Smooth Density Research Articles

ON IMPROVED GAUSSIAN CORRELATION INEQUALITIES FOR SYMMETRICAL -RECTANGLES EXTENDED TO CERTAIN MULTIVARIATE GAMMA DISTRIBUTIONS AND SOME FURTHER PROBABILITY INEQUALITIES

The Gaussian correlation inequality (GCI) for symmetrical n-rectangles is improved if the absolute components have a joint cumulative distribution function (cdf), which is MTP2 (multivariate totally positive of order 2). Inequalities of the given type hold at least for all MTP2-cdfs on or with everywhere positive smooth densities. In particular, at least some infinitely divisible multivariate chi-square distributions (gamma distributions in the sense of Krishnamoorthy and Parthasarathy) with any positive real “degree of freedom” are shown to be MTP2. Moreover, further numerically calculable probability inequalities for a broader class of multivariate gamma distributions are derived. A different improvement for inequalities of the GCI-type, and of a similar type with three instead of two groups of components with more special correlation structures is also obtained. The main idea behind these inequalities is to find for a given correlation matrix with positive correlations, a further correlation matrix with smaller correlations whose inverse is an M-matrix and where the corresponding multivariate gamma distribution function is numerically available.

Intestinal Region-Dependent Impact of NFκB-Nrf Crosstalk in Myenteric Neurons and Adjacent Muscle Cells in Type 1 Diabetic Rats.

Type 1 diabetes affects cytokines as potential inducers of NFκB signalling involved in inflammation and neuronal survival. Our goal was to assess the expression of NFκB p65 and its negative regulator, Nrf2, in myenteric neurons and adjacent smooth muscle of different gut segments after chronic hyperglycaemia and immediate insulin treatment. After ten weeks of hyperglycaemia, intestinal samples of control, streptozotocin-induced diabetic and insulin-treated diabetic rats were prepared for fluorescent immunohistochemistry, immunogold electron microscopy, ELISA and qPCR. In the diabetic rats, the proportion of NFκB p65-immunoreactive myenteric neurons decreased significantly in the duodenum and increased in the ileum. The density of NFκB p65-labelling gold particles increased in the ileal but remained unchanged in the duodenal ganglia. Meanwhile, both total and nuclear Nrf2 density increased in the myenteric neurons of the diabetic duodenum. In smooth muscle, NFκB p65 and Nrf2 density increased in the small intestine of diabetic rats. While on the mRNA level, NFκB p65 and Nrf2 were induced, on the protein level, NFκB p65 increased and Nrf2 decreased in muscle/myenteric plexus homogenates. Insulin treatment had protective effects. Our findings reveal a segment-specific NFκB and Nrf expression in myenteric neurons and ganglionic muscular environments, which may contribute to regional neuronal survival and motility disturbances in diabetes.

Effects of age, elastin density, and glycosaminoglycan accumulation on the delamination strength of human thoracic and abdominal aortas

Aortic dissection is a life-threatening condition caused by layer separation. Despite extensive research, the relationship between the aortic wall's structural integrity and dissection risk remains unclear. Glycosaminoglycan (GAG) accumulation and elastin loss are suspected to play significant roles. We investigated how age-related changes in aortic structure affect dissection susceptibility. Peeling tests were performed on longitudinal and circumferential thoracic (TA) and abdominal aortic (AA) strips from 35 donors aged 13–76 years (mean 38 ± 15 years, 34 % female). GAG, elastin, collagen, and smooth muscle cell (SMC) contents were assessed using bidirectional histology. Young TAs resisted longitudinal peeling better than circumferential, with delamination strengths of 65.4 mN/mm and 44.2 mN/mm, respectively. Delamination strength decreased with age in both directions, more rapidly longitudinally, equalizing at ∼20–25 mN/mm in older TAs. Delamination strength in AAs was 22 % higher than in TAs. No sex differences were observed. GAG density increased, while elastin density decreased by 2.5 % and 4 % per decade, respectively. Collagen density did not change with age, while SMC density decreased circumferentially. GAGs partially mediated the reduction in longitudinal delamination strength due to aging, while circumferential strength reduction was not mediated by changes in either GAG or elastin densities. This study explains why aortic dissections are more common in TAs, especially in older individuals, and why they typically propagate spirally. TAs exhibit lower delamination strength compared to AAs and experience strength reduction with age, a phenomenon linked to increased GAG accumulation and elastin loss. These findings enhance our understanding of the pathophysiological mechanisms behind aortic dissection. Statement of significanceThis work explores the age-dependent relationships between delamination strength in human aortas and wall structural content. We investigated 35 human aortas from donors aged 13 to 76 years, providing new insights into the biomechanical and histological factors that influence aortic dissection risk. Our findings elucidate how variations in elastin, glycosaminoglycan, collagen, and smooth muscle cell densities impact the structural integrity of the aorta, contributing significantly to the understanding of aortic dissection mechanisms.

Topology optimization with graph neural network enabled regularized thresholding

Topology optimization algorithms often employ a smooth density function to implicitly represent geometries in a discretized domain. While this implicit representation offers great flexibility to parametrize the optimized geometry, it also leads to a transition region. Previous approaches, such as the Solid Isotropic Material Penalty (SIMP) method, have been proposed to modify the objective function aiming to converge toward integer density values and eliminate this non-physical transition region. However, the iterative nature of topology optimization renders this process computationally demanding, emphasizing the importance of achieving fast convergence. Accelerating convergence without significantly compromising the final solution can be challenging. In this work, we introduce a machine learning approach that leverages the message-passing Graph Neural Network (GNN) to eliminate the non-physical transition zone for the topology optimization problems. By representing the optimized structures as weighted graphs, we introduce a generalized filtering algorithm based on the topology of the spatial discretization. As such, the resultant algorithm can be applied to two- and three-dimensional space for both Cartesian (structured grid) and non-Cartesian discretizations (e.g. polygon finite element). The numerical experiments indicate that applying this filter throughout the optimization process may avoid excessive iterations and enable a more efficient optimization procedure.

Random thermal-vibration mechanisms of sandwich ventral fin-type plate-shell systems with porous functionally graded core

The stochastic thermal-vibration mechanisms within a sandwich ventral fin-type plate-shell system, featuring a porous functionally graded (FG) core, are exhaustively analyzed under various random loading conditions employing an innovative node-based, meshless computational approach. The studied structure is decoupled into several plates and open cylindrical panel according to the geometric characteristics, and the mechanical relationships at the structural boundaries or connection interfaces are equivalently simulated by using penalty parameters. Following the general Hamilton's principle, the meshless approach combined with the first-order shear deformation theory (FSDT) incorporating thermal effects is employed to derive the vibration equations of the sandwich ventral fin-type plate-shell systems. Also, the pseudo excitation method (PEM) is introduced to calculate stationary and nonstationary random responses. In order to verify the accuracy of the meshless algorithm in this study, the convergence and correctness are studied comprehensively. And then, the effects of some parameters such as temperature variation, porosity parameters, power-law index and random excitations on the thermal vibration characteristics of the sandwich ventral fin-type plate-shell systems with porous FG core are presented. The results show that the power-law index and temperature can increase the frequency parameter of the structure. The smooth power spectral density (PSD) excitation only affects the amplitude of the response curve, and does not affect the frequency corresponding to the peak. In the analysis of non-stationary random vibration, the influence of modulation parameters on response is very significant.

On invariant distributions of Feller Markov chains with applications to dynamical systems with random switching

AbstractWe introduce simple conditions ensuring that invariant distributions of a Feller Markov chain on a compact Riemannian manifold are absolutely continuous with a lower semi-continuous, continuous or smooth density with respect to the Riemannian measure. This is applied to Markov chains obtained by random composition of maps and to piecewise deterministic Markov processes obtained by random switching between flows.

Rotating machine bearing health prognosis using a data driven approach based on KS‐density and BiLSTM

AbstractRolling element bearings are vital components within rotating machinery, making them a central focus of maintenance in the prognostics and health management sector. This involves closely monitoring their condition to accurately predict the remaining useful life, increasing reliability while minimizing unexpected breakdowns, thereby enabling cost savings through planned maintenance, and enhancing operational stability and security. To achieve this goal, it is necessary to build an online intelligent system for degradation monitoring and failure prognosis by the construction of a robust health indicator and making quantitative measure for bearing degradation. In this paper, an efficient and reliable approach is proposed to estimate the remaining useful life of bearing. A new prediction method is presented by the combination of kernel smoothing density (KS‐density) and bidirectional long short‐term memory (BiLSTM). Firstly, KS‐density smoothens the preliminarily estimated probability distribution function using machinery degradation data. Secondly, the obtained KS‐density is used in feed deep learning technique based on BiLSTM models. On this basis, the variation of the signal distribution models between the current faulty state and the normal conditions state is quantified for bearing health assessment. The effective recognition of bearing degradation by the proposed Weibull‐based health index is demonstrated through experimental validations utilizing run‐to‐failure datasets, provided by the centre for intelligent maintenance systems. The comparison with the literature's review show that the prediction results of the proposed approach are more accurate.

Flexible Bayesian estimation of incubation times.

The incubation period is of paramount importance in infectious disease epidemiology as it informs about the transmission potential of a pathogenic organism and helps to plan public health strategies to keep an epidemic outbreak under control. Estimation of the incubation period distribution from reported exposure times and symptom onset times is challenging as the underlying data is coarse. We develop a new Bayesian methodology using Laplacian-P-splines that provides a semi-parametric estimation of the incubation density based on a Langevinized Gibbs sampler. A finite mixture density smoother informs a set of parametric distributions via moment matching and an information criterion arbitrates between competing candidates. Algorithms underlying our method find a natural nest within the EpiLPS package, which has been extended to cover estimation of incubation times. Various simulation scenarios accounting for different levels of data coarseness are considered with encouraging results. Applications to real data on COVID-19, MERS and Mpox reveal results that are in alignment with what has been obtained in recent studies. The proposed flexible approach is an interesting alternative to classic Bayesian parametric methods for estimation of the incubation distribution.

The origin and evolution of wide Jupiter mass binary objects in young stellar clusters

The recently observed population of 540 free-floating Jupiter-mass objects, including 40 dynamically soft pairs, and two triples, in the Trapezium cluster have raised interesting questions on their formation and evolution. We test various scenarios for the origin and survivability of these free floating Jupiter-mass objects and Jupiter-mass Binary Objects (JuMBOs) in the Trapezium cluster. The numerical calculations are performed by direct NN-body integration of the stars and planets in the Trapezium cluster starting with a wide variety of planets in various configurations. We discuss four models: \mathcal{SPP}𝒮𝒫𝒫, in which selected stars have two outer orbiting Jupiter-mass planets; \mathcal{SPM}𝒮𝒫ℳ, where selected stars are orbited by Jupiter-mass planet-moon pairs; \mathcal{ISF}ℐ𝒮ℱ in which JuMBOs form in situ with the stars, and \mathcal{FFC}ℱℱ𝒞, where we introduce a population of free-floating single Jupiter-mass objects, but no initialised binaries. Models \mathcal{FFC}ℱℱ𝒞 and \mathcal{SPP}𝒮𝒫𝒫 fail to produce enough JuMBOs. Models \mathcal{SPM}𝒮𝒫ℳ can produce sufficient free-floaters and JuMBOs, but requires unusually wide orbits for the planet-moon system around the star. The observed JuMBOs and free-floating Jupiter-mass objects in the Trapezium cluster are best reproduced if they formed in pairs and as free-floaters together with the other stars in a smooth (Plummer) density profile with a virial radius of \sim 0.5∼0.5pc. A fractal (with fractal dimension 1.6) stellar density distribution also works, but requires relatively recent formations (⪆ 0.2⪆0.2Myr after the other stars formed) or a high (⪆ 50⪆50%) initial binary fraction. This would make the primordial binary fraction of JuMBOs even higher than the already large observation fraction of \sim 8∼8% (42/540). The fraction of JuMBOs will continue to drop with time, and the lack of JuMBOs in Upper Scorpius could then result in its higher age, causing more JuMBOs to be ionized. We then also predict that the interstellar density of Jupiter-mass objects (mostly singles with some \sim 2∼2% lucky surviving binaries) is \sim 0.05∼0.05 per pc^{-3}−3 (or around 0.24 per star).

A Chua’s Chaotic Chirp Spread-Spectrum Power Spectral Homogenization Strategy Based on Distribution Transformation

When utilizing high-dimensional chaotic signals for frequency modulation, achieving a uniformly distributed power spectrum is a challenging task. This paper addresses this challenge by proposing a power spectrum homogenization strategy based on distribution transformation. The strategy transforms the task of achieving a uniformly distributed power spectrum in frequency modulation of high-dimensional chaotic signals to solve and equalize the probability density function of the chaotic signals, thereby further enhancing the ability of high-dimensional chaotic signals to suppress electromagnetic interference. Firstly, the difficulty of obtaining a smooth probability density function of chaotic modulation signals is solved using the kernel density estimation algorithm. Then, a distribution transformation algorithm is proposed to convert non-uniformly distributed chaotic modulation signals into uniformly distributed chaotic modulation signals. By using uniformly distributed chaotic modulation signals for frequency modulation, the objective of power spectrum equalization is achieved. Finally, taking the Chua’s chaotic signal as an example, the effectiveness of the proposed strategy is verified using an experimental platform based on a digital signal processor-controlled active clamping flyback converter.

Phase space geometry of general quantum energy transitions

The mixed density operator for coarsegrained eigenlevels of a static Hamiltonian is represented in phase space by the spectral Wigner function, which has its peak on the corresponding classical energy shell. The action of trajectory segments along the shell determine the phase of the Wigner oscillations in its interior. The classical transitions between any pair of energy shells, driven by a general external time dependent Hamiltonian, also have a smooth probability density. It is shown here that a further contribution to the transition between the corresponding pair of coarsegrained energy levels, which oscillates with either energy, or the driving time, is determined by four trajectory segments (two in the pair of energy shells and two generated by the driving Hamiltonian) that join exactly to form a closed compound orbit (CCO). In its turn, this sequence of segments belongs to the semiclassical expression of a compound unitary operator that combines four quantum evolutions: a pair generated by the static internal Hamiltonian and a pair generated by the driving Hamiltonian. The CCOs are shown to belong to continuous families, which are initially seeded at points where the classical flow generated by both Hamiltonians commute.

Variable transformations in combination with wavelets and ANOVA for high-dimensional approximation

We use hyperbolic wavelet regression for the fast reconstruction of high-dimensional functions having only low-dimensional variable interactions. Compactly supported periodic Chui-Wang wavelets are used for the tensorized hyperbolic wavelet basis on the torus. With a variable transformation, we are able to transform the approximation rates and fast algorithms from the torus to other domains. We perform and analyze scattered data approximation for smooth but arbitrary density functions by using a least squares method. The corresponding system matrix is sparse due to the compact support of the wavelets, which leads to a significant acceleration of the matrix vector multiplication. For non-periodic functions, we propose a new extension method. A proper choice of the extension parameter together with the piecewise polynomial Chui-Wang wavelets extends the functions appropriately. In every case, we are able to bound the approximation error with high probability. Additionally, if the function has a low effective dimension (i.e., only interactions of a few variables), we qualitatively determine the variable interactions and omit ANOVA terms with low variance in a second step in order to decrease the approximation error. This allows us to suggest an adapted model for the approximation. Numerical results show the efficiency of the proposed method.

Evaluation of Neuromuscular Morphometry of the Vaginal Wall Using Protein Gene Product 9.5 (Pgp 9.5) and Smooth Muscle α-Actin (Sma) in Patients with Posterior Vaginal Wall Prolapse.

Background and Objectives: This study aims to compare the neuromuscular structure of the vagina in women with posterior vaginal wall prolapse with the neuromuscular structure of the vagina in women without prolapse, to determine the difference, and to demonstrate the role of neuromuscular structure in the physiopathology of prolapse. Materials and Methods: In this prospective study, women aged between 40 and 75 years who had not undergone any vaginal surgery and had not undergone any abdominal prolapse surgery were included. Thirty-one women diagnosed with rectocele on examination were included in the study group. Thirty-one patients who underwent vaginal intervention and hysterectomy for reasons other than rectocele (colposcopy, conization, etc.) without anterior or posterior wall prolapse were included in the control group. Biopsy material was obtained from the epithelium of the posterior wall of the vagina, including the fascia that fits the Ap point. Immunohistochemical staining with Protein Gene Product 9.5 and smooth muscle α-actin was performed in the pathology laboratory. The epithelial thickness measurement and smooth muscle density parameters obtained with these immunohistochemical stainings were compared between the two groups. The collected data were analyzed using the SPSS 23 package program. p values less than 0.05 were considered statistically significant. Results: In the control group, muscle thickness and the number of nerves per mm2 of fascia were statistically significantly higher than in the study group (p < 0.05). Conclusions: We found that smooth muscle tissue and the number of nerves per mm2 of fascia were decreased in posterior vaginal wall prolapse compared to the general population. Based on the correlation coefficients, age was the parameter that most affected the degree of prolapse, followed by parity, number of live births, and number of vaginal deliveries.

Discrete and continuous mathematical models of sharp-fronted collective cell migration and invasion.

Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion are routinely employed and known to capture key experimental observations, linear diffusion fails to predict well-defined sharp fronts that are often observed experimentally. This observation has motivated the use of nonlinear degenerate diffusion; however, these nonlinear models and the associated parameters lack a clear biological motivation and interpretation. Here, we take a different approach by developing a stochastic discrete lattice-based model incorporating biologically inspired mechanisms and then deriving the reaction-diffusion continuum limit. Inspired by experimental observations, agents in the simulation deposit extracellular material, which we call a substrate, locally onto the lattice, and the motility of agents is taken to be proportional to the substrate density. Discrete simulations that mimic a two-dimensional circular barrier assay illustrate how the discrete model supports both smooth and sharp-fronted density profiles depending on the rate of substrate deposition. Coarse-graining the discrete model leads to a novel partial differential equation (PDE) model whose solution accurately approximates averaged data from the discrete model. The new discrete model and PDE approximation provide a simple, biologically motivated framework for modelling the spreading, growth and invasion of cell populations with well-defined sharp fronts. Open-source Julia code to replicate all results in this work is available on GitHub.

Variants of Bernstein’s theorem for variational integrals with linear and nearly linear growth

AbstractUsing a Caccioppoli-type inequality involving negative exponents for a directional weight we establish variants of Bernstein’s theorem for variational integrals with linear and nearly linear growth. We give some mild conditions for entire solutions of the equation $$\begin{aligned} {\text {div}} \Big [Df(\nabla u)\Big ] = 0 \,, \end{aligned}$$ div [ D f ( ∇ u ) ] = 0 , under which solutions have to be affine functions. Here f is a smooth energy density satisfying $$D^2 f&gt;0$$ D 2 f &gt; 0 together with a natural growth condition for $$D^2 f$$ D 2 f .

Wasserstein upper bounds of [formula omitted]-norms for multivariate densities in Besov spaces

While the total variation between two probability measures cannot be bounded by Wasserstein metrics in general, it is possible if they possess smooth densities. More generally, we demonstrate that Lp-distances between densities in Besov spaces can be bounded by powers of the Wasserstein metrics.

Using strain hardening to predict the stress crack resistance of unaged and aged smooth black HDPE geomembranes

The correlation between the single-point notched constant tensile load-stress crack resistance (SP-NCTL SCR) Test (ASTM D5397; Appendix) of smooth high density polyethylene (HDPE) geomembranes and their strain hardening modulus is investigated for both unaged and aged specimens. The strain hardening modulus was calculated based on the (force-elongation) raw data from the tensile strength test conducted at room temperature using Type IV and/or Type V specimens (as described in ASTM D638) at a test speed of 7 mm/min. Three different approaches are used to define the strain hardening modulus and to compare the representative strain hardening modulus with the SP-NCTL SCR. It is shown that the high test speed of 7 mm/min performed at room temperature provides a good correlation with the SP-NCTL SCR of different smooth black HDPE geomembranes. Additionally, the proposed method using Type V specimens predicts the SCR values during oxidative degradation close to those observed using the SP-NCTL SCR test. For the resins and conditions examined, the proposed method provides a quick assessment of the SP-NCTL SCR of unaged geomembranes when the SP-NCTL SCR takes long testing times (e.g., >1000 h) or in jurisdictions in which the use of surfactants becomes prohibited to allow conducting the SP-NCTL SCR tests.

Extension of finite particle method simulating thermal-viscoelastic flow and fluid–rigid body interactional process in weakly compressible smoothed particle hydrodynamics scheme

In computational non-Newtonian fluid dynamics, heat transfer has obvious effects on motions of viscoelastic fluids, mechanical mechanism of elasticity, and flow regimes. This study suggests an extended numerical scheme of smoothed particle hydrodynamics and finite particle method within density smoothing (SPH_DSFPM), which involves the discretization of smoothed particle hydrodynamics (SPH) and finite particle method (FPM) within density smoothing (DS) in the weakly compressible flow scheme. A corrected particle shifting technique is incorporated to eliminate tensile instability and inhomogeneity near solid boundaries. A corrected dynamic solid coupled boundary is introduced to deal with casting molding within high-pressure operations, which has a good compatibility between virtual particle method and repulsive force model. Numerical results show that the present scheme has the nearly lower relative error (0.5%) than conventional SPH (2.6%) in the case of evolutionary thermal-viscoelastic Poiseuille flow and heat effects have active influences on velocity, pressure variations for viscoelastic fluid flow around periodic circular cylinders. Three different printing modes of moving printers significantly generate into differentiated forming regimes through high-pressure extrusion. Adaptive particle distributions possess robust flow evolutions, by which the shocked jets can be tracked well and the sinking velocities of wedge entering into solutions can be numerically probed well considering different cuspidal biting angles. In the case of macroscopic fluid–rigid body interactions, the statistical degree of deviation on probed forces with experiments is relatively 4.35% and that is 12.5% for SPH. The proposed numerical scheme has a good performance on improved accuracy, convergence, and stability for simulating transient thermal-viscoelastic flows.

Can towed-streamer seismic data be used for elastic wave imaging? Synthetic and field data examples

In marine seismic exploration, towed-streamer seismic data acquisition stands out as a prevalent and economical approach. These data record scalar pressure and capture P waves, including those that are converted from subseabed S waves. Theoretically, towed-streamer seismic data can be used to reconstruct S wavefields for elastic wave imaging via backward extrapolation. Our research applies an acoustic-elastic coupled equation that includes a pressure term to perform elastic reverse time migration (ERTM), using the pressure seismic data as the boundary condition for backward extrapolation. The feasibility of using towed-streamer seismic data for elastic wave imaging of complex subsurface structures is confirmed through synthetic and field data examples. The investigation demonstrates how the smoothness of velocity and density models impacts the quality of ERTM using towed-streamer seismic data. We find that using smooth velocity and density models for elastic wave imaging can enhance imaging quality by using transmitted S waves. Furthermore, certain nonphysical S waves generated during backward extrapolation can contribute to PS images, as evidenced by a synthetic data example. Overall, the results indicate that the towed-streamer seismic data for elastic wave imaging have potential in marine seismic exploration. Moving forward, it is crucial to focus on refining the quality of PS images and reducing artifacts caused by the backward-extrapolated nonphysical waves.

Higher order phase-field modeling of brittle fracture via isogeometric analysis

AbstractThe evolution of brittle fracture in a material can be conveniently investigated by means of the phase-field technique introducing a smooth crack density functional. Following Borden et al. (2014), two distinct types of phase-field functional are considered: (i) a second-order model and (ii) a fourth-order one. The latter approach involves the bi-Laplacian of the phase field and therefore the resulting Galerkin form requires continuously differentiable basis functions: a condition we easily fulfill via Isogeometric Analysis. In this work, we provide an extensive comparison of the considered formulations performing several tests that progressively increase the complexity of the crack patterns. To measure the fracture length necessary in our accuracy evaluations, we propose an image-based algorithm that features an automatic skeletonization technique able to track complex fracture patterns. In all numerical results, damage irreversibility is handled in a straightforward and rigorous manner using the Projected Successive Over-Relaxation algorithm that is suitable to be adopted for both phase-field formulations since it can be used in combination with higher continuity isogeometric discretizations. Based on our results, the fourth-order approach provides higher rates of convergence and a greater accuracy. Moreover, we observe that fourth- and second-order models exhibit a comparable accuracy when the former methods employ a mesh-size approximately two times larger, entailing a substantial reduction of the computational effort.