scholarly journals From linear to metric functional analysis

2021 ◽  
Vol 118 (28) ◽  
pp. e2107069118
Author(s):  
Anders Karlsson
Keyword(s):  
Game Theory ◽  
Functional Analysis ◽  
Fixed Point ◽  
Deep Learning ◽  
Evolution Equations ◽  
Complex Dynamics ◽  
Surface Topology ◽  
Metric Geometry ◽  
Pure Mathematics ◽  
The Mean

This article presents the beginning of a metric functional analysis. A major notion is metric functionals which extends that of horofunctions in metric geometry. Applications of the main tools are found in a wide variety of subjects such as random walks on groups, complex dynamics, surface topology, deep learning, evolution equations, and game theory, thus branching well outside of pure mathematics. In several cases, linear notions fail to describe linear phenomena that are naturally captured by metric concepts. An extension of the mean ergodic theorem testifies to this. A general metric fixed-point theorem is also proved.

scholarly journals Cotton Stand Counting from Unmanned Aerial System Imagery Using MobileNet and CenterNet Deep Learning Models

2021 ◽  
Vol 13 (14) ◽  
pp. 2822
Author(s):  
Zhe Lin ◽  
Wenxuan Guo
Keyword(s):  
Deep Learning ◽  
Cotton Plant ◽  
Unmanned Aerial System ◽  
Learning Models ◽  
Training Images ◽  
Testing Dataset ◽  
Cotton Plants ◽  
Detection And Counting ◽  
Different Dimensions ◽  
The Mean

An accurate stand count is a prerequisite to determining the emergence rate, assessing seedling vigor, and facilitating site-specific management for optimal crop production. Traditional manual counting methods in stand assessment are labor intensive and time consuming for large-scale breeding programs or production field operations. This study aimed to apply two deep learning models, the MobileNet and CenterNet, to detect and count cotton plants at the seedling stage with unmanned aerial system (UAS) images. These models were trained with two datasets containing 400 and 900 images with variations in plant size and soil background brightness. The performance of these models was assessed with two testing datasets of different dimensions, testing dataset 1 with 300 by 400 pixels and testing dataset 2 with 250 by 1200 pixels. The model validation results showed that the mean average precision (mAP) and average recall (AR) were 79% and 73% for the CenterNet model, and 86% and 72% for the MobileNet model with 900 training images. The accuracy of cotton plant detection and counting was higher with testing dataset 1 for both CenterNet and MobileNet models. The results showed that the CenterNet model had a better overall performance for cotton plant detection and counting with 900 training images. The results also indicated that more training images are required when applying object detection models on images with different dimensions from training datasets. The mean absolute percentage error (MAPE), coefficient of determination (R2), and the root mean squared error (RMSE) values of the cotton plant counting were 0.07%, 0.98 and 0.37, respectively, with testing dataset 1 for the CenterNet model with 900 training images. Both MobileNet and CenterNet models have the potential to accurately and timely detect and count cotton plants based on high-resolution UAS images at the seedling stage. This study provides valuable information for selecting the right deep learning tools and the appropriate number of training images for object detection projects in agricultural applications.

scholarly journals Design and Implementation of Intelligent Inspection and Alarm Flight System for Epidemic Prevention

Drones ◽  
2021 ◽  
Vol 5 (3) ◽  
pp. 68
Author(s):  
Jiwei Fan ◽  
Xiaogang Yang ◽  
Ruitao Lu ◽  
Xueli Xie ◽  
Weipeng Li
Keyword(s):  
Deep Learning ◽  
Autonomous Navigation ◽  
Detection Method ◽  
Active Role ◽  
Absolute Error ◽  
Face Mask ◽  
Learning Technology ◽  
Flight System ◽  
Crowd Density ◽  
The Mean

Unmanned aerial vehicles (UAV) and related technologies have played an active role in the prevention and control of novel coronaviruses at home and abroad, especially in epidemic prevention, surveillance, and elimination. However, the existing UAVs have a single function, limited processing capacity, and poor interaction. To overcome these shortcomings, we designed an intelligent anti-epidemic patrol detection and warning flight system, which integrates UAV autonomous navigation, deep learning, intelligent voice, and other technologies. Based on the convolution neural network and deep learning technology, the system possesses a crowd density detection method and a face mask detection method, which can detect the position of dense crowds. Intelligent voice alarm technology was used to achieve an intelligent alarm system for abnormal situations, such as crowd-gathering areas and people without masks, and to carry out intelligent dissemination of epidemic prevention policies, which provides a powerful technical means for epidemic prevention and delaying their spread. To verify the superiority and feasibility of the system, high-precision online analysis was carried out for the crowd in the inspection area, and pedestrians’ faces were detected on the ground to identify whether they were wearing a mask. The experimental results show that the mean absolute error (MAE) of the crowd density detection was less than 8.4, and the mean average precision (mAP) of face mask detection was 61.42%. The system can provide convenient and accurate evaluation information for decision-makers and meets the requirements of real-time and accurate detection.

scholarly journals Image Enhanced Mask R-CNN: A Deep Learning Pipeline with New Evaluation Measures for Wind Turbine Blade Defect Detection and Classification

2021 ◽  
Vol 7 (3) ◽  
pp. 46
Author(s):  
Jiajun Zhang ◽  
Georgina Cosma ◽  
Jason Watkins
Keyword(s):  
Deep Learning ◽  
Wind Turbine ◽  
Turbine Blade ◽  
Defect Detection ◽  
Recognition Rate ◽  
Weighted Average ◽  
Wind Turbine Blade ◽  
Evaluation Measures ◽  
Augmentation Techniques ◽  
The Mean

Demand for wind power has grown, and this has increased wind turbine blade (WTB) inspections and defect repairs. This paper empirically investigates the performance of state-of-the-art deep learning algorithms, namely, YOLOv3, YOLOv4, and Mask R-CNN for detecting and classifying defects by type. The paper proposes new performance evaluation measures suitable for defect detection tasks, and these are: Prediction Box Accuracy, Recognition Rate, and False Label Rate. Experiments were carried out using a dataset, provided by the industrial partner, that contains images from WTB inspections. Three variations of the dataset were constructed using different image augmentation settings. Results of the experiments revealed that on average, across all proposed evaluation measures, Mask R-CNN outperformed all other algorithms when transformation-based augmentations (i.e., rotation and flipping) were applied. In particular, when using the best dataset, the mean Weighted Average (mWA) values (i.e., mWA is the average of the proposed measures) achieved were: Mask R-CNN: 86.74%, YOLOv3: 70.08%, and YOLOv4: 78.28%. The paper also proposes a new defect detection pipeline, called Image Enhanced Mask R-CNN (IE Mask R-CNN), that includes the best combination of image enhancement and augmentation techniques for pre-processing the dataset, and a Mask R-CNN model tuned for the task of WTB defect detection and classification.

scholarly journals On Almost Automorphic Mild Solutions for Nonautonomous Stochastic Evolution Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Jing Cui ◽  
Litan Yan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Banach Fixed Point Theorem ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Almost Automorphic ◽  
Composition Theorem

We consider a class of nonautonomous stochastic evolution equations in real separable Hilbert spaces. We establish a new composition theorem for square-mean almost automorphic functions under non-Lipschitz conditions. We apply this new composition theorem as well as intermediate space techniques, Krasnoselskii fixed point theorem, and Banach fixed point theorem to investigate the existence of square-mean almost automorphic mild solutions. Some known results are generalized and improved.

scholarly journals Lesion-Based Bone Metastasis Detection in Chest Bone Scintigraphy Images of Prostate Cancer Patients Using Pre-Train, Negative Mining, and Deep Learning

Diagnostics ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 518
Author(s):  
Da-Chuan Cheng ◽  
Te-Chun Hsieh ◽  
Kuo-Yang Yen ◽  
Chia-Hung Kao
Keyword(s):  
Breast Cancer ◽  
Prostate Cancer ◽  
Deep Learning ◽  
Bone Metastasis ◽  
Cancer Patients ◽  
Bone Scintigraphy ◽  
Breast Cancer Patients ◽  
Location Detection ◽  
The Mean ◽  
Mean Sensitivity

This study aimed to explore efficient ways to diagnose bone metastasis early using bone scintigraphy images through negative mining, pre-training, the convolutional neural network, and deep learning. We studied 205 prostate cancer patients and 371 breast cancer patients and used bone scintigraphy data from breast cancer patients to pre-train a YOLO v4 with a false-positive reduction strategy. With the pre-trained model, transferred learning was applied to prostate cancer patients to build a model to detect and identify metastasis locations using bone scintigraphy. Ten-fold cross validation was conducted. The mean sensitivity and precision rates for bone metastasis location detection and classification (lesion-based) in the chests of prostate patients were 0.72 ± 0.04 and 0.90 ± 0.04, respectively. The mean sensitivity and specificity rates for bone metastasis classification (patient-based) in the chests of prostate patients were 0.94 ± 0.09 and 0.92 ± 0.09, respectively. The developed system has the potential to provide pre-diagnostic reports to aid in physicians’ final decisions.

scholarly journals A study on controllability of impulsive fractional evolution equations via resolvent operators

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Haide Gou ◽  
Yongxiang Li
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Resolvent Operator ◽  
Evolution Equations ◽  
Validity Study ◽  
Resolvent Operators ◽  
Fractional Evolution Equations ◽  
Mönch Fixed Point Theorem ◽  
Alpha Beta

AbstractIn this article, we study the controllability for impulsive fractional integro-differential evolution equation in a Banach space. The discussions are based on the Mönch fixed point theorem as well as the theory of fractional calculus and the $(\alpha ,\beta )$ ( α , β ) -resolvent operator, we concern with the term $u'(\cdot )$ u ′ ( ⋅ ) and finding a control v such that the mild solution satisfies $u(b)=u_{b}$ u ( b ) = u b and $u'(b)=u'_{b}$ u ′ ( b ) = u b ′ . Finally, we present an application to support the validity study.

Applications of General Infimum Principles to Fixed-Point Theory and Game Theory

2007 ◽  
Vol 16 (4) ◽  
pp. 375-398 ◽  
Author(s):  
Władysław Kulpa ◽  
Andrzej Szymanski
Keyword(s):  
Game Theory ◽  
Fixed Point ◽  
Fixed Point Theory ◽  
Point Theory

Fractional evolution equations with nonlocal conditions in partially ordered Banach space

2018 ◽  
Vol 34 (3) ◽  
pp. 379-390
Author(s):  
HEMANT KUMAR NASHINE ◽  
◽  
HE YANG ◽  
RAVI P. AGARWAL ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Coupled Fixed Point ◽  
Positive Cone ◽  
Bounded Linear ◽  
Partially Ordered ◽  
C0 Semigroup ◽  
Uniformly Bounded

In the present work, we discuss the existence of mild solutions for the initial value problem of fractional evolution equation of the form where C Dσ t denotes the Caputo fractional derivative of order σ ∈ (0, 1), −A : D(A) ⊂ X → X generates a positive C0-semigroup T(t)(t ≥ 0) of uniformly bounded linear operator in X, b > 0 is a constant, f is a given functions. For this, we use the concept of measure of noncompactness in partially ordered Banach spaces whose positive cone K is normal, and establish some basic fixed point results under the said concepts. In addition, we relaxed the conditions of boundedness, closedness and convexity of the set at the expense that the operator is monotone and bounded. We also supply some new coupled fixed point results via MNC. To justify the result, we prove an illustrative example that rational of the abstract results for fractional parabolic equations.

Vesseg: An Open-Source Tool for Deep Learning-Based Atherosclerotic Plaque Quantification in Histopathology Image

2021 ◽  
Author(s):  
J.M. Murray ◽  
P. Pfeffer ◽  
R. Seifert ◽  
A. Hermann ◽  
J. Handke ◽  
...  
Keyword(s):  
Deep Learning ◽  
Open Source ◽  
Atherosclerotic Plaque ◽  
State Of The Art ◽  
The Mean ◽  
Time Savings ◽  
Plaque Quantification ◽  
Atherosclerosis Research ◽  
Hematoxylin Eosin ◽  
Microscopy Images

Objective: Manual plaque segmentation in microscopy images is a time-consuming process in atherosclerosis research and potentially subject to unacceptable user-to-user variability and observer bias. We address this by releasing Vesseg a tool that includes state-of-the-art deep learning models for atherosclerotic plaque segmentation. Approach and Results: Vesseg is a containerized, extensible, open-source, and user-oriented tool. It includes 2 models, trained and tested on 1089 hematoxylin-eosin stained mouse model atherosclerotic brachiocephalic artery sections. The models were compared to 3 human raters. Vesseg can be accessed at https://vesseg .online or downloaded. The models show mean Soerensen-Dice scores of 0.91±0.15 for plaque and 0.97±0.08 for lumen pixels. The mean accuracy is 0.98±0.05. Vesseg is already in active use, generating time savings of >10 minutes per slide. Conclusions: Vesseg brings state-of-the-art deep learning methods to atherosclerosis research, providing drastic time savings, while allowing for continuous improvement of models and the underlying pipeline.

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