Oscillations in deviating difference equations using an iterative technique.
Ontology highlight
ABSTRACT:
SUBMITTER: Chatzarakis GE
PROVIDER: S-EPMC5529606 | biostudies-other | 2017
REPOSITORIES: biostudies-other
Similar Datasets
Project description:In this talk I will present the recompression technique on the running example of word equations. In word equation problem we are given an equation The approach turned out to be quite robust and can be applied to various generalized, simplified and related problems, in particular, to problems in the area of grammar compressed words. I will comment on some of those applications.
| S-EPMC7206631 | biostudies-literature
Project description:This article describes a quantitative evaluation of visualizing small vessels using several image reconstruction methods in computed tomography. Simulated vessels with diameters of 1-6 mm made by 3D printer was scanned using 320-row detector computed tomography (CT). Hybrid iterative reconstruction (hybrid IR) and model-based iterative reconstruction (MBIR) were performed for the image reconstruction.
| S-EPMC5484979 | biostudies-literature
Project description:The purpose of this paper is to employ an alternative approach to reconstruct the standard variational iteration algorithm II proposed by He, including Lagrange multiplier, and to give a simpler formulation of Adomian decomposition and modified Adomian decomposition method in terms of newly proposed variational iteration method-II (VIM). Through careful investigation of the earlier variational iteration algorithm and Adomian decomposition method, we find unnecessary calculations for Lagrange multiplier and also repeated calculations involved in each iteration, respectively. Several examples are given to verify the reliability and efficiency of the method.
| S-EPMC3976783 | biostudies-other
Project description:Biological tissues are rarely transparent, presenting major challenges for deep tissue optical microscopy. The achievable imaging depth is fundamentally limited by wavefront distortions caused by aberration and random scattering. Here, we report an iterative wavefront compensation technique that takes advantage of the nonlinearity of multiphoton signals to determine and compensate for these distortions and to focus light inside deep tissues. Different from conventional adaptive optics methods, this technique can rapidly measure highly complicated wavefront distortions encountered in deep tissue imaging and provide compensations for not only aberration but random scattering. The technique is tested with a variety of highly heterogeneous biological samples including mouse brain tissue, skull, and lymph nodes. We show that high quality three-dimensional imaging can be realized at depths beyond the reach of conventional multiphoton microscopy and adaptive optics methods, albeit over restricted distances for a given correction. Moreover, the required laser excitation power can be greatly reduced in deep tissues, deviating from the power requirement of ballistic light excitation and thus significantly reducing photo damage to the biological tissue.
| S-EPMC3365222 | biostudies-literature
Project description:ObjectiveTo assess the feasibility of applying a deep learning-based denoising technique to coronary CT angiography (CCTA) along with iterative reconstruction for additional noise reduction.Materials and methodsWe retrospectively enrolled 82 consecutive patients (male:female = 60:22; mean age, 67.0 ± 10.8 years) who had undergone both CCTA and invasive coronary artery angiography from March 2017 to June 2018. All included patients underwent CCTA with iterative reconstruction (ADMIRE level 3, Siemens Healthineers). We developed a deep learning based denoising technique (ClariCT.AI, ClariPI), which was based on a modified U-net type convolutional neural net model designed to predict the possible occurrence of low-dose noise in the originals. Denoised images were obtained by subtracting the predicted noise from the originals. Image noise, CT attenuation, signal-to-noise ratio (SNR), and contrast-to-noise ratio (CNR) were objectively calculated. The edge rise distance (ERD) was measured as an indicator of image sharpness. Two blinded readers subjectively graded the image quality using a 5-point scale. Diagnostic performance of the CCTA was evaluated based on the presence or absence of significant stenosis (≥ 50% lumen reduction).ResultsObjective image qualities (original vs. denoised: image noise, 67.22 ± 25.74 vs. 52.64 ± 27.40; SNR [left main], 21.91 ± 6.38 vs. 30.35 ± 10.46; CNR [left main], 23.24 ± 6.52 vs. 31.93 ± 10.72; all p < 0.001) and subjective image quality (2.45 ± 0.62 vs. 3.65 ± 0.60, p < 0.001) improved significantly in the denoised images. The average ERDs of the denoised images were significantly smaller than those of originals (0.98 ± 0.08 vs. 0.09 ± 0.08, p < 0.001). With regard to diagnostic accuracy, no significant differences were observed among paired comparisons.ConclusionApplication of the deep learning technique along with iterative reconstruction can enhance the noise reduction performance with a significant improvement in objective and subjective image qualities of CCTA images.
| S-EPMC7458859 | biostudies-literature
Project description:This paper presents the approximate analytical solutions to solve the nonlinear gas dynamics and coupled Burger's equations with fractional time derivative. By using initial values, the explicit solutions of the equations are solved by using a reliable algorithm. Numerical results show that the new iterative method is easy to implement and accurate when applied to time-fractional partial differential equations.
| S-EPMC4391695 | biostudies-other
Project description:How epithelia transport fluid is a fundamental issue that is unresolved. Explanations offered include molecular engines, local transcellular osmosis, local paracellular osmosis, and paracellular fluid transport. On the basis of experimental and theoretical work done on corneal endothelium, a fluid transporting epithelium, we suggest electroosmotic coupling at the level of the intercellular junctions driven by the transendothelial electrical potential difference as an explanation of paracellular fluid transport. We collect frequency spectra of that potential difference in real-time. For what we believe is the first time for any epithelium, we report that, unexpectedly, the potential difference displays oscillations at many characteristic frequencies. We also show that on both stimulating cell activity and inhibiting ion transport mechanisms, there are corresponding changes in the oscillations amplitudes that mirror changes known previously in rates of fluid transport. We believe these findings provide a novel tool to study the kinetics of electrogenic elements such as channels and transporters, which from this evidence would give rise to current oscillations with characteristic periods going from 150 ms to 8 s.
| S-EPMC2741586 | biostudies-literature
Project description:BackgroundThe number of children with obesity has increased in Saudi Arabia, which is a significant public health concern. Early diagnosis of childhood obesity and screening of the prevalence is needed using a simple in situ method. This study aims to generate statistical equations to predict body fat percentage (BF%) for Saudi children by employing machine learning technology and to establish gender and age-specific body fat reference range.MethodsData was combined from two cross-sectional studies conducted in Saudi Arabia for 1,292 boys and girls aged 8-12 years. Body fat was measured in both studies using bio-electrical impedance analysis devices. Height and weight were measured and body mass index was calculated and classified according to CDC 2,000 charts. A total of 603 girls and 374 boys were randomly selected for the learning phase, and 153 girls and 93 boys were employed in the validation set. Analyses of different machine learning methods showed that an accurate, sensitive model could be created. Two regression models were trained and fitted with the construction samples and validated. Gradient boosting algorithm was employed to achieve a better estimation and produce the equations, then the root means squared error (RMSE) equation was performed to decrease the error. Body fat reference ranges were derived for children aged 8-12 years.ResultsFor the gradient boosting models, the predicted fat percentage values were more aligned with the true value than those in regression models. Gradient boosting achieved better performance than the regression equation as it combined multiple simple models into a single composite model to take advantage of that weak classifier. The developed predictive model archived RMSE of 3.12 for girls and 2.48 boys. BF% and Fat mass index charts were presented in which cut-offs for 5th, 75th and 95th centiles are used to define 'under-fat', 'normal', 'overfat' and 'subject with obesity'.ConclusionMachine learning models could represent a significant advancement for investigators studying adiposity-related issues in children. These models and newly developed centile charts could be useful tools for the estimation and classification of BF%.
| S-EPMC7908871 | biostudies-literature
Project description:Purpose. The purpose of this study was to evaluate the technical and diagnostic performance of sub-milliSievert ultralow-dose (ULD) CT colonograpy (CTC) in the detection of colonic and extracolonic lesions. Materials and Methods. CTC with standard dose (SD) and ULD acquisitions of 64 matched patients, half of them with colonic findings, were reconstructed with filtered back projection (FBP), hybrid (HIR) and iterative model reconstruction techniques (IMR). Image noise in six colonic segments, in the left psoas muscle and aorta were measured. Image quality of the left adrenal gland and of the colon in the endoscopic and 2D view was rated on a five point Likert scale by two observers, who also completed the reading of CTC for colonic and extracolonic findings. Results. The mean radiation dose estimate was 4.1 ± 1.4 mSv for SD and 0.86 ± 0.17 mSv for ULD for both positions (p < 0.0001). In ULD-IMR, SD-IMR and SD-HIR, the endoluminal noise was decreased in all colonic segments compared to SD-FBP (p < 0.001). There were 27 small (6-9 mm) and 17 large (≥10 mm) colonic lesions that were classified as sessile polyps (n = 38), flat lesions (n = 3), or as a mass (n = 3). Per patient sensitivity and specificity were 0.82 and 0.93 for ULD-FBP, 0.97 and 0.97 for ULD-HIR, 0.97 and 1.0 for ULD-IMR. Per polyp sensitivity was 0.84 for ULD-FBP, 0.98 for ULD-HIR, 0.98 for ULD-IMR. Significantly less extracolonic findings were detected in ULD-FBP and ULD-HIR, but in the E4 category by C-RADS (potentially important findings), the detection was similar. Conclusion. Both HIR and IMR are suitable for sub-milliSievert ULD CTC without sacrificing diagnostic performance of the study.
| S-EPMC4824919 | biostudies-literature
Project description:Crowdsourcing, understood as outsourcing work to a large network of people in the form of an open call, has been utilized successfully many times, including a very interesting concept involving the implementation of computer games with the objective of solving a scientific problem by employing users to play a game-so-called crowdsourced serious games. Our main objective was to verify whether such an approach could be successfully applied to the discovery of mathematical equations that explain experimental data gathered during the observation of a given dynamic system. Moreover, we wanted to compare it with an approach based on artificial intelligence that uses symbolic regression to find such formulae automatically. To achieve this, we designed and implemented an Internet game in which players attempt to design a spaceship representing an equation that models the observed system. The game was designed while considering that it should be easy to use for people without strong mathematical backgrounds. Moreover, we tried to make use of the collective intelligence observed in crowdsourced systems by enabling many players to collaborate on a single solution. The idea was tested on several hundred players playing almost 10,000 games and conducting a user opinion survey. The results prove that the proposed solution has very high potential. The function generated during weeklong tests was almost as precise as the analytical solution of the model of the system and, up to a certain complexity level of the formulae, it explained data better than the solution generated automatically by Eureqa, the leading software application for the implementation of symbolic regression. Moreover, we observed benefits of using crowdsourcing; the chain of consecutive solutions that led to the best solution was obtained by the continuous collaboration of several players.
| S-EPMC4701001 | biostudies-literature