17 research outputs found
Stark Effect in Lax-Phillips Theory
The scattering theory of Lax and Phillips, originally developed to describe
resonances associated with classical wave equations, has been recently extended
to apply as well to the case of the Schroedinger equation in the case that the
wave operators for the corresponding Lax-Phillips theory exist. It is known
that the bound state levels of an atom become resonances (spectral
enhancements) in the continuum in the presence of an electric field (in all
space) in the quantum mechanical Hilbert space. Such resonances appear as
states in the extended Lax-Phillips Hilbert space. We show that for a simple
version of the Stark effect, these states can be explicitly computed, and
exhibit the (necessarily) semigroup property of decay in time. The widths and
location of the resonances are those given by the poles of the resolvent of the
standard quantum mechanical form.Comment: Plain TeX, 19 page
Deep convolution neural network for screening carotid calcification in dental panoramic radiographs
Ischemic stroke, a leading global cause of death and disability, is commonly caused by carotid arteries atherosclerosis. Carotid artery calcification (CAC) is a well-known marker of atherosclerosis. Such calcifications are classically detected by ultrasound screening. In recent years it was shown that these calcifications can also be inferred from routine panoramic dental radiographs. In this work, we focused on panoramic dental radiographs taken from 500 patients, manually labelling each of the patientsâ sides (each radiograph was treated as two sides), which were used to develop an artificial intelligence (AI)-based algorithm to automatically detect carotid calcifications. The algorithm uses deep learning convolutional neural networks (CNN), with transfer learning (TL) approach that achieved true labels for each corner, and reached a sensitivity (recall) of 0.82 and a specificity of 0.97 for individual arteries, and a recall of 0.87 and specificity of 0.97 for individual patients. Applying and integrating the algorithm in healthcare units and dental clinics has the potential of reducing stroke events and their mortality and morbidity consequences. Author summary Stroke is a leading global cause of death and disability. One major cause of stroke is carotid arteries atherosclerosis. Carotid artery calcification (CAC) is a well-known marker of atherosclerosis. Traditional approaches for CAC detection are doppler ultrasound screening and angiography computerized tomography (CT), medical procedures that incur financial expenses, and are time consuming and discomforting to the patient. Of note, angiography CT involves the injection of contrast material and exposure to X-ray ionizing irradiation. In recent years researchers have shown that CAC can also be detected by analyzing routine panoramic dental radiographs, a non-invasive, cheap and easily accessible procedure. This study takes us one step further, in developing artificial intelligence (AI)-based algorithms trained to detect such calcifications in panoramic dental radiographs. The models developed are based on deep learning convolutional neural networks and transfer learning, that enable an accurate automated detection of carotid calcifications, with a recall of 0.82 and a specificity of 0.97. Statistical approaches for assessing predictions per individual (i.e.: predicting the risk of calcification in at least one artery) were developed, showing a recall of 0.87 and specificity of 0.97. Applying and integrating this approach in healthcare units may significantly contribute to identifying at-risk patients
The probabilities and quantities of prediction CAC or âCleanâ on three types of patients based on the performance of a single side.
The cells in the table consist of the probabilities and the patient numbers are presented in italic in parentheses.</p
Sample size sufficiency analysis.
Ischemic stroke, a leading global cause of death and disability, is commonly caused by carotid arteries atherosclerosis. Carotid artery calcification (CAC) is a well-known marker of atherosclerosis. Such calcifications are classically detected by ultrasound screening. In recent years it was shown that these calcifications can also be inferred from routine panoramic dental radiographs. In this work, we focused on panoramic dental radiographs taken from 500 patients, manually labelling each of the patientsâ sides (each radiograph was treated as two sides), which were used to develop an artificial intelligence (AI)-based algorithm to automatically detect carotid calcifications. The algorithm uses deep learning convolutional neural networks (CNN), with transfer learning (TL) approach that achieved true labels for each corner, and reached a sensitivity (recall) of 0.82 and a specificity of 0.97 for individual arteries, and a recall of 0.87 and specificity of 0.97 for individual patients. Applying and integrating the algorithm in healthcare units and dental clinics has the potential of reducing stroke events and their mortality and morbidity consequences.</div
Gradient-weighted class activation mapping (Grad-CAM) of a correct prediction of CAC and âcleanâ classes.
The colors indicate the region that has the greatest impact on the CAC prediction. The color range is presented below (ranging from red, representing the regions with the greatest impact on the CAC prediction, to blue, representing the regions with the lowest impact). It can be noticed that the classifier indeed focused on the region of the calcification signs. Other Grad-CAM of CAC and clean predications can be found in the S3 Fig and S4 Fig.</p
Sample size assessment: F1 score as a function of the sample size, based on random subsampling of 40%-80% of the original data.
Sample size assessment: F1 score as a function of the sample size, based on random subsampling of 40%-80% of the original data.</p
Probability calculations of the three patient types.
Probability calculations of the three patient types.</p
Figures E and F are panoramic corners with Triticeous Cartilage calcification.
The blue arrows point toward the calcification. Figures G and H are clean normal corners. (TIF)</p
Sequence of layers in the CNN used to predict CAC.
Sequence of layers in the CNN used to predict CAC.</p
Summaryâperformances âper corner âand âper patientâ.
Summaryâperformances âper corner âand âper patientâ.</p