Temporal Splitting Research Articles

Heedful proactivity: How individual tactical considerations contribute to pre‐screening of innovative ideas in the hierarchy

Purposefully fostering creativity and innovation through stimulating proactivity requires grappling with an apparent trade‐off. On the one hand, organization members need some autonomy to initiate change. On the other hand, managers might want to steer initiatives and retain control over outcomes. The current paper advances recent work on how proactivity is enacted as a compromise between autonomy and control by studying the process through which bottom‐up ideas are shared in highly hierarchical organizations. Based on an abductive analysis of data from informants in 42 organizations, we develop the concept of pre‐screening, which denotes collective action patterns geared towards qualifying individuals' innovative ideas before they are made subject to formal decision making. We explain how proactive individuals' tactical considerations—informed by their holistic prospective thinking, risk hedging, temporal splitting, and a both/and approach to proactivity and hierarchy—influence the actions through which ideas are shared and who are approached first (e.g., supervisors vs. peers). We also exemplify how action patterns accomplishing idea sharing and pre‐screening are entangled with more mundane workplace routines. Overall, the paper sheds new light on ideas' journeys in the context of hierarchy and opens up multiple avenues for future research.

Partially explicit splitting scheme with explicit–implicit-null method for nonlinear multiscale flow problems

In this work, we present an efficient approach to solve nonlinear high-contrast multiscale diffusion problems. We incorporate the explicit–implicit-null (EIN) method to separate the nonlinear term into a linear term and a damping term, and then utilize the implicit and explicit time marching scheme for the two parts respectively. Due to the multiscale property of the linear part, we further introduce a temporal partially explicit splitting scheme and construct suitable multiscale subspaces to speed up the computation. The approximated solution is split into these subspaces associated with different physics. The temporal splitting scheme employs implicit discretization in the subspace with small dimension that representing the high-contrast property and uses explicit discretization for the other subspace. We exploit the stability of the proposed scheme and give the condition for the choice of the linear diffusion coefficient. The convergence of the proposed scheme is provided. Several numerical tests are performed to show the efficiency and accuracy of the proposed scheme.

Single-shot observation of nonlinear pulse splitting in a Kerr medium.

We report single-shot, time-resolved observation of self-steepening and temporal splitting of near-infrared, 50 fs, micro-joule pulses propagating nonlinearly in flint (SF11) glass. A coherent, smooth-profiled, 60-nm-bandwidth probe pulse that propagated obliquely to the main pulse through the Kerr medium recorded a time sequence of longitudinal projections of the main pulse's induced refractive index profile in the form of a phase-shift "streak," in which frequency-domain interferometry recovered with ∼10 fs temporal resolution. A three-dimensional simulation based on a unidirectional pulse propagation equation reproduced observed pulse profiles.

Intelligent Optical Fiber‐Integrated Near‐Infrared Polarimeter Based on Upconversion Nanoparticles

AbstractThe near‐infrared (NIR) light polarization metrology is crucial in a broad area of applications, such as optical sensing, imaging, and communications. The conventional measurement of NIR light polarization requires bulky polarization optics by the spatial or temporal splitting of the input light beam with expensive infrared detectors. Here, an intelligent fiber‐integrated NIR polarimeter based on upconversion nanoparticles (UCNPs) is demonstrated. Er‐doped UCNPs are synthesized in core–shell structures for bright upconversion luminescence (UCL), and the tapered multimode fiber (MMF) is designed for random Rayleigh‐distributed speckles. It is demonstrated for the first time that spectra‐polarization‐dependent upconverted speckle patterns captured by a cost‐effective visible image sensor can be accurately decoded via a deep neural network (ResNet50). The experimental results show that ResNet50 has a recognition accuracy of over 99.5% for the full‐Stokes parameters of NIR light polarization, along with 100% accuracy for the light wavelength ranging from 1535 nm to 1565 nm. The developed intelligent optical sensors provide a new design paradigm for fiber‐integrated multi‐dimensional NIR light field detection and can be applied in fiber‐optic sensors and communications networks.

An adaptive space and time method in partially explicit splitting scheme for multiscale flow problems

We propose a space and time adaptive framework for a partially explicit splitting scheme of flow problems in multiscale media. We consider the parabolic equation with high-contrast multiscale coefficients. It is known that sufficient number of multiscale basis are needed to capture non-local features and information across all scales. Moreover, the time step size in an explicit discretization of the problem is affected by the magnitude of the coefficient. To improve computational efficiency, in this work, we introduce an adaptive algorithm to refine temporal size and enrich multiscale spaces. We first utilize a stable temporal splitting scheme with an appropriate construction of multiscale spaces to ensure that the time step size is independent of the contrast. The multiscale subspaces are then constructed to handle the fast-flow and slow-flow parts separately, and implicit and explicit discretization is adopted for the degrees of freedom with respect to the two multiscale subspaces, respectively. A multirate time stepping is introduced for the two parts considering that the flow rates vary significantly in different regions due to the high-contrast features of the multiscale coefficients. We derive both temporal and spatial error estimators to identify local regions for two components of the solutions. Start with coarser time step sizes and a few important multiscale basis functions in each subspace, we can adaptively refine time stepping and add additional basis with constraint energy minimizing properties based on the derived error indicators. The stability and convergence of the method are studied, and several numerical tests are presented to demonstrate the performance of the proposed method.

An industrial evaluation of proteochemometric modelling: Predicting drug-target affinities for kinases

Deep learning proteochemometric (PCM) models have been reported to achieve excellent performances on public benchmarking datasets. Nevertheless, numerous papers have cast doubt on commonly used evaluation metrics, suggesting they do not reflect true prospective predictive abilities. The aim of this study is to provide a comprehensive assessment of performance of a state-of-the-art PCM model on proprietary data and evaluate its potential over other modelling approaches as a virtual screening tool for kinase inhibitors. Whilst the model has been shown to achieve an RMSE of 0.48 on a public benchmarking dataset, an impaired overall performance was observed for the proprietary dataset in this study, with an RMSE of 0.85 and a Pearson Correlation Coefficient of 0.65 using a temporal splitting strategy. We hypothesise that the more limited performance can be in part attributed to a shift in the chemical space observed over time in an industrial setting, which is not considered by the more lenient random ligand splitting strategy, more commonly used on benchmarking datasets. The overall performance of the PCM model was statistically similar to a multitask model and only slightly superior to a KNN and random forest PCM model. A comprehensive analysis of performance was performed to capture the key challenges faced in the design of competitive kinase inhibitors, which revealed the key limitations of PCM modelling. For example, the model showed poor predictive abilities for understudied targets, and a limited ability to assess ligand selectivity and promiscuity, with no improved performance over a multitask model or a random forest PCM model. Overall, these findings reveal that the PCM model assessed in this study does not provide significant benefits over less complex models such as multitask model or a random forest PCM model as a virtual screening tool for kinase inhibitors in an industrial setting. Taken together, this study highlights the need for more robust evaluations of PCM models by using stricter splitting strategies, more extensive benchmarking and more comprehensive performance analysis beyond traditional metrics.

Chirp characteristics and the effect of chirp on the beam quality of laser pulses propagating upwards in the atmosphere

The chirp characteristics and the effect of chirp on the beam quality of laser pulses propagating from the ground through the atmosphere to the space orbit are studied. The analytical expressions of the additional chirp caused by group-velocity dispersion (GVD) and self-focusing effects in the atmosphere are derived, respectively. It is shown that the behavior of the additional chirp caused by GVD effect is quite different from that caused by self-focusing effect. On the other hand, it is found that there exists a minimum of pulse width on the target when a certain negative initial chirp arrives. In particular, it is demonstrated that the beam quality on the target can be optimized (i.e., the target intensity can be improved and the temporal pulse splitting on the target can be avoided) by the preliminary chirp method.

Long-term reconstruction of satellite-based precipitation, soil moisture, and snow water equivalent in China

Abstract. A long-term high-resolution national dataset of precipitation (P), soil moisture (SM), and snow water equivalent (SWE) is necessary for predicting floods and droughts and assessing the impacts of climate change on streamflow in China. Current long-term daily or sub-daily datasets of P, SM, and SWE are limited by a coarse spatial resolution or the lack of local correction. Although SM and SWE data derived from hydrological simulations at a national scale have fine spatial resolutions and take advantage of local forcing data, hydrological models are not directly calibrated with SM and SWE data. In this study, we produced a daily 0.1∘ dataset of P, SM, and SWE in 1981–2017 across China, using global background data and local on-site data as forcing input and satellite-based data as reconstruction benchmarks. Global 0.1∘ and local 0.25∘P data in 1981–2017 are merged to reconstruct the historical P of the 0.1∘ China Merged Precipitation Analysis (CMPA) available in 2008–2017 using a stacking machine learning model. The reconstructed P data are used to drive the HBV hydrological model to simulate SM and SWE data in 1981–2017. The SM simulation is calibrated by Soil Moisture Active Passive Level 4 (SMAP-L4) data. The SWE simulation is calibrated by the national satellite-based snow depth dataset in China (Che and Dai, 2015) and the Moderate Resolution Imaging Spectroradiometer (MODIS) snow cover data. Cross-validated by the spatial and temporal splitting of the CMPA data, the median Kling–Gupta efficiency (KGE) of the reconstructed P is 0.68 for all grids at a daily scale. The median KGE of SM in calibration is 0.61 for all grids at a daily scale. For grids in two snow-rich regions, the median KGEs of SWE in calibration are 0.55 and −2.41 in the Songhua and Liaohe basins and the northwest continental basin respectively at a daily scale. Generally, the reconstruction dataset performs better in southern and eastern China than in northern and western China for P and SM and performs better in northeast China than in other regions for SWE. As the first long-term 0.1∘ daily dataset of P, SM, and SWE that combines information from local observations and satellite-based data benchmarks, this reconstruction product is valuable for future national investigations of hydrological processes.

Globally hyperbolic spacetimes: slicings, boundaries and counterexamples

The Cauchy slicings for globally hyperbolic spacetimes and their relation with the causal boundary are surveyed and revisited, starting at the seminal conformal boundary constructions by R. Penrose. Our study covers: (1) adaptive possibilities and techniques for their Cauchy slicings, (2) global hyperbolicity of sliced spacetimes, (3) critical review on the conformal and causal boundaries for a globally hyperbolic spacetime, and (4) procedures to compute the causal boundary of a Cauchy temporal splitting by using isocausal comparison with a static product. New simple counterexamples on $\mathbb{R}^2$ illustrate a variety of possibilities related to these splittings, such as the logical independence (for normalized sliced spacetimes) between the completeness of the slices and global hyperbolicity, the necessity of uniform bounds on the slicings in order to ensure global hyperbolicity, or the insufficience of these bounds for the computation of the causal boundary. A refinement of one of these examples shows that the space of all the (normalized, conformal classes of) globally hyperbolic metrics on a smooth product manifold $\mathbb{R}\times S$ is not convex, even though it is path connected by means of piecewise convex combinations.

Storage and manipulation of single x-ray photons via nuclear hyperfine splitting

We introduce a technique to store and manipulate single x-ray photons, which relies on dynamically controlled absorption via nuclear hyperfine magnetic splitting. This scheme is inherently suitable for storage, on-demand generation, and dynamical manipulation of single x-ray photons, for instance, the manipulation of the temporal shape, temporal splitting, the interference between x-ray photons, and the control of the polarization. Our approach provides more opportunities in x-ray quantum information.

Multirate Partially Explicit Scheme for Multiscale Flow Problems

For time-dependent problems with high-contrast multiscale coefficients, the time step size for explicit methods is affected by the magnitude of the coefficient parameter. With a suitable construction of multiscale space, one can achieve a stable temporal splitting scheme where the time step size is independent of the contrast. Consider the parabolic equation with heterogeneous diffusion parameter, the flow rates vary significantly in different regions due to the high-contrast features of the diffusivity. In this work, we aim to introduce a multirate partially explicit splitting scheme to achieve efficient simulation with the desired accuracy. We first design multiscale subspaces to handle flow with different speed. For the fast flow, we obtain a low-dimensional subspace with respect to the high-diffusive component and adopt an implicit time discretization scheme. The other multiscale subspace will take care of the slow flow, and the corresponding degrees of freedom are treated explicitly. Then a multirate time stepping is introduced for the two parts. The stability of the multirate methods is analyzed for the partially explicit scheme. Moreover, we derive local error estimators corresponding to the two components of the solutions and provide an upper bound of the errors. An adaptive local temporal refinement framework is then proposed to achieve higher computational efficiency. Several numerical tests are presented to demonstrate the performance of the proposed method.

Efficient hybrid explicit-implicit learning for multiscale problems

Splitting method is a powerful method to handle application problems by splitting physics, scales, domain, and so on. Many splitting algorithms have been designed for efficient temporal discretization. In this paper, our goal is to use temporal splitting concepts in designing machine learning algorithms and, at the same time, help splitting algorithms by incorporating data and speeding them up. We propose a machine learning assisted splitting scheme which improves the efficiency of the scheme meanwhile preserves the accuracy. We consider a recently introduced multiscale splitting algorithms, where the multiscale problem is solved on a coarse grid. To approximate the dynamics, only a few degrees of freedom are solved implicitly, while others explicitly. This splitting concept allows identifying degrees of freedom that need implicit treatment. In this paper, we use this splitting concept in machine learning and propose several strategies. First, the implicit part of the solution can be learned as it is more difficult to solve, while the explicit part can be computed. This provides a speed-up and data incorporation for splitting approaches. Secondly, one can design a hybrid neural network architecture because handling explicit parts requires much fewer communications among neurons and can be done efficiently. Thirdly, one can solve the coarse grid component via PDEs or other approximation methods and construct simpler neural networks for the explicit part of the solutions. We discuss these options and implement one of them by interpreting it as a machine translation task. This interpretation of the splitting scheme successfully enables us using the Transformer since it can perform model reduction for multiple time series and learn the connection between them. We also find that the splitting scheme is a great platform to predict the coarse solution with insufficient information of the target model: the target problem is partially given and we need to solve it through a known problem which approximates the target. Our machine learning model can incorporate and encode the given information from two different problems and then solve the target problems. We conduct four numerical examples and the results show that our method is stable and accurate.

Contrast-Independent Partially Explicit Time Discretizations for Quasi Gas Dynamics

In the paper, we study a design and stability of contrast-independent partially explicit time discretizations for Quasi-Gas-Dynamics (QGD) Equations in multiscale high-contrast media. In our previous works, we have introduced contrast-independent partially explicit time discretizations. In this paper, we extend these ideas to multiscale QGD problems. Because of high contrast, explicit methods require a very small time stepping. By designing appropriate spatial splitting and temporal splitting, partially explicit methods remove this constraint. The proposed partially explicit time discretization consists of two steps. First, we split the space into contrast dependent (fast) and contrast independent (slow) components on a coarse grid that is much larger compared to spatial heterogeneities. Secondly, we design a temporal splitting algorithm in a such way that it is stable and the time step is independent of the contrast and only depends on the coarse mesh size. Using proposed method, a few degrees of freedom are treated implicitly and the approach is mostly explicit. We prove that the proposed splitting is unconditionally stable under some suitable conditions formulated for the second space (slow). We present numerical results and show that the proposed methods provide results similar to implicit methods with the time step that is independent of the contrast.

Cutoff Values for Diagnosing Hepatic Steatosis Using Contemporary MRI-Proton Density Fat Fraction Measuring Methods.

To propose standardized MRI-proton density fat fraction (PDFF) cutoff values for diagnosing hepatic steatosis, evaluated using contemporary PDFF measuring methods in a large population of healthy adults, using histologic fat fraction (HFF) as the reference standard. A retrospective search of electronic medical records between 2015 and 2018 identified 1063 adult donor candidates for liver transplantation who had undergone liver MRI and liver biopsy within a 7-day interval. Patients with a history of liver disease or significant alcohol consumption were excluded. Chemical shift imaging-based MRI (CS-MRI) PDFF and high-speed T2-corrected multi-echo MR spectroscopy (HISTO-MRS) PDFF data were obtained. By temporal splitting, the total population was divided into development and validation sets. Receiver operating characteristic (ROC) analysis was performed to evaluate the diagnostic performance of the MRI-PDFF method. Two cutoff values with sensitivity > 90% and specificity > 90% were selected to rule-out and rule-in, respectively, hepatic steatosis with reference to HFF ≥ 5% in the development set. The diagnostic performance was assessed using the validation set. Of 921 final participants (624 male; mean age ± standard deviation, 31.5 ± 9.0 years), the development and validation sets comprised 497 and 424 patients, respectively. In the development set, the areas under the ROC curve for diagnosing hepatic steatosis were 0.920 for CS-MRI-PDFF and 0.915 for HISTO-MRS-PDFF. For ruling-out hepatic steatosis, the CS-MRI-PDFF cutoff was 2.3% (sensitivity, 92.4%; specificity, 63.0%) and the HISTO-MRI-PDFF cutoff was 2.6% (sensitivity, 88.8%; specificity, 70.1%). For ruling-in hepatic steatosis, the CS-MRI-PDFF cutoff was 3.5% (sensitivity, 73.5%; specificity, 88.6%) and the HISTO-MRI-PDFF cutoff was 4.0% (sensitivity, 74.7%; specificity, 90.6%). In a large population of healthy adults, our study suggests diagnostic thresholds for ruling-out and ruling-in hepatic steatosis defined as HFF ≥ 5% by contemporary PDFF measurement methods.

Contrast-Independent, Partially-Explicit Time Discretizations for Nonlinear Multiscale Problems

This work continues a line of work on developing partially explicit methods for multiscale problems. In our previous works, we considered linear multiscale problems where the spatial heterogeneities are at the subgrid level and are not resolved. In these works, we have introduced contrast-independent, partially explicit time discretizations for linear equations. The contrast-independent, partially explicit time discretization divides the spatial space into two components: contrast dependent (fast) and contrast independent (slow) spaces defined via multiscale space decomposition. Following this decomposition, temporal splitting was proposed, which treats fast components implicitly and slow components explicitly. The space decomposition and temporal splitting are chosen such that they guarantees stability, and we formulated a condition for the time stepping. This condition was formulated as a condition on slow spaces. In this paper, we extend this approach to nonlinear problems. We propose a splitting approach and derive a condition that guarantees stability. This condition requires some type of contrast-independent spaces for slow components of the solution. We present numerical results and show that the proposed methods provide results similar to implicit methods with a time step that is independent of the contrast.

Time-resolved microscopy of femtosecond laser filaments in fused quartz

Detailed picture of continuous shape evolution of femtosecond laser pulse has been recorded directly in the process of filament formation in fused silica using time-resolved polarization microscopy with ∼70 fs temporal resolution. The main stages of the pulse transformation (temporal self-compression and splitting, formation of conical wave) have been studied. The maximum temporal compression has been found to be achieved by the leading subpulse after the time splitting event. It was found that the Bessel zone of conical wave formation is shifted backwards from the pulse front. Sub- and superluminal propagation velocities of the pulse maxima after the time splitting have been measured.

Phase I prognostic online (PIPO): A web tool to improve patient selection for oncology early phase clinical trials

PurposePatient selection in phase 1 clinical trials (Ph1t) continues to be a challenge. The aim of this study was to develop a user-friendly prognostic calculator for predicting overall survival (OS) outcomes in patients to be included in Ph1t with immune checkpoint inhibitors (ICIs) or targeted agents (TAs) based on clinical parameters assessed at baseline. MethodsUsing a training cohort with consecutive patients from the VHIO phase 1 unit, we constructed a prognostic model to predict median OS (mOS) as a primary endpoint and 3-month (3m) OS rate as a secondary endpoint. The model was validated in an internal cohort after temporal data splitting and represented as a web application. ResultsWe recruited 799 patients (training and validation sets, 558 and 241, respectively). Median follow-up was 21.2 months (m), mOS was 10.2 m (95% CI, 9.3–12.7) for ICIs cohort and 7.7 m (95% CI, 6.6–8.6) for TAs cohort. In the multivariable analysis, six prognostic variables were independently associated with OS – ECOG, number of metastatic sites, presence of liver metastases, derived neutrophils/(leukocytes minus neutrophils) ratio [dNLR], albumin and lactate dehydrogenase (LDH) levels. The phase 1 prognostic online (PIPO) calculator showed adequate discrimination and calibration performance for OS, with C-statistics of 0.71 (95% CI 0.64–0.78) in the validation set. The overall accuracy of the model for 3m OS prediction was 87.2% (95% CI 85%–90%). ConclusionsPIPO is a user-friendly objective and interactive tool to calculate specific survival probabilities for each patient before enrolment in a Ph1t. The tool is available at https://pipo.vhio.net/.

Beam Quality of Annular Pulsed Laser Beams Propagating Through the Nonlinear and Dispersive Atmosphere

The Kerr self-focusing and group-velocity dispersion (GVD) effects play important roles when a high-power pulsed laser beam propagates from the ground through the nonlinear and dispersive atmosphere to space orbits. For an annular pulsed laser beam, the Kerr self-focusing and GVD effects on the beam quality on the target is studied in this paper. Due to self-focusing, the maximum intensity I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> on the target arrives when the beam power P = P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">opt</sub> (P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">opt</sub> is called the optimal beam power), and the intensity on the target will decrease as the beam power P increases further when P > P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">opt</sub> . The P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">opt</sub> of nanosecond and picosecond pulsed beams is lower than that of femtosecond pulsed beams, while the maximum intensity I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> on the target of nanosecond and picosecond pulsed beams is higher than that of femtosecond pulsed beams. The P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">opt</sub> and I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> of annular pulsed beams are higher than those of Gaussian pulsed beams. In addition, the B integral and the Strehl ratio are also adopted to describe the beam quality on the target. On the other hand, because of the interplay of Kerr self-focusing and GVD effects, the temporal pulse splitting and self-healing may take place on propagation, and the temporal pulse splitting may take place more than once. The results obtained in this paper are useful for laser ablation propulsion's applications in space.

Temporal splitting algorithms for non-stationary multiscale problems

In this paper, we study temporal splitting algorithms for multiscale problems. The exact fine-grid spatial problems typically require some reduction in degrees of freedom. Multiscale algorithms are designed to represent the fine-scale details on a coarse grid and, thus, reduce the problems' size. When solving time-dependent problems, one can take advantage of the multiscale decomposition of the solution and perform temporal splitting by solving smaller-dimensional problems, which is studied in the paper. In the proposed approach, we consider the temporal splitting based on various low dimensional spatial approximations. Because a multiscale spatial splitting gives a “good” decomposition of the solution space, one can achieve an efficient implicit-explicit temporal discretization. We present a recently developed theoretical result in [15] and adopt in this paper for multiscale problems. Numerical results are presented to demonstrate the efficiency of the proposed splitting algorithm.

A mathematical model for thermal single-phase flow and reactive transport in fractured porous media

In this paper we present a mathematical model and a numerical workflow for the simulation of a thermal single-phase flow with reactive transport in porous media, in the presence of fractures. The latter are thin regions which might behave as high or low permeability channels depending on their physical parameters, and are thus of paramount importance in underground flow problems. Chemical reactions may alter the local properties of the porous media as well as the fracture walls, changing the flow path and possibly occluding some portions of the fractures or zones in the porous media. To solve numerically the coupled problem we propose a temporal splitting scheme so that the equations describing each physical process are solved sequentially. Numerical tests show the accuracy of the proposed model and the ability to capture complex phenomena, where one or multiple fractures are present.