Integration Step Research Articles

Coordination of force-generating actin-based modules stabilizes and remodels membranes in vivo.

Membrane remodeling drives a broad spectrum of cellular functions, and it is regulated through mechanical forces exerted on the membrane by cytoplasmic complexes. Here, we investigate how actin filaments dynamically tune their structure to control the active transfer of membranes between cellular compartments with distinct compositions and biophysical properties. Using intravital subcellular microscopy in live rodents we show that a lattice composed of linear filaments stabilizes the granule membrane after fusion with the plasma membrane and a network of branched filaments linked to the membranes by Ezrin, a regulator of membrane tension, initiates and drives to completion the integration step. Our results highlight how the actin cytoskeleton tunes its structure to adapt to dynamic changes in the biophysical properties of membranes.

Enhancing Accuracy and Efficiency in Stiff ODE Integration Using Variable Step Diagonal BBDF Approaches

Recent advancements in mathematical modelling have uncovered a growing number of systems exhibiting stiffness, a phenomenon that challenges the effectiveness of traditional numerical methods. Motivated by the need for more robust numerical techniques to address this issue, this paper presents an enhanced version of the Diagonally Block Backward Differentiation Formula (BBDF) that incorporates intermediate points, known as off-step points, to improve the accuracy and efficiency of solutions for stiff ordinary differential equations (ODEs). The new scheme leverages an adaptive step-size strategy to refine accuracy and efficiency between regular and off-grid integration steps. Theoretical analysis confirms that the proposed scheme is an A-stable and convergent method, as it satisfies the fundamental criteria of consistency, zero-stability, and A-stability. Numerical experiments on single and multivariable systems across varying time scales demonstrate significant improvements in solving stiff ODEs compared to existing techniques. Therefore, the new proposed method is an effective solver for stiff ODEs.

A GENERALIZED APPROACH TO INTEGRATION PROCESS BY AUXILIARY FUNCTIONS

Analytical integrals of functions in closed form are rare and one has to resort frequently to numerical integration techniques. In this work, approximate auxiliary functions that can be integrated are replaced by the original function to determine approximate analytical and numerical integrals. Information on one and two points of the function is used in determining the parameters of the auxiliary trial functions. Three alternative methods are proposed. Once the function without an available closed-form integral is replaced with an integrable one, analytical and numerical integration results can be found. The integration step size can be substantially increased by the employment of the methods.

Multicohort study testing the generalisability of the SASKit-ML stroke and PDAC prognostic model pipeline to other chronic diseases

ObjectivesTo validate and test the generalisability of the SASKit-ML pipeline, a prepublished feature selection and machine learning pipeline for the prediction of health deterioration after a stroke or pancreatic adenocarcinoma...

A dual-modified implicit time integration method for three-dimensional impact modelling within the framework of the SBFEM

This paper presents a dual-modified implicit time integration method (DMITIM) for three-dimensional impact modelling within the framework of the scaled boundary finite element method (SBFEM). Controlled by a single parameter, this method effectively dissipates high-frequency responses in impact problems without affecting low-frequency responses, ensuring time integration stability. To address the issue of false oscillations during impacts, additional Lagrange multipliers are introduced to supplement the velocity and acceleration corrections at each time integration step. For nonmatching meshes, by leveraging the mesh flexibility of the SBFEM, a rapid and straightforward remeshing method is utilized to establish a node-to-node contact scheme. The numerical results demonstrate that the DMITIM significantly reduces false oscillations in the velocity and contact force during impact events. It also showcases the flexibility of the SBFEM in handling nonmatching meshes. The combination of the SBFEM with the DMITIM provides enhanced simulation accuracy and stability for impact problems compared to the results from ABAQUS using the HHT-α time integration algorithm.

Full shape cosmology analysis from BOSS in configuration space using neural network acceleration

Recently, a new wave of full modeling analyses have emerged within the Large-Scale Structure community, leading mostly to tighter constraints on the estimation of cosmological parameters, when compared with standard approaches used over the last decade by collaboration analyses of stage III experiments. However, the majority of these full-shape analyses have primarily been conducted in Fourier space, with limited emphasis on exploring the configuration space. Investigating n-point correlations in configuration space demands a higher computational cost compared to Fourier space because it typically requires an additional integration step. This can pose a limitation when using these approaches, especially when considering higher-order statistics. One avenue to mitigate the high computation time is to take advantage of neural network acceleration techniques. In this work, we present a full shape analysis of Sloan Digital Sky Survey III/BOSS in configuration space using a neural network accelerator. We show that the efficacy of the pipeline is enhanced by a time factor 103 without sacrificing precision, making it possible to reduce the error associated with the surrogate modeling to below 10-2 percent which is compatible with the precision required for current stage IV experiments such as DESI. We find Ω m = 0.286±0.009, H 0 = 68.8±1.2 kms-1Mpc-1 and A s × 109 = 2.09 +0.25 -0.29. Our results on public BOSS data are in good agreement with BOSS official results and compatible with other independent full modeling analyses. We explore relaxing the prior on ωb and varying ns , without significant changes in the mean values of the cosmological parameters posterior distributions, but enlarging their widths. Finally, we explore the information content of the multipoles when constraining cosmological parameters.

HIV-1 Intasomes Assembled with Excess Integrase C-Terminal Domain Protein Facilitate Structural Studies by Cryo-EM and Reveal the Role of the Integrase C-Terminal Tail in HIV-1 Integration.

Retroviral integration is mediated by intasome nucleoprotein complexes wherein a pair of viral DNA ends are bridged together by a multimer of integrase (IN). Atomic-resolution structures of HIV-1 intasomes provide detailed insights into the mechanism of integration and inhibition by clinical IN inhibitors. However, previously described HIV-1 intasomes are highly heterogeneous and have the tendency to form stacks, which is a limiting factor in determining high-resolution cryo-EM maps. We have assembled HIV-1 intasomes in the presence of excess IN C-terminal domain protein, which was readily incorporated into the intasomes. The purified intasomes were largely homogeneous and exhibited minimal stacking tendencies. The cryo-EM map resolution was further improved to 2.01 Å, which will greatly facilitate structural studies of IN inhibitor action and drug resistance mechanisms. The C-terminal 18 residues of HIV-1 IN, which are critical for virus replication and integration in vitro, have not been well resolved in previous intasome structures, and its function remains unclear. We show that the C-terminal tail participates in intasome assembly, resides within the intasome core, and forms a small alpha helix (residues 271-276). Mutations that disrupt alpha helix integrity impede IN activity in vitro and disrupt HIV-1 infection at the step of viral DNA integration.

Accelerated Simulation of Passive Analog Circuits Over GPU Using Explicit Integration Methods

Analog circuits composed by large number of nodes in a tightly coupled structure pose significant challenges due to their prohibitive CPU simulation time. This work describes a method to speed up the simulation of such circuits by means of the combination of space state formulation of circuit equations with explicit integration methods parallelized over a many-core processor such as a GPU. Although stability of explicit techniques require smaller integration steps compared to implicit methods, the proposed method employs a fast estimate of the maximum allowed step size to guarantee numerical stability, which yields a shorter simulation time for increasing complexity circuit architectures. Moreover, the proposed technique can be straightforward parallelized on a many core architecture. The proposed method is demonstrated with two examples using constant and variable coefficients respectively: an RLC interconnect and a MOS-C network to perform Gaussian filtering of medium resolution images. The results obtained have been compared to a parallel version of SPICE and show improvements up to two orders of magnitude for transient simulations depending of the circuit size.

Loss of pre-stress in impregnated superconducting magnets, experimental results and numerical analysis

The SMC (Short Model Coil) R&D program was started at CERN around 2007 to develop the Nb3Sn technology. The small magnet structure allowed relatively cheap and fast testing of various superconducting coils. One of the key questions to be answered, was related to the relation between the pre-stress and the magnet’s performance. To measure this dozens of strain gauges were installed on the coils, the axial tie-rods and the external shell. The experimental results of the strain measurements during all stages of the load: room temperature (RT) pre-stress, cool-down, powering, warm-up were analyzed in an extensive report [56]. A repeatable pattern of a decreasing strain after the warm-up, compared to the value before the cool-down, was observed on the external cylinder for all the tested coils. Values from 2 % to 50 % were reported.In this work a viscoelastic model was used to explain this effect. The Nb3Sn coil was treated as a composite material with decreasing stiffness due to mechanical damage. The Generalized Maxwell Solid model (Prony series model) was employed, including one spring and one damper, leading to a relatively simple model characterized by only two parameters. The two constants of the viscoelastic model were found: 1st – the relative relaxation moduli α based on a calibration curve derived from the experimental results of the SMC program and the 2nd one – relaxation time τ – based on minimizing the computational cost, by finding the asymptotic solution in one integration step. The model showed the capability of explaining the strain drop (loss of pre-stress) of more than 80 %. In addition to the viscoelastic effects, the role of friction coefficient was studied revealing the possibility of explaining up to 14 % of the strain drop. Yet, to fit with the experimentally measures strains on the SMC cylinder, especially during the RT pre-load, the most-probable value of the friction coefficient should be μ<0.4. The strong impact of the stiffness of the G-10/G-11 laminate used to spread the load on the coil was found, indicating the need of knowing the elastic properties of this material very precisely. In addition, the experimentally measured strain values showed strong asymmetric, both in plane and along the magnet’s axis, revealing the potential sensitivity to the geometric imperfections and the need for 360° magnet models.

The possible origin of three Apollo asteroids. 3200 Phaethon, 2005UD, and 1999YC

We study the possible dynamical background of three Apollo asteroids: 3200 Phaethon, 2005 UD, and 1999 YC. The source regions under consideration are the asteroid families (2) Pallas, in the outer belt, and two inner-belt families (329) Svea and (142) Polana. We also aim to explain some of the contradictions in the literature in regards to the origin of Phaethon. Our methodology relies on the precise dynamical mapping of several mean motion resonances (MMRs), which are considered the main transport channels. This approach allows the clear detection of chaotic structures in an MMR and efficent selection of test asteroids for diffusion. We tracked the orbital evolution of the selected particles over 5 million years and registered all their eventual entries into the orbital neighborhood of the asteroids 3200 Phaethon, 2005 UD and 1999 YC. We performed massive calculations for different orbital and integration parameters using Orbit9 and Rebound software packages. We observed possible connections between three targeted Apollo asteroids and asteroid families we considered as their sources. The (2) Pallas family has the highest chance of being the origin of targeted asteroids, and (142) Polana has the lowest. The amount of transported material largely depends on the integrator, the integration step, and even the choice of the initial epoch, though to a lesser extent. There is a systematic discrepancy between the results obtained with Orbit9 and Rebound regarding the efficiency of the transport, but they show good agreement over delivery times and dynamical maps. A non-negligible number of objects approached all three target asteroids, which could indicate that the breakup of the precursor body occurred during its dynamical evolution.

Automatic adjustment of the parameters of the temperature measurement algorithm in a wide range

Existing methods and devices for measuring temperature are described, and it is noted that resistance thermometers are most widely used as temperature sensors in systems for collecting and monitoring environmental parameters. It is shown that the main source of temperature measurement errors when connecting sensors remotely is the resistance of the connecting lines, determined by their length. The main methods for reducing the measurement error caused by the influence of the resistance of the vehicle connection line on the temperature measurement results are considered. The advantages of two-wire circuits in comparison with three- and four-wire circuits are formulated. As an analogue, a two-wire method of measuring temperature with an integrating converter is considered in detail, implemented on the basis of a device with a built-in microcontroller, and allowing to obtain such advantages as reducing measurement time, detuning from interference and quantization noise and, as a result, reducing the temperature measurement error in comparison with similar two-wire measurement methods. An alternative two-wire method for measuring temperature with automatic adjustment of the parameters of the measurement algorithm is proposed, aimed at increasing the measurement accuracy by weakening the influence of the time constant. The search for the optimal time of the first integration step was carried out. Experimental studies and evaluation calculations were carried out to confirm the effectiveness of the proposed solution. The coefficient of variation when the resistance of the vehicle changes in the range of 1–4 kOhm lies in the range, and the range of change in the relative error of resistance measurement when using auto-tuning within the specified range has decreased by more than 4 times. The results of the experiment allow us to count on the possibility of using the method in control and regulation systems with remote connection of temperature sensors.

Finite Elements with Switch Detection for numerical optimal control of nonsmooth dynamical systems with set-valued heaviside step functions

This paper develops high-accuracy methods for the numerical solution of optimal control problems subject to nonsmooth differential equations with set-valued Heaviside step functions. An important subclass of these systems are Filippov systems. By writing the Heaviside step function as the solution map of a linear program and using its optimality conditions, the initial nonsmooth system is rewritten into an equivalent Dynamic Complementarity System (DCS). The Finite Elements with Switch Detection (FESD) method (Nurkanović et al., 2024) was originally developed for Filippov systems transformed via Stewart’s reformulation into DCS (Stewart, 1990). This paper extends it to the above mentioned class of nonsmooth systems. The key ideas are to start with a standard Runge–Kutta method for the DCS and to let the integration step sizes to be degrees of freedom. Then, additional conditions are introduced to allow implicit but accurate switch detection and to remove possible spurious degrees of freedom when no switches occur. The theoretical properties of the FESD method are studied. The motivation for these developments is to obtain a computationally tractable formulation of nonsmooth optimal control problems. Numerical simulations and optimal control examples are used to illustrate the favorable properties of the proposed approach. All methods introduced in this paper are implemented in the open-source software package nosnoc (Nurkanović and Diehl, 2022).

Numerical Calculations of Adiabatic Invariants From MHD‐Driven Magnetic Fields

AbstractThe adiabatic invariants (M, J, Φ) and the related invariants (M, K, L*) have been established as effective coordinate systems for describing radiation belt dynamics at a theoretical level, and through numerical techniques, can be paired with in situ observations to order phase‐space density. To date, methods for numerical techniques to calculate adiabatic invariants have focused on empirical models such the Tsyganenko models TS05, T96, and T89. In this work, we develop methods based on numerical integration and variable step size iteration for the calculation of adiabatic invariants, applying the method to the Lyon‐Fedder‐Mobarry (LFM) global magnetohydrodynamics (MHD) simulation code, with optional coupling to the Rice Convection Model (RCM). By opening the door to adiabatic invariant modeling with MHD magnetic fields, the opportunity for exploratory modeling work of radiation belt dynamics is enabled. Calculations performed using LFM are cross‐referenced with the same code applied to the T96 and TS05 Tsyganenko models evaluated on the LFM grid. Important aspects of the adiabatic invariant calculation are reviewed and discussed, including (a) sensitivity to magnetic field model used, (b) differences in the problem between quiet and disturbed geomagnetic states, and (c) the selection of key parameters, such as the magnetic local time step size for drift shell determination. The rigorous development and documentation of this algorithm additionally acts as preliminary step for future thorough reassessment of in situ phase‐space density results using alternative magnetic field models.

A comparative study of sensitivity computations in ESDIRK-based optimal control problems

This paper compares the impact of iterated and direct approaches to sensitivity computation in fixed step-size explicit singly diagonally implicit Runge–Kutta (ESDIRK) methods when applied to optimal control problems (OCPs). We strictly use the principle of internal numerical differentiation (IND) for the iterated approach, i.e., reusing iteration matrix factorizations, the number of Newton-type iterations, and Newton iterates, to compute the sensitivities. The direct method computes the sensitivities without using the Newton schemes. We compare the impact of these sensitivity computations in OCPs for the quadruple tank system (QTS). We discretize the OCPs using multiple shooting and solve these with a sequential quadratic programming (SQP) solver. We benchmark the iterated and direct approaches against a base case. This base case applies the ESDIRK methods with exact Newton schemes and a direct approach for sensitivity computations. In these OCPs, we vary the number of integration steps between control intervals and evaluate the performance based on the number of SQP and QPs iterations, KKT violations, function evaluations, Jacobian updates, and iteration matrix factorizations. We also provide examples using the continuous-stirred tank reactor (CSTR), and the IPOPT algorithm instead of the SQP. For OCPs solved using SQP, the QTS results show the direct method converges only once, while the iterated approach and base case converges in all situations. Similar results are seen with the CSTR. Using IPOPT, both the iterated approach and base case converge in all cases. In contrast, the direct method only converges in all cases regarding the CSTR.

A decade of Eurasian integration: An ex-post non-parametric assessment of the Eurasian economic union

This paper provides a sound ex-post evaluation of the impact of the Eurasian integration on member countries’ bilateral trade after a decade of implementation. We overcome the main limitations of current empirical analyses on the effects of trade agreements, namely the aggregation of tariff and non-tariff barriers and the likely self-selection bias, by applying a non-parametric method specifically designed to fully exploit time-series cross-sectional data. We thus compare the trade flows of the member countries in the Eurasian agreement with the exporter-importer pairs located in the Eurasian continent, which are most similar in terms of pre-treatment trends and features. Our results confirm the previous literature about the lack of a significant impact of the Eurasian customs union but find more positive net effects of the more recent integration steps. Our results ask for additional efforts to complete the Eurasian integration and let its member countries fully benefit from its hoped-for long-term effects.

Jacobian-free Locally Linearized Runge–Kutta method of Dormand and Prince for large systems of differential equations

This paper introduces Jacobian-free Locally Linearized Runge–Kutta formulas of Dormand and Prince for integrating large systems of initial value problems. With these new Jacobian-free formulas, an adaptive time-stepping variable-order scheme with regulated Krylov dimension is constructed with new developments in the computation of the phi-function action over vectors through Jacobian-free Krylov–Padé approximations, and in the procedures for controlling the approximation errors and for estimating the dimension of the Krylov subspaces. At each integration step, the implemented scheme performs only one Krylov subspace decomposition and a few computations of low dimensional exponential matrices, which contrasts with the implementation of other exponential-type integrators of high order. Regarding to existing schemes, the performed numerical study demonstrates a higher effectiveness of the constructed scheme in the integration of a variety of test equations.

The Role of the Implementation Matrix in Designing and Reporting Integration Decisions in a Mixed Methods Study

The purpose of this article is to illustrate the process and insights gleaned from developing an implementation matrix to convey a concise, yet detailed representation of the project integration steps in a single diagram. The article is based on an explanatory sequential study conducted with 248 teachers exploring how beliefs shaped their use of technology. This article contributes to mixed methods research (MMR) by providing an example that can be used as guide by other researchers in developing and using the implementation matrix as a tool for communicating procedurally the mixed methods project integration steps for an explanatory sequential study. It also provides analytical insights gleaned and recommendations for how the implementation matrix can be developed and utilized.

Asymptotically consistent and computationally efficient modeling of short-ranged molecular interactions between curved slender fibers undergoing large 3D deformations

This article proposes a novel computational modeling approach for short-ranged molecular interactions between curved slender fibers undergoing large 3D deformations, and gives a detailed overview how it fits into the framework of existing fiber or beam interaction models, either considering microscale molecular or macroscale contact effects. The direct evaluation of a molecular interaction potential between two general bodies in 3D space would require to integrate molecule densities over two 3D volumes, leading to a sixfold integral to be solved numerically. By exploiting the short-range nature of the considered class of interaction potentials as well as the fundamental kinematic assumption of undeformable fiber cross-sections, as typically applied in mechanical beam theories, a recently derived, closed-form analytical solution is applied for the interaction potential between a given section of the first fiber (slave beam) and the entire second fiber (master beam), whose geometry is linearly expanded at the point with smallest distance to the given slave beam section. This novel approach based on a pre-defined section–beam interaction potential (SBIP) requires only one single integration step along the slave beam length to be performed numerically. In addition to significant gains in computational efficiency, the total beam–beam interaction potential resulting from this approach is shown to exhibit an asymptotically consistent angular and distance scaling behavior. Critically for the numerical solution scheme, a regularization of the interaction potential in the zero-separation limit as well as the finite element discretization of the interacting fibers, modeled by the geometrically exact beam theory, are presented. In addition to elementary two-fiber systems, carefully chosen to verify accuracy and asymptotic consistence of the proposed SBIP approach, a potential practical application in form of adhesive nanofiber-grafted surfaces is studied. Involving a large number of helicoidal fibers undergoing large 3D deformations, arbitrary mutual fiber orientations as well as frequent local fiber pull-off and snap-into-contact events, this example demonstrates the robustness and computational efficiency of the new approach.

Log-Euclidean metric based covariance propagation on SPD manifold for continuous–discrete extended Kalman filtering

For nonlinear systems with continuous dynamic and discrete measurements, a Log-Euclidean metric (LEM) based novel scheme is proposed to refine the covariance integration steps of continuous–discrete Extended Kalman filter (CDEKF). In CDEKF, the covariance differential equation is usually integrated with regular Euclidean matrix operations, which actually ignores the Riemannian structure of underlying space and poses a limit on the further improvement of estimation accuracy. To overcome this drawback, this work proposes to define the covariance variable on the manifold of symmetric positive definite (SPD) matrices and propagate it using the Log-Euclidean metric. To embed the LEM based novel propagation scheme, the manifold integration of the covariance for LEMCDEKF is proposed together with the details of efficient realization, which can integrate the covariance on SPD manifold and avoid the drawback of Euclidean scheme. Numerical simulations certify the new method’s superior accuracy than conventional methods.

Physics-Based Self-Learning Spiking Neural Network enhanced time-integration scheme for computing viscoplastic structural finite element response

The present study introduces a new physics-based self-learning spiking neural framework to compute geometrically and physically nonlinear structural response. While the so-called traditional or second-generation deep neural networks are used in many applications in the class of physics-informed neural networks, we propose a hybrid model that consists of third-generation Leaky-Integrated and Fire (LIF) neurons, Recurrent Leaky-Integrated and Fire (RLIF) neurons and second-generation dense transformation. The third-generation neurons are inspired by the human brain’s energy-efficient functioning which introduces inherent temporal and sparse behavior leading to a more sustainable AI approach. However, the sparse nature of the spiking neurons poses a challenge to tackle nonlinear regression tasks. Thus, in the present study, we use an autoencoding strategy that converts the real-valued signals to its spiking representation and enables the spiking neurons to learn nonlinear material response. The proposed hybrid network is firstly pretrained with combined data-driven and physics-based loss functions and then deployed in the plastic corrector step of the implicit integration which is used in the Finite Element solver and is validated on a series of Boundary Value Problems (BVPs) consisting of plate elements. A self-learning strategy is introduced for the hybrid network to train itself during FE simulation using the proposed physics-based loss function. Two major advantages were observed: an overall computational gain in the excess of 30% and the self-learning/online training ability of the model that bolsters its convergence behavior. Finally, the proposed third-generation layers are deployed on the Xylo-Av2 neuromorphic chip and its energy performance is compared with the second-generation Recurrent Neural Networks (RNNs).