Search results for: Intuitionistic L-fuzzy convex sub l-group

Authors: Zahid Ullah, Atlas Khan

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This abstract focuses on the advancements in mathematical modeling and optimization techniques that play a crucial role in enhancing the efficiency, reliability, and performance of these systems. In this era of rapidly evolving technology, mathematical modeling and optimization offer powerful tools to tackle the complex challenges faced by control, signal processing, and energy systems. This abstract presents the latest research and developments in mathematical methodologies, encompassing areas such as control theory, system identification, signal processing algorithms, and energy optimization. The abstract highlights the interdisciplinary nature of mathematical modeling and optimization, showcasing their applications in a wide range of domains, including power systems, communication networks, industrial automation, and renewable energy. It explores key mathematical techniques, such as linear and nonlinear programming, convex optimization, stochastic modeling, and numerical algorithms, that enable the design, analysis, and optimization of complex control and signal processing systems. Furthermore, the abstract emphasizes the importance of addressing real-world challenges in control, signal processing, and energy systems through innovative mathematical approaches. It discusses the integration of mathematical models with data-driven approaches, machine learning, and artificial intelligence to enhance system performance, adaptability, and decision-making capabilities. The abstract also underscores the significance of bridging the gap between theoretical advancements and practical applications. It recognizes the need for practical implementation of mathematical models and optimization algorithms in real-world systems, considering factors such as scalability, computational efficiency, and robustness. In summary, this abstract showcases the advancements in mathematical modeling and optimization techniques for control, signal processing, and energy systems. It highlights the interdisciplinary nature of these techniques, their applications across various domains, and their potential to address real-world challenges. The abstract emphasizes the importance of practical implementation and integration with emerging technologies to drive innovation and improve the performance of control, signal processing, and energy.

Keywords: mathematical modeling, optimization, control systems, signal processing, energy systems, interdisciplinary applications, system identification, numerical algorithms

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Authors: M. Amparo Nunez-Andres, Nieves Lantada

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One of the most harmful geological risks is rockfalls. They cause both economic lost, damaged in buildings and infrastructures, and personal ones. Therefore, in order to estimate the risk of the exposed elements, it is necessary to know the mechanism of this kind of events, since the characteristics of the rock walls, to the propagation of fragments generated by the initial detached rock mass. In the framework of the research RockModels project, several inventories of rockfalls were carried out along the northeast of the Spanish peninsula and the Mallorca island. These inventories have general information about the events, although the important fact is that they contained detailed information about fragmentation. Specifically, the IBSD (Insitu Block Size Distribution) is obtained by photogrammetry from drone or TLS (Terrestrial Laser Scanner) and the RBSD (Rock Block Size Distribution) from the volume of the fragment in the deposit measured by hand. In order to share all this information with other scientists, engineers, members of civil protection, and stakeholders, it is necessary a platform accessible from the internet and following interoperable standards. In all the process, open-software have been used: PostGIS 2.1., Geoserver, and OpenLayers library. In the first step, a spatial database was implemented to manage all the information. We have used the data specifications of INSPIRE for natural risks adding specific and detailed data about fragmentation distribution. The next step was to develop a WMS with Geoserver. A previous phase was the creation of several views in PostGIS to show the information at different scales of visualization and with different degrees of detail. In the first view, the sites are identified with a point, and basic information about the rockfall event is facilitated. In the next level of zoom, at medium scale, the convex hull of the rockfall appears with its real shape and the source of the event and fragments are represented by symbols. The queries at this level offer a major detail about the movement. Eventually, the third level shows all elements: deposit, source, and blocks, in their real size, if it is possible, and in their real localization. The last task was the publication of all information in a web mapping site (www.rockdb.upc.edu) with data classified by levels using libraries in JavaScript as OpenLayers.

Keywords: geological risk, web mapping, WMS, rockfalls

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Authors: Yousif M. Makeen

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This study presents the results of the sedimentological and petrographical analyses on the cored samples from the Bentiu Formation. The cored intervals consist of thick beds of sandstone, which are sometimes intercalated with beds of fine-grained sandstone and, in a minor case, with a siltstone bed. Detailed sedimentological facies analysis revealed the presence of six facies types, which can be clarified in order of their great percentage occurrences as follows: (i) Massive sandstone, (ii) Planar cross-bedded sandstone, (iii) Trough cross-bedded sandstone, (iv) Fine laminated sandstone (v) Fine laminated siltstone and (vi) Horizontally parted sandstone. The petrographical analyses under the plane polarized microscope and the scanning electron microscope (SEM) for the sandstone lithofacies types that exist within the cored intervals allowed classifying these lithofacies into Kaolinitic Subfeldspathic Arenites. Among the detrital components, quartz grains are the most abundant (mainly monocrystalline quartz), followed by feldspars, micas, detrital and authigenic clays, and carbonaceous debris. However, traces of lithic fragments, iron oxides and heavy minerals were observed in some of the analyzed samples, where they occur in minor amounts. Kaolinite is present mainly as an authigenic component in most of the analyzed samples, while quartz overgrowths occur in variable amounts in most of the investigated samples. Carbonates (calcite & siderite) are present in considerable amounts. The grain roundness in most of the investigated sandstone samples ranges from well-rounded to round, and, in fewer samples, is sub-angular to angular. Most of the sandstone samples are moderately compacted and display point, concavo-convex and long grain contacts, whereas the sutured grain contacts, which reflect a higher degree of compaction, are relatively observed in lesser amounts, while the float grain contact has also been observed in minor quantity. Pore types in the analyzed samples are dominantly primary and secondary interparticle forms. Point-counted porosity values range from 19.6% to 30%. Average pore sizes are highly variable and range from 20 to 350 microns. Pore interconnectivity ranges from good to very good.

Keywords: sandstone, sedimentological facies, porosity, quartz overgrowths

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Authors: Xiangtuo Chen, Paul-Henry Cournéde

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Crop yield prediction is a paramount issue in agriculture. The main idea of this paper is to find out efficient way to predict the yield of corn based meteorological records. The prediction models used in this paper can be classified into model-driven approaches and data-driven approaches, according to the different modeling methodologies. The model-driven approaches are based on crop mechanistic modeling. They describe crop growth in interaction with their environment as dynamical systems. But the calibration process of the dynamic system comes up with much difficulty, because it turns out to be a multidimensional non-convex optimization problem. An original contribution of this paper is to propose a statistical methodology, Multi-Scenarios Parameters Estimation (MSPE), for the parametrization of potentially complex mechanistic models from a new type of datasets (climatic data, final yield in many situations). It is tested with CORNFLO, a crop model for maize growth. On the other hand, the data-driven approach for yield prediction is free of the complex biophysical process. But it has some strict requirements about the dataset. A second contribution of the paper is the comparison of these model-driven methods with classical data-driven methods. For this purpose, we consider two classes of regression methods, methods derived from linear regression (Ridge and Lasso Regression, Principal Components Regression or Partial Least Squares Regression) and machine learning methods (Random Forest, k-Nearest Neighbor, Artificial Neural Network and SVM regression). The dataset consists of 720 records of corn yield at county scale provided by the United States Department of Agriculture (USDA) and the associated climatic data. A 5-folds cross-validation process and two accuracy metrics: root mean square error of prediction(RMSEP), mean absolute error of prediction(MAEP) were used to evaluate the crop prediction capacity. The results show that among the data-driven approaches, Random Forest is the most robust and generally achieves the best prediction error (MAEP 4.27%). It also outperforms our model-driven approach (MAEP 6.11%). However, the method to calibrate the mechanistic model from dataset easy to access offers several side-perspectives. The mechanistic model can potentially help to underline the stresses suffered by the crop or to identify the biological parameters of interest for breeding purposes. For this reason, an interesting perspective is to combine these two types of approaches.

Keywords: crop yield prediction, crop model, sensitivity analysis, paramater estimation, particle swarm optimization, random forest

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Authors: Lana Damaj, Vincent Laur, Azar Maalouf, Alexis Chevalier

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Matched termination is an important part of the passive waveguide components. It is typically used at the end of a waveguide transmission line to prevent reflections and improve signal quality. Waveguide terminations (loads) are commonly used in microwave and RF applications. In traditional microwave architectures, usually, waveguide termination consists of a standard rectangular waveguide made by a lossy resistive material, and ended by shorting metallic plate. These types of terminations are used, to dissipate the energy as heat. However, these terminations may increase the size and the weight of the overall system. New alternative solution consists in developing terminations based on 3D-printing of materials. Designing such terminations is very challenging since it should meet the requirements imposed by the system. These requirements include many parameters such as the absorption, the power handling capability in addition to the cost, the size and the weight that have to be minimized. 3D-printing is a shaping process that enables the production of complex geometries. It allows to find best compromise between requirements. In this paper, a comparison study has been made between different existing and new shapes of waveguide terminations. Indeed, 3D printing of absorbers makes it possible to study not only standard shapes (wedge, pyramid, tongue) but also more complex topologies such as exponential ones. These shapes have been designed and simulated using CST MWS®. The loads have been printed using the carbon-filled PolyLactic Acid, conductive PLA from ProtoPasta. Since the terminations has been characterized in the X-band (from 8GHz to 12GHz), the rectangular waveguide standard WR-90 has been selected. The classical wedge shape has been used as a reference. First, all loads have been simulated with the same length and two parameters have been compared: the absorption level (level of |S11|) and the dissipated power density. This study shows that the concave exponential pyramidal shape has the better absorption level and the convex exponential pyramidal shape has the better dissipated power density level. These two loads have been printed in order to measure their properties. A good agreement between the simulated and measured reflection coefficient has been obtained. Furthermore, a study of material structuring based on the honeycomb hexagonal structure has been investigated in order to vary the effective properties. In the final paper, the detailed methodology and the simulated and measured results will be presented in order to show how 3D-printing can allow controlling mass, weight, absorption level and power behaviour.

Keywords: additive manufacturing, electromagnetic composite materials, microwave measurements, passive components, power handling capacity (PHC), 3D-printing

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Authors: Vixen Joshua Tan, Siyuan He

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Scanners have been implemented within single point laser rangefinders, to determine the ranges within an environment by sweeping the laser spot across the surface of interest. The research motivation is to exploit a smaller and cheaper alternative scanning component for the emitting portion within current designs of laser rangefinders. This research implements an FPCB (Flexible Programmable Circuit Board) Electromagnetic 1-Dimensional scanning micro-mirror as a scanning component for laser rangefinding by means of triangulation. The prototype uses a laser module, micro-mirror, and receiver. The laser module is infrared (850 nm) with a power output of 4.5 mW. The receiver consists of a 50 mm convex lens and a 45mm 1-dimensional PSD (Position Sensitive Detector) placed at the focal length of the lens at 50 mm. The scanning component is an elliptical Micro-Mirror attached onto an FPCB Structure. The FPCB structure has two miniature magnets placed symmetrically underneath it on either side, which are then electromagnetically actuated by small solenoids, causing the FPCB to mechanically rotate about its torsion beams. The laser module projects a laser spot onto the micro-mirror surface, hence producing a scanning motion of the laser spot during the rotational actuation of the FPCB. The receiver is placed at a fixed distance from the micro-mirror scanner and is oriented to capture the scanning motion of the laser spot during operation. The elliptical aperture dimensions of the micro-mirror are 8mm by 5.5 mm. The micro-mirror is supported by an FPCB with two torsion beams with dimensions of 4mm by 0.5mm. The overall length of the FPCB is 23 mm. The voltage supplied to the solenoids is sinusoidal with an amplitude of 3.5 volts and 4.5 volts to achieve optical scanning angles of +/- 10 and +/- 17 degrees respectively. The operating scanning frequency during experiments was 5 Hz. For an optical angle of +/- 10 degrees, the prototype is capable of detecting objects within the ranges from 0.3-1.2 meters with an error of less than 15%. As for an optical angle of +/- 17 degrees the measuring range was from 0.3-0.7 meters with an error of 16% or less. Discrepancy between the experimental and actual data is possibly caused by misalignment of the components during experiments. Furthermore, the power of the laser spot collected by the receiver gradually decreased as the object was placed further from the sensor. A higher powered laser will be tested to potentially measure further distances more accurately. Moreover, a wide-angled lens will be used in future experiments when higher scanning angles are used. Modulation within the current and future higher powered lasers will be implemented to enable the operation of the laser rangefinder prototype without the use of safety goggles.

Keywords: FPCB electromagnetic 1-D scanning micro-mirror, laser rangefinder, position sensitive detector, PSD, triangulation

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Authors: Ibrahim Rassoul, A. Serir, E-K. Si Ahmed, J. Legrand

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The acronym PEM refers to Proton Exchange Membrane or alternatively Polymer Electrolyte Membrane. Due to its high efficiency, low operating temperature (30–80 °C), and rapid evolution over the past decade, PEMFCs are increasingly emerging as a viable alternative clean power source for automobile and stationary applications. Before PEMFCs can be employed to power automobiles and homes, several key technical challenges must be properly addressed. One technical challenge is elucidating the mechanisms underlying water transport in and removal from PEMFCs. On one hand, sufficient water is needed in the polymer electrolyte membrane or PEM to maintain sufficiently high proton conductivity. On the other hand, too much liquid water present in the cathode can cause “flooding” (that is, pore space is filled with excessive liquid water) and hinder the transport of the oxygen reactant from the gas flow channel (GFC) to the three-phase reaction sites. The experimental transparent fuel cell used in this work was designed to represent actual full scale of fuel cell geometry. According to the operating conditions, a number of flow regimes may appear in the microchannel: droplet flow, blockage water liquid bridge /plug (concave and convex forms), slug/plug flow and film flow. Some of flow patterns are new, while others have been already observed in PEMFC microchannels. An algorithm in MATLAB was developed to automatically determine the flow structure (e.g. slug, droplet, plug, and film) of detected liquid water in the test microchannels and yield information pertaining to the distribution of water among the different flow structures. A video processing algorithm was developed to automatically detect dynamic and static liquid water present in the gas channels and generate relevant quantitative information. The potential benefit of this software allows the user to obtain a more precise and systematic way to obtain measurements from images of small objects. The void fractions are also determined based on images analysis. The aim of this work is to provide a comprehensive characterization of two-phase flow in an operating fuel cell which can be used towards the optimization of water management and informs design guidelines for gas delivery microchannels for fuel cells and its essential in the design and control of diverse applications. The approach will combine numerical modeling with experimental visualization and measurements.

Keywords: polymer electrolyte fuel cell, air-water two phase flow, gas diffusion layer, microchannels, advancing contact angle, receding contact angle, void fraction, surface tension, image processing

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Authors: Mir Jalil Razavi, Tianming Liu, Xianqiao Wang

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Cortical folding, characterized by convex gyri and concave sulci, has an intrinsic relationship to the brain’s functional organization. Understanding the mechanism of the brain’s convoluted patterns can provide useful clues into normal and pathological brain function. During the development, the cerebral cortex experiences a noticeable expansion in volume and surface area accompanied by tremendous tissue folding which may be attributed to many possible factors. Despite decades of endeavors, the fundamental mechanism and key regulators of this crucial process remain incompletely understood. Therefore, to taking even a small role in unraveling of brain folding mystery, we present a mechanical model to find mechanism of 3-hinges formation in a growing brain that it has not been addressed before. A 3-hinge is defined as a gyral region where three gyral crests (hinge-lines) join. The reasons that how and why brain prefers to develop 3-hinges have not been answered very well. Therefore, we offer a theoretical and computational explanation to mechanism of 3-hinges formation in a growing brain and validate it by experimental observations. In theoretical approach, the dynamic behavior of brain tissue is examined and described with the aid of a large strain and nonlinear constitutive model. Derived constitute model is used in the computational model to define material behavior. Since the theoretical approach cannot predict the evolution of cortical complex convolution after instability, non-linear finite element models are employed to study the 3-hinges formation and secondary morphological folds of the developing brain. Three-dimensional (3D) finite element analyses on a multi-layer soft tissue model which mimics a small piece of the brain are performed to investigate the fundamental mechanism of consistent hinge formation in the cortical folding. Results show that after certain amount growth of cortex, mechanical model starts to be unstable and then by formation of creases enters to a new configuration with lower strain energy. By further growth of the model, formed shallow creases start to form convoluted patterns and then develop 3-hinge patterns. Simulation results related to 3-hinges in models show good agreement with experimental observations from macaque, chimpanzee and human brain images. These results have great potential to reveal fundamental principles of brain architecture and to produce a unified theoretical framework that convincingly explains the intrinsic relationship between cortical folding and 3-hinges formation. This achieved fundamental understanding of the intrinsic relationship between cortical folding and 3-hinges formation would potentially shed new insights into the diagnosis of many brain disorders such as schizophrenia, autism, lissencephaly and polymicrogyria.

Keywords: brain, cortical folding, finite element, three hinge

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Authors: Miranda E. Karban

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A distinctive pattern of occipital squama convexity, known as the occipital bun or chignon, has traditionally been considered a derived Neandertal trait. However, some early modern and extant Homo sapiens share similar occipital bone morphology, showing pronounced internal and external occipital squama curvature and paralambdoidal flattening. It has been posited that these morphological patterns are homologous in the two groups, but this claim remains disputed. Many developmental hypotheses have been proposed, including assertions that the chignon represents a developmental response to a long and narrow cranial vault, a narrow or flexed basicranium, or a prognathic face. These claims, however, remain to be metrically quantified in a large subadult sample, and little is known about the feature’s developmental, functional, or evolutionary significance. This study assesses patterns of chignon development and covariation in a comparative sample of extant human growth study cephalograms. Cephalograms from a total of 549 European-derived North American subjects (286 male, 263 female) were scored on a 5-stage ranking system of chignon prominence. Occipital squama shape was found to exist along a continuum, with 34 subjects (6.19%) possessing defined chignons, and 54 subjects (9.84%) possessing very little occipital squama convexity. From this larger sample, those subjects represented by a complete radiographic series were selected for metric analysis. Measurements were collected from lateral and posteroanterior (PA) cephalograms of 26 subjects (16 male, 10 female), each represented at 3 longitudinal age groups. Age group 1 (range: 3.0-6.0 years) includes subjects during a period of rapid brain growth. Age group 2 (range: 8.0-9.5 years) includes subjects during a stage in which brain growth has largely ceased, but cranial and facial development continues. Age group 3 (range: 15.9-20.4 years) includes subjects at their adult stage. A total of 16 landmarks and 153 sliding semi-landmarks were digitized at each age point, and geometric morphometric analyses, including relative warps analysis and two-block partial least squares analysis, were conducted to study covariation patterns between midsagittal occipital bone shape and other aspects of craniofacial morphology. A convex occipital squama was found to covary significantly with a low, elongated neurocranial vault, and this pattern was found to exist from the youngest age group. Other tested patterns of covariation, including cranial and basicranial breadth, basicranial angle, midcoronal cranial vault shape, and facial prognathism, were not found to be significant at any age group. These results suggest that the chignon, at least in this sample, should not be considered an independent feature, but rather the result of developmental interactions relating to neurocranial elongation. While more work must be done to quantify chignon morphology in fossil subadults, this study finds no evidence to disprove the developmental homology of the feature in modern humans and Neandertals.

Keywords: chignon, craniofacial covariation, human cranial development, longitudinal growth study, occipital bun

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Authors: Armin Nabaei, M. Omair Ahmad, M. N. S. Swamy

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Many facial expression and emotion recognition methods in the traditional approaches of using LDA, PCA, and EBGM have been proposed. In recent years deep learning models have provided a unique platform addressing by automatically extracting the features for the detection of facial expression and emotions. However, deep networks require large training datasets to extract automatic features effectively. In this work, we propose an efficient emotion detection algorithm using face images when only small datasets are available for training. We design a deep network whose feature extraction capability is enhanced by utilizing several parallel modules between the input and output of the network, each focusing on the extraction of different types of coarse features with fined grained details to break the symmetry of produced information. In fact, we leverage long range dependencies, which is one of the main drawback of CNNs. We develop this work by introducing a Dynamic Soft-Margin SoftMax.The conventional SoftMax suffers from reaching to gold labels very soon, which take the model to over-fitting. Because it’s not able to determine adequately discriminant feature vectors for some variant class labels. We reduced the risk of over-fitting by using a dynamic shape of input tensor instead of static in SoftMax layer with specifying a desired Soft- Margin. In fact, it acts as a controller to how hard the model should work to push dissimilar embedding vectors apart. For the proposed Categorical Loss, by the objective of compacting the same class labels and separating different class labels in the normalized log domain.We select penalty for those predictions with high divergence from ground-truth labels.So, we shorten correct feature vectors and enlarge false prediction tensors, it means we assign more weights for those classes with conjunction to each other (namely, “hard labels to learn”). By doing this work, we constrain the model to generate more discriminate feature vectors for variant class labels. Finally, for the proposed optimizer, our focus is on solving weak convergence of Adam optimizer for a non-convex problem. Our noteworthy optimizer is working by an alternative updating gradient procedure with an exponential weighted moving average function for faster convergence and exploiting a weight decay method to help drastically reducing the learning rate near optima to reach the dominant local minimum. We demonstrate the superiority of our proposed work by surpassing the first rank of three widely used Facial Expression Recognition datasets with 93.30% on FER-2013, and 16% improvement compare to the first rank after 10 years, reaching to 90.73% on RAF-DB, and 100% k-fold average accuracy for CK+ dataset, and shown to provide a top performance to that provided by other networks, which require much larger training datasets.

Keywords: computer vision, facial expression recognition, machine learning, algorithms, depp learning, neural networks

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Authors: A. C. Facin, M. C. Maronezi , M. P. Menezes, G. L. Montanhim, L. Pavan, M. A. R. Feliciano, R. P. Nociti, R. A. R. Uscategui, P. C. Moraes

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The incidence of brachycephalic syndrome (BS) in the clinical routine of small animals has increased significantly giving the higher proportion of brachycephalic pets in the last years and has been considered as an animal welfare problem. The treatment of BS is surgical and the clinical signs related can be considerably attenuated. Nevertheless, the systemic effects of the BS are still poorly reported and little is known about these when the surgical correction is not performed early. Affected dogs are more likely to develop cardiopulmonary, gastrointestinal and sleep disorders in which the chronic hypoxemia plays a major role. This syndrome is compared with the obstructive sleep apnea (OSA) in humans, both considered as causes of systemic and metabolic dysfunction. Among the several consequences of the BS little is known if the syndrome also affects the hepatic tissue of brachycephalic patients. Elastography is a promising ultrasound technique that evaluates tissue elasticity and has been recently used with the purpose of diagnosis of liver fibrosis. In medicine, it is a growing concern regarding the hepatic injury of patients affected by OSA. This prospective study hypothesizes if there is any consequence of BS in the hepatic parenchyma of brachycephalic dogs that don’t receive any surgical treatment. This study was conducted following the approval of the Animal Ethics and Welfare Committee of the Faculdade de Ciências Agrárias e Veterinárias, UNESP, Campus Jaboticabal, Brazil (protocol no 17944/2017) and funded by Sao Paulo Research Foundation (FAPESP, process no 2017/24809-4). The methodology was based in ARFI elastography using the ACUSON S2000/SIEMENS device, with convex multifrequential transducer and specific software as well as clinical evaluation of the syndrome, in order to determine if they can be used as a prognostic non-invasive tool. On quantitative elastography, it was collected three measures of shear wave velocity (meters per second) and depth in centimeters in the left lateral, left medial, right lateral, right medial and caudate lobe of the liver. The brachycephalic patients, 16 pugs and 30 french bulldogs, were classified using a previously established 4-point functional grading system based on clinical evaluation before and after a 3-minute exercise tolerance test already established and validated. The control group was based on the same features collected in 22 beagles. The software R version 3.3.0 was used for the analysis and the significance level was set at 0.05. The data were analysed for normality of residuals and homogeneity of variances by Shapiro-Wilks test. Comparisons of parametric continuous variables between breeds were performed by using ANOVA with a post hoc test for pair wise comparison. The preliminary results show significant statistic differences between the brachycephalic groups and the control group in all lobes analysed (p ≤ 0,05), with higher values of shear wave velocities in the hepatic tissue of brachycephalic dogs. In this context, the results obtained in this study contributes to the understanding of BS as well as its consequences in our patients, reflecting in evidence that one more systemic consequence of the syndrome may occur in brachycephalic patients, which was not related in the veterinary literature yet.

Keywords: airway obstruction, brachycephalic airway obstructive syndrome, hepatic injury, obstructive sleep apnea

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Authors: Adrian W. Egger, Savvas P. Triantafyllou, Eleni N. Chatzi

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The scaled boundary finite element method (SBFEM) is a semi-analytical numerical method, which introduces a scaling center in each element’s domain, thus transitioning from a Cartesian reference frame to one resembling polar coordinates. Consequently, an analytical solution is achieved in radial direction, implying that only the boundary need be discretized. The only limitation imposed on the resulting polygonal elements is that they remain star-convex. Further arbitrary p- or h-refinement may be applied locally in a mesh. The polygonal nature of SBFEM elements has been exploited in quadtree meshes to alleviate all issues conventionally associated with hanging nodes. Furthermore, since in 2D this results in only 16 possible cell configurations, these are precomputed in order to accelerate the forward analysis significantly. Any cells, which are clipped to accommodate the domain geometry, must be computed conventionally. However, since SBFEM permits polygonal elements, significantly coarser meshes at comparable accuracy levels are obtained when compared with conventional quadtree analysis, further increasing the computational efficiency of this scheme. The generalized stress intensity factors (gSIFs) are computed by exploiting the semi-analytical solution in radial direction. This is initiated by placing the scaling center of the element containing the crack at the crack tip. Taking an analytical limit of this element’s stress field as it approaches the crack tip, delivers an expression for the singular stress field. By applying the problem specific boundary conditions, the geometry correction factor is obtained, and the gSIFs are then evaluated based on their formal definition. Since the SBFEM solution is constructed as a power series, not unlike mode superposition in FEM, the two modes contributing to the singular response of the element can be easily identified in post-processing. Compared to the extended finite element method (XFEM) this approach is highly convenient, since neither enrichment terms nor a priori knowledge of the singularity is required. Computation of the gSIFs by SBFEM permits exceptional accuracy, however, when combined with hybrid quadtrees employing linear elements, this does not always hold. Nevertheless, it has been shown that crack propagation schemes are highly effective even given very coarse discretization since they only rely on the ratio of mode one to mode two gSIFs. The absolute values of the gSIFs may still be subject to large errors. Hence, we propose a post-processing scheme, which minimizes the error resulting from the approximation space of the cracked element, thus limiting the error in the gSIFs to the discretization error of the quadtree mesh. This is achieved by h- and/or p-refinement of the cracked element, which elevates the amount of modes present in the solution. The resulting numerical description of the element is highly accurate, with the main error source now stemming from its boundary displacement solution. Numerical examples show that this post-processing procedure can significantly improve the accuracy of the computed gSIFs with negligible computational cost even on coarse meshes resulting from hybrid quadtrees.

Keywords: linear elastic fracture mechanics, generalized stress intensity factors, scaled finite element method, hybrid quadtrees

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Authors: Hyohun Kim, Dongwha Shin, Yeonseok Kim, Ji-Su Ahn, Kensuke Nakamura, Dongeun Choi, Byung-Woo Hong

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Artefacts are commonly encountered in the imaging process of clinical computed tomography (CT) where the artefact refers to any systematic discrepancy between the reconstructed observation and the true attenuation coefficient of the object. It is known that CT images are inherently more prone to artefacts due to its image formation process where a large number of independent detectors are involved, and they are assumed to yield consistent measurements. There are a number of different artefact types including noise, beam hardening, scatter, pseudo-enhancement, motion, helical, ring, and metal artefacts, which cause serious difficulties in reading images. Thus, it is desired to remove nuisance factors from the degraded image leaving the fundamental intrinsic information that can provide better interpretation of the anatomical and pathological characteristics. However, it is considered as a difficult task due to the high dimensionality and variability of data to be recovered, which naturally motivates the use of machine learning techniques. We propose an image restoration algorithm based on the deep neural network framework where the denoising auto-encoders are stacked building multiple layers. The denoising auto-encoder is a variant of a classical auto-encoder that takes an input data and maps it to a hidden representation through a deterministic mapping using a non-linear activation function. The latent representation is then mapped back into a reconstruction the size of which is the same as the size of the input data. The reconstruction error can be measured by the traditional squared error assuming the residual follows a normal distribution. In addition to the designed loss function, an effective regularization scheme using residual-driven dropout determined based on the gradient at each layer. The optimal weights are computed by the classical stochastic gradient descent algorithm combined with the back-propagation algorithm. In our algorithm, we initially decompose an input image into its intrinsic representation and the nuisance factors including artefacts based on the classical Total Variation problem that can be efficiently optimized by the convex optimization algorithm such as primal-dual method. The intrinsic forms of the input images are provided to the deep denosing auto-encoders with their original forms in the training phase. In the testing phase, a given image is first decomposed into the intrinsic form and then provided to the trained network to obtain its reconstruction. We apply our algorithm to the restoration of the corrupted CT images by the artefacts. It is shown that our algorithm improves the readability and enhances the anatomical and pathological properties of the object. The quantitative evaluation is performed in terms of the PSNR, and the qualitative evaluation provides significant improvement in reading images despite degrading artefacts. The experimental results indicate the potential of our algorithm as a prior solution to the image interpretation tasks in a variety of medical imaging applications. This work was supported by the MISP(Ministry of Science and ICT), Korea, under the National Program for Excellence in SW (20170001000011001) supervised by the IITP(Institute for Information and Communications Technology Promotion).

Keywords: auto-encoder neural network, CT image artefact, deep learning, intrinsic image representation, noise reduction, total variation

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