Diffuse Functions Research Articles

Multifeature Contrast Enhancement Algorithm for Digital Media Images Based on the Diffusion Equation

This paper studies the processing of digital media images using a diffusion equation to increase the contrast of the image by stretching or extending the distribution of luminance data of the image to obtain clearer information of digital media images. In this paper, the image enhancement algorithm of nonlinear diffusion filtering is used to add a velocity term to the diffusion function using a coupled denoising model, which makes the diffusion of the original model smooth, and the interferogram is solved numerically with the help of numerical simulation to verify the denoising processing effect before and after the model correction. To meet the real-time applications in the field of video surveillance, this paper focuses on the optimization of the algorithm program, including software pipeline optimization, operation unit balancing, single instruction multiple data optimization, arithmetic operation optimization, and onchip storage optimization. These optimizations enable the nonlinear diffusion filter-based image enhancement algorithm to achieve high processing efficiency on the C674xDSP, with a processing speed of 25 posts per second for 640 × 480 size video images. Finally, the significance means a value of super pixel blocks is calculated in superpixel units, and the image is segmented into objects and backgrounds by combining with the Otsu threshold segmentation algorithm to mention the image. In this paper, the proposed algorithm experiments with several sets of Kor Kor resolution remote sensing images, respectively, and the Markov random field model and fully convolutional network (FCN) algorithm are used as the comparison algorithm. By comparing the experimental results qualitatively and quantitatively, it is shown that the algorithm in this paper has an obvious practical effect on contrast enhancement of digital media images and has certain practicality and superiority.

Approach with DFT for non-linear optical properties of organic molecular complexes

Studies of nonlinear optical phenomena are prominent in research and technology for their molecular and electronic properties. In particular, properties of organic molecules gain sufficient impact in transition arising between coherent states influencing intrinsic geometry that occur due to interactions with stability. In the present work, distinct benzaldehydes, the host molecules H1and H2 are influenced by guest molecule p-chloro-aniline (G1) that changes the geometry for molecular and electronic properties using density functional theory (DFT). The method is implemented using B3LYP hybrid method that focuses on nonlinear phenomena for molecular geometry, vibrational frequencies, and quantum descriptors with the basis set 6-311++** of Gaussian 16 package and Gaussview 6.1 for analysis as polarizing and diffusion functions. Studies of these optimized structures provide Fourier Transform Infrared Spectra (FTIR) and Fourier Transform Raman spectra. The Molecular mechanism is attributed to changes in wavenumbers between host and guest molecules indicating the formation of bonding. Studies with Raman spectra indicated the presence of a shift towards the lower side in complexes with increased intensities. Quantum mechanical descriptors influenced factors responsible for the transition between coherent states, influencing non-linear optical properties.

Spatial populations with seed-bank: well-posedness, duality and equilibrium

We consider a system of interacting Fisher-Wright diffusions with seed-bank. Individuals live in colonies and are subject to resampling and migration as long as they are active. Each colony has a structured seed-bank into which individuals can retreat to become dormant, suspending their resampling and migration until they become active again. As geographic space labeling the colonies we consider a countable Abelian group G endowed with the discrete topology. The key example of interest is the Euclidean lattice G= Zd, d∈N. Our goal is to classify the long-time behaviour of the system in terms of the underlying model parameters. In particular, we want to understand in what way the seed-bank enhances genetic diversity. We introduce three models of increasing generality, namely, individuals become dormant: (1) in the seed-bank of their colony; (2) in the seed-bank of their colony while adopting a random colour that determines their wake-up time; (3) in the seed-bank of a random colony while adopting a random colour. The extension in (2) allows us to model wake-up times with fat tails while preserving the Markov property of the evolution. The extension in (3) allows us to place individuals in different colony when they become dormant. For each of the three models we show that the system of continuum stochastic differential equations, describing the population in the large-colony-size limit, has a unique strong solution. We also show that the system converges to a unique equilibrium depending on a single density parameter that is determined by the initial state, and exhibits a dichotomy of coexistence (= locally multi-type equilibrium) versus clustering (= locally mono-type equilibrium) depending on the parameters controlling the migration and the seed-bank. The seed-bank slows down the loss of genetic diversity. In model (1), the dichotomy between clustering and coexistence is determined by migration only. In particular, clustering occurs for recurrent migration and coexistence occurs for transient migration, as for the system without seed-bank. In models (2) and (3), an interesting interplay between migration and seed-bank occurs. In particular, the dichotomy is affected by the seed-bank when the wake-up time has infinite mean. For instance, for critically recurrent migration the system exhibits clustering for finite mean wake-up time and coexistence for infinite mean wake-up time. Hence, at the critical dimension for the system without seed-bank, new universality classes appear when the seed-bank is added. If the wake-up time has a sufficiently fat tail, then the seed-bank determines the dichotomy and migration has no effect at all. The presence of the seed-bank makes the proof of convergence to a unique equilibrium a conceptually delicate issue. By combining duality arguments with coupling techniques, we show that our results also hold when we replace the Fisher-Wright diffusion function by a more general diffusion function, drawn from an appropriate class.

Long-time behavior of a size-structured population model with diffusion and delayed birth process

<p style='text-indent:20px;'>This work focuses on the long time behavior for a size-dependent population system with diffusion and Riker type birth function. Some dynamical properties of the considered system is investigated by using <inline-formula><tex-math id="M1">\begin{document}$ C_0 $\end{document}</tex-math></inline-formula>-semigroup theory and spectral analysis arguments. Some sufficient conditions are obtained respectively for asymptotical stability, asynchronous exponential growth at the null equilibrium as well as Hopf bifurcation occurring at the positive steady state of the system. In the end several examples and their simulations are also provided to illustrate the achieved results.</p>

Threshold reweighted Nadaraya–Watson estimation of jump-diffusion models

<p style='text-indent:20px;'>In this paper, we propose a new method to estimate the diffusion function in the jump-diffusion model. First, a threshold reweighted Nadaraya–Watson-type estimator is introduced. Then, we establish asymptotic normality for the estimator and conduct Monte Carlo simulations through two examples to verify the better finite-sampling properties. Finally, our estimator is demonstrated through the actual data of the Shanghai Interbank Offered Rate in China.</p>

A Deterministic Approximation to Neural SDEs.

Neural Stochastic Differential Equations (NSDEs) model the drift and diffusion functions of a stochastic process as neural networks. While NSDEs are known to make accurate predictions, their uncertainty quantification properties have been remained unexplored so far. We report the empirical finding that obtaining well-calibrated uncertainty estimations from NSDEs is computationally prohibitive. As a remedy, we develop a computationally affordable deterministic scheme which accurately approximates the transition kernel, when dynamics is governed by a NSDE. Our method introduces a bidimensional moment matching algorithm: vertical along the neural net layers and horizontal along the time direction, which benefits from an original combination of effective approximations. Our deterministic approximation of the transition kernel is applicable to both training and prediction. We observe in multiple experiments that the uncertainty calibration quality of our method can be matched by Monte Carlo sampling only after introducing high computational cost. Thanks to the numerical stability of deterministic training, our method also improves prediction accuracy.

Pixel Difference Function and Local Entropy-Based Speckle Reducing Anisotropic Diffusion

Speckles destroy the texture details of synthetic aperture radar (SAR) images, thereby constraining their high-precision application. Speckle suppression and edge preservation are two aspects that need to be balanced in despeckling. Although a conventional anisotropic diffusion filter can theoretically achieve this balance, it still triggers many edge losses. To better improve the balance, a novel anisotropic diffusion (AD) filter based on the pixel difference function and local entropy is proposed. The proposed filter utilizes a pixel difference function to update the original diffusion function of the AD filter and introduces local entropy to recover the edge loss from the ratio image generated by noisy and filtered images. In addition, a neighborhood weighting approach and a new adaptive iterative rule are proposed for better AD filtering. Simulated data and real SAR images were applied to evaluate the performance of the proposed algorithm. Experimental results show that the proposed filter both effectively smooths speckles and reduces edge loss. Furthermore, the effectiveness and superiority of the proposed method were confirmed by comparison with other state-of-the-art methods.

Bifurcation Points of Periodic Triangular Patterns Obtained in Reaction-Diffusion System with Anisotropic Diffusion

Turing demonstrated that spatially heterogeneous patterns can be self-organized, when the two substances interact locally and diffuse randomly. Turing systems have been applied not only to explain patterns observed within the biological and chemical fields, but also to develop image information processing tools. In a twin study, to evaluate the V-shaped bundle of the inner ear outer hair, we developed a method that utilizes a reaction-diffusion system with anisotropic diffusion that exhibited triangular patterns with the introduction of a certain anisotropy strength. In this study, we explored the parameter range over which these periodic triangular patterns were obtained. First, we defined an index for triangular clearness, TC. Triangular patterns can be obtained by introducing a large anisotropy δ, but the range of δ depends on the diffusion coefficient. We found an explanatory variable that can explain the change in TC based on a heuristic argument of the relative distance of the pitchfork bifurcation point between the maximum and minimum anisotropic diffusion function values. Clear periodic triangular patterns were obtained when the distance between the minimum anisotropic function value and pitchfork bifurcation point was over 2.5 times the distance to the anisotropic diffusion function maximum value. By changing the diffusion coefficients or the reaction terms, we further confirmed the accuracy of this condition using computer simulation. Its relevance to diffusion instability has also been discussed.

Some comparison results and a partial bang-bang property for two-phases problems in balls

<abstract><p>In this paper, we present two type of contributions to the study of two-phases problems. In such problems, the main focus is on optimising a diffusion function $ a $ under $ L^\infty $ and $ L^1 $ constraints, this function $ a $ appearing in a diffusive term of the form $ -{{\nabla}} \cdot(a{{\nabla}}) $ in the model, in order to maximise a certain criterion. We provide a parabolic Talenti inequality and a partial bang-bang property in radial geometries for a general class of elliptic optimisation problems: namely, if a radial solution exists, then it must saturate, at almost every point, the $ L^\infty $ constraints defining the admissible class. This is done using an oscillatory method.</p></abstract>

Application of Image Denoising Method Based on Two-Way Coupling Diffusion Equation in Public Security Forensics

This paper uses the web live broadcast and on-demand platform based on the B/S architecture as the application side and designs a video image forensic system that can meet multiple police types and multiple application scenarios. The system uses mobile phones as the video image capture terminal to solve the problem of rapid response and concealment and uses 5G communication technology as the transmission medium to solve the problem of device mobility and link maintenance. The problem of diversification of the use and application modes of multiple police types is solved; the video image evidence is managed in a centralized storage, audit, and export method, and the security and authenticity of the evidence are solved. While the system realizes a series of functions such as the collection, transmission, storage, and application of video image evidence, it also realizes the application-side video image live broadcast function according to actual work needs and solves the large-scale case command and decision-making problem that has been plagued by public security organs. In order to remove the noise in the public security forensic images and to smooth the noise while retaining the details of the image, this paper proposes a denoising algorithm based on the two-way coupling diffusion equation. By improving the second-order partial differential equation, a new diffusion function with better diffusion effect than the original model is constructed. We combined the adaptive edge threshold and stop criterion to establish a new denoising algorithm model, which can get better denoising results. When the noise level is low, the PSNR value and SSIM value of several denoising methods are relatively ideal, and the result is at a higher level, the denoising picture effect is better, and there is no obvious incomplete noise removal or detail problems. As the noise level increases, the denoising results will gradually decrease, and the effects will also vary to different degrees. When the noise intensity increases, visually, it can be clearly seen that the two-way coupled diffusion equation and DnCNN have better denoising effects. When the noise level is high, the two-way coupled diffusion equation network is used to use the clear image and the denoised image for indistinguishable calculation. The method in this paper almost retains all the texture details in the clear image, and there are almost no artifacts and images. On the other hand, the color of the image after denoising by the method in this paper is more vivid, and it is closer to the target picture in terms of picture definition and tone, the denoising effect is ideal, and the generated image has a higher degree of restoration. Compared with the residual GAN, the two-way coupling diffusion equation network converges faster and the network performance is improved.

Evaluation of oxygen-vacancy concentration through simulated hydrogen diffusion in amorphous In-Ga-Zn-O

A multiscale approach is presented to calculate the hydrogen diffusion in amorphous In-Ga-Zn-O (a-IGZO). Based on the fact that the presence of oxygen vacancy (VO) defects suppresses the hydrogen diffusion in a-IGZO, the simulated H diffusion depth is utilized to evaluate the VO concentration (nVo). The kinetic Monte Carlo (kMC) simulation is carried out to obtain the depth profiles of H diffusion in a-IGZO, which uses input of the H migration energy barriers (EA) calculated within the density functional theory (DFT) method. The DFT calculations showed that when H occupies the VO defects, its EA becomes higher than that of the interstitial H, which eventually suppresses H diffusion. The H diffusion function depending on nVo and temperature, fD(nVo,T), is readily obtained fitting the complementary error function to the simulated H diffusion profile. It is observed that fD(nVo,T) can closely reproduce the experimentally measured H diffusion from literature with nVo being comparable to the measured carrier concentration that can be speculated as the upper limit of nVo. The properties of H diffusion in a-IGZO are examined in detail to address the application of the presented approach for estimation of nVo.

Improved Intra-Pixel Sensitivity Characterization Based on Diffusion and Coupling Model for Infrared Focal Plane Array Photodetector.

The high-precision characterization of the intra-pixel sensitivity (IPS) for infrared focal plane array (FPA) photodetector is of great significance to high-precision photometry and astrometry in astronomy, as well as target tracking in under-sampled remote sensing images. The discrete sub-pixel response (DSPR) model and fill factor model have been used for IPS characterization in some studies. However, these models are incomplete and lack the description of physical process of charge diffusion and capacitance coupling, leading to the inaccuracy of IPS characterization. In this paper, we propose an improved IPS characterization method based on the diffusion and coupling physical (DCP) model for infrared FPA photodetector, which considering the processes of generation and collection of the charge, can improve the accuracy of IPS characterization. The IPS model can be obtained by convolving the ideal rectangular response function with the charge diffusion function and the capacitive coupling function. Then, the IPS model is convolved with the beam spot profile to obtain the beam spot scanning response model. Finally, we calculate the parameters of IPS by fitting the beam spot scanning response map with the proposed DCP model based on the Trust-Region-Reflective algorithm. Simulated results show that when using a 3 μm beam spot to scan, the error of IPS characterization based on DCP model is 0.63%, which is better than that of DSPR model’s 3.70%. Experimental results show that the fitting error of the beam spot scan response model based on DCP model is 4.29%, which is better than that of DSPR model’s 8.31%.

Asymptotic properties of penalized spline estimators in concave extended linear models: Rates of convergence

This paper develops a general theory on rates of convergence of penalized spline estimators for function estimation when the likelihood functional is concave in candidate functions, where the likelihood is interpreted in a broad sense that includes conditional likelihood, quasi-likelihood and pseudo-likelihood. The theory allows all feasible combinations of the spline degree, the penalty order and the smoothness of the unknown functions. According to this theory, the asymptotic behaviors of the penalized spline estimators depends on interplay between the spline knot number and the penalty parameter. The general theory is applied to obtain results in a variety of contexts, including regression, generalized regression such as logistic regression and Poisson regression, density estimation, conditional hazard function estimation for censored data, quantile regression, diffusion function estimation for a diffusion type process and estimation of spectral density function of a stationary time series. For multidimensional function estimation, the theory (presented in the Supplementary Material) covers both penalized tensor product splines and penalized bivariate splines on triangulations.

Image denoising for magnetic resonance imaging medical images using improved generalized cross‐validation based on the diffusivity function

AbstractVarious image denoising algorithms have been developed for medical imaging. But some disadvantages have been found, including the block effect, which increases smoothing, and the loss of image detail. Using the statistical properties of observed noisy images, we propose a new diffusivity function‐based partial differential equation method for image denoising. This model incorporates a Quaternion Wavelet Transform for the generation of the various noisy image coefficients, an improved generalized cross‐validation function for generating the optimal threshold value via the soft threshold function, and a new diffusivity function for controlling the diffusion process. The fourth‐order PDE diffusivity function, which is presented in this article, is a novel diffusion coefficient that is more effective at removing noise and preserving edges than previous approaches. Finally, the performance of the proposed method is evaluated using the peak signal‐to‐noise ratio, mean square error, structural similarity index, and comparisons to other traditional methods.

Serum levels of laminin and von Willebrand factor in COVID-19 survivors 6 months after discharge

ObjectivesThe aim of this study was to evaluate the clinical characteristics, pulmonary diffusion function, chest computed tomography (CT), and serum lung cell damage indicators of coronavirus disease 2019 (COVID-19) survivors 6 months after discharge. MethodsData of COVID-19 survivors discharged from hospital between January 21, 2020 and January 11, 2021 and healthy controls were collected. Serum levels of surfactant protein D (SP-D), the receptor for advanced glycation end products (RAGE), laminin, and von Willebrand factor (vWF) were measured in the healthy controls and COVID-19 survivors 6 months after discharge. The relationships between serum lung cell damage indicator levels and various parameters were explored. ResultsFifty-two COVID-19 survivors (31 with non-severe disease and 21 with severe disease) and 30 controls were included. Serum levels of laminin in COVID-19 survivors 6 months after discharge were significantly higher than those in the controls. The increase was more significant in elderly and female patients. Serum levels of RAGE and vWF were not statistically different from those of the controls. However, 6 months after discharge, COVID-19 survivors with abnormal chest CT and those in the severe group had higher vWF levels. ConclusionsCOVID-19 patients had abnormal lung injury indicators 6 months after discharge. The recovery time after infection is currently unknown, and long-term observation is required.

Noise Data Removal and Image Restoration Based on Partial Differential Equation in Sports Image Recognition Technology

With the rapid development of image processing technology, the application range of image recognition technology is becoming more and more extensive. Processing, analyzing, and repairing graphics and images through computer and big data technology are the main methods to obtain image data and repair image data in complex environment. Facing the low quality of image information in the process of sports, this paper proposes to remove the noise data and repair the image based on the partial differential equation system in image recognition technology. Firstly, image recognition technology is used to track and obtain the image information in the process of sports, and the fourth-order partial differential equation is used to optimize and process the image. Finally, aiming at the problem of low image quality and blur in the transmission process, denoising is carried out, and image restoration is studied by using the adaptive diffusion function in partial differential equation. The results show that the research content of this paper greatly improves the problems of blurred image and poor quality in the process of sports and realizes the function of automatically tracking the target of sports image. In the image restoration link, it can achieve the standard repair effect and reduce the repair time. The research content of this paper is effective and applicable to image processing and restoration.

ZORA double zeta basis sets for fifth row elements: Application in studies of electronic structures of atoms and molecules

Segmented all-electron basis set of double zeta valence quality plus polarization functions (DZP) to be used with the zero-order regular approximation (ZORA) scalar relativistic Hamiltonian was developed for the elements Cs, Ba, La, and from Hf to Rn. This set was augmented with diffuse functions for the purpose of describing electrons distant from atomic nuclei. Using the ZORA-B3LYP method, some atomic and molecular properties are computed. Benchmark theoretical results and experimental data were used to evaluate the performance of the DZP-ZORA and ADZP-ZORA basis sets. Despite their small sizes, these sets have proven to be accurate and reliable and can also be used in property calculations involving electrons not only from the outer shells, but also from the inner shells. Comparison of second order Douglas-Kroll-Hess and ZORA results was made.

Phase congruency-based filtering approach combined with a convolutional network for lung CT image analysis

ABSTRACT Computed tomography (CT) imaging was confirmed as one of the important evolving radiological features of disease diagnosis. In this work, we propose an image filtering method for CT images that fuses the spatial and the transform domain. Filters in the transform domain work well in restoring low-contrast details that are usually smoothed by spatial domain filters. The new filter is based on a modified anisotropic diffusion approach combined with the phase congruency (PC) feature. The PC feature is a scale-invariant compared to the classical gradient, where weak edges are usually omitted and undetected with gradient-based feature detectors. This feature is incorporated in the diffusion function to enhance image edges while eliminating noise and texture background. In a further step, a U-net convolutional network is used to segment the lung-infected area. Comparative tests and results show the efficiency of our method, which permits to enhance image features while removing noise perfectly.

Reexamination of the ground-state Born-Oppenheimer Yb2 potential

The precision of the photoassociation spectroscopy of Yb dimer in degenerate gases is enough to improve the constraints on the new short-range gravity-like forces if the theoretical knowledge of the Born-Oppenheimer interatomic potential and non-Born-Oppenheimer interactions is refined [M. Borkowski et al. Sci. Rep. A {\bf 9}, 14807 (2019)]. The ground-state interaction potential of ytterbium dimer is investigated at the eXact 2-component core-correlated CCSD(T) level of {\it ab initio} theory in the complete basis set limit with extensive augmentation by diffuse functions. For the small basis set the comparison is made with the four-component relativistic finite-nuclei CCSD(T) calculations to identify the contraction of the dimer bond length as the main unrecoverable consequence of the scalar-relativistic approximation. Empirical constraint on the number of bound vibrational energy levels of the $^{174}$Yb$_2$ dimer is accounted for by representing the global {\it ab initio}-based Born-Oppenheimer potential with the model semianalytical function containing the scale and shift parameters. The results support the previous evaluation of the Yb dimer potentials from the photoassociation spectroscopy data and provide an accurate and flexible reference for future refinement of the constraints on the short-range gravity-like forces by ultracold atomic spectroscopy.

The effect of midbond functions on interaction energies computed using MP2 and CCSD(T).

In this article we use MP2 and CCSD(T) calculations for the A24 and S66 data sets to explore how midbond functions can be used to generate cost effective counterpoise corrected supramolecular interaction energies of noncovalent complexes. We use the A24 data set to show that the primary role of midbond functions is not to approach the complete basis set limit, but rather to ensure a balanced description of the molecules and the interaction region (unrelated to the basis set superposition error). The need for balance is a consequence of using atom centered basis sets. In the complete basis set limit, the error will disappear, but reaching the complete basis set limit is not feasible beyond small systems. For S66 we investigate the need for increasing the number of midbond centers. Results show that adding a second midbond center increases the accuracy, but the effect is secondary to changing the atom centered basis set. Further, by comparing calculations using the 3s3p2d1f1g midbond set with using aug-cc-pVDZ and aug-cc-pVTZ as midbond sets, we see that the requirements for the midbond set to be effective, is not just that it contains diffuse functions, but also that high angular momentum functions are included. By comparing two approaches for placing midbond centers we show that results are not particularly sensitive to placement as long as the placement is reasonable.