Integration-based Methods Research Articles

Boosting integral-based human pose estimation through implicit heatmap learning

Human pose estimation typically encompasses three categories: heatmap-, regression-, and integral-based methods. While integral-based methods possess advantages such as end-to-end learning, full-convolution learning, and being free from quantization errors, they have garnered comparatively less attention due to inferior performance. In this paper, we revisit integral-based approaches for human pose estimation and propose a novel implicit heatmap learning framework. The framework learns the true distribution of keypoints from the perspective of maximum likelihood estimation, aiming to mitigate inherent ambiguity in shape and variance associated with implicit heatmaps. Specifically, Simple Implicit Heatmap Normalization (SIHN) is first introduced to calculate implicit heatmaps as an efficient and effective representation for keypoint localization, which replaces the vanilla softmax normalization method. As implicit heatmaps may introduce potential challenges related to variance and shape ambiguity arising from the inherent nature of implicit heatmaps, we thus propose a Differentiable Spatial-to-Distributive Transform (DSDT) method to aptly map those implicit heatmaps onto the transformation coefficients of a deformed distribution. The deformed distribution is predicted by a likelihood-based generative model to unravel the shape ambiguity quandary effectively, and the transformation coefficients are learned by a regression model to resolve the variance ambiguity issue. Additionally, to expedite the acquisition of precise shape representations throughout the training process, we introduce a Wasserstein Distance-based Constraint (WDC) to ensure stable and reasonable supervision during the initial generation of implicit heatmaps. Experimental results on both the MSCOCO and MPII datasets demonstrate the effectiveness of our proposed method, achieving competitive performance against heatmap-based approaches while maintaining the advantages of integral-based approaches. Our source codes and pre-trained models are available at https://github.com/ducongju/IHL.

Pulse pile-up correction by auto-regression on linear operations (ARLO) method: A comparison with integration-based algorithms

Radiation detection at high count rate suffers from pulse pile-up, where the counting data and energy information of the system are affected by the overlapping of the system output pulses. There exist various pile-up correction strategies to recover the true information of the pulses, among which pulse-tail extrapolation is a well-known method focused on in this study.Present work aims to use a mono-exponential model for extrapolating the pileup-distorted trailing edge of a pulse, to provide a reference line for calculating the true amplitude of its subsequent overlapping pulse. To this goal, the auto-regression on linear operations (ARLO) method is examined and compared with two integration-based methods (the Foss and the Matheson methods), as well as the non-linear least squares (NLS) method.Despite a higher sensitivity to noise, the ARLO method was able to provide a simple, non-iterative solution with a performance over 400 times faster than the NLS algorithm, according to the analysis of a high count rate set of experimental pulses from a NaI(Tl) detection system. Foss and Matheson methods also provided solutions reasonably faster than NLS (but not surpassing ARLO), performing exactly the same as each other with results very close to NLS, benefiting from their non-iterative nature.

Phenomenon-Based Learning in Teaching a Foreign Language: Experiences of Lithuanian Teachers

Phenomenon-based learning (hereinafter PhenoBL) is widely studied in the majority of European countries, especially given that research data indicate that PhenoBL is more successful in providing effective learning, better student achievement, a stronger interest in science, and even a higher happiness index. However, there are sparse data on the educational practice of this method in Lithuania, particularly in foreign language teaching (FLT). Thus, teachers’ professional preparation for the effective implementation of PhenoBL remains one of the most relevant research problems. For this reason, this study aims to analyse the experiences of Lithuanian foreign language teachers in incorporating PhenoBL into FLT. Fifteen individual semi-structured interviews were conducted, and the obtained data were analysed by applying qualitative inductive content analysis. An inductive content analysis of the interview reports revealed six themes and related categories: the perception of student-centred teaching, the development of subject integration competencies, teamwork development competencies, research-planning skills, the positioning of personal responsibilities and duties, and foreign language usage emancipation, i.e. setting free from personal fears (fear to make grammar, vocabulary mistakes, while speaking in public) to speak a foreign languages. The content of the revealed themes indicated that teachers highlighted the flexibility of PhenoBL from the perspective of its application to different language learning levels within one group. The majority of the respondents underlined the necessity for the development of an active didactic competence. Other respondents mentioned the importance of the correlation between personal creativity competence development and success in PhenoBL. It was also stressed that if a teacher wants to be successful while using PhenoB, they must to be prepared to work with integration-based and communication-emancipatory methods, must be student-centred, must have competencies in teaching several subjects, must be good at teamwork, and must be good at managing learning time.

Impact of Spatial Inhomogeneity on Excitation Energy Transport in the Fenna-Matthews-Olson Complex.

The dynamics of the excitation energy transfer (EET) in photosynthetic complexes is an interesting question both from the perspective of fundamental understanding and the research in artificial photosynthesis. Over the past decade, very accurate spectral densities have been developed to capture spatial inhomogeneities in the Fenna-Matthews-Olson (FMO) complex. However, challenges persist in numerically simulating these systems, both in terms of parameterizing them and following their dynamics over long periods of time because of long non-Markovian memories. We investigate the dynamics of FMO with the exact treatment of various theoretical spectral densities using the new tensor network path integral-based methods, which are uniquely capable of addressing the difficulty of long memory length and incoherent Förster theory. It is also important to be able to analyze the pathway of EET flow, which can be difficult to identify given the non-trivial structure of connections between bacteriochlorophyll molecules in FMO. We use the recently introduced ideas of relating coherence to population derivatives to analyze the transport process and reveal some new routes of transport. The combination of exact and approximate methods sheds light on the role of coherences in affecting the fine details of the transport and promises to be a powerful toolbox for future exploration of other open systems with quantum transport.

Comparison of Single Control Loop Performance Monitoring Methods

Well-performing control loops have an integral role in efficient and sustainable industrial production. Control performance monitoring (CPM) tools are necessary to establish further process optimization and preventive maintenance. Data-driven, model-free control performance monitoring approaches are studied in this research by comparing the performance of nine CPM methods in an industrially relevant process simulation. The robustness of some of the methods is considered with varying fault intensities. The methods are demonstrated on a simulator which represents a validated state-space model of a supercritical carbon dioxide fluid extraction process. The simulator is constructed with a single-input single-output unit controller for part of the process and a combination of relevant faults in the industry are introduced into the simulation. Of the demonstrated methods, Kullback–Leibler divergence, Euclidean distance, histogram intersection, and Overall Controller Efficiency performed the best in the first simulation case and could identify all the simulated fault scenarios. In the second case, integral-based methods Integral Squared Error and Integral of Time-weighted Absolute Error had the most robust performance with different fault intensities. The results highlight the applicability and robustness of some model-free methods and construct a solid foundation in the application of CPM in industrial processes.

Accelerating Hybrid Density Functional Theory Molecular Dynamics Simulations by Seminumerical Integration, Resolution-of-the-Identity Approximation, and Graphics Processing Units.

The computationally very demanding evaluation of the 4-center-2-electron (4c2e) integrals and their respective integral derivatives typically represents the major bottleneck within hybrid Kohn-Sham density functional theory molecular dynamics simulations. Building upon our previous works on seminumerical exact-exchange (sn-LinK) [Laqua, H., Thompsons, T. H., Kussmann, J., Ochsenfeld, C., J. Chem. Theory Comput. 2020, 16, 1465] and resolution-of-the-identity Coulomb (RI-J) [Kussmann, J., Laqua, H., Ochsenfeld, C., J. Chem. Theory Comput. 2021, 17, 1512], the expensive 4c2e integral evaluation can be avoided entirely, resulting in a highly efficient electronic structure theory method, allowing for fast ab initio molecular dynamics (AIMD) simulations even with large basis sets. Moreover, we propose to combine the final self-consistent field (SCF) step with the subsequent nuclear forces evaluation, providing the forces at virtually no additional cost after a converged SCF calculation, reducing the total runtime of an AIMD simulation by about another 25%. In addition, multiple independent MD trajectories can be computed concurrently on a single node, leading to a greatly increased utilization of the available hardware─especially when combined with graphics processing unit acceleration─improving the overall throughput by up to another 5 times in this way. With all of those optimizations combined, our proposed method provides nearly 3 orders of magnitude faster execution times than traditional 4c2e integral-based methods. To demonstrate the practical utility of the approach, quantum-mechanical/molecular-mechanical dynamics simulations on double-stranded DNA were performed, investigating the relative hydrogen bond strength between adenine-thymine and guanine-cytosine base pairs. In addition, this illustrative application also contains a general accuracy assessment of the introduced approximations (integration grids, resolution-of-the-identity) within AIMD simulations, serving as a protocol on how to apply these new methods to practical problems.

An efficient and accurate chatter prediction method of milling processes with a transition matrix reduction scheme

Efficient and accurate chatter prediction is essential for selection of chatter-free process parameters in order to improve machining productivity and surface quality of the workpiece. This paper proposes a five-point Gaussian quadrature-based chatter prediction method of milling processes together with a transition matrix reduction scheme to improve the computational accuracy and efficiency. The five-point Gauss–Legendre quadrature rule is utilized to approximate the equations of motion of milling systems represented in the form of integral equation. By this means, the convergence rate of the chatter prediction method can be improved. Since the transition matrix describing the relation between the states of current and previous tooth or spindle period is used to evaluate chatter stability, its dimension has a significant effect on the computational efficiency. In this paper, it is theoretically proved that the dimension of the transition matrix constructed by numerical integration-based methods can be reduced by half. Based on this, an efficient scheme is firstly proposed to further decrease the computational time. Typical benchmark examples are employed to verify the proposed method. The results demonstrate that the proposed method with the transition matrix reduction scheme is more efficient and accurate than the existing methods. Meanwhile, experimental validation shows the proposed method can predict the milling chatter accurately.

Analytical calibration of slope response of Zernike modes in a Shack-Hartmann wavefront sensor based on matrix product.

The Shack-Hartmann wavefront sensor (SH-WFS) is widely used as a slope-based wavefront sensing device. The modal method is favored for wavefront reconstruction from SH-WFS output because of its excellent performance. In this case, the calibration of modal (commonly Zernike modes) slope is required in advance. Traditional numerical or symbolic integral-based methods are not satisfactory because of their low accuracy or efficiency, particularly when an extremely large number of microlenses are involved. In this Letter, a novel method based on matrix product is proposed in which two key matrix operators are utilized. The first, namely the derivative matrix operator, is used to obtain the derivative of the Zernike modes; the second, that is, the transformation matrix operator, is then used to map the Zernike derivative defined in the original, whole circular pupil into modes defined in a scaled, translated circle pupil enveloping a specific microlens. With these two operators, the evaluation of slope response of Zernike modes could be unified into a matrix-product framework, which contributes its high efficiency. Numerical simulations show the superior advantages of the proposed method in accuracy and efficiency over traditional ones.

A machine learning framework for predicting drug\u2013drug interactions

Understanding drug–drug interactions is an essential step to reduce the risk of adverse drug events before clinical drug co-prescription. Existing methods, commonly integrating heterogeneous data to increase model performance, often suffer from a high model complexity, As such, how to elucidate the molecular mechanisms underlying drug–drug interactions while preserving rational biological interpretability is a challenging task in computational modeling for drug discovery. In this study, we attempt to investigate drug–drug interactions via the associations between genes that two drugs target. For this purpose, we propose a simple f drug target profile representation to depict drugs and drug pairs, from which an l2-regularized logistic regression model is built to predict drug–drug interactions. Furthermore, we define several statistical metrics in the context of human protein–protein interaction networks and signaling pathways to measure the interaction intensity, interaction efficacy and action range between two drugs. Large-scale empirical studies including both cross validation and independent test show that the proposed drug target profiles-based machine learning framework outperforms existing data integration-based methods. The proposed statistical metrics show that two drugs easily interact in the cases that they target common genes; or their target genes connect via short paths in protein–protein interaction networks; or their target genes are located at signaling pathways that have cross-talks. The unravelled mechanisms could provide biological insights into potential adverse drug reactions of co-prescribed drugs.

Beyond integration: modeling every pixel to obtain better structure factors from stills

Most crystallographic data processing methods use pixel integration. In serial femtosecond crystallography (SFX), the intricate interaction between the reciprocal lattice point and the Ewald sphere is integrated out by averaging symmetrically equivalent observations recorded across a large number (104-106) of exposures. Although sufficient for generating biological insights, this approach converges slowly, and using it to accurately measure anomalous differences has proved difficult. This report presents a novel approach for increasing the accuracy of structure factors obtained from SFX data. A physical model describing all observed pixels is defined to a degree of complexity such that it can decouple the various contributions to the pixel intensities. Model dependencies include lattice orientation, unit-cell dimensions, mosaic structure, incident photon spectra and structure factor amplitudes. Maximum likelihood estimation is used to optimize all model parameters. The application of prior knowledge that structure factor amplitudes are positive quantities is included in the form of a reparameterization. The method is tested using a synthesized SFX dataset of ytterbium(III) lysozyme, where each X-ray laser pulse energy is centered at 9034 eV. This energy is 100 eV above the Yb3+ L-III absorption edge, so the anomalous difference signal is stable at 10 electrons despite the inherent energy jitter of each femtosecond X-ray laser pulse. This work demonstrates that this approach allows the determination of anomalous structure factors with very high accuracy while requiring an order-of-magnitude fewer shots than conventional integration-based methods would require to achieve similar results.

Vector Field Topology of Time-Dependent Flows in a Steady Reference Frame.

The topological analysis of unsteady vector fields remains to this day one of the largest challenges in flow visualization. We build up on recent work on vortex extraction to define a time-dependent vector field topology for 2D and 3D flows. In our work, we split the vector field into two components: a vector field in which the flow becomes steady, and the remaining ambient flow that describes the motion of topological elements (such as sinks, sources and saddles) and feature curves (vortex corelines and bifurcation lines). To this end, we expand on recent local optimization approaches by modeling spatially-varying deformations through displacement transformations from continuum mechanics. We compare and discuss the relationships with existing local and integration-based topology extraction methods, showing for instance that separatrices seeded from saddles in the optimal frame align with the integration-based streakline vector field topology. In contrast to the streakline-based approach, our method gives a complete picture of the topology for every time slice, including the steps near the temporal domain boundaries. With our work it now becomes possible to extract topological information even when only few time slices are available. We demonstrate the method in several analytical and numerically-simulated flows and discuss practical aspects, limitations and opportunities for future work.

A Dynamic Parameter Identification Method for Flexible Joints Based on Adaptive Control

This paper investigates the dynamic parameter identification for flexible joints without additional sensors. The estimation accuracy of traditional methods based on the original dynamic model is limited by measurement of angular acceleration. Recently, approaches using integral operations are raised to solve this problem. However, the integral operations easily result in error accumulation and deteriorate the parameter estimation accuracy. This study proposes a new dynamic parameter identification method for flexible joints. By constructing an alternative system function and estimating its outputs through nonmodel-based adaptive control, we avoid the measurement of angular acceleration and integral operations. On this basis, dynamic parameters of flexible joints are estimated using the recursive least squares (RLS) method. The experimental results indicate that the proposed method possesses better estimation accuracy than the general RLS- and integral-based methods. It is also validated that the proposed method can provide accurate estimation even under a relatively low-resolution system. Applications to model-based motion control and physical human-robot interaction are also verified.

Convergence of integration-based methods for the solution of standard and generalized Hermitian eigenvalue problems

Recently, methods based on spectral projection and numerical integration have been proposed in the literature as candidates for reliable high-performance eigenvalue solvers. The key ingredients of this type of eigenvalue solver are a Rayleigh-Ritz process and a routine to compute an approximation to the desired eigenspace. The latter computation can be performed by numerical integration of the resolvent. In this article we investigate the progress of the Rayleigh-Ritz process and the achievable quality of the computed eigenpairs for the case that an upper bound for the normwise difference between the currently used subspace and the desired eigenspace is available. Then, such bounds are derived for the Gauß-Legendre rule and the trapezoidal rule.

Integral-equation based methods for parameter estimation in output pulses of radiation detectors: Application in nuclear medicine and spectroscopy

Model based analysis methods are relatively new approaches for processing the output data of radiation detectors in nuclear medicine imaging and spectroscopy. A class of such methods requires fast algorithms for fitting pulse models to experimental data. In order to apply integral-equation based methods for processing the preamplifier output pulses, this article proposes a fast and simple method for estimating the parameters of the well-known bi-exponential pulse model by solving an integral equation. The proposed method needs samples from only three points of the recorded pulse as well as its first and second order integrals. After optimizing the sampling points, the estimation results were calculated and compared with two traditional integration-based methods. Different noise levels (signal-to-noise ratios from 10 to 3000) were simulated for testing the functionality of the proposed method, then it was applied to a set of experimental pulses. Finally, the effect of quantization noise was assessed by studying different sampling rates. Promising results by the proposed method endorse it for future real-time applications.

Relationships among contour integral-based methods for solving generalized eigenvalue problems

Recently, contour integral-based methods have been actively studied for solving interior eigenvalue problems that find all eigenvalues located in a certain region and their corresponding eigenvectors. In this paper, we reconsider the algorithms of the five typical contour integral-based eigensolvers from the viewpoint of projection methods, and then map the relationships among these methods. From the analysis, we conclude that all contour integral-based eigensolvers can be regarded as projection methods and can be categorized based on their subspace used, the type of projection and the problem to which they are applied implicitly.

Integrative methods for analyzing big data in precision medicine.

We provide an overview of recent developments in big data analyses in the context of precision medicine and health informatics. With the advance in technologies capturing molecular and medical data, we entered the area of "Big Data" in biology and medicine. These data offer many opportunities to advance precision medicine. We outline key challenges in precision medicine and present recent advances in data integration-based methods to uncover personalized information from big data produced by various omics studies. We survey recent integrative methods for disease subtyping, biomarkers discovery, and drug repurposing, and list the tools that are available to domain scientists. Given the ever-growing nature of these big data, we highlight key issues that big data integration methods will face.

Understanding the variability of compound quantification from targeted profiling metabolomics of 1D-1H-NMR spectra in synthetic mixtures and urine with additional insights on choice of pulse sequences and robotic sampling

The growing use of ‘targeted profiling’ approaches for the deconvolution of 1D-1H-NMR spectra by comparison to a pure compound library has created a need for an in-depth characterization of quantification variability that is beyond what is currently available in the literature. In this study, we explore the underlying source of quantification variability (tube insertion, spectra acquisition, and profiling) as well as a number of other factors, such as temporal consistency of repeated NMR scans, human consistency in repeated profiles, and human versus machine sampling. We also look at the effect of different pulse sequences on the differences between acquired spectra and the peak reference library. Two sample types were considered for this work—a synthetic five compound mixture as well as human urine. The result is a comprehensive examination of 1D-1H-NMR quantification error. Our investigation into variability sources revealed that apart from profiling, sample insertion and/or shimming can play a significant role in final quantification, a finding that is equally applicable to all integration-based methods of quantification. Both sources of error were also found to have temporal relationships, with bias identified as a function of both scan and profiling order, reinforcing the need for randomization in scanning and profiling. As well as presenting a practical estimate of variability in human urine samples, we have uncovered a considerable amount of complexity in underlying NMR variability that will hopefully serve as impetus for future exploration in this area.

Hygrothermal Fracture Analysis of Orthotropic Functionally Graded Materials UsingJk-Integral-Based Methods

This paper puts forward two differentJk-integral-based methods, which can be used to perform mixed-mode fracture analysis of orthotropic functionally graded materials subjected to hygrothermal stresses. The first method requires the evaluation of both components ofJk-integral, whereas the second method employs the first componentJ1and the asymptotic crack tip displacement fields. Plane orthotropic hygrothermoelasticity is the basic theory behind theJk-integral formulation, which is carried out by assuming that all material properties are functions of the spatial coordinates. Developed procedures are implemented by means of the finite element method and integrated into a general purpose finite element analysis software. Temperature and specific moisture concentration fields needed in the fracture analyses are also computed through finite element analysis. Each of the developed methods is utilized in conjunction with the superposition technique to calculate the hygrothermal fracture parameters. An inclined crack located in a hygrothermally loaded orthotropic functionally graded layer is examined in parametric analyses. Comparisons of the results generated by the proposed methods do indicate that both methods lead to numerical results of high accuracy and that the developed form of theJk-integral is domain independent. Further results are presented so as to illustrate the influences of crack inclination angle, crack length, and crack location upon the modes I and II stress intensity factors.

2011 IEEE Visualization Contest winner: Visualizing unsteady vortical behavior of a centrifugal pump.

In the 2011 IEEE Visualization Contest, the dataset represented a high-resolution simulation of a centrifugal pump operating below optimal speed. The goal was to find suitable visualization techniques to identify regions of rotating stall that impede the pump's effectiveness. The winning entry split analysis of the pump into three parts based on the pump's functional behavior. It then applied local and integration-based methods to communicate the unsteady flow behavior in different regions of the dataset. This research formed the basis for a comparison of common vortex extractors and more recent methods. In particular, integration-based methods (separation measures, accumulated scalar fields, particle path lines, and advection textures) are well suited to capture the complex time-dependent flow behavior. This video (http://youtu.be/oD7QuabY0oU) shows simulations of unsteady flow in a centrifugal pump.

Analysis of Time-Dependent Flow-Sensitive PC-MRI Data

Many flow visualization techniques, especially integration-based methods, are problematic when the measured data exhibit noise and discretization issues. Particularly, this is the case for flow-sensitive phase-contrast magnetic resonance imaging (PC-MRI) data sets which not only record anatomic information, but also time-varying flow information. We propose a novel approach for the visualization of such data sets using integration-based methods. Our ideas are based upon finite-time Lyapunov exponents (FTLE) and enable identification of vessel boundaries in the data as high regions of separation. This allows us to correctly restrict integration-based visualization to blood vessels. We validate our technique by comparing our approach to existing anatomy-based methods as well as addressing the benefits and limitations of using FTLE to restrict flow. We also discuss the importance of parameters, i.e., advection length and data resolution, in establishing a well-defined vessel boundary. We extract appropriate flow lines and surfaces that enable the visualization of blood flow within the vessels. We further enhance the visualization by analyzing flow behavior in the seeded region and generating simplified depictions.