A/cm2K2 at R2, and 7.07 and 8.13 A/cm2K2 at R3 for low- and high-temperature ranges, respectively. It is clear that especially HTR results are quite close to the known theoretical A* value of 8.16 A/cm2K2 for n-GaAs.

Neurons transmit information as action potentials or spikes. Due to the inherent randomness of the inter-spike intervals (ISIs), probabilistic models are often used for their description. Cumulative damage (CD) distributions are a family of probabilistic models that has been widely considered for describing time-related cumulative processes. This family allows us to consider certain deterministic principles for modeling ISIs from a probabilistic viewpoint and to link its parameters to values with biological interpretation. The CD family includes the Birnbaum–Saunders and inverse Gaussian distributions, which possess distinctive properties and theoretical arguments useful for ISI description. We expand the use of CD distributions to the modeling of neural spiking behavior, mainly by testing the suitability of the Birnbaum–Saunders distribution, which has not been studied in the setting of neural activity. We validate this expansion with original experimental and simulated electrophysiological data.