User-defined Region Research Articles

Calcium Signal Analysis in the Zebrafish Heart via Phase Matching of the Cardiac Cycle.

Calcium signalling in the endocardium is critical for heart valve development. Calcium ion pulses in the endocardium are generated in response to mechanical forces due to blood flow and can be visualised in the beating zebrafish heart using a genetically encoded calcium indicator such as GCaMP7a. Analysing these pulses is challenging because of the rapid movement of the heart during heartbeat. This protocol outlines an imaging analysis method used to phase-match the cardiac cycle in single z-slice movies of the beating heart, allowing easy measurement of the calcium signal. Key features • Software to synchronise and analyse frames from movies of the beating heart corresponding to a user-defined phase of the cardiac cycle. • Software to measure the fluorescence intensity of the beating heart corresponding to a user-defined region of interest.

Adaptive fuzzy prescribed time tracking control for nonlinear systems with input saturation

This article investigates the adaptive fuzzy prescribed time tracking control problem for a class of strict-feedback systems simultaneously considering the user-defined asymmetric tracking performance, input saturation, and external disturbances. From the perspective of ensuring the reliability for control implementation, a saturation-based fixed-time funnel boundary is constructed by embedding the modification signals related to input saturation errors into a funnel function, which is capable of automatically enlarging or recovering itself when input saturation occurs or disappears, thereby reducing the risk of system singularity. Subsequently, by constructing a fixed-time tracking performance function, any known bounded tracking error is recast into a new variable with a zero initial value. With such a treatment, funnel boundaries are no longer redeveloped for different initial tracking errors, and meanwhile the behavior of the tracking error is pre-specified as needed over a finite time interval. Also, auxiliary systems are devised to generate the aforesaid modification signals, while compensating for the adverse impact resulting from input saturation. Remarkably, by feat of the backstepping design based on the fuzzy approximation, it is proven that the tracking error converges to a user-defined region within a prescribed time (known as the practically prescribed time tracking), which is achieved without the fractional power feedback of system states. Finally, two simulation examples are presented to confirm the feasibility and effectiveness of the developed approach.

A consistent volume-of-fluid approach for direct numerical simulation of the aerodynamic breakup of a vaporizing drop

A novel simulation framework has been developed in this study for the direct numerical simulation of the aerodynamic breakup of a vaporizing drop. The interfacial multiphase flow with phase change is resolved using a consistent geometric volume-of-fluid method. The bulk fluids are viscous and incompressible with surface tension at the interface. The newly-developed numerical methods have been implemented in the Basilisk solver, in which the adaptive octree/quadtree mesh is used for spatial discretization, allowing flexibility in dynamically refining the mesh in a user-defined region. The simulation framework is extensively validated by a series of benchmark cases, including the 1D Stefan and sucking problems, the growth of a 3D spherical bubble in a superheated liquid, and a 2D film boiling problem. The simulation results agree very well with the exact solution and previous numerical studies. 2D axisymmetric simulations were performed to resolve the vaporization of a moving drop with a low Weber number in a high-temperature free stream. The computed rate of volume loss agrees well with the empirical model of drop evaporation. Finally, the validated solver is used to simulate the aerodynamic breakup of an acetone drop at a high Weber number. A fully 3D simulation is performed and the morphological evolution of the drop is accurately resolved. The rate of vaporization is found to be significantly enhanced due to the drop deformation and breakup. The drop volume decreases nonlinearly in time and at a much higher rate than the empirical correlation for a spherical drop.

Window function design via fractional programming

The window functions formed from simple functions (e.g. trigonometric functions) have not utilized the degree of freedom (DOF) sufficiently, and thus they may not be optimal. In this paper, we derive two new window design algorithms via optimizing all window elements rather than the weighting coefficients of such simple functions, which are formulated as fractional programming models that only focus on minimizing the ratio of the maximum sidelobe level to the minimum level of the user-defined main energy region and that do not require masks or particular sidelobe level constraints. Especially, the first method is based on only the spectral mainlobe and sidelobe region information, whereas the second method is developed with only the range sidelobe region information from the view of pulse compression. Moreover, the solutions to the resultant nonlinear and nonconvex optimization problems are derived. Finally, simulation results show that proposed windows have advantages of enhanced spectral characteristics, better filtering performance, and improved range sidelobe suppression over their counterparts.

Traffic Monitoring from the Perspective of an Unmanned Aerial Vehicle

The paper is focused on the development of the experimental web-based solution for image processing from the perspective of an Unmanned Aerial Vehicle (UAV). Specifically, the research is carried out as part of the broader study on drone utilization in traffic at the Technical University of Kosice. This contribution explores the possibility of using the UAV as a tool to detect the temporal state of the traffic in multiple locations. Road traffic analysis is enabled through the detection of vehicles from the user-defined region of interest (ROI). Its content then serves as the input for motion detection, followed by the detection of vehicles using the YOLOv4 model. Detection of other types of objects is possible, thus making the system more universal. The vehicle is tracked after recognition in two consecutive frames. The tracking algorithm is based on the calculation of the Euclidean distance and the intersection of the rectangles. The experimental verification yields lower hardware requirements for CPU and GPU by about two FPS when using optimization techniques, such as ROI or reference dimensions of objects. The accuracy of detection and the subsequent tracking of cars reaches almost 100% while providing accurate trajectory determination.

Large-Scale Autonomous Flight With Real-Time Semantic SLAM Under Dense Forest Canopy

Semantic maps represent the environment using a set of semantically meaningful objects. This representation is storage-efficient, less ambiguous, and more informative, thus facilitating large-scale autonomy and the acquisition of actionable information in highly unstructured, GPS-denied environments. In this letter, we propose an integrated system that can perform large-scale autonomous flights and real-time semantic mapping in challenging under-canopy environments. We detect and model tree trunks and ground planes from LiDAR data, which are associated across scans and used to constrain robot poses as well as tree trunk models. The autonomous navigation module utilizes a multi-level planning and mapping framework and computes dynamically feasible trajectories that lead the UAV to build a semantic map of the user-defined region of interest in a computationally and storage efficient manner. A drift-compensation mechanism is designed to minimize the odometry drift using semantic SLAM outputs in real time, while maintaining planner optimality and controller stability. This leads the UAV to execute its mission accurately and safely at scale. Code is released at: https://github.com/KumarRobotics/kr_autonomous_flight and https://github.com/KumarRobotics/sloam.

An automated liver segmentation in liver iron concentration map using fuzzy c-means clustering combined with anatomical landmark data

BackgroundTo estimate median liver iron concentration (LIC) calculated from magnetic resonance imaging, excluded vessels of the liver parenchyma region were defined manually. Previous works proposed the automated method for excluding vessels from the liver region. However, only user-defined liver region remained a manual process. Therefore, this work aimed to develop an automated liver region segmentation technique to automate the whole process of median LIC calculation.Methods553 MR examinations from 471 thalassemia major patients were used in this study. LIC maps (in mg/g dry weight) were calculated and used as the input of segmentation procedures. Anatomical landmark data were detected and used to restrict ROI. After that, the liver region was segmented using fuzzy c-means clustering and reduced segmentation errors by morphological processes. According to the clinical application, erosion with a suitable size of the structuring element was applied to reduce the segmented liver region to avoid uncertainty around the edge of the liver. The segmentation results were evaluated by comparing with manual segmentation performed by a board-certified radiologist.ResultsThe proposed method was able to produce a good grade output in approximately 81% of all data. Approximately 11% of all data required an easy modification step. The rest of the output, approximately 8%, was an unsuccessful grade and required manual intervention by a user. For the evaluation matrices, percent dice similarity coefficient (%DSC) was in the range 86–92, percent Jaccard index (%JC) was 78–86, and Hausdorff distance (H) was 14–28 mm, respectively. In this study, percent false positive (%FP) and percent false negative (%FN) were applied to evaluate under- and over-segmentation that other evaluation matrices could not handle. The average of operation times could be reduced from 10 s per case using traditional method, to 1.5 s per case using our proposed method.ConclusionThe experimental results showed that the proposed method provided an effective automated liver segmentation technique, which can be applied clinically for automated median LIC calculation in thalassemia major patients.

InterPhon: Ab initio interface phonon calculations within a 3D electronic structure framework

This work provides the community with an easily executable open-source Python package designed to automize the evaluation of Interfacial Phonons (InterPhon). Its strategy of arbitrarily defining the interfacial region and periodicity alleviates the excessive computational cost in applying ab initio phonon calculations to interfaces and enables efficient extraction of interfacial phonons. InterPhon makes it possible to apply all of the phonon-based predictions that have been available for bulk systems, to interfacial systems. The first example, in which this package was applied to InAs surfaces, demonstrates a systematic structure search for unexplored surface reconstructions, navigated by the imaginary mode of surface phonons. It eventually explains the anisotropic surface vibrations of the polar crystal. The second example, involving oxygen adsorption on Cu, reveals adsorption-induced vibrational change and its contribution to energetic stability. The third example, on a Si/GaAs interface, shows distinct vibrational patterns depending on interfacial structures. It leads to a prediction regarding the structural transition of interfaces and unveils the processing conditions for spontaneous growth of GaAs nanowires on Si. High-level automation in InterPhon will be of great help in elucidating interfacial atomic dynamics and in implementing an automated computational workflow for diverse interfacial systems. Program summaryProgram title: InterPhonCPC Library link to program files:https://doi.org/10.17632/9xjh66g4z2.1Developer's repository link:https://github.com/inwonyeu/interphonCode Ocean capsule:https://codeocean.com/capsule/4380849Licensing provisions: LGPLv2.1Programming language: PythonSupplementary material: a PDF file describing details of phonon formalism using FDM, validation of symmetry functionality, InterPhon package architecture, method to define the interfacial region and convergence test, and calculation details for all of the results in this work.Nature of problem: The interface possesses diverse atomic structures and lattice vibrations, which are distinct from the bulk. In particular, interfacial phonons play the key roles to unveil the largely unexplored atomic dynamics within the localized region, and this information is essential to make a prediction regarding the dependence of interface structures on process conditions. However, there has been a limitation in applying ab initio phonon calculations to interfaces due to the excessive computational cost, introduced by their large number of atoms and broken symmetry. The problems are intrinsically inevitable within a three-dimensional (3D) DFT framework representing interfacial systems by supercells.Solution method: Although the main obstacles are unavoidable, distinct interfacial phonons are confined to the vicinity of the interface. By limiting the range of phonon calculations to user-defined interfacial region, the enormous computational cost is mitigated. The strategy is efficiently implemented in a Python library capable of calculation setup, evaluation, analysis, and visualization for arbitrary interfacial systems in conjunction with any 3D DFT code. All of the functionality is fully automated and the program execution can be managed through high-level user interfaces without difficulty.Additional comments: At the time of writing, the latest version of InterPhon is 1.3.0, in which the conjunction with VASP, Quantum ESPRESSO, and FHI-aims is supported.

Core-CT: A MATLAB application for the quantitative analysis of sediment and coral cores from X-ray computed tomography (CT)

X-ray computed tomography (CT) is a non-destructive imaging technique that provides three-dimensional (3D) visualisation and high-resolution quantitative data in the form of CT numbers. CT numbers are derived from the X-ray energy, effective atomic number and density of the analysed material. The sensitivity of the CT number to changes in material density means that it can be used to identify facies changes within sediment cores by detecting downcore shifts in sediment properties, and to quantify skeletal linear extension rates and internal biological erosion from coral cores. Here we present two algorithms to analyse CT scan images for geoscience research and package them within an open-source MATLAB application (Core-CT) that is freely available at GitHub (https://github.com/yuting-yan/Core-CT). The first algorithm computes CT numbers from a user-defined region of interest to identify boundaries of density change (e.g., sedimentary facies, laminations, coral growth bands). The second algorithm segments regions with major density contrast (e.g., internal void space or biogenic material) and provides 3D geometrical measurements of these irregularities. The versatility of Core-CT for geoscience is demonstrated for a range of environmental settings using both lake and marine sediment cores (Chile and Singapore) and coral cores (Red Sea). Core-CT analysis of sediment cores shows the application is able to: (1) distinguish episodic tsunami deposits from lacustrine sediments, (2) generate rapid and detailed measurement of varved sediments, and (3) identify sedimentary facies from an unsplit marine sediment core. When applied to coral cores, Core-CT can measure skeletal linear extension of annual growth bands and provide 3D visualisation and volumetric quantification of internal bioerosion cavities. Other potential applications of Core-CT include the identification of cryptotephra in sediment cores, or laminations in speleothem samples.

Perspective registration and multi-frame super-resolution of license plates in surveillance videos

One task often encountered in surveillance videos is the recognition of a target—e.g. the license plate of a vehicle. Often, the quality of a single video frame does not permit a reliable recognition. If multiple frames are available, it is possible to combine them in order to generate a single image with lower noise (frame averaging) and/or higher resolution (super-resolution). In order for these techniques to work, it is necessary to accurately estimate the motion of the object of interest in the recorded footage.In this paper, we introduce a method capable of accurately computing the perspective transformation that describes the motion of a planar object. The method minimizes the squared distance between the transformed image and a reference, computed over a user-defined region of interest, and uses the partial derivatives in order to significantly speed up the computation. This approach is inspired by the well known Kanade–Lucas–Tomasi feature tracker.

SnowCloudMetrics: Snow Information for Everyone

Snow is a critical component of the climate system, provides fresh water for millions of people globally, and affects forest and wildlife ecology. Snowy regions are typically data sparse, especially in mountain environments. Remotely-sensed snow cover data are available globally but are challenging to convert into accessible, actionable information. SnowCloudMetrics is a web portal for on-demand production and delivery of snow information including snow cover frequency (SCF) and snow disappearance date (SDD) using Google Earth Engine (GEE). SCF and SDD are computed using the Moderate Resolution Imaging Spectroradiometer (MODIS) Snow Cover Binary 500 m (MOD10A1) product. The SCF and SDD metrics are assessed using 18 years of Snow Telemetry records at more than 750 stations across the Western U.S. SnowCloudMetrics provides users with the capacity to quickly and efficiently generate local-to-global scale snow information. It requires no user-side data storage or computing capacity, and needs little in the way of remote sensing expertise. SnowCloudMetrics allows users to subset by year, watershed, elevation range, political boundary, or user-defined region. Users can explore the snow information via a GEE map interface and, if desired, download scripts for access to tabular and image data in non-proprietary formats for additional analyses. We present global and hemispheric scale examples of SCF and SDD. We also provide a watershed example in the transboundary, snow-dominated Amu Darya Basin. Our approach represents a new, user-driven paradigm for access to snow information. SnowCloudMetrics benefits snow scientists, water resource managers, climate scientists, and snow related industries providing SCF and SDD information tailored to their needs, especially in data sparse regions.

Top-k term publish/subscribe for geo-textual data streams

Massive amounts of data that contain spatial, textual, and temporal information are being generated at a rapid pace. With streams of such data, which includes check-ins and geo-tagged tweets, available, users may be interested in being kept up-to-date on which terms are popular in the streams in a particular region of space. To enable this functionality, we aim at efficiently processing two types of general top-k term subscriptions over streams of spatio-temporal documents: region-based top-k spatial-temporal term (RST) subscriptions and similarity-based top-k spatio-temporal term (SST) subscriptions. RST subscriptions continuously maintain the top-k most popular trending terms within a user-defined region. SST subscriptions free users from defining a region and maintain top-k locally popular terms based on a ranking function that combines term frequency, term recency, and term proximity. To solve the problem, we propose solutions that are capable of supporting real-life location-based publish/subscribe applications that process large numbers of SST and RST subscriptions over a realistic stream of spatio-temporal documents. The performance of our proposed solutions is studied in extensive experiments using two spatio-temporal datasets.

Bitmap generation from computer-aided design for potential layer-quality evaluation in electron beam additive manufacturing

PurposeElectron beam additive manufacturing (EBAM) is a popular additive manufacturing (AM) technique used by many industrial sectors. In EBAM process monitoring, data analysis is focused on information extraction directly from the raw data collected in-process, i.e. thermal/optical/electronic images, and the comparison between the collected data and the computed tomography/microscopy images generated after the EBAM process. This paper aims to postulate that a stack of bitmaps could be generated from the computer-aided design (CAD) at a range of Z heights and user-defined region of interest during file preparation of the EBAM process, and serve as a reference image set.Design/methodology/approachComparison between that and the workpiece images collected during the EBAM process could then be used for quality assessment purposes. In spite of the extensive literature on CAD slicing and contour generation for AM process preparation, the method of bitmap generation from the CAD model at different field of views (FOVs) has not been disseminated in detail. This article presents a piece of custom CAD-bitmap generation software and an experiment demonstrating the application of the software alongside an electronic imaging system prototype.FindingsResults show that the software is capable of generating binary bitmaps with user-defined Z heights, image dimensions and image FOVs from the CAD model; and can generate reference bitmaps to work with workpiece electronic images for potential pixel-to-pixel image comparison.Originality/valueIt is envisaged that this CAD-bitmap image generation ability opens up new opportunities in quality assessment for the in-process monitoring of the EBAM process.

Optimal Geometry for Ultra-wideband Localization using Bayesian Optimization

Abstract This paper introduces a novel algorithm to find a geometric configuration of ultra-wideband sources in order to provide optimal position estimation performance with Time-Difference-of-Arrival measurements. Different from existing works, we aim to achieve the best localization performance for a user-defined region of interest instead of a single target point. We employ an analysis based on the Cramer-Rao lower bound and dilution of precision to formulate an optimization problem. A Bayesian optimization-based algorithm is proposed to find an optimal geometry that achieves the smallest estimation variance upper bound while ensuring source placement constraints. The approach is validated through simulation and experimental results in 2D scenarios, showing an improvement over a naive source placement.

CoastSat: A Google Earth Engine-enabled Python toolkit to extract shorelines from publicly available satellite imagery

CoastSat is an open-source software toolkit written in Python that enables the user to obtain time-series of shoreline position at any sandy coastline worldwide from 30+ years (and growing) of publicly available satellite imagery. The toolkit exploits the capabilities of Google Earth Engine to efficiently retrieve Landsat and Sentinel-2 images cropped to any user-defined region of interest. The resulting images are pre-processed to remove cloudy pixels and enhance spatial resolution, before applying a robust and generic shoreline detection algorithm. This novel shoreline detection technique combines a supervised image classification and a sub-pixel resolution border segmentation to map the position of the shoreline with an accuracy of ~10 m. The purpose of CoastSat is to provide coastal managers, engineers and scientists a user-friendly and practical toolkit to monitor and explore their coastlines. The software is freely-available on GitHub (https://github.com/kvos/CoastSat) and is accompanied by guided examples (Jupyter Notebook) plus step-by-step README documentation.

A Novel CNN-Based CAD System for Early Assessment of Transplanted Kidney Dysfunction

This paper introduces a deep-learning based computer-aided diagnostic (CAD) system for the early detection of acute renal transplant rejection. For noninvasive detection of kidney rejection at an early stage, the proposed CAD system is based on the fusion of both imaging markers and clinical biomarkers. The former are derived from diffusion-weighted magnetic resonance imaging (DW-MRI) by estimating the apparent diffusion coefficients (ADC) representing the perfusion of the blood and the diffusion of the water inside the transplanted kidney. The clinical biomarkers, namely: creatinine clearance (CrCl) and serum plasma creatinine (SPCr), are integrated into the proposed CAD system as kidney functionality indexes to enhance its diagnostic performance. The ADC maps are estimated for a user-defined region of interest (ROI) that encompasses the whole kidney. The estimated ADCs are fused with the clinical biomarkers and the fused data is then used as an input to train and test a convolutional neural network (CNN) based classifier. The CAD system is tested on DW-MRI scans collected from 56 subjects from geographically diverse populations and different scanner types/image collection protocols. The overall accuracy of the proposed system is 92.9% with 93.3% sensitivity and 92.3% specificity in distinguishing non-rejected kidney transplants from rejected ones. These results demonstrate the potential of the proposed system for a reliable non-invasive diagnosis of renal transplant status for any DW-MRI scans, regardless of the geographical differences and/or imaging protocol.

Simultaneous Pu and U Isotope Nuclear Forensics on an Environmentally Recovered Hot Particle.

An environmentally recovered, mixed Pu-U hot particle from the Thule accident, Greenland has been analyzed by Scanning Electron Microscopy and a large-geometry Secondary Ion Mass Spectrometry based Scanning Ion Imaging (SII) method for simultaneous 235,236,238U and 239,240Pu isotope compositions. This SII technique permits the visual assessment of the spatial distribution of the isotopes of U and Pu and can be used to obtain quantitative isotope ratios in any user-defined square region up to a few 100 μm in size. The particle measured here has two resolvable U isotopic compositions with a single composition of weapons grade Pu. The bulk of the particle has enriched U and weapons-grade Pu with 235U/238U, 236U/238U, and 240Pu/239Pu of 1.12 ± 0.04, 0.006 ± 0.002, 0.054 ± 0.004, respectively (2σ). The Pu isotopic ratio was consistent across the sample but 239Pu/238Uraw decreased from 1.99 ± 0.07 to 0.11 ± 0.04 (2σ) corresponding to the area of the particle with a resolvably different U isotope composition. This portion of the particle has 235U/238U, 236U/238U, and 240Pu/239Pu ratios of 0.11 ± 0.04, 0.001 ± 0.002, and 0.05 ± 0.04, respectively (2σ). The origin of the less enriched U could be environmental that mixed with the particle or heterogeneously enriched U from the weapons. The heterogeneity of hot particles on a micrometer scale highlights the need for spatially resolved techniques to avoid mixing during a bulk or whole particle analysis, as the mixing end-members here would have been lost, and the measured ratios would have been inaccurate.

Dosimetric Impact of MRI Distortions: A Study on Head and Neck Cancers

To evaluate the effect of magnetic resonance (MR) imaging (MRI) geometric distortions on head and neck radiation therapy treatment planning (RTP) for an MRI-only RTP. We also assessed the potential benefits of patient-specific shimming to reduce the magnitude of MR distortions for a 3-T scanner. Using an in-house Matlab algorithm, shimming within entire imaging volumes and user-defined regions of interest were simulated. We deformed 21 patient computed tomography (CT) images with MR distortion fields (gradient nonlinearity and patient-induced susceptibility effects) to create distorted CT (dCT) images using bandwidths of 122 and 488Hz/mm at 3T. Field parameters from volumetric modulated arc therapy plans initially optimized on dCT data sets were transferred to CT data to compute a new plan. Both plans were compared to determine the impact of distortions on dose distributions. Shimming across entire patient volumes decreased the percentage of voxels with distortions of more than 2mm from 15.4% to 2.0%. Using the user-defined region of interest (ROI) shimming strategy, (here the Planning target volume (PTV) was the chosen ROI volume) led to increased geometric for volumes outside the PTV, as such voxels within the spinal cord with geometric shifts above 2 mm increased from 11.5% to 32.3%. The worst phantom-measured residual system distortions after 3-dimensional gradient nonlinearity correction within a radial distance of 200mm from the isocenter was 2.17mm. For all patients, voxels with distortion shifts of more than 2mm resulting from patient-induced susceptibility effects were 15.4% and 0.0% using bandwidths of 122Hz/mm and 488Hz/mm at 3T. Dose differences between dCT and CT treatment plans in D50 at the planning target volume were 0.4%±0.6% and 0.3%±0.5% at 122 and 488Hz/mm, respectively. The overall effect of MRI geometric distortions on data used for RTP was minimal. Shimming over entire imaging volumes decreased distortions, but user-defined subvolume shimming introduced significant errors in nearby organs and should probably be avoided.

Does acoustic radiation force elastography improve the diagnostic capability of ultrasound in the preoperative characterization of masses of the parotid gland?

Ultrasound is the method of choice for preoperative evaluation of tumours of the parotid glands. However, existing methods do not allow for clear differentiation between the most common benign tumours and malignant tumours. The aim of our study was to evaluate if acoustic radiation force, Virtual Touch Quantification (VTQ) elastography helps to improve the preoperative evaluation of parotid masses. We investigated the parenchyma of 102 parotid glands, 14 lymph nodes of healthy volunteers and 51 tumours of the parotid gland via ultrasound, colour Doppler ultrasound and VTQ. The results were matched with histopathology and analyzed. The perfusion in pleomorphic adenoma, the most frequent benign tumour of the parotid gland, was significantly lower in comparison to malignant tumours. All tumours showed statistically significant higher perfusion in comparison to the parenchyma or the lymph nodes of the gland. Shear wave velocity of the user-defined region of interest was statistically significant more frequently an overflow value higher than 8.5 m/s in total tumours in comparison to parenchyma or lymph nodes. The different tumour types presented no significant difference in the shear wave velocity. VTQ in combination with classical ultrasound examination provides additional data useful in distinguishing between benign and malignant tumours and thus shows promise for integration into preexisting ultrasound protocols. However, despite the improvement, clear differentiation of tumours is still not possible and further investigation is recommended.

FEAST eigensolver for nonlinear eigenvalue problems

The linear FEAST algorithm is a method for solving linear eigenvalue problems. It uses complex contour integration to calculate the eigenvectors associated with eigenvalues that are located inside some user-defined region in the complex plane. This makes it possible to parallelize the process of solving eigenvalue problems by simply dividing the complex plane into a collection of disjoint regions and calculating the eigenpairs in each region independently of the eigenpairs in the other regions. In this paper we present a generalization of the linear FEAST algorithm that can be used to solve nonlinear eigenvalue problems. Like its linear progenitor, the nonlinear FEAST algorithm can be used to solve nonlinear eigenvalue problems for the eigenpairs corresponding to eigenvalues that lie in a user-defined region in the complex plane, thereby allowing for the calculation of large numbers of eigenpairs in parallel. We describe the nonlinear FEAST algorithm, and use several physically motivated examples to demonstrate its properties.