scholarly journals A MATHEMATICAL MODEL FOR THE RELATIVE ASSESSMENT OF SURFACE AND DEEP LEARNING

2015 ◽  
Vol 7 (3) ◽  
Author(s):  
L. Nikolova ◽  
M. Hristova ◽  
D. Kolev ◽  
H. Georgiev
Keyword(s):  
Mathematical Model ◽  
Deep Learning

scholarly journals Mathematical model for implementing Non Linear Time Series Forecasting using Deep Learning

2020 ◽  
Vol 981 ◽  
pp. 022021
Author(s):  
Imran Qureshi ◽  
Burhanuddin Mohammad ◽  
Mohammed Abdul Habeeb ◽  
Mohammed Ali Shaik
Keyword(s):  
Mathematical Model ◽  
Time Series ◽  
Deep Learning ◽  
Linear Time ◽  
Time Series Forecasting ◽  
Non Linear

scholarly journals Deep learning on butterfly phenotypes tests evolution’s oldest mathematical model

2019 ◽  
Vol 5 (8) ◽  
pp. eaaw4967 ◽  
Author(s):  
Jennifer F. Hoyal Cuthill ◽  
Nicholas Guttenberg ◽  
Sophie Ledger ◽  
Robyn Crowther ◽  
Blanca Huertas
Keyword(s):  
Mathematical Model ◽  
Deep Learning ◽  
Wing Pattern ◽  
Neighbor Joining ◽  
Phenotypic Analysis ◽  
Frequency Dependent ◽  
Comparative Analyses ◽  
Müllerian Mimicry ◽  
Heliconius Melpomene ◽  
Mullerian Mimicry

Traditional anatomical analyses captured only a fraction of real phenomic information. Here, we apply deep learning to quantify total phenotypic similarity across 2468 butterfly photographs, covering 38 subspecies from the polymorphic mimicry complex of Heliconius erato and Heliconius melpomene. Euclidean phenotypic distances, calculated using a deep convolutional triplet network, demonstrate significant convergence between interspecies co-mimics. This quantitatively validates a key prediction of Müllerian mimicry theory, evolutionary biology’s oldest mathematical model. Phenotypic neighbor-joining trees are significantly correlated with wing pattern gene phylogenies, demonstrating objective, phylogenetically informative phenome capture. Comparative analyses indicate frequency-dependent mutual convergence with coevolutionary exchange of wing pattern features. Therefore, phenotypic analysis supports reciprocal coevolution, predicted by classical mimicry theory but since disputed, and reveals mutual convergence as an intrinsic generator for the unexpected diversity of Müllerian mimicry. This demonstrates that deep learning can generate phenomic spatial embeddings, which enable quantitative tests of evolutionary hypotheses previously only testable subjectively.

Deep Learning Approach Applied to Prediction of Bone Age Based on Computed Tomography Orthopedic Image Processing

2020 ◽  
Vol 10 (5) ◽  
pp. 1242-1248
Author(s):  
Gefei Tan ◽  
Daoshun Wang
Keyword(s):  
Computed Tomography ◽  
Mathematical Model ◽  
Deep Learning ◽  
Image Recognition ◽  
Bone Age ◽  
Research Progress ◽  
Age Assessment ◽  
Black And White ◽  
Significant Difference ◽  
Bone Age Assessment

Objective: Deep learning and neural network models are new research directions in the field of machine learning and artificial intelligence. Deep learning has made breakthroughs in image recognition and speech recognition applications, and has also shown unique advantages in face recognition and information retrieval, and has been widely used. Methods: Thin-layer computed tomography (CT) scan and multiplanar reconstruction (MPR) and volume reconstruction (VR) techniques were used to perform CT thin-slice scan and volume of the bilateral clavicle sternum at 548 number of l5~25 years old. Reproduction (volume rendering, VR) and three-dimensional image recombination, measuring and calculating the longest diameter of the sternal end of the bilateral clavicle, the longest diameter of the metaphysis and its length ratio, the area of the epiphysis, the area of the metaphysis and its area ratio, etc. We establish a mathematical model of bone age inference, and then substitute 50 training samples into the mathematical model to test the accuracy of the model. Results: There was a statistically significant difference between the male and female sex ratios in the same age group (P < 0.05). The established mathematical model shows that the developmental law of the sternal skeletal bone is highly correlated with the biological age. The accuracy of all models is 70.5% (±1.0 years old) and 82.5% (±1.5 years). Skeletal X-ray images show different gradation changes in black and white, with black-and-white contrast and hierarchical image features. Based on the advantages of deep learning in image recognition, we combine it with bone age assessment research to build a forensic bone age automation. Conclusions: This paper harnesses the basic concepts of deep learning and its network structure, and expounds the research progress of deep learning in image recognition in different research fields at home and abroad in recent years, as well as the advantages and application prospects of deep learning in bone age assessment.

RANDOM NEURAL NETWORK METHODS AND DEEP LEARNING

2019 ◽  
pp. 1-31 ◽  
Author(s):  
Yonghua Yin
Keyword(s):  
Neural Network ◽  
Machine Learning ◽  
Mathematical Model ◽  
Deep Learning ◽  
Energy Expenditure ◽  
Great Success ◽  
Integrate And Fire ◽  
Random Neural Network ◽  
Network Methods ◽  
Spiking Network

The random neural network (RNN) is a mathematical model for an “integrate and fire” spiking network that closely resembles the stochastic behavior of neurons in mammalian brains. Since its proposal in 1989, there have been numerous investigations into the RNN's applications and learning algorithms. Deep learning (DL) has achieved great success in machine learning. Recently, the properties of the RNN for DL have been investigated, in order to combine their power. Recent results demonstrate that the gap between RNNs and DL can be bridged and the DL tools based on the RNN are faster and can potentially be used with less energy expenditure than existing methods.

Abstract TP224: A Deep Learning Based-Algorithm to Automatically Measure Carotid Stenosis Using Cine-Images of Carotid Duplex Ultrasonography

Stroke ◽  
2020 ◽  
Vol 51 (Suppl_1) ◽  
Author(s):  
Kiwan Jeon ◽  
Hee Jin Chang ◽  
Gyeongmi Yook ◽  
Yun Kyong Hyon ◽  
Tae Young Ha ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Deep Learning ◽  
Standard Deviation ◽  
Carotid Stenosis ◽  
Vessel Wall ◽  
Gaussian Mixture ◽  
Dice Coefficient ◽  
Vessel Lumen ◽  
Segmentation Algorithms ◽  
Carotid Duplex Ultrasonography

Background and Objective: The present study was performed to develop an automated algorithm to measure the carotid stenosis by considering both deep learning and mathematical model using carotid duplex ultrasonography (CDU) images. Methods: We first obtained cine images of CDU from right and left carotid arteries of 18 ischemic stroke patients by continuous moving from supraclavicular to submandibular area. Then, we collected raw axial-CDU images from the cine-CDU images, and then, labelled segmentation of the stenosis caused by atherosclerotic plaque from the vessel wall in the individual axial image by two experts. To develop segmentation algorithm from the axial-CDU images, we first applied a deep learning algorithm to segment vessel lumen from vessel wall. Next, a mathematical algorithm using Gaussian mixture was used to segment atherosclerotic stenosis from the vessel lumen. Dice coefficient was obtained to evaluate whether the segmentation algorithms could accurately segment lumen of carotid artery and predict the stenosis severity measured by the experts using python packages including TensorFlow and scikit-learn on a workstation (Intel i9-7900X CPU, Nvidia Titan Xp GPU and 128G 2400GHz memory). Results: We finally collected total 13,586 raw axial-CDU images from the cine-CDU images of the 18 patients. After application of two steps of segmentation algorithms to the axial-CDU images, accuracy of the algorithm to segment lumen from the carotid vessel wall was mean 0.92 (±standard deviation 0.46) of dice coefficient. And, accuracy to estimate the stenotic area was mean 0.201 (±standard deviation 0.137) of dice coefficient. Conclusions: We proposed an algorithm to automatically quantify the carotid stenosis using two steps of approach. First, a deep learning based-algorithm to segment lumen of carotid artery; second, a mathematical model based-algorithm using Gaussian mixture to segment carotid stenosis from the lumen. Even though we need more studies to increase the accuracy to predict the stenosis, the present prediction algorithms provide a possible tool to automatically measure the severity and regional characteristics of carotid stenosis using cine-CDU images.

scholarly journals Susceptible-Infected-Removed Mathematical Model under Deep Learning in Hospital Infection Control of Novel Coronavirus Pneumonia

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Ting Liu ◽  
Yanling Bai ◽  
Mingmei Du ◽  
Yueming Gao ◽  
Yunxi Liu
Keyword(s):  
Mathematical Model ◽  
Deep Learning ◽  
Infection Control ◽  
Model Fitting ◽  
Sir Model ◽  
Hospital Infection ◽  
Model Based ◽  
Hospital Infection Control ◽  
Stochastic Sir ◽  
Novel Coronavirus

Objective. This research aimed to explore the application of a mathematical model based on deep learning in hospital infection control of novel coronavirus (COVID-19) pneumonia. Methods. First, the epidemic data of Beijing, China, were utilized to make a definite susceptible-infected-removed (SIR) model fitting to determine the estimated value of the COVID-19 removal intensity β, which was then used to do a determined SIR model and a stochastic SIR model fitting for the hospital. In addition, the reasonable β and γ estimates of the hospital were determined, and the spread of the epidemic in hospital was simulated, to discuss the impact of basal reproductive number changes, isolation, vaccination, and so forth on COVID-19. Results. There was a certain gap between the fitting of SIR to the remover and the actual data. The fitting of the number of infections was accurate. The growth rate of the number of infections decreased after measures, such as isolation, were taken. The effect of herd immunity was achieved after the overall immunity reached 70.9%. Conclusion. The SIR model based on deep learning and the stochastic SIR fitting model were accurate in judging the development trend of the epidemic, which can provide basis and reference for hospital epidemic infection control.

Sign in / Sign up

Export Citation Format

Share Document