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Introduction Pyroptosis, also known as inflammatory necrosis, is a programmed cell death caused by inflammation. Multiple studies suggest that Mycobacterium tuberculosis (MTB) infection causes tissue pyroptosis. However, there are currently no protective drugs against inflammatory damage caused by pyroptosis. In this study, the anti-pyroptotic effects of the natural compound Astaxanthin (ASTA) in a simulated pulmonary tuberculosis-associated inflammatory environment were explored. Methods In the established LPS-induced apoptosis co-culture system of MEL-12 cells and RAW246.7 macrophages，we detected the expression of key proteins Caspase4, Caspase11 and Gasdermin D in the pyroptosis pathway.Results The results showed that ASTA was able to maintain the stability of MLE-12 lung epithelial cell numbers in the inflammatory environment established by LPS. But the reason is not to promote cell proliferation, but to inhibit LPS-induced pyroptosis. The results showed that ASTA significantly inhibited the expression of key proteins in the Caspase4/11-Gasdermin D pathway and the release of pyroptosis-related inflammatory mediators. Conclusion Therefore, ASTA inhibits inflammation-induced pyroptosis by inhibiting the G pathway, and has the potential to protect lung tissue from tuberculosis-related inflammatory injury. ASTA, a functional food component, is a promising candidate for protection against tuberculosis-associated inflammatory lung injury.

Binarization has always been a very challenging task for degraded document images because of the variety and complexity of degradations. This paper proposed a nonlinear diffusion equation with selective source for restoration of degraded document images, followed by a binary projection for binarization. The source is composed of two parts: one is used for the restoration of contaminated background, and another is responsible for the fidelity of texts. The evolution equation is numerically solved by the simplest finite differencing. The proposed method is tested on publicly available datasets (DIBCO (Document Image Binarization Competition) 2009–2014, 2016) and is compared with five models based on partial differential equation (PDE). The experimental results show that the proposed method is effective for degraded document images and has achieved generally the best performance of binarization compared to the other five PDE methods.

In this paper, we propose a noise-robust online convolutional coding model for image representation, which can use the noisy images as training data. Then an alternating algorithm is utilized to convert the model into two sub-problems, the image pursuit problem and the dictionary learning problem. For the image pursuit problem, the Gauss elimination method is used to solve the equation set which is derived by the Euler equation and discrete Fourier transform. For the dictionary learning problem, a gradient-descent flow is derived to solve it. Experimental results show that our method can output more meaningful feature representations compared to the related models while the training data was corrupted by Poisson noise.

Sepsis-associated encephalopathy (SAE) is characterized by the activation of inflammatory cascades, in which microglia play a key role. The activation of Recombinant Sirtuin 3 (SIRT3) was shown to significantly reduce the susceptibility of microglia to inflammatory stress. The purpose of this study is to determine whether miRNA-494 can regulate the activation and oxidative stress of SAE microglia through SIRT3.An SAE rat model was established, and the expression of Ionized calcium bindingadaptor molecule-1 (Iba-1) in rat brain tissue was detected by immunohistochemistry. Enzyme-linked immuno sorbent assay was performed to detect the expression of tumor necrosis factor alpha (TNF-α) and interleukin-6 (IL-6) in brain tissue. Real time quantitative PCR was performed to detect the relative expression of SIRT3 and related miRNAs, while Western blot was used to detect the protein expression of SIRT3. Rat microglia cells were culturedThe results showed that the expression of Iba-1 in the brain tissue of the SAE model group increased, and the expression of inflammatory factors TNF-α and IL-6 increased significantly (P0.01). The expression of SIRT3 protein and mRNA in the brain tissue of the SAE model group also significantly increased (P0.05). The relative expression of miRNA-494 in the SAE model group was significantly lower than that in the control group (P0.01). After miRNA-494 was transfected into microglia, cells were treated with lipopolysaccharide. In the miRNA transfection group, the expression levels of TNF-α and IL-6 were significantly lower than those in the negative control (NC) group (P0.01), and the protein expression levels of Iba-1 and SIRT3 were also significantly lower than those in the NC (P0.01).MiRNA-494 may further regulate the activation of microglia in SAE by regulating mitochondrial function, providing basic research data for the development of new SAE treatment methods.

Binarization has always been a challenging problem in document image processing because of various types of degradation. In this paper, we present a nonlinear reaction–diffusion model for binarization of bleed-through document images, which is the Perona–Malik equation involving diffusion coefficient based on structure tensor along with a nonlinear reaction term. The Perona–Malik diffusion is utilized to selectively smooth document images with bleed-through removal. Meanwhile, the nonlinear reaction term takes the responsibility for the desired binarization. In order to solve our model numerically, we develop a parallel–series splitting algorithm by combining finite differencing with two kinds of splitting methods in the literature. Our algorithm is tested on seven publicly available datasets (DIBCO 2009 to 2014 and 2016). The experimental results show that our method averagely outperforms six relevant models for the nineteen document images with bleed-through in the DIBCO series datasets.

This paper presents an adaptive enhancement model with selective smoothing for restoration of degraded document images with blur, noise and bleed-through, which involves adaptive shock filtering and selective diffusion processes. A novel hybrid scheme is developed to solve the proposed model numerically, which combines explicit finite difference and exponential smoothing. Numerical experiments show that the proposed model is very effective for restoration of degraded document images with blur, noise and bleed-through, and has averagely the best performance on the DIBCO (Document Image Binarization Competition) series datasets, compared to five PDE (partial differential equation)-based models for restoration of degraded document images.

Tissue engineering techniques have enabled to replicate the geometrical architecture of native tissues but usually fail to reproduce their exact cellular arrangements during the fabricating process, while it is critical for manufacturing physiologically relevant tissues. To address this problem, a "sewing-like" method of controlling cellular alignment during the fabricating process is reported here. By integrating the stretching step into the fabricating process, a static mechanical environment is created which, in turn, regulates the subsequent cellular alignment, elongation, and differentiation in the generated tissues. With this method, patterned cellular constructs can be fabricated with controlled cellular alignment. Moreover, this method shows a potent capability to fabricate physiologically relevant skeletal muscle constructs in vitro by mechanically inducing myoblast fusion and maturation. As a potential clinical application, aligned myofibers are directly fabricated onto injured muscles in vivo, which repair the damaged tissues effectively. This study shows that the "sewing-like" method can produce engineered tissues with precise control of cellular arrangements and more clinically viable functionalities. This study was supported by the Major International Cooperation Project of National Natural Science Foundation of China (No. 62120106004) and the Key R&D project of Ministry of Science and Technology of China (No. 2021YFB3200801).

BACKGROUND: China ranks second in the incidence of tuberculosis (TB), and the virulence and infectivity of Mycobacterium tuberculosis (M.tb) in different lineages are different. The variation of virulence genes in the M.tb regions of difference (RD) may be the reason for differences in pathogenicity. Studying the relationship between virulence gene mutations in the RD region of clinical strains of M.tb and TB relapse can provide basic data for the study of TB prevention and control. METHODS: A total of 155 M.tb clinical strains were collected in Kashgar Prefecture. Whole-genome sequencing (WGS) was conducted, and mutations in virulence genes in the M.tb RD region were analyzed. The maximum likelihood method was implemented using IQ-TREE software. Logistic regression was used to analyze the relationship between lineage, RD region virulence gene variation, and patient relapse. RESULTS: The 155 strains of M.tb in Kashgar Prefecture belong to 3 M.tb lineages: L2 (45.80%), L3 (32.90%), and L4 (21.30%). In relapsed patients, L2 (70.83%, 17/24) was significantly higher than the other lineages (29.17%, 7/24; P

In this paper, we propose a variational level set model for multiscale image segmentation that can extract desired object from the background under various scales. The new model consists of three terms: A boundary extraction term, a regularization term and a multiscale representation term. The boundary extraction term is based on the Chan–Vese (CV) functional, which drives the active contour toward the boundaries of the objects. The regularization term penalizes the length of the active contour and keeps the level set function close to a signed distance function , which enables the active contour to maintain its stability during the evolution process. The multiscale representation term is based on the total variation (TV) energy that can provide a multiscale representation of the input image by tuning the scale parameter. We use an alternating iterative algorithm that combines the gradient descent algorithm and the alternating direction method of multipliers (ADMM) to numerically solve the model. The experimental results for both synthetic and real images demonstrate the robustness and effectiveness of the proposed model for multiscale image segmentation. In addition, the proposed model is a promising model for image denoising applications.

In this paper, a vector total fractional-order variation (VTV-β) is proposed. Then, VTV-β model and Gβ(Ω) model are proposed for color image denoising and decomposition, respectively. Some properties of the VTV-β are investigated and an alternative algorithm is used to solve the two models. Some experimental results are given to show the effectiveness and advantages of our methods.

In this paper, we put forward an idea of indirect diffusion and further develope an indirect diffusion-based level set model for image segmentation. This model is based on the dynamic process of diffusion that is posed indirectly on level set function by way of auxiliary function, coupled with a transition region-based force that exhibits the desired sign-changing property. It is formulated as a coupled system of two evolution equations, in which the first equation drives the motion of zero level set toward the object edges and makes it possible to set a termination criterion on the algorithm, while the second equation (indirect diffusion) smoothens the auxiliary function and keeps the auxiliary function as close to the level set function as possible. The derived model can effectively be solved purely by the simplest explicit finite difference. Experimental results show that the proposed model not only has the strong capability of noise immunity, but it also can much better conduce to extraction of deeply concave edges and preservation of sharp corners, compared with the direct diffusion-based counterpart.

Urolithiasis commonly occurs in kidney and ureteral, and may cause local organ/tissue damage, even kidney failure. The incidence of this disease is increasing worldwide, in which calcium oxalate is the major composition forming the urinary calculus. Therefore, to monitor this disease for the prevention and treatment, measuring the oxalate in the urine is of great significance. Here, a rapid and sensitive colorimetric method was developed based on 3,3',5,5'-tetramethylbenzidine-manganese dioxide (TMB-MnO2) nanosheets for oxalate detection. MnO2 nanosheets acted as an efficient biomimetic oxidase to catalyze the reaction with TMB and oxalate. Pale yellow TMB can be oxidized to blue oxide TMB catalyzed by BSA-stabilized MnO2 nanosheets, and oxalate can selectively inhibit this reaction by consuming and reacting with MnO2 nanosheets, thus achieving the quantitative detection of oxalate. Moreover, a home-made bionic electronic-eye (E-eye) system was developed as a portable in-situ detection platform to efficiently measure the oxalate concentrations in 10 s by direct photographing. By optimizing experimental conditions, this method shows a wide linear range (7.8 μM to 250 μM) and a low detection limit (0.91 μM) for oxalate detection. Besides, this method exhibits high selectivity even with 80-fold interfering chemicals. Furthermore, the performance of the method was validated by testing the artificial urine samples, indicating its great potential for monitoring and diagnosis of urolithiasis in point-of-care applications.

Bioprinting is a common method to replicate geometrical architecture of native tissues. However, it usually fails to modulate cellular arrangements, which is critical for the tissue’s functionality. To our knowledge, no method has successfully addressed this challenge. Here, we report a method of controlling cellular orientation during the bioprinting process by integrating a stretch process into a modified bioprinting frame. We demonstrate that the cellular orientation is a result of cells’ sensing and responding to the tensile stress, instead of shear stress or topographical patterns. Moreover, our method shows a potent capability to induce myoblast differentiation, fusion and maturation without the presence of differentiation medium. As a potential clinical application, we demonstrate that aligned myofibers directly printed onto injured muscle in vivo, can not only repair the structure of damaged tissue, but also recover the muscle functionalities effectively. This study shows that the new method can produce tissues with precise control of cellular arrangements and more clinically viable functionalities.Significance StatementDue to no method could reproduce the exact cellular arrangements of native tissues in engineered tissues, tissue engineering facing difficult in fabricating 3D tissues that possess desirable biological and mechanical functionalities for biomedical applications. For the first time, we report a method of controlling cellular orientation during 3D bio-printing process. This method can be used to produce engineered tissues with controlled cellular arrangement with several different cell types. Moreover, this method shows a potent capability of fabricating fully mature and aligned myofibers in vitro in the absence of differentiation medium. As potential clinical applications, with this method, engineered tissues could be directly printed in vivo with high efficacy of tissue repair and function recovery.

The segmentation of images with severe noise has always been a very challenging task because noise has great influence on the accuracy of segmentation. This paper proposes a robust variational level set model for image segmentation, involving the kernel metric based on the Gaussian radial basis function (GRBF) kernel as the data fidelity metric. The kernel metric can adaptively emphasize the contribution of pixels close to the mean intensity value inside (or outside) the evolving curve and so reduce the influence of noise. We prove that the proposed energy functional is strictly convex and has a unique global minimizer in B V ( Ω ) . A three-step time-splitting scheme, in which the evolution equation is decomposed into two linear differential equations and a nonlinear differential equation, is developed to numerically solve the proposed model efficiently. Experimental results show that the proposed method is very robust to some types of noise (namely, salt & pepper noise, Gaussian noise and mixed noise) and has better performance than six state-of-the-art related models.

Exosomes are common membrane-bound nanovesicles that contain diverse biomolecules, such as lipids, proteins, and nucleic acids. Exosomes are derived from cells through exocytosis, are ingested by target cells, and can transfer biological signals between local or distant cells. Exosome secretion is a constitutive phenomenon that is involved in both physiological and pathological processes and determines both the exosomal surface molecules and the contents. Hence, we can exploit exosomes as biomarkers, vaccines and drug carriers and modify them rationally for therapeutic interventions. However, it is still a challenge to identify, isolate and quantify exosomes accurately, efficiently and selectively. Further studies on exosomes will explore their potential in translational medicine and provide new avenues for the creation of effective clinical diagnostics and therapeutic strategies; the use of exosomes in these applications can be called exosome theranostics. This review describes the fundamental processes of exosome formation and uptake. In addition, the physiological and pathological roles of exosomes in biology are also illustrated with a focus on how exosomes can be exploited or engineered as powerful tools in translational medicine.

Robust and accurate segmentation of oil slick regions from synthetic aperture radar satellite images plays a fundamental role for detecting and monitoring of oil spills. However, uneven intensity, high noise, and blurry boundary, which always exist in oil spill images, make the automatic segmentation of such images very difficult. In this paper, a two-stage method is developed for the segmentation of oil spill images. The first stage of our method is to obtain the enhanced image by suppressing the backscattering from an oil spill image. Once the enhanced image is obtained, then in the second stage, a variational segmentation model is presented for dealing with the enhanced image. The data term of the energy functional is constructed for the enhanced image in a piecewise constant way. In addition, a Cahn–Hilliard-type regularization term is introduced into the energy functional. The variational model is numerically solved by alternating minimization. Numerical experiments on $\text{65}$ oil spill images from ENVISAT show that the proposed method can obtain an overall accuracy of $\text{94} \%$ for dark spot segmentation and create limited false alarms and outperforms the two representative state-of-the-art methods in terms of the efficiency and accuracy.

In this letter, we present a fast and effective algorithm for solving the Poisson-modified total variation model proposed in [Le et al. , “A variational approach to reconstructing images corrupted by Poisson noise,” J. Math. Imag. Vis. , vol. 27, no 3, pp. 257–263, Apr. 2007]. The existence and uniqueness of solution for the model are proved by using a different method. A semi-implicit difference scheme is designed to discretize the derived gradient descent flow with a large time step. Different from the original numerical scheme, our scheme is conditional stable with a less stringent condition and can ensure that the numerical solution is strictly positive in image domain. Experimental results show the efficiency and effectiveness of our algorithm.

Electronic tongues (ETs) have been developed and widely used in food, beverage and pharmaceutical fields, but limited in sensitivity and specificity. In recent years, bioelectronic tongues (BioETs) integrating biological materials and various types of transducers are proposed to bridge the gap between ET system and biological taste. In this work, a bionic in vitro cell-based BioET is developed for bitter and umami detection, utilizing rat cardiomyocytes as a primary taste sensing element and microelectrode arrays (MEAs) as a secondary transducer for the first time. The primary cardiomyocytes of Sprague Dawley (SD) rats, which endogenously express bitter and umami taste receptors, were cultured on MEAs. Cells attached and grew well on the sensor surface, and syncytium was formed for potential conduction and mechanical beating, indicating the good biocompatibility of surface coating. The specificity of this BioET was verified by testing different tastants and bitter compounds. The results show that the BioET responds to bitter and umami compounds specifically among five basic tastants. For bitter recognition, only those can activate receptors in cardiomyocytes can be recognized by the BioET, and different bitter substances could be discriminated by principal component analysis (PCA). Moreover, the specific detections of two bitters (Denatonium Benzoate, Diphenidol) and an umami compound (Monosodium Glutamate) were realized with a detection limit of 10−6 M. The cardiomyocytes-based BioET proposed in this work provides a new approach for the construction of BioETs and has promising applications in taste detection and pharmaceutical study.

Alzheimer's disease (AD) is a chronic central neurodegenerative disease. The pathological features of AD are the extracellular deposition of senile plaques formed by amyloid-β oligomers (AβOs) and the intracellular accumulation of neurofibrillary tangles. However, due to the lack of effective method and experimental models to study the cognitive decline, communication at cell resolution and the implementation of interventions, the diagnosis and treatment on AD still progress slowly. In this paper, we established a pathological model of AD in vitro based on AβOs-induced hippocampal neuronal network chip for multi-site dynamic analysis of the neuronal electrical activity and network connection. The multiple characteristic parameters, including positive and negative spike intervals, firing rate and peak-to-peak values, were extracted through the analysis of spike signals, and two firing patterns from the interneurons and pyramidal neurons were recorded. The spatial firing patterns mapping and cross-correlation between channels were performed to validate the degeneration of neuronal network connectivity. Moreover, an electrical stimulation with frequency at 40 Hz was exerted to preliminarily explore the therapeutic effect on the pathological model of AD. This neuronal network chip enables the implementation of AD models in vitro for studying basic mechanisms of neurodegeneration within networks and for the parallel testing of various potential therapies. It can be a novel technique in the research of AD pathological model in vitro.

A variety of mammalian or insect behaviors rely on the recognition of relevant odor stimuli. The olfactory system detects and translates complex olfactory stimuli (odors) through the unique and reproducible dynamic ensembles of neuronal activities. This process is involved in various types of neurons of olfactory parts, thereby encoding olfactory information or predicting progression in some neuropsychiatric diseases. In this paper, we constructed a biomimetic model including olfactory sensing system and olfactory bulb processing system to map olfactory-associated ensembles of neuronal activity. The olfactory receptor neurons (ORNs) and olfactory bulb (OB) neurons were primarily cultured and the immunofluorescence images were performed to identify the types of neurons. Diacetyl solution was used as an odor stimulus, and the spike bursts and random spike firing patterns of concentration-dependent excitatory responses were obtained from the ORNs network. The spike waveform and feature parameters were extracted including the spike number and interval in per burst to program the stimulation unit and sequences. The sequences containing odor information were applied to the OB neuronal network for the simulation of the primary olfactory processing. The response pattern and change rule of the OB neuronal network were consistent with the OB neurons affected by the neurotransmitter, which is the carrier of olfactory information transmission in vivo. This biomimetic integrated olfactory sensory and processing system can serve as a novel model for studying the physiological and pathological mechanisms of olfaction, and the pharmacological application in vitro.

Display Omitted We propose a multiscale variational decomposition model.We apply the proposed model for hierarchical image restoration and reconstruction.We prove the nontrivial property and the convergence of our model.Experimental results verify the correctness of the theoretical analysis. Variational decomposition has been widely used in image denoising, however, it can't distinguish texture from noise well. Replacing the fixed parameter in the (BV, G) decomposition with a monotone increasing sequence, and iteratively taking the residual of the previous step as the input to decompose, we propose a multiscale variational decomposition model in this paper. Unlike the fixed-scale decomposition, the new model can decompose the input image into a sum of a series of features with different scales. So, texture can be distinguished from noise. In addition, we prove the nontrivial property and the convergence of this multiscale decomposition, and introduce a hybrid iteration algorithm that combines the first-order primal-dual algorithm with the gradient decent method to numerically solve the multiscale decomposition model. Numerical results validate the effectiveness of the proposed model. Furthermore, we apply this multiscale decomposition for image hierarchical restoration. Compared with the classical hierarchical (BV, L2) decomposition, hierarchical wavelet decomposition and fixed-scale (BV, G) decomposition, our model has better performance for both synthetic and real images in terms of PSNR and MSSIM.

Urolithiasis commonly occurs in kidney and ureteral, and may cause local organ/tissue damage, even kidney failure. The incidence of this disease is increasing worldwide, in which calcium oxalate is the major composition forming the urinary calculus. Therefore, to monitor this disease for the prevention and treatment, measuring the oxalate in the urine is of great significance. Here, a rapid and sensitive colorimetric method was developed based on 3,3',5,5'-tetramethylbenzidine-manganese dioxide (TMB-MnO

In this paper, we generalize some determinantal inequalities for Hadamard product of $M$-matrices and inverse $M$-matrices obtained by Chen [Linear Algebra Appl. $\textbf{426}$ (2007), no. 2-3, 610--618.].

The purpose of this paper is to discuss inequalities related to operator versions of the classical Bohr inequality. We obtain refinements of some inequalities due to Cheung and Pecaric [J. Math. Anal. Appl. 323 (2006) 403–412] and Zhang [J. Math. Anal. Appl. 333 (2007) 1264–1271]. Moreover, we present two inequalities for multiple operators, which are similar to ones proposed by Chansangiam et al. [J. Math. Anal. Appl. 356 (2009) 525–536]. Mathematics subject classification (2010): 47A63.

We present refinements of an inequality which is due to Saito and Tominaga [Linear Algebra Appl. 432 (2010) 3258–3264], and other inequalities for absolute value operators.

We propose a new active contour model which integrates a local intensity fitting (LIF) energy with an auxiliary global intensity fitting (GIF) energy. The LIF energy is responsible for attracting the contour toward object boundaries and is dominant near object boundaries, while the GIF energy incorporates global image information to improve the robustness to initialization of the contours. The proposed model not only can provide desirable segmentation results in the presence of intensity inhomogeneity but also allows for more flexible initialization of the contour compared to the RSF and LIF models, and we give a theoretical proof to compute a unique steady state regardless of the initialization; that is, the convergence of the zero-level line is irrespective of the initial function. This means that we can obtain the same zero-level line in the steady state, if we choose the initial function as a bounded function. In particular, our proposed model has the capability of detecting multiple objects or objects with interior holes or blurred edges.

In this paper, we refine an inequality due to Bhatia and Kittaneh [Linear Algebra Appl. 308 (2000) 203–211], and generalize another inequality by Bhatia and Kittaneh [Lett. Math. Phys. 43 (1998) 225–231]. Mathematics subject classification (2010): 15A18, 15A42, 47A63.

In this paper, we develop a novel active contour model in PDE (partial differential equation) formulation, which is based on the Chan–Vese “active contours without edges” model and the Sobolev gradient. Our evolution PDE consists of an adaptive force which is derived from the L 2 gradient of the fidelity term of the Chan–Vese functional, and a regularized force which is the Sobolev gradient of the contour length. For a two-phase piecewise constant image, we prove that the adaptive force has exactly opposite sign in the interior and exterior of objects, and the zero-level set of the evolution function can match with the boundary between objects and background in a single iteration if the initial function is suitably chosen as a sign-changing and bounded function. The proposed model has the advantages of flexible initialization and very fast segmentation process (so re-initialization is not necessary). The proposed model has been applied to both synthetic and real images with promising results.

In this paper, we first generalize an inequality and improve another one for unitarily invariant norms, which are established by Kittaneh and Manasrah in [Improved Young and Heinz inequalities for matrices. J. Math. Anal. Appl.361(2010)262-269]. Then we present a new inequality for unitarily invariant norms, which is equivalent to an inequality presented by Kittaneh and Manasrah in the case of the Hilbert-Schmidt norm.

This paper aims to present some inequalities for unitarily invariant norms. We first give inverses of Young and Heinz type inequalities for scalars. Then we use these inequalities to establish some inequalities for unitarily invariant norms. Mathematics subject classification (2010): 15A45, 15A60.

We propose anLp(|∇I|)-based adaptively active contours model for image segmentation which is derived from the well-known Chan-Vese (C-V) model. Unlike the C-V model, the proposed model uses theLp(|∇I|) (p(|∇I|)>2)norm instead of theL2norm to define the external energy and incorporates an extra internal energy into the overall energy. Due to the variable exponentp(|∇I|) which could fit the image gradient information adaptively, the proposedLp(|∇I|)-based model has the hope of segmenting those images with low contrast and blurred boundaries. Experimental results show that the proposed model withp(|∇I|)>2really can effectively and quickly segment those images with low contrast and blurred boundaries.

An adaptive regularized level set method for image segmentation is proposed. A weightedp(x)-Dirichlet integral is presented as a geometric regularization on zero level curve, which is used to diminish the influence of image noise on level set evolution while ensuring the active contours not to pass through weak object boundaries. The idea behind the new energy integral is that the amount of regularization on the zero level curve can be adjusted automatically by the variable exponentp(x)to fit the image data. This energy is then incorporated into a level set formulation with an external energy term that drives the motion of the zero level set toward the desired objects boundaries, and a level set function regularization term that is necessary for maintaining stable level set evolution. The proposed model has been applied to a wide range of both real and synthetic images with promising results.

In this note, we give some refinements of Fischer-type determinantal inequalities for accretive-dissipative matrices which are due to Lin (Linear Algebra Appl. 438:2808-2812, 2013) and Ikramov (J. Math. Sci. (N.Y.) 121:2458-2464, 2004).

In this paper, we establish some new inequalities of Simpson’s type based on -convexity for differentiable mappings. This contributes to new better estimates than presented already. Some applications for special means of real numbers and error estimates for some numerical quadrature rules are also given. MSC:26D15, 26D10.

The purpose of the paper is to present some inequalities for eigenvalues of positive semidefinite matrices.