scholarly journals Lipschitz Bounds and Nonautonomous Integrals

2021 ◽  
Author(s):  
Cristiana De Filippis ◽  
Giuseppe Mingione
Keyword(s):  
Variational Problems ◽  
Growth Conditions ◽  
Regularity Criteria ◽  
Regularity Of Solutions ◽  
Optimal Regularity ◽  
Lipschitz Regularity ◽  
Elliptic Case ◽  
Different Types ◽  
Vector Valued

AbstractWe provide a general approach to Lipschitz regularity of solutions for a large class of vector-valued, nonautonomous variational problems exhibiting nonuniform ellipticity. The functionals considered here range from those with unbalanced polynomial growth conditions to those with fast, exponential type growth. The results obtained are sharp with respect to all the data considered and also yield new, optimal regularity criteria in the classical uniformly elliptic case. We give a classification of different types of nonuniform ellipticity, accordingly identifying suitable conditions to get regularity theorems.

Boundary regularity of flows under perfect slip boundary conditions

2013 ◽  
Vol 11 (7) ◽  
Author(s):  
Petr Kaplický ◽  
Jakub Tichý
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Boundary Regularity ◽  
Growth Conditions ◽  
Regularity Of Solutions ◽  
Slip Boundary Conditions ◽  
Optimal Regularity ◽  
Slip Boundary ◽  
Nonlinear Elliptic ◽  
Perfect Slip Boundary Conditions

AbstractWe investigate boundary regularity of solutions of generalized Stokes equations. The problem is complemented with perfect slip boundary conditions and we assume that the nonlinear elliptic operator satisfies non-standard ϕ-growth conditions. We show the existence of second derivatives of velocity and their optimal regularity.

Dual stain kit for the microscopic gram classification of ocular infection bacteria

1993 ◽  
Vol 51 ◽  
pp. 248-249
Author(s):  
Jacob S. Hanker ◽  
Dale N. Holdren ◽  
Kenneth L. Cohen ◽  
Beverly L. Giammara
Keyword(s):  
Contact Lenses ◽  
Ocular Infection ◽  
Gram Negative Bacteria ◽  
Gram Negative ◽  
Gram Staining ◽  
Ocular Infections ◽  
Different Types ◽  
Culture Positive ◽  
Increased Susceptibility

Keratitis and conjunctivitis (infections of the cornea or conjunctiva) are ocular infections caused by various bacteria, fungi, viruses or parasites; bacteria, however, are usually prominent. Systemic conditions such as alcoholism, diabetes, debilitating disease, AIDS and immunosuppressive therapy can lead to increased susceptibility but trauma and contact lens use are very important factors. Gram-negative bacteria are most frequently cultured in these situations and Pseudomonas aeruginosa is most usually isolated from culture-positive ulcers of patients using contact lenses. Smears for staining can be obtained with a special swab or spatula and Gram staining frequently guides choice of a therapeutic rinse prior to the report of the culture results upon which specific antibiotic therapy is based. In some cases staining of the direct smear may be diagnostic in situations where the culture will not grow. In these cases different types of stains occasionally assist in guiding therapy.

Explanatory Power for Medical Expert Systems: Studies in the Representation of Causal Relationships for Clinical Consultations

1982 ◽  
Vol 21 (03) ◽  
pp. 127-136 ◽  
Author(s):  
J. W. Wallis ◽  
E. H. Shortliffe
Keyword(s):  
Explanatory Power ◽  
Prototype System ◽  
Inference Rules ◽  
Medical Expert ◽  
Comprehensive Knowledge ◽  
Different Types ◽  
Medical Expert Systems ◽  
Explanation System ◽  
Systems Studies

This paper reports on experiments designed to identify and implement mechanisms for enhancing the explanation capabilities of reasoning programs for medical consultation. The goals of an explanation system are discussed, as is the additional knowledge needed to meet these goals in a medical domain. We have focussed on the generation of explanations that are appropriate for different types of system users. This task requires a knowledge of what is complex and what is important; it is further strengthened by a classification of the associations or causal mechanisms inherent in the inference rules. A causal representation can also be used to aid in refining a comprehensive knowledge base so that the reasoning and explanations are more adequate. We describe a prototype system which reasons from causal inference rules and generates explanations that are appropriate for the user.

scholarly journals Variational Problems with Time Delay and Higher-Order Distributed-Order Fractional Derivatives with Arbitrary Kernels

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1665
Author(s):  
Fátima Cruz ◽  
Ricardo Almeida ◽  
Natália Martins
Keyword(s):  
Time Delay ◽  
Fractional Derivatives ◽  
Variational Problems ◽  
Higher Order ◽  
Sufficient Optimality Conditions ◽  
Fractional Operator ◽  
Different Types ◽  
Generalized Fractional Derivatives ◽  
Necessary And Sufficient ◽  
Distributed Order

In this work, we study variational problems with time delay and higher-order distributed-order fractional derivatives dealing with a new fractional operator. This fractional derivative combines two known operators: distributed-order derivatives and derivatives with respect to another function. The main results of this paper are necessary and sufficient optimality conditions for different types of variational problems. Since we are dealing with generalized fractional derivatives, from this work, some well-known results can be obtained as particular cases.

Glycans in scaffold design in tissue reconstruction

2021 ◽  
pp. 088391152199784
Author(s):  
Nipun Jain ◽  
Shashi Singh
Keyword(s):  
Cell Attachment ◽  
Low Cost ◽  
Growth Conditions ◽  
Downstream Signaling ◽  
Cell Carrier ◽  
Wide Range ◽  
Proliferation And Differentiation ◽  
Different Types ◽  
Tissue Reconstruction ◽  
A Cell

Development of an artificial tissue by tissue engineering is witnessed to be one of the long lasting clarified solutions for the damaged tissue function restoration. To accomplish this, a scaffold is designed as a cell carrier in which the extracellular matrix (ECM) performs a prominent task of controlling the inoculated cell’s destiny. ECM composition, topography and mechanical properties lead to different types of interactions between cells and ECM components that trigger an assortment of cellular reactions via diverse sensing mechanisms and downstream signaling pathways. The polysaccharides in the form of proteoglycans and glycoproteins yield better outcomes when included in the designed matrices. Glycosaminoglycan (GAG) chains present on proteoglycans show a wide range of operations such as sequestering of critical effector morphogens which encourage proficient nutrient contribution toward the growing stem cells for their development and endurance. In this review we discuss how the glycosylation aspects are of considerable importance in everyday housekeeping functions of a cell especially when placed in a controlled environment under ideal growth conditions. Hydrogels made from these GAG chains have been used extensively as a resorbable material that mimics the natural ECM functions for an efficient control over cell attachment, permeability, viability, proliferation, and differentiation processes. Also the incorporation of non-mammalian polysaccharides can elicit specific receptor responses which authorize the creation of numerous vigorous frameworks while prolonging the low cost and immunogenicity of the substance.

scholarly journals Deep Learning Methods for Classification of Certain Abnormalities in Echocardiography

Electronics ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 495
Author(s):  
Imayanmosha Wahlang ◽  
Arnab Kumar Maji ◽  
Goutam Saha ◽  
Prasun Chakrabarti ◽  
Michal Jasinski ◽  
...  
Keyword(s):  
Deep Learning ◽  
Short Term Memory ◽  
Support Vector ◽  
Variational Autoencoder ◽  
Different Types ◽  
Static Images ◽  
Long Short Term Memory ◽  
2D And 3D ◽  
Better Than

This article experiments with deep learning methodologies in echocardiogram (echo), a promising and vigorously researched technique in the preponderance field. This paper involves two different kinds of classification in the echo. Firstly, classification into normal (absence of abnormalities) or abnormal (presence of abnormalities) has been done, using 2D echo images, 3D Doppler images, and videographic images. Secondly, based on different types of regurgitation, namely, Mitral Regurgitation (MR), Aortic Regurgitation (AR), Tricuspid Regurgitation (TR), and a combination of the three types of regurgitation are classified using videographic echo images. Two deep-learning methodologies are used for these purposes, a Recurrent Neural Network (RNN) based methodology (Long Short Term Memory (LSTM)) and an Autoencoder based methodology (Variational AutoEncoder (VAE)). The use of videographic images distinguished this work from the existing work using SVM (Support Vector Machine) and also application of deep-learning methodologies is the first of many in this particular field. It was found that deep-learning methodologies perform better than SVM methodology in normal or abnormal classification. Overall, VAE performs better in 2D and 3D Doppler images (static images) while LSTM performs better in the case of videographic images.

scholarly journals Preventing corneal blindness caused by keratitis using artificial intelligence

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Zhongwen Li ◽  
Jiewei Jiang ◽  
Kuan Chen ◽  
Qianqian Chen ◽  
Qinxiang Zheng ◽  
...  
Keyword(s):  
Early Diagnosis ◽  
Vision Loss ◽  
Learning System ◽  
Automated Classification ◽  
Slit Lamp ◽  
Resource Limited ◽  
The World ◽  
Different Types ◽  
Corneal Blindness

AbstractKeratitis is the main cause of corneal blindness worldwide. Most vision loss caused by keratitis can be avoidable via early detection and treatment. The diagnosis of keratitis often requires skilled ophthalmologists. However, the world is short of ophthalmologists, especially in resource-limited settings, making the early diagnosis of keratitis challenging. Here, we develop a deep learning system for the automated classification of keratitis, other cornea abnormalities, and normal cornea based on 6,567 slit-lamp images. Our system exhibits remarkable performance in cornea images captured by the different types of digital slit lamp cameras and a smartphone with the super macro mode (all AUCs>0.96). The comparable sensitivity and specificity in keratitis detection are observed between the system and experienced cornea specialists. Our system has the potential to be applied to both digital slit lamp cameras and smartphones to promote the early diagnosis and treatment of keratitis, preventing the corneal blindness caused by keratitis.

scholarly journals Higher differentiability results for solutions to a class of non-autonomous obstacle problems with sub-quadratic growth conditions

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Andrea Gentile
Keyword(s):  
Besov Space ◽  
Lipschitz Space ◽  
Growth Conditions ◽  
Obstacle Problems ◽  
Quadratic Growth ◽  
Regularity Assumption ◽  
Lipschitz Regularity ◽  
Fixed Boundary ◽  
Higher Differentiability ◽  
Admissible Functions

Abstract We establish some higher differentiability results of integer and fractional order for solutions to non-autonomous obstacle problems of the form min ⁡ { ∫ Ω f ⁢ ( x , D ⁢ v ⁢ ( x ) ) : v ∈ K ψ ⁢ ( Ω ) } , \min\biggl{\{}\int_{\Omega}f(x,Dv(x)):v\in\mathcal{K}_{\psi}(\Omega)\biggr{\}}, where the function 𝑓 satisfies 𝑝-growth conditions with respect to the gradient variable, for 1 < p < 2 1<p<2 , and K ψ ⁢ ( Ω ) \mathcal{K}_{\psi}(\Omega) is the class of admissible functions v ∈ u 0 + W 0 1 , p ⁢ ( Ω ) v\in u_{0}+W^{1,p}_{0}(\Omega) such that v ≥ ψ v\geq\psi a.e. in Ω, where u 0 ∈ W 1 , p ⁢ ( Ω ) u_{0}\in W^{1,p}(\Omega) is a fixed boundary datum. Here we show that a Sobolev or Besov–Lipschitz regularity assumption on the gradient of the obstacle 𝜓 transfers to the gradient of the solution, provided the partial map x ↦ D ξ ⁢ f ⁢ ( x , ξ ) x\mapsto D_{\xi}f(x,\xi) belongs to a suitable Sobolev or Besov space. The novelty here is that we deal with sub-quadratic growth conditions with respect to the gradient variable, i.e. f ⁢ ( x , ξ ) ≈ a ⁢ ( x ) ⁢ | ξ | p f(x,\xi)\approx a(x)\lvert\xi\rvert^{p} with 1 < p < 2 1<p<2 , and where the map 𝑎 belongs to a Sobolev or Besov–Lipschitz space.

NEURAL CLASSIFICATION OF MASS ABNORMALITIES WITH DIFFERENT TYPES OF FEATURES IN DIGITAL MAMMOGRAPHY

2006 ◽  
Vol 06 (01) ◽  
pp. 61-75 ◽  
Author(s):  
R. PANCHAL ◽  
B. VERMA
Keyword(s):  
Breast Cancer ◽  
Research Work ◽  
Breast Cancer Diagnosis ◽  
Classification Rate ◽  
Test Dataset ◽  
Benchmark Database ◽  
Different Types ◽  
Breast Tissues ◽  
Mass Type

Early detection of breast abnormalities remains the primary prevention against breast cancer despite the advances in breast cancer diagnosis and treatment. Presence of mass in breast tissues is highly indicative of breast cancer. The research work presented in this paper investigates the significance of different types of features using proposed neural network based classification technique to classify mass type of breast abnormalities in digital mammograms into malignant and benign. 14 gray level based features, four BI-RADS features, patient age feature and subtlety value feature have been explored using the proposed research methodology to attain maximum classification on test dataset. The proposed research technique attained a 91% testing classification rate with a 100% training classification rate on digital mammograms taken from the DDSM benchmark database.

scholarly journals Space Precession Target Classification Based on Radar High-Resolution Range Profiles

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Yizhe Wang ◽  
Cunqian Feng ◽  
Yongshun Zhang ◽  
Sisan He
Keyword(s):  
Parameter Extraction ◽  
Classification Performance ◽  
Support Vector ◽  
Electromagnetic Data ◽  
Feature Extractor ◽  
Different Types ◽  
Radar Echo ◽  
High Level ◽  
Cone Target

Precession is a common micromotion form of space targets, introducing additional micro-Doppler (m-D) modulation into the radar echo. Effective classification of space targets is of great significance for further micromotion parameter extraction and identification. Feature extraction is a key step during the classification process, largely influencing the final classification performance. This paper presents two methods for classifying different types of space precession targets from the HRRPs. We first establish the precession model of space targets and analyze the scattering characteristics and then compute electromagnetic data of the cone target, cone-cylinder target, and cone-cylinder-flare target. Experimental results demonstrate that the support vector machine (SVM) using histograms of oriented gradient (HOG) features achieves a good result, whereas the deep convolutional neural network (DCNN) obtains a higher classification accuracy. DCNN combines the feature extractor and the classifier itself to automatically mine the high-level signatures of HRRPs through a training process. Besides, the efficiency of the two classification processes are compared using the same dataset.

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