Orders Of Magnitude Research Articles

Accelerating Globally Optimal Consensus Maximization in Geometric Vision.

Branch-and-bound-based consensus maximization stands out due to its important ability of retrieving the globally optimal solution to outlier-affected geometric problems. However, while the discovery of such solutions caries high scientific value, its application in practical scenarios is often prohibited by its computational complexity growing exponentially as a function of the dimensionality of the problem at hand. In this work, we convey a novel, general technique that allows us to branch over an n-1 dimensional space for an n-dimensional problem. The remaining degree of freedom can be solved globally optimally within each bound calculation by applying the efficient interval stabbing technique. While each individual bound derivation is harder to compute owing to the additional need for solving a sorting problem, the reduced number of intervals and tighter bounds in practice lead to a significant reduction in the overall number of required iterations. Besides an abstract introduction of the approach, we present applications to four fundamental geometric computer vision problems: camera resectioning, relative camera pose estimation, point set registration, and rotation and focal length estimation. Through our exhaustive tests, we demonstrate significant speed-up factors at times exceeding two orders of magnitude, thereby increasing the viability of globally optimal consensus maximizers in online application scenarios.

Study of the Accuracy of the Ronen Method at Material Interfaces

The Ronen Method (RM) is a nonlinear iterative scheme that demands successive resolutions of the diffusion equation, where local diffusion constants are modified to reproduce more accurate estimates of the neutron currents by a transport operator. The methodology is currently formulated using the formalism of the collision probability method for evaluation of the current. The RM was recently tested on a complete suite of one-dimensional (1-D) multigroup benchmark problems. Small differences in the flux (less than 2%) were reported at material interfaces and close to the vacuum boundary with respect to the reference solution from transport. This work investigates first a possible numerical equivalence between transport and diffusion in some representative 1-D problems from the same benchmark test suite. The equivalence is sought with optimal diffusion coefficients computed using reference transport solutions that allow for adjusting the diffusion model. The RM, which attempts to obtain such equivalent diffusion coefficients without knowing the reference solution, is then compared to the optimal coefficients. The accuracy of the flux distribution at material interfaces is investigated for different approximations of the vacuum boundary and by decreasing progressively the RM convergence tolerance set in the iterative scheme. Using tighter convergence criteria, the RM calculates more accurate flux distributions at all material interfaces, regardless of the value of the diffusion coefficient and the extrapolated distance set at the beginning of the iterative scheme. Maximum flux deviations are remarkably reduced when the RM convergence tolerance is set to eight or more significant digits, leading to improvements in the flux deviation of two orders in magnitude and providing numerical proof for equivalence with transport in the tested configurations.

Ultra-Sensitive Detection of the SARS-CoV-2 Nucleocapsid Protein via a Clustered Regularly Interspaced Short Palindromic Repeat/Cas12a-Mediated Immunoassay.

Tracking trace protein analytes in precision diagnostics is an ongoing challenge. Here, we developed an ultrasensitive detection method for the detection of SARS-CoV-2 nucleocapsid (N) protein by combining enzyme-linked immunosorbent assay (ELISA) with the clustered regularly interspaced short palindromic repeat/CRISPR-associated protein (CRISPR/Cas) system. First, the SARS-CoV-2 N protein bound by the capture antibody adsorbed on the well plate was sequentially coupled with the primary antibody, biotinylated secondary antibody, and streptavidin (SA), followed by biotin primer binding to SA. Subsequently, rolling circle amplification was initiated to generate ssDNA strands, which were targeted by CRISPR/Cas12a to cleave the FAM-ssDNA-BHQ1 probe in trans to generate fluorescence signals. We observed a linear relationship between fluorescence intensity and the logarithm of N protein concentration ranging from 3 fg/mL to 3 × 107 fg/mL. The limit of detection (LOD) was 1 fg/mL, with approximately nine molecules in 1 μL of the sample. This detection sensitivity was 4 orders magnitude higher than that of commercially available ELISA kits (LOD: 5.7 × 104 fg/mL). This method was highly specific and sensitive and could accurately detect SARS-CoV-2 pseudovirus and clinical samples, providing a new approach for ultrasensitive immunoassay of protein biomarkers.

Combustion performance of hydrogen fueled parallel wall-jet used for drag reduction in a supersonic combustor

Hydrogen fueled parallel wall-jet combustion is considered to be one of the most promising drag reduction technologies in supersonic combustors, researchers mainly focus on its drag reduction mechanism, while balancing its combustion efficiency and drag reduction performance is of great significance for engine performance and energy conservation. In this paper, combustion performance of hydrogen fueled parallel wall-jet is numerically investigated. Kinetic reaction rate and scalar dissipation rate are defined to decouple the chemical reaction and mixing processes. Results indicate that although hydrogen fueled parallel wall-jet combustion is a nonequilibrium chemical reaction process, the combustion process is dominated by mixing due to the much larger magnitude order of kinetic reaction rate. The investigation also reveals that, compared to the effects of mainstream total temperature, mainstream Mach number presents a more significant effect on combustion efficiency. Moreover, combustion efficiency increase first brings negative and then brings beneficial effects on drag reduction performance, which is due to the different sensibilities of the two skin friction determinants viscosity and velocity gradient to combustion efficiency. It is found that, viscosity is more sensitive to combustion efficiency, with combustion efficiency increases by 5.4 %, viscosity increases by 4.15 %, while velocity gradient only decreases by 2.19 %.

Effects of cell parameters on accurate calculation of activation dose after DT explosion for local hot spots in laser-driven ICF facilities

Instruments placed in the target chamber will be highly activated after DT explosion in laser-driven ICF experiments, especially for the part near the chamber center. Operations near those local hot spots are the main concern for radiation protection due to its high contribution to the occupation exposure dose, therefore it becomes very important to calculate the dose during the operating process accurately. Cell-based rigorous two-step (R2S) method has been introduced to deal with the activated objects with highly heterogeneous distribution, and the effects of cell size, materials as well as radiation source have also been specified to improve the accuracy of simulations. Results for a typical model sample show that with a given distribution of radiation source, cell size in the simulations placed a significant influence on the accuracy of the radiation field. A cell size of 50 cm for a 100 cm cone-shaped sample will lead to the inaccuracy of the radiation field as large as an order in magnitude within the location 50 cm from the surface of the sample. While for the same sample model, cell size should be limited to smaller than 2 cm to ensure an accuracy lower than ±10 %. In addition, the effects of the material and source energy on the calculation accuracy for the radiation field could be neglected if the cell size is limited to smaller than 5 cm. Furthermore, the influence of cell size increased as the distance from the sample surface decreased, which indicates that appropriate cell size must be chosen to ensure the accuracy of dose estimation, especially for surface contact operations. Besides, a significant difference between the effective dose and skin-equivalent dose has been observed for the typical mode used in the calculations.

FLASH FLOODS: RISK ASSESSMENT AND MITIGATION

In recent years, United Arab Emirates has experienced several flash flood events and extreme cyclonic events that resulted in flooding various parts of the country. This in return raised concerns on the preparedness of the infrastructure to such events considering the damage caused by them. Roads were blocked from the excessive rainfall water leading to heavy traffic jams, houses were drowned and cars were swept away. Therefore, an in-depth study was performed on a selected area of interest in the city of Ras Al-Khaimah (UAE) to explore the risks associated with flash flood events and to propose solutions for flood management. Hydrological and hydraulic models were used to simulate precipitation runoffs and calculate flood magnitudes in order to plan and design new flood control and hydraulic structures. Using the output of the hydrologic and hydraulic models, a dam and a protection channel were proposed as possible solutions to resolve flood issues in the selected area. It was concluded that with proper hydrologic modelling, flash floods can be managed to a great extent and damage to the infrastructure can be minimized. It is even more important in context of climate change that such modelling techniques should be part of urban planning and design of infrastructure drainage systems for areas that are prone to heavy rainfall and floods.

MPSketch: Message Passing Networks via Randomized Hashing for Efficient Attributed Network Embedding.

Given a network, it is well recognized that attributed network embedding represents each node of the network in a low-dimensional space, and, thus, brings considerable benefits for numerous graph mining tasks. In practice, a diverse set of graph tasks can be processed efficiently via the compact representation that preserves content and structure information. The majority of attributed network embedding approaches, especially, the graph neural network (GNN) algorithms, are substantially costly in either time or space due to the expensive learning process, while the randomized hashing technique, locality-sensitive hashing (LSH), which does not need learning, can speedup the embedding process at the expense of losing some accuracy. In this article, we propose the MPSketch model, which bridges the performance gap between the GNN framework and the LSH framework by adopting the LSH technique to pass messages and capture high-order proximity in a larger aggregated information pool from the neighborhood. The extensive experimental results confirm that in node classification and link prediction, the proposed MPSketch algorithm enjoys performance comparable to the state-of-the-art learning-based algorithms and outperforms the existing LSH algorithms, while running faster than the GNN algorithms by 3-4 orders of magnitude. More precisely, MPSketch runs 2121, 1167, and 1155 times faster than GraphSAGE, GraphZoom, and FATNet on average, respectively.

Testing analytical methods to derive the cosmic-ray ionisation rate in cold regions via synthetic observations

Context. Cosmic rays (CRs) heavily impact the chemistry and physics of cold and dense star-forming regions. However, the characterisation of their ionisation rate continues to pose a challenge from the observational point of view. Aims. In the past, a few analytical formulas have been proposed to infer the cosmic-ray ionisation rate, ζ2, from molecular line observations. These have been derived from the chemical kinetics of the involved species, but they have not yet been validated using synthetic data processed with a standard observative pipeline. In this work, we aim to bridge this gap. Methods. We performed a radiative transfer on a set of three-dimensional magneto-hydrodynamical simulations of prestellar cores, exploring different initial ζ2, evolutionary stages, types of radiative transfer (for instance assuming local-thermodynamic-equilibrium conditions), and telescope responses. We then computed the column densities of the involved tracers to determine ζ2, employing a recently proposed method based on the detection of H2D+. We compared this approach with a previous method, based on more common tracers. Both approaches are commonly used. Results. Our results confirm that the equation based on the detection of H2D+ accurately retrieves the actual ζ2 within a factor of two to three in the physical conditions explored in our tests. Since we have also explored a non-local thermodynamic equilibrium (non-LTE) radiative transfer, this work indirectly offers insights into the excitation temperatures of common transitions at moderate volume densities (n ≈ 105 cm−3). We also performed a few tests using a previous methodology that is independent of H2D+, which overestimates the actual ζ2 by at least two orders of magnitude. We considered a new derivation of this method, however, we found that it still leads to high over-estimations. Conclusions. The method based on H2D+ is further validated in this work and demonstrates a reliable method for estimating ζ2 in cold and dense gas. On the contrary, the former analytical equation, as already pointed out by its authors, has no global domain of application. Thus, we find that it ought to be employed with caution.

Correlation of quantum well periods on the 3rd order nonlinear optical responses of InGaN/GaN heterostructures

Semiconductor multi quantum well (MQW) design allows for the compression of electron-interaction dimensions, offering advantages for various applications, particularly in nonlinear optics. Despite the potential improvements in nonlinear optical responses, the influence of quantum well periods remains unexplored. In this study, we report the correlation of quantum well periods on the 3rd order nonlinear optical properties in In0.15 Ga0.85 N/GaN MQW using z-scan technique under femtosecond and continous wave laser regime. In0.15 Ga0.85 N well/GaN barrier with x1, x5, x10, x15 periods were grown by MOCVD technique. Good structural quality of grown MQWs were confirmed via HRTEM imaging, EDS, AFM and XRD. Absorption coefficient from UV-Vis coupled with PL emission spectrum shows systematic response of optical linear properties which provide an insight on the overall band gap structure. Positive nonlinear refraction, n2 and nonlinear absoprtion, β trends is observed under femtosecond an CW laser albeit differences of one order magnitude in χ3 value. The increase in χ3 value is shown to be monotonous with the increasing number of quantum well suggesting that compounding effect took place. This findings indicate the possibility of manipulating and tuning nonlinear reponses of MQW structures leading to improvement in semiconductor design in various areas such as optoelectronics, photonics, solar cell research, as well as quantum information processing.

Tunneling splittings using modified WKB method in Cartesian coordinates: The test case of vinyl radical.

Modified WKB theory for calculating tunneling splittings in symmetric multi-well systems in full dimensionality is re-derived using Cartesian coordinates. It is explicitly shown that the theory rests on the wavefunction that is exact for harmonic potentials. The theory was applied to calculate tunneling splittings in vinyl radical and some of its deuterated isotopologues in their vibrational ground states and the low-lying vibrationally excited states and compared to exact variational results. The exact results are reproduced within a factor of 2 in most states. Remarkably, all large enhancements of tunneling splittings relative to the ground state, up to three orders in magnitude in some excited mode combinations, are well reproduced. It is also shown that in the asymmetrically deuterated vinyl radical, the theory correctly predicts the states that are localized in a single well and the delocalized tunneling states. Modified WKB theory on the minimum action path is computationally inexpensive and can also be applied without modification to much larger systems in full dimensionality; the results of this test case serve to give insight into the expected accuracy of the method.

Multi-attribute decision-making analysis based on the bipolar N-soft PROMETHEE method

The multi-attribute decision-making (MADM) methods can deeply mine hidden information in data and make a more reliable decision with actual needs and human cognition. For this reason, this paper proposes the bipolar N-soft PROMETHEE (preference ranking organization method for enrichment of evaluation) method. The method fully embodies the advantages of the PROMETHEE method, which can limit the unconditional compensation between attribute values and effectively reflect the priority between attribute values. Further, by introducing an attribute threshold to filter research objects, the proposed method not only dramatically reduces the amount of computation but also considers the impact of the size of the attribute value itself on decision-making. Secondly, the paper proposes the concepts of attribute praise, attribute popularity, total praise, and total popularity for the first time, fully mining information from bipolar N-soft sets, which can effectively handle situations where attribute values have different orders of magnitude. In addition, this paper presents the decision-making process of the new method, closely integrating theoretical models with real life. Finally, this paper analyses and compares the proposed method with the existing ones, further verifying the effectiveness and flexibility of the proposed method.

Defects in Se, As2S3, and GeS2 glasses: Ab initio analyses of related clusters

Dangling bonds in Se, As2S3, and GeS2 glasses and wrong bonds in the compounds have been comparatively studied using an ab initio molecular-orbital software. Defect energies and the densities in the chalcogenide glasses are estimated from the total energy Et of small clusters such as H-nSe-H, As3S4H, and Ge4S4H. Properties of corner- and edge-shared connections are also explored for the As-S and Ge-S systems. The three kinds of clusters show for a meta-stable energy ΔEt, relative to the total energy Et of normal bonding structures, a magnitude order of ΔEt(IVAP) < ΔEt(2D0) < ΔEt(D+/D−). Based on this result, we discuss why only GeS2 exhibits unpaired electron spins. The analysis also manifests that ΔEts of clusters containing wrong bonds (As-As, Ge-Ge, and S-S) are comparable with those of ΔEt(IVAP). Regarding electronic levels, the three glasses seem to possess marked gap states having different origins.

The structure of the incidence of acute intestinal infections in children of the Southern Aral Sea region and bioimmune correction of intestinal microbiocenosis in shigellosis

BACKGROUND: The microbiome of the gastrointestinal tract ensures colonization resistance of the intestinal epithelium, produces enzymes, and participates in nutrient metabolism. Changes in its composition lead to pathological conditions of the intestines.AIM: To determine the structure of the incidence of acute intestinal infections in children living in the Southern Aral Sea region and to characterize the effect of bioimmune correction of changes in the intestinal microbiome in children with shigellosis.&#x0D; MATERIAL AND METHODS: In the period from 06.07.2020 to 05.10.2020, 179 children with intestinal infections aged 2 to 7 years living in an environmentally unfavorable zone of Southern Uzbekistan were examined. The children were divided into two groups: the first (32 children) received basic therapy (pathogenetic therapy, antibiotic therapy, diet), the second (11 children) received basic therapy with bioimmune correction with bifidobacteria bifidum (bifidumbacterin PL) and thymus peptides of sheep embryos and newborn lambs (immunomodulin). To characterize the microbiome, the material was screened on differential diagnostic media, identifying obligate, facultative and opportunistic microflora. To assess the statistical significance of differences between data groups, the Student's t test was used, taking p ≤0.05 as a significant level.&#x0D; RESULTS: Shigellosis was diagnosed in 43 sick children (24% of those examined), escherichiosis was diagnosed in 34 (19%), salmonellosis was diagnosed in 30 (16.3%), and diarrhea of other bacterial etiology was diagnosed in 23 (13%) patients. In all variants, changes in the intestinal microbiome were detected. Etiotropic therapy led to an improvement in the general condition of patients, but did not affect dysbiotic changes in the intestines and did not contribute to the restoration of the microbiome. Bioimmune correction of dysbiosis in shigellosis in 11 patients using preparations of bifidobacteria bifidum and fetal thymic peptides led to the restoration of intestinal microflora to normal values: the number of lactose-negative E. coli significantly decreased by more than 5 orders of magnitude (p=0.037), fungi of the genus Candida (p=0.030) and enterococci (p=0.019) by 3 orders of magnitude, and staphylococci by 2 orders of magnitude (p=0.048).&#x0D; CONCLUSION: The use of preparations of bifidobacteria bifidum and fetal thymus peptides as bioimmunocorrectors is a promising therapeutic strategy for shigellosis in children.

Quantifying Exhaled Particles in Healthy Humans During Various Respiratory Activities Under Realistic Conditions.

Background: Quantitatively collecting and characterizing exhaled aerosols is vital for infection risk assessment, but the entire droplet size spectrum has often been neglected. We analyzed particle number and size distribution of healthy participants in various respiratory activities, considering inter-individual variability, and deployed a simplified far-field model to inform on infection risks. Methods: Participants repeated the same respiratory activities on two visits. Particles were collected using an airtight extraction helmet supplied with High Efficiency Particulate Air (HEPA) filtered air. The sampling volume flow was transported to two particle counters covering the small and large particle spectrum. The applied simple mass balance model included respiratory activity, viral load, room size, and air exchange rates. Results: Thirty participants completed the study. The major fraction of the number-based size distribution was <5 μm in all respiratory activities. In contrast, the major fraction of the volume-based size distribution was 2-12 μm in tidal breathing, but >60 μm in all other activities. Aerosol volume flow was lowest in tidal breathing, 10-fold higher in quiet/normal speaking, deep breathing, coughing, and 100-fold higher in loud speaking/singing. Intra-individual reproducibility was high. Between participants, aerosol volume flow varied by two orders of magnitude in droplets <80 μm, and three orders of magnitude in droplets >80 μm. Simple model calculations not accounting for potential particle size-dependent differences in viral load and infection-related differences were used to model airborne pathogen concentrations. Conclusions: Quantitative analysis of exhaled aerosols for the entire droplet size spectrum as well as the variability in aerosol emission between individuals provides information that can support infection research. Clinical Trial Registration number: NCT04771585.

Evidence of apsidal motion and a possible co-moving companion star detected in the WASP-19 system

Context. Love numbers measure the reaction of a celestial body to perturbing forces, such as the centrifugal force caused by rotation, or tidal forces resulting from the interaction with a companion body. These parameters are related to the interior density profile. The non-point mass nature of the host star and a planet orbiting around each other contributes to the periastron precession. The rate of this precession is characterized mainly by the second-order Love number, which offers an opportunity to determine its value. When it is known, the planetary interior structure can be studied with one additional constraint beyond the mass, radius, and orbital parameters. Aims. We aim to re-determine the orbital period, eccentricity, and argument of the periastron for WASP-19Ab, along with a study of its periastron precession rate. We calculated the planetary Love number from the observed periastron precession rate, based on the assumption of the stellar Love number from stellar evolutionary models. Methods. We collected all available radial velocity (RV) data, along with the transit and occultation times from the previous investigations of the system. We supplemented the data set with 19 new RV data points of the host star WASP-19A obtained by HARPS. Here, we summarize the technique for modeling the RV observations and the photometric transit timing variations (TTVs) to determine the rate of periastron precession in this system for the first time. Results. We excluded the presence of a second possible planet up to a period of ~4200 d and with a radial velocity amplitude bigger than ≃ 1 m s−1. We show that a constant period is not able to reproduce the observed radial velocities. We also investigated and excluded the possibility of tidal decay and long-term acceleration in the system. However, the inclusion of a small periastron precession term did indeed improve the quality of the fit. We measured the periastron precession rate to be 233−35+25″d−1. By assuming synchronous rotation for the planet, it indicates a k2 Love number of 0.20−0.03+0.02 for WASP-19Ab. Conclusions. The derived k2,p value of the planet has the same order of magnitude as the estimated fluid Love number of other Jupiter-sized exoplanets (WASP-18Ab, WASP-103b, and WASP-121b). A low value of k2,p indicates a higher concentration of mass toward the planetary nucleus.

Quantifying the diffusion of suprathermal electrons by whistler waves between 0.2 and 1 AU with Solar Orbiter and Parker Solar Probe

Context. The evolution of the solar wind electron distribution function with heliocentric distance exhibits different features that are still unexplained, in particular, the fast decrease in the electron heat flux and the increase in the Strahl pitch angle width. Wave-particle interactions between electrons and whistler waves are often proposed to explain these phenomena. Aims. We aim to quantify the effect of whistler waves on suprathermal electrons as a function of heliocentric distance. Methods. We first performed a statistical analysis of whistler waves (occurrence and properties) observed by Solar Orbiter and Parker Solar Probe between 0.2 and 1 AU. The wave characteristics were then used to compute the diffusion coefficients for solar wind suprathermal electrons in the framework of quasi-linear theory. These coefficients were integrated to deduce the overall effect of whistler waves on electrons along their propagation. Results. About 110 000 whistler wave packets were detected and characterized in the plasma frame, including their direction of propagation with respect to the background magnetic field and their radial direction of propagation. Most waves are aligned with the magnetic field and only ∼0.5% of them have a propagation angle greater than 45°. Beyond 0.3 AU, it is almost exclusively quasi-parallel waves propagating anti-sunward (some of them are found sunward but are within switchbacks with a change of sign of the radial component of the background magnetic) that are observed. Thus, these waves are found to be Strahl-aligned and not counter-streaming. At 0.2 AU, we find both Strahl-aligned and counter-streaming quasi-parallel whistler waves. Conclusions. Beyond 0.3 AU, the integrated diffusion coefficients show that the observed waves are sufficient to explain the measured Strahl pitch angle evolution and effective in isotropizing the halo. Strahl diffusion is mainly attributed to whistler waves with a propagation angle of θ ∈ [15.45]°, although their origin has not yet been fully determined. Near 0.2 AU, counter-streaming whistler waves are able to diffuse the Strahl electrons more efficiently than the Strahl-aligned waves by two orders of magnitude.

Three Dimensional Microwave Data Inversion in Feature Space for Stroke Imaging.

Microwave imaging is a promising method for early diagnosing and monitoring brain strokes. It is portable, non-invasive, and safe to the human body. Conventional techniques solve for unknown electrical properties represented as pixels or voxels, but often result in inadequate structural information and high computational costs. We propose to reconstruct the three dimensional (3D) electrical properties of the human brain in a feature space, where the unknowns are latent codes of a variational autoencoder (VAE). The decoder of the VAE, with prior knowledge of the brain, acts as a module of data inversion. The codes in the feature space are optimized by minimizing the misfit between measured and simulated data. A dataset of 3D heads characterized by permittivity and conductivity is constructed to train the VAE. Numerical examples show that our method increases structural similarity by 14% and speeds up the solution process by over 3 orders of magnitude using only 4.8% number of the unknowns compared to the voxel-based method. This high-resolution imaging of electrical properties leads to more accurate stroke diagnosis and offers new insights into the study of the human brain.

Composing MPC With LQR and Neural Network for Amortized Efficiency and Stable Control

Model predictive control (MPC) is a powerful control method that handles dynamical systems with constraints. However, solving MPC iteratively in real time, i.e., implicit MPC, remains a computational challenge. To address this, common solutions include explicit MPC and function approximation. Both methods, whenever applicable, may improve the computational efficiency of the implicit MPC by several orders of magnitude. Nevertheless, explicit MPC often requires expensive pre-computation and does not easily apply to higher-dimensional problems. Meanwhile, function approximation, although scales better with dimension, still requires pre-training on a large dataset and generally cannot guarantee to find an accurate surrogate policy, the failure of which often leads to closed-loop instability. To address these issues, we propose a triple-mode hybrid control scheme, named Memory-Augmented MPC, by combining a linear quadratic regulator, a neural network, and an MPC. From its standard form, we derive two variants of such hybrid control scheme: one customized for chaotic systems and the other for slow systems. The proposed scheme does not require pre-computation and is capable of improving the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">amortized</i> running time of the composed MPC with a well-trained neural network. In addition, the scheme maintains closed-loop stability with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">any</i> neural networks of proper input and output dimensions, alleviating the need for certifying optimality of the neural network in safety-critical applications. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This article was motivated by the need to reduce the amortized cost of MPC in repetitive industrial robotic applications, where long-term operational cost is important and safety is critical. Examples of such applications include factory robotic arm manipulation and fixed-route quadcopter payload transport. Unlike explicit MPC or function approximation, our approach does not require any pre-computation or pre-training. Rather, it attains task proficiency over time by learning a surrogate neural network on the spot and by gradually replacing the costly MPC with the more efficient surrogate model so long as safety permits. Consequently, the proposed scheme incurs a learning cost during the initial phase of the deployment but usually becomes more adept on the task afterwards, leading to amortized efficiency.

Parallel Computation of Piecewise Linear Morse-Smale Segmentations.

This article presents a well-scaling parallel algorithm for the computation of Morse-Smale (MS) segmentations, including the region separators and region boundaries. The segmentation of the domain into ascending and descending manifolds, solely defined on the vertices, improves the computational time using path compression and fully segments the border region. Region boundaries and region separators are generated using a multi-label marching tetrahedra algorithm. This enables a fast and simple solution to find optimal parameter settings in preliminary exploration steps by generating an MS complex preview. It also poses a rapid option to generate a fast visual representation of the region geometries for immediate utilization. Two experiments demonstrate the performance of our approach with speedups of over an order of magnitude in comparison to two publicly available implementations. The example section shows the similarity to the MS complex, the useability of the approach, and the benefits of this method with respect to the presented datasets. We provide our implementation with the paper.

Discrete Morse Sandwich: Fast Computation of Persistence Diagrams for Scalar Data - An Algorithm and A Benchmark.

This paper introduces an efficient algorithm for persistence diagram computation, given an input piecewise linear scalar field f defined on a d-dimensional simplicial complex K, with d ≤ 3. Our work revisits the seminal algorithm "PairSimplices" [31], [103] with discrete Morse theory (DMT) [34], [80], which greatly reduces the number of input simplices to consider. Further, we also extend to DMT and accelerate the stratification strategy described in "PairSimplices" [31], [103] for the fast computation of the 0th and (d-1)th diagrams, noted D0(f) and Dd-1(f). Minima-saddle persistence pairs ( D0(f)) and saddle-maximum persistence pairs ( Dd-1(f)) are efficiently computed by processing , with a Union-Find , the unstable sets of 1-saddles and the stable sets of (d-1)-saddles. We provide a detailed description of the (optional) handling of the boundary component of K when processing (d-1)-saddles. This fast pre-computation for the dimensions 0 and (d-1) enables an aggressive specialization of [4] to the 3D case, which results in a drastic reduction of the number of input simplices for the computation of D1(f), the intermediate layer of the sandwich. Finally, we document several performance improvements via shared-memory parallelism. We provide an open-source implementation of our algorithm for reproducibility purposes. We also contribute a reproducible benchmark package, which exploits three-dimensional data from a public repository and compares our algorithm to a variety of publicly available implementations. Extensive experiments indicate that our algorithm improves by two orders of magnitude the time performance of the seminal "PairSimplices" algorithm it extends. Moreover, it also improves memory footprint and time performance over a selection of 14 competing approaches, with a substantial gain over the fastest available approaches, while producing a strictly identical output. We illustrate the utility of our contributions with an application to the fast and robust extraction of persistent 1-dimensional generators on surfaces, volume data and high-dimensional point clouds.