Depth Function Research Articles

Structural, morphological and optical properties of the La2W2O9/Fe2O3 composite for UV-shielding applications

Currently, research has been conducted on the individual oxides La2W2O9 and Fe2O3 but not on its composite form. Using a solid-state reaction technique, a La2W2O9/Fe2O3 composite was created. A particular calcination cycle was followed by mixing the raw precursors. Scanning electron microscopy (SEM) was used to investigate the morphological microstructure, and X-ray diffraction (XRD) was used to examine the structural characteristics. The thermal and gravimetric properties were examined via differential thermal analysis (DTA) and thermogravimetric analysis (TGA). The optical characteristics were investigated via UV–visible spectroscopy, which investigated included the transmittance, absorbance, absorption coefficient, band gap (Eg), penetration depth (β), Urbach energy (EU), refractive index, optical conductivity, and dielectric function. These findings indicate that the optical properties improved after the addition of Fe2O3 compared with those of pure La2W2O9. The La2W2O9/Fe2O3 composite holds promise as a prospective material for use in the fields of sunscreen products, UV shielding or solar filtration.

Tsg101 knockout in the mammary gland leads to a decrease in small extracellular vesicles in milk from C57BL/6J dams and contributes to leakiness of the gut mucosa and reduced postnatal weight gain in suckling pups

Human milk contains 2.2 ± 1.5×1011 small extracellular vesicles (sEVs) per milliliter and human infants consume 1.7×1014 milk sEVs (sMEVs) daily in 800 mL milk. Infant formula contains trace amounts of sMEVs. To date, eight adverse effects of milk depletion and five beneficial effects of sMEV supplementation have been reported including studies in infants and neonate mice. Formula-fed infants do not realize the benefits of sMEVs. Most of the phenotyping studies reported to date have the limitation that sMEV depletion and supplementation were initiated after mice were weaned. Here, we used a genetics approach for assessing effects of sMEV depletion on the development of suckling mice. Newborn C57BL/6J pups were fostered to Tumor Susceptibility Gene 101 (Tsg101) mammary-specific knockout (KO) dams or C57BL/6J dams (controls) in synchronized pregnancies. Tsg101 KO was associated with an 80% decrease of sMEVs. Postnatal weight gain and gut health (histology, morphology, and barrier function) were assessed until weaning at age three weeks. We observed a significant decrease in weight gain, length of small intestine, villi height, crypt depth, and intestinal barrier function in male and female pups fostered to Tsg101 dams compared to pups fostered to control dams. The effect size varied between 11 and 32 percent. Maternal Tsg101 KO did not affect the dams’ health, content of macronutrients and dry mass of milk and had no effect on the amount of milk consumed by pups. We conclude that sMEVs are important for growth and gut health in neonate mice.

Mathematical Morphology on Directional Data

AbstractWe define morphological operators and filters for directional images whose pixel values are unit vectors. This requires an ordering relation for unit vectors which is obtained by using depth functions. They provide a centre-outward ordering with respect to a specified centre vector. We apply our operators on synthetic directional images and compare them with classical morphological operators for grey-scale images. As application examples, we enhance the fault region in a compressed glass foam and segment misaligned fibre regions of glass fibre-reinforced polymers.

Data depth functions for non-standard data by use of formal concept analysis

In this article we introduce a notion of depth functions for data types that are not given in standard statistical data formats. We focus on data that cannot be represented by one specific data structure, such as normed vector spaces. This covers a wide range of different data types, which we refer to as non-standard data. Depth functions have been studied intensively for normed vector spaces. However, a discussion of depth functions for non-standard data is lacking. In this article, we address this gap by using formal concept analysis to obtain a unified data representation. Building on this representation, we then define depth functions for non-standard data. Furthermore, we provide a systematic basis by introducing structural properties using the data representation provided by formal concept analysis. Finally, we embed the generalised Tukey depth into our concept of data depth and analyse it using the introduced structural properties. Thus, this article presents the mathematical formalisation of centrality and outlyingness for non-standard data and increases the number of spaces in which centrality can be discussed. In particular, we provide a basis for defining further depth functions and statistical inference methods for non-standard data.

Extraction of Acoustic Normal Mode Depth Functions Using Range-Difference Method with Vertical Linear Array Data

Extraction of Acoustic Normal Mode Depth Functions Using Range-Difference Method with Vertical Linear Array Data

Harmonic Source Depth Estimation by a Single Hydrophone under Unknown Seabed Geoacoustic Property

The passive estimation of harmonic sound source depth is of great significance for underwater target localization and identification. Passive source depth estimation using a single hydrophone with an unknown seabed geoacoustic property is a crucial challenge. To address this issue, a harmonic sound source depth estimation algorithm, seabed independent depth estimation (SIDE) algorithm, is proposed. This algorithm combines the estimated mode depth functions, modal amplitudes, and the sign of each modal to estimate the sound source depth. The performance of the SIDE algorithm is analyzed by simulations. Results show that the SIDE is insensitive to the initial range of the sound source, the source depth, the hydrophone depth, the source velocity, and the type of the seabed. Finally, the effectiveness of the SIDE algorithm is verified by the SWellEX-96 data.

Capacity bounds for hyperbolic neural network representations of latent tree structures

We study the representation capacity of deep hyperbolic neural networks (HNNs) with a ReLU activation function. We establish the first proof that HNNs can ɛ-isometrically embed any finite weighted tree into a hyperbolic space of dimension d at least equal to 2 with prescribed sectional curvature κ<0, for any ɛ>1 (where ɛ=1 being optimal). We establish rigorous upper bounds for the network complexity on an HNN implementing the embedding. We find that the network complexity of HNN implementing the graph representation is independent of the representation fidelity/distortion. We contrast this result against our lower bounds on distortion which any ReLU multi-layer perceptron (MLP) must exert when embedding a tree with L>2d leaves into a d-dimensional Euclidean space, which we show at least Ω(L1/d); independently of the depth, width, and (possibly discontinuous) activation function defining the MLP.

Depth in arrangements: Dehn–Sommerville–Euler relations with applications

The depth of a cell in an arrangement of n (non-vertical) great-spheres in Sd\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {S}}^d$$\\end{document} is the number of great-spheres that pass above the cell. We prove Euler-type relations, which imply extensions of the classic Dehn–Sommerville relations for convex polytopes to sublevel sets of the depth function, and we use the relations to extend the expressions for the number of faces of neighborly polytopes to the number of cells of levels in neighborly arrangements.

Projection depth and Lr-type depths for fuzzy random variables

Statistical depth functions are a standard tool in nonparametric statistics to extend order-based univariate methods to the multivariate setting. Since there is no universally accepted total order for fuzzy data (even in the univariate case) and there is a lack of parametric models, a fuzzy extension of depth-based methods is very interesting. In this paper, we adapt the multivariate depths projection depth and Lr-type depth functions to the fuzzy setting, proposing different generalizations for the Lr-type depths. We prove that the proposed fuzzy depth functions have very good properties, obtaining that the fuzzy projection depth is the second example in the literature to satisfy simultaneously the notion of semilinear and of geometric depth. This implies that the fuzzy projection depth is extremely well behave, to order fuzzy sets with respect to fuzzy random variables. Furthermore, we illustrate the good empirical behavior of the proposed fuzzy depth functions with a real data example of trapezoidal fuzzy sets and the used of fuzzy depths in depth-based classification procedures. Finally, as trapezoidal fuzzy sets can be represented by elements of R4, we justify our proposals by also showing empirically the superiority of the fuzzy depths over the multivariate projection depth applied to fuzzy sets.

Digital modeling of surface and subsurface soil salinity in Golestan Province, Iran

Soil salinity is a challenging issue in many arid and semiarid regions and requires suitable management strategies. In the present study, the ability of three ML algorithms (random forest (RF), quantile regression forest (QRF), and cubist (Cu)) together with a depth function were evaluated to predict and compare the spatial distribution of soil salinity, and to identify the main environmental variables that influence soil salinity spatial distribution in 105 soil profiles in 90,000 ha in Northern Iran, Golestan Province. Environmental variables to support modeling included land parameters obtained from the digital elevation model, remote sensing information retrieved from Landsat 7 ETM+ images, rainfall, and piezometric maps. The electrical conductivity was estimated (ECe – dS m−1) at five depth intervals (i.e., 0–25, 25–50, 50–75, 75–100, and 100–125 cm) by spline model in all soil profiles. The model performance was assessed using root mean squared error (RMSEcv), mean absolute error (MAEcv), and coefficient of determination (R2cv). RF, QRF, and Cu methods similarly predicted ECe at the soil surface (0 to 25 cm). At 25–50 cm depth, the QRF model (R2cv = 0.55 and RMSEcv = 12.10) outperformed the other two models. QRF produced more consistent results with the expected ECe distribution on Taylor diagrams. This result showed that QRF is a well-suited model for mapping soil salinity at different depths in the studied region. The produced maps indicated a similar trend of increasing salinity as depth increased. Additionally, results showed that rainfall, NDVI, MRVBF, and piezometer were the most important variables to predict salinity in the study area.

A convex-hull based method with manifold projections for detecting cell protrusions

Cell protrusions play an important role in a variety of cell physiological processes. In this paper, we propose a convex-hull based method, combined with manifold projections, to detect cell protrusions. A convex hull is generated based on the cell surface. We consider the cell surface and the boundary of its convex hull as two manifolds, which are diffeomorphic, and define a depth function based on the distance between the cell surface and its convex hull boundary. The extreme points of the depth function represent the positions of cell protrusions. To find the extreme points easily, we project the points on the cell surface onto the boundary of the convex hull and expand them in spherical polar coordinates. We conducted experiments on three types of cell protrusions. The proposed method achieved the average precision of 98.9%, 95.6%, and 94.7% on blebs, filopodia, and lamellipodia, respectively. Experiments on three datasets show that the proposed method has a robust performance.

Quantitative coarse graining of laminar fluid flow penetration in rough boundaries

The interaction between a fluid and a wall is described with a certain boundary condition for the fluid velocity at the wall. To understand how fluids behave near a rough wall in a completely laminar flow regime, the fluid velocity at every point on the rough surface may be provided. This approach requires detailed knowledge of, and likely depends strongly on the roughness. Another approach of modelling the boundary conditions of a rough wall is to coarse grain and extract a penetration depth over which on average the fluid penetrates into the roughness. In this work, we examine the impact of well-defined patterned surfaces on the fluid flow behaviour. We considered two extreme cases: one with horizontal ridges and another with vertical ridges on the wall and an intermediate case with ridges at an angle on the wall. We show that for a broad range of periodic roughness patterns and relative flow velocities, a universal penetration depth function can be obtained. We obtain these results with experiments and complementary numerical simulations. We evaluate how this penetration depth depends on the various roughness parameters such as ridge depth, ridge spacing and ridge angle. Our results present a novel approach to investigating wall roughness boundary conditions by considering the penetration depth δ that captures the spatially averaged behaviour of the decaying velocity profile between the asperities. We find that this penetration depth δ can be rescaled into a simple exponential master curve δ = δ∞(1 − e−kD/S) for horizontal ridges with varying depth D and spacing S. A similar variation of δ with D and S is observed for vertical ridges, but with a smaller magnitude δ∞, while for ridges at an angle, the penetration depth lies between the two extreme cases.

Integration of RS and GIS in assessing flood risk: A Case Study on Istanbul - Esenyurt

Floods, exacerbated by escalating urbanization, pose significant threats to life and property globally. Over the past decade, the Esenyurt district in Istanbul has witnessed a series of floods, highlighting existing flood risks. Rapid population growth in this area and dense urbanization caused by intensive construction increase flood risks. Given these factors, the study focuses on examining the historical impact of urbanization on flood risks, considering spatial and temporal changes. Landsat-8 satellite data, specifically examining NDVI, NDBI, and BU, was employed to detect building imprints and reveal their historical backgrounds for temporal risk calculations. The analysis showed a sudden increase in urbanization rates in 2016, 2017, and 2021. In the flood risk calculations, 2014 data for a return period of 100 years were used and flood inundation depth, economic damages, affected population and depth-damage function were taken into consideration. The results indicate that from 2014 to 2022, increasing urbanization led to a 32.9% increase in the population affected by floods, a 22.3% rise in potential economic damage, and a 13.6% increase in total flood risk. The relationship between flood risks, contemporary urbanization, and its economic dimensions has been evaluated to reduce risks and achieve sustainable cities.

Comparing machine learning algorithms by union-free generic depth

We propose a framework for descriptively analyzing sets of partial orders based on the concept of depth functions. Despite intensive studies in linear and metric spaces, there is very little discussion on depth functions for non-standard data types such as partial orders. We introduce an adaptation of the well-known simplicial depth to the set of all partial orders, the union-free generic (ufg) depth. Moreover, we utilize our ufg depth for a comparison of machine learning algorithms based on multidimensional performance measures. Concretely, we provide two examples of classifier comparisons on samples of standard benchmark data sets. Our results demonstrate promisingly the wide variety of different analysis approaches based on ufg methods. Furthermore, the examples outline that our approach differs substantially from existing benchmarking approaches, and thus adds a new perspective to the vivid debate on classifier comparison.1

A modular neural network to quickly approximate the modal dispersion in coastal waters

Low-frequency acoustic propagation modeling in coastal waters usually relies on numerical models based on modal theory such as Kraken and Orca. These models compute the modal parameters (e.g., modal wavenumbers and depth functions) that can be used in the calculation of the acoustic field. Their repeated use in broadband applications, or for inversion purposes, comes with a notable computational cost. To mitigate this, a modular neural network (NN) was trained to approximate modal parameters for varying modes and frequencies, across diverse environments, with variable water sound speed profile and variable seabed geoacoustic parameters. The training dataset is generated using Kraken and the NN is evaluated on many environments not seen during training. Once trained, the NN can make broadband predictions without prior knowledge on the number of modes, even when the number of modes changes over the frequency-band of interest. This approach reduces computation time compared to the original forward propagation model, while maintaining high precision. The effectiveness of our method is demonstrated through transmission loss calculations and a simulated geoacoustic inversion scenario.

Moving harmonic source depth estimation by MDFMD-v in a weakly range-depend waveguide

To estimate the depth of a non-cooperative moving sound source in a range-depend waveguide, a passive depth estimation method combining depth-polarity search for a harmonic moving source is proposed in this paper. Firstly, the method obtains each mode parameters at the source and horizontal linear array (HLA) locations by utilizing the modal depth function constrained modal Doppler velocity estimation (MDFMD-v) and matrix pencil (MP) methods, respectively. Subsequently, mode amplitudes are calculated by compressive sensing. To determine the polarity of each mode amplitude, a depth-polarity search method is given in this paper. Finally, a depth ambiguity function with mode amplitude polarity is used to obtain the depth estimation results. Simulation results verify the effectiveness of the method.

Mode-informed complex-valued neural processes for matched field processing

Matched field processing (MFP) is a key technique for passive underwater source localization, estimating the source position by matching array measurements with acoustic model replicas. Its effectiveness relies on matching environmental parameters with the actual oceanic environment, but performance declines with environmental mismatches and lower signal-to-noise ratios. This paper proposes a novel approach that integrates neural networks (NNs) and complex Gaussian processes with modal depth functions for acoustic field reconstruction that is more accurate and efficient compared to Gaussian process regression. A meta-learning strategy is used to optimize parameters of the NN. The reconstructed data are denoised and interpolated, generating densely populated acoustic fields at virtual arrays, which are then used as data in MFP. Replicas are also computed at the virtual receivers. This mode-informed complex-valued neural processes enhance MFP performance, particularly in low SNR and mismatched environments. It captures the propagation properties of underwater acoustic fields more comprehensively, showing superior localization performance in both simulated and real-world data from the SWellEx-96 Event S5 environment.

Need for Objective Task-Based Evaluation of Image Segmentation Algorithms for Quantitative PET: A Study with ACRIN 6668/RTOG 0235 Multicenter Clinical Trial Data.

Reliable performance of PET segmentation algorithms on clinically relevant tasks is required for their clinical translation. However, these algorithms are typically evaluated using figures of merit (FoMs) that are not explicitly designed to correlate with clinical task performance. Such FoMs include the Dice similarity coefficient (DSC), the Jaccard similarity coefficient (JSC), and the Hausdorff distance (HD). The objective of this study was to investigate whether evaluating PET segmentation algorithms using these task-agnostic FoMs yields interpretations consistent with evaluation on clinically relevant quantitative tasks. Methods: We conducted a retrospective study to assess the concordance in the evaluation of segmentation algorithms using the DSC, JSC, and HD and on the tasks of estimating the metabolic tumor volume (MTV) and total lesion glycolysis (TLG) of primary tumors from PET images of patients with non-small cell lung cancer. The PET images were collected from the American College of Radiology Imaging Network 6668/Radiation Therapy Oncology Group 0235 multicenter clinical trial data. The study was conducted in 2 contexts: (1) evaluating conventional segmentation algorithms, namely those based on thresholding (SUVmax40% and SUVmax50%), boundary detection (Snakes), and stochastic modeling (Markov random field-Gaussian mixture model); (2) evaluating the impact of network depth and loss function on the performance of a state-of-the-art U-net-based segmentation algorithm. Results: Evaluation of conventional segmentation algorithms based on the DSC, JSC, and HD showed that SUVmax40% significantly outperformed SUVmax50%. However, SUVmax40% yielded lower accuracy on the tasks of estimating MTV and TLG, with a 51% and 54% increase, respectively, in the ensemble normalized bias. Similarly, the Markov random field-Gaussian mixture model significantly outperformed Snakes on the basis of the task-agnostic FoMs but yielded a 24% increased bias in estimated MTV. For the U-net-based algorithm, our evaluation showed that although the network depth did not significantly alter the DSC, JSC, and HD values, a deeper network yielded substantially higher accuracy in the estimated MTV and TLG, with a decreased bias of 91% and 87%, respectively. Additionally, whereas there was no significant difference in the DSC, JSC, and HD values for different loss functions, up to a 73% and 58% difference in the bias of the estimated MTV and TLG, respectively, existed. Conclusion: Evaluation of PET segmentation algorithms using task-agnostic FoMs could yield findings discordant with evaluation on clinically relevant quantitative tasks. This study emphasizes the need for objective task-based evaluation of image segmentation algorithms for quantitative PET.

Nearshore Bathymetry from ICESat-2 LiDAR and Sentinel-2 Imagery Datasets Using Physics-Informed CNN

The recently developed Ice, Cloud, and Land Elevation Satellite 2 (ICESat-2), furnished with the Advanced Terrain Laser Altimeter System (ATLAS), delivers considerable benefits in providing accurate bathymetric data across extensive geographical regions. By integrating active lidar-derived reference seawater depth data with passive optical remote sensing imagery, efficient bathymetry mapping is facilitated. In recent times, machine learning models are frequently used to define the nonlinear connection between remote sensing spectral data and water depths, which consequently results in the creation of bathymetric maps. A salient model among these is the convolutional neural network (CNN), which effectively integrates contextual information concerning bathymetric points. However, current CNN models and other machine learning approaches mainly concentrate on recognizing mathematical relationships within the data to determine a water depth function and remote sensing spectral data, while oftentimes disregarding the physical light propagation process in seawater before reaching the seafloor. This study presents a physics-informed CNN (PI-CNN) model which incorporates radiative transfer-based data into the CNN structure. By including the shallow water double-band radiative transfer physical term (swdrtt), this model enhances seawater spectral features and also considers the context surroundings of bathymetric pixels. The effectiveness and reliability of our proposed PI-CNN model are verified using in situ data from St. Croix and St. Thomas, validating its correctness in generating bathymetric maps with a broad experimental R2 accuracy exceeding 95% and remaining errors below 1.6 m. Preliminary results suggest that our PI-CNN model surpasses conventional methodologies.

Regression Depth for Statistical Depth Function

The statistical depth function is one of the modern approaches that can be used for developing multivariate robust regression based on robust estimates of the location and dispersion matrix. One merit advantage of the depth concept is that it can be used directly to provide deeper estimation functions for data location and regression parameters in a multidimensional environment. The deeper estimation functions induced by depth are expected to inherit the desired and inherent robustness properties (such as limited maximum bias, impact function, and high breaking point) as do their counterparts at univariate sites. Investigation. The main objective of this article is to check the power of the statistical depth function throw the depth regression, it turns out that the deepest functional projection possesses a finite effect function and the best possible asymptotic breakpoint as well as the best breaking point of a finite sample compared with some classical and robust existed method.