Approximate Estimation Research Articles

Recurrent Event Analysis in the Presence of Real-Time High Frequency Data via Random Subsampling

Digital monitoring studies collect real-time high frequency data via mobile sensors in the subjects’ natural environment. This data can be used to model the impact of changes in physiology on recurrent event outcomes such as smoking, drug use, alcohol use, or self-identified moments of suicide ideation. Likelihood calculations for the recurrent event analysis, however, become computationally prohibitive in this setting. Motivated by this, a random subsampling framework is proposed for computationally efficient, approximate likelihood-based estimation. A subsampling-unbiased estimator for the derivative of the cumulative hazard enters into an approximation of log-likelihood. The estimator has two sources of variation: the first due to the recurrent event model and the second due to subsampling. The latter can be reduced by increasing the sampling rate; however, this leads to increased computational costs. The approximate score equations are equivalent to logistic regression score equations, allowing for standard, “off-the-shelf” software to be used in fitting these models. Simulations demonstrate the method and efficiency-computation tradeoff. We end by illustrating our approach using data from a digital monitoring study of suicidal ideation. Supplementary materials for this article are available online.

Scalable Approximate Butterfly and Bi-triangle Counting for Large Bipartite Networks

A bipartite graph is a graph that consists of two disjoint sets of vertices and only edges between vertices from different vertex sets. In this paper, we study the counting problems of two common types of em motifs in bipartite graphs: (i) butterflies (2x2 bicliques) and (ii) bi-triangles (length-6 cycles). Unlike most of the existing algorithms that aim to obtain exact counts, our goal is to obtain precise enough estimations of these counts in bipartite graphs, as such estimations are already sufficient and of great usefulness in various applications. While there exist approximate algorithms for butterfly counting, these algorithms are mainly based on the techniques designed for general graphs, and hence, they are less effective on bipartite graphs. Not to mention that there is still a lack of study on approximate bi-triangle counting. Motivated by this, we first propose a novel butterfly counting algorithm, called one-sided weighted sampling, which is tailored for bipartite graphs. The basic idea of this algorithm is to estimate the total butterfly count with the number of butterflies containing two randomly sampled vertices from the same side of the two vertex sets. We prove that our estimation is unbiased, and our technique can be further extended (non-trivially) for bi-triangle count estimation. Theoretical analyses under a power-law random bipartite graph model and extensive experiments on multiple large real datasets demonstrate that our proposed approximate counting algorithms can reach high accuracy, yet achieve up to three orders (resp. four orders) of magnitude speed-up over the state-of-the-art exact butterfly (resp. bi-triangle) counting algorithms. Additionally, we present an approximate clustering coefficient estimation framework for bipartite graphs, which shows a similar speed-up over the exact solutions with less than 1% relative error.

Approximation of classes of periodic functions of several variables with given majorant of mixed moduli of continuity

We obtain the exact-order estimates of approximation of the Nikol'skii-Besov-type classes $B^{\Omega}_{\infty,\theta}$ of periodic functions of several variables with a given function $\Omega(t)$ of a special form by using linear operators satisfying certain conditions. The approximation error is estimated in the metric of the space $L_{\infty}$. The obtained estimates of the considered approximation characteristic, in addition to independent interest, can be used to establish the lower bounds of the orthowidths of the corresponding functional classes.

On existence, uniqueness and stability of solutions to Cahn–Hilliard/Allen–Cahn systems with cross-kinetic coupling

A system of phase-field equations with strong-coupling through state and gradient dependent non-diagonal mobility matrices is studied. Existence of weak solutions is established by the Galerkin approximation and a-priori estimates in strong norms. Relative energy estimates are used to derive a general nonlinear stability estimate. As a consequence, a weak–strong uniqueness principle is obtained and stability with respect to model parameters is investigated.

Effect of SUVR reference region selection on sampled iterative local approximation estimates of amyloid onset age

AbstractBackgroundAmyloid PET imaging quantifies Aß plaques informing longitudinal modeling methods such as sampled iterative local approximation (SILA) that provide individualized estimated amyloid onset age (EAOA). EAOA is defined as the transition to abnormal Aß accumulation that occurs in Alzheimer’s disease. This work investigates the effect of SUVR reference region selection on EAOA by comparing DVR‐trained versus SUVR‐trained SILA models with three different SUVR reference regions.MethodN = 585 participants (mean (SD) baseline age = 66.40 (7.89) years, 512 unimpaired, 44 MCI, 28 dementia, 1 unknown) from the Wisconsin Registry for Alzheimer’s Prevention and Wisconsin Alzheimer’s Disease Research Center underwent T1‐weighted MRI and dynamic 11C‐Pittsburgh Compound B (PiB) amyloid PET imaging (0‐70 minutes after bolus injection). Reconstructed dynamic PET time series were processed and quantified using MR‐guided imaging pipelines optimized for DVR (Logan, k2’ = 0.149 min‐1, cerebellum gray matter (CBLM‐GM) reference region) and SUVR (50‐70 min frames) quantification with CBLM‐GM, whole cerebellum (WHOLE‐CBLM), or subcortical white matter (WM) as a reference region. Mean cortical PiB DVR and SUVR were each calculated by averaging across eight bilateral ROIs. Group‐based trajectory modeling was applied to longitudinal DVR data to establish an amyloid positivity (A+) threshold (DVR>1.14; equivalent to 14 centiloids). LME was used to define the relationship between DVR and SUVR and translate the DVR threshold to SUVR (SUVRCBLM GM>1.28; SUVRWHOLE CBLM>1.07; SUVRWM>0.68). Within‐person paired differences between EAOADVR and EAOASUVR_REFERENCE_REGION are reported as (mean; [95% CI]).ResultEAOA derived from DVR and SUVR were compared for n = 198 (34%) DVR A+ participants. Amyloid vs. age data are shown for each quantification approach in Figure 1. EAOASUVR‐WHOLE‐CBLM (‐1.29 years; [‐1.51, ‐1.08]) had the highest agreement with EAOADVR compared to EAOASUVR‐CBLM‐GM (‐1.44 years; [‐1.75, ‐1.12]) and EAOASUVR‐WM (‐0.67 years; [‐2.13, 0.79]; Figure 2). EAOA variability was highest for DVR>1.8 where fewer longitudinal observations were available for model training.ConclusionSUVR with whole cerebellum as a reference region resulted in the smallest difference in EAOA compared to DVR from the SILA model. Future work is ongoing to define SUVR thresholds that will optimize agreement with DVR‐trained EAOA results for harmonization of temporal estimates.

Associative Rules for Modeling International Security Decisions in the Context of the Ukrainian-Russian War. Preliminary Evaluations

Abstract Research background By launching a war against Ukraine, Russia changed the entire world system and demonstrated the ineffectiveness of the global security system. Today it is necessary to look for effective solutions to support the adoption of security decisions and develop effective strategies for the formation of a new architecture of the international security system. Purpose The paper aims to obtain preliminary approximate estimates of the state commitments of the countries of the world that support Ukraine in the war with Russia and to reveal non-obvious connections and regularities in the provision of various types of aid. Research methodology The data were collected on the rough refugee cost estimate, quantitative assessment of the government-to-government commitments, and preliminary data on non-bilateral aid transferred by governments to Ukraine of 40 countries. We used the FP-Growth algorithm to identify non-obvious connections and patterns between different types of support for Ukraine. Results We created an associative rules model to detect non-obvious patterns and relationships between the different types of bilateral commitments of the countries, that support Ukraine. Novelty Preliminary estimates were obtained between various types of international support for Ukraine in the war against Russia covering February 24 to November 20, 2022, the number of Ukrainian refugees accepted by the respective countries, and the sale of arms to Russia by some of them after the ban.

Effect of SUVR reference region selection on sampled iterative local approximation estimates of amyloid onset age

AbstractBackgroundAmyloid PET imaging quantifies Aβ plaques informing longitudinal modeling methods such as sampled iterative local approximation (SILA) that provide individualized estimated amyloid onset age (EAOA). EAOA is defined as the transition to abnormal Aβ accumulation that occurs in Alzheimer’s disease. This work investigates the effect of SUVR reference region selection on EAOA by comparing DVR‐trained versus SUVR‐trained SILA models with three different SUVR reference regions.MethodN = 585 participants (mean (SD) baseline age = 66.40 (7.89) years, 512 unimpaired, 44 MCI, 28 dementia, 1 unknown) from the Wisconsin Registry for Alzheimer’s Prevention and Wisconsin Alzheimer’s Disease Research Center underwent T1‐weighted MRI and dynamic 11C‐Pittsburgh Compound B (PiB) amyloid PET imaging (0‐70 minutes after bolus injection). Reconstructed dynamic PET time series were processed and quantified using MR‐guided imaging pipelines optimized for DVR (Logan, k2’ = 0.149 min−1, cerebellum gray matter (CBLM‐GM) reference region) and SUVR (50‐70 min frames) quantification with CBLM‐GM, whole cerebellum (WHOLE‐CBLM), or subcortical white matter (WM) as a reference region. Mean cortical PiB DVR and SUVR were each calculated by averaging across eight bilateral ROIs. Group‐based trajectory modeling was applied to longitudinal DVR data to establish an amyloid positivity (A+) threshold (DVR>1.14; equivalent to 14 centiloids). LME was used to define the relationship between DVR and SUVR and translate the DVR threshold to SUVR (SUVRCBLM GM>1.28; SUVRWHOLE CBLM>1.07; SUVRWM>0.68). Within‐person paired differences between EAOADVR and EAOASUVR_REFERENCE_REGION are reported as (mean; [95% CI]).ResultEAOA derived from DVR and SUVR were compared for n = 198 (34%) DVR A+ participants. Amyloid vs. age data are shown for each quantification approach in Figure 1. EAOASUVR‐WHOLE‐CBLM (‐1.29 years; [‐1.51, ‐1.08]) had the highest agreement with EAOADVR compared to EAOASUVR‐CBLM‐GM (‐1.44 years; [‐1.75, ‐1.12]) and EAOASUVR‐WM (‐0.67 years; [‐2.13, 0.79]; Figure 2). EAOA variability was highest for DVR>1.8 where fewer longitudinal observations were available for model training.ConclusionSUVR with whole cerebellum as a reference region resulted in the smallest difference in EAOA compared to DVR from the SILA model. Future work is ongoing to define SUVR thresholds that will optimize agreement with DVR‐trained EAOA results for harmonization of temporal estimates.

Discontinuous Galerkin Two-Grid Method for the Transient Navier–Stokes Equations

Abstract In this paper, we apply a two-grid scheme to the DG formulation of the 2D transient Navier–Stokes model. The two-grid algorithm consists of the following steps: Step 1 involves solving the nonlinear system on a coarse mesh with mesh size 𝐻, and Step 2 involves linearizing the nonlinear system by using the coarse grid solution on a fine mesh of mesh size ℎ and solving the resulting system to produce an approximate solution with desired accuracy. We establish optimal error estimates of the two-grid DG approximations for the velocity and pressure in energy and L 2 L^{2} -norms, respectively, for an appropriate choice of coarse and fine mesh parameters. We further discretize the two-grid DG model in time, using the backward Euler method, and derive the fully discrete error estimates. Finally, numerical results are presented to confirm the efficiency of the proposed scheme.

Deep reinforcement learning in finite-horizon to explore the most probable transition pathway

In many scientific and engineering problems, noise and nonlinearity are unavoidable, which could induce interesting mathematical problem such as transition phenomena. This paper focuses on efficiently discovering the most probable transition pathway for stochastic dynamical systems employing reinforcement learning. With the Onsager–Machlup action functional theory to quantify rare events in stochastic dynamical systems, finding the most probable pathway is equivalent to solving a variational problem on the action functional. When the action function cannot be explicitly expressed by paths near the reference orbit, the variational problem needs to be converted into an optimal control problem. First, by integrating terminal prediction into the reinforcement learning framework, we develop a Terminal Prediction Deep Deterministic Policy Gradient (TP-DDPG) algorithm to deal with the finite-horizon optimal control issue in a forward way. Next, we present the convergence analysis of our algorithm for the value function in terms of the neural network’s approximation error and estimation error. Finally, we conduct various experiments in different dimensions for the transition problems in applications to illustrate the effectiveness of our algorithm.

Stability estimates for an inverse problem for Schrödinger operators at high frequencies from arbitrary partial boundary measurements

In this paper, we study the partial data inverse boundary value problem for the Schrödinger operator at a high frequency in a bounded domain with smooth boundary in , . Assuming that the potential is known in a neighborhood of the boundary, we obtain the logarithmic stability when both Dirichlet data and Neumann data are taken on arbitrary open subsets of the boundary where the two sets can be disjointed. Our results also show that the logarithmic stability can be improved to the one of Hölder type in the high frequency regime. To achieve those goals, we used a method by combining the CGO solution, Runge approximation and Carleman estimate.

Approximate Bayesian Estimation of Stochastic Volatility in Mean Models Using Hidden Markov Models: Empirical Evidence from Emerging and Developed Markets

Approximate Bayesian Estimation of Stochastic Volatility in Mean Models Using Hidden Markov Models: Empirical Evidence from Emerging and Developed Markets

Semi-tensor product-based one-bit compressed sensing

The area of one-bit compressed sensing (1-bit CS) focuses on the recovery of sparse signals from binary measurements. Over the past decade, this field has witnessed the emergence of well-developed theories. However, most of the existing literature is confined to fully random measurement matrices, like random Gaussian and random sub-Gaussian measurements. This limitation often results in high generation and storage costs. This paper aims to apply semi-tensor product-based measurements to 1-bit CS. By utilizing the semi-tensor product, this proposed method can compress high-dimensional signals using lower-dimensional measurement matrices, thereby reducing the cost of generating and storing fully random measurement matrices. We propose a regularized model for this problem that has a closed-form solution. Theoretically, we demonstrate that the solution provides an approximate estimate of the underlying signal with upper bounds on recovery error. Empirically, we conduct a series of experiments on both synthetic and real-world data to demonstrate the proposed method’s ability to utilize a lower-dimensional measurement matrix for signal compression and reconstruction with enhanced flexibility, resulting in improved recovery accuracy.

A convergent finite volume scheme for the stochastic barotropic compressible Euler equations

In this paper, we analyze a semi-discrete finite volume scheme for the three-dimensional barotropic compressible Euler equations driven by a multiplicative Brownian noise. We derive necessary a priori estimates for numerical approximations, and show that the Young measure generated by the numerical approximations converge to a dissipative measure-valued martingale solution to the stochastic compressible Euler system. These solutions are probabilistically weak in the sense that the driving noise and associated filtration are integral part of the solution. Moreover, we demonstrate strong convergence of numerical solutions to the regular solution of the limit systems at least on the lifespan of the latter, thanks to the weak (measure-valued)–strong uniqueness principle for the underlying system. To the best of our knowledge, this is the first attempt to prove the convergence of numerical approximations for the underlying system.

Estimation of stress-strength reliability for generalized Gompertz distribution under progressive type-II censoring

In this study, the stress-strength reliability, $R=P(Y

Numerical modelling of myocardial infarction. II. Analysis of macrophage polarization mechanism as a therapeutic target

In this study, we explore the mechanism of macrophage polarization and its significance in the development of large-scale infarction with favorable outcomes, using a minimal mathematical model of aseptic inflammation dynamics. The problem is considered in the local approximation and in the two-dimensional non-stationary formulation. The study aims to address the pertinent problem of analyzing general principles governing macrophage polarization in the context of devising therapeutic strategies and refining the "therapeutic window". Key trends are identified to enhance the effectiveness of macrophage polarization for therapeutic purposes, along with providing approximate estimations of optimal macrophage interventions that yield organ-preserving and regenerative effects. Our findings reveal that M1/M2 macrophage polarization results from an additive interplay of at least two mechanisms - cytokine-dependent activation and reprogramming of activated macrophages. Furthermore, our modeling data demonstrate the pivotal role of macrophage reprogramming as a direct response to microenvironmental changes, facilitating favorable disease progression and its outcomes. Moreover, we establish that the process of macrophage polarization plays a crucial role in localizing focal inflammation, leading to the formation of the infarction core within finite dimensions and quasi-stationary structure at the periphery, comprising immune cell clusters. The modeling results exhibit qualitative and quantitative agreement with the experimental data. Importantly, the computational experiments results align with the majority of laboratory and clinical studies, emphasizing the therapeutic potential of macrophage polarization management as a promising treatment strategy. The paper is a follow-up of the previously published work series, devoted to the study of spatial and temporal aspects of the inflammation and death processes development in heart muscle cells.

A novel methodology for water-sensitive papers analysis focusing on the segmentation of overlapping droplets to better characterize deposition pattern

Water-sensitive papers (WSPs), as an artificial target, have been generally used to evaluate spray quality in pesticide applications. Though many tools were available to analyze WSPs, they were not effective in processing the presented overlapping droplets, which prevented accurate quantification of spray quality. Here, a novel methodology was proposed to analyze WSPs, focusing on the segmentation of overlapping droplets based on concave point detection and ellipse fitting. Up to 553 WSPs obtained from field trials in apple trees were used to validate this methodology. A high overall segmentation accuracy of 77.8% was achieved for the WSPs with coverage below 25%, which allowed to precisely characterize the corresponding deposition pattern. A universal linear relationship was observed between the droplet density and coverage, independent of the sprayer and canopy characteristics. In addition, the droplet size distributions for all spray applications showed a similar trend. As the proposed methodology was not effective to segment the complex overlapping spots on the WSP with high coverage (>25%), simulated WSPs were generated to estimate the deposition pattern of high coverage based on the droplet size distribution deposited on the WSPs with low coverage. A linear relationship with a much higher slope was observed between droplet density and coverage for the high deposition, which enabled an approximate estimation of the corresponding droplet density. In general, the proposed approaches allowed to obtain more accurate spray quality indicators from the WSP collectors and could be widely used for spray application evaluation to promote precision spraying.

О моделировании гидродинамического режима течений в системах речных русел в период прохождения волны половодья на примере участка р. Оби

Рассмотрен пример численного моделирования прохождения волны половодья на участке верхней и средней Оби ниже плотины Новосибирской ГЭС. Расчеты выполнены с использованием численной модели для описания распространения и трансформации волн половодий и паводков в системе русел (STREAM), разрабо танной в ИВЭП СО РАН. Модель основана на одномерных уравнениях Сен-Венана. Система русел моделируется в виде графа типа дерево, в вершинах которого за даются условия сопряжения основных гидродинамических параметров. Приведена приближенная численная оценка порядка точности метода решения. Результаты моделирования хорошо согласуются c данными наблюдений. The goal of the study is to analyze the possibility of using the numerical model STREAM for performing research on the passage of a flood wave in a system of channels. The model was developed at IWEP SB RAS on the basis of one-dimensional Saint-Venant equations. It allows describing the flow regimes in channels, represented as a directed graph of the tree type. In the nodes of the graph (channel gates), the conjugation conditions for the main hydrodynamic parameters flow rates and water levels are set. The finite difference method is used to solve the system of equations. The difference scheme has a second order of accuracy in space and a first order in time. An approximate numerical estimate of the order of accuracy of the model using the Runge method is obtained. Numerical simulation of the Ob river section under the conditions of a high-water year 2014 has been carried out. To construct the morphometric model of the graph, data from the pilot map of the river and data of the expedition studies of IWEP SB RAS were used. The hydrological information is taken from the open access source “Automated information System of State monitoring of water bodies”. As a simulated object, a section of the Ob river from the Novosibirsk hydroelectric power station to Alexandrovskoye village is taken. The length of the site is 1210 km. The flow rates of six tributaries are taken into account. The graph consists of 12 segments. In the closing section, a boundary condition is set for water flow in the form of a flow rate versus level. To estimate the influence of the boundary condition on the simulation results, two water flow curves were constructed according to the data of 2013 and 2014 years. Qualitative and quantitative estimates of the difference in levels using two different curves, as well as comparison with the measurement data, were obtained. It is shown that the calculation method provides an acceptable agreement between the calculated values of water levels and the observational data. The possibility of using the water flow curve according to the data of the previous year as a boundary condition in the closing gate is demonstrated.

Modified control variates method based on second-order saddle-point approximation for practical reliability analysis

Abstract. A novel method is presented for efficiently analyzing the reliability of engineering components and systems with highly nonlinear complex limit state functions. The proposed method begins by transforming the integral of the limit state function into an integral of a highly correlated limit state function using the control variates method. The second-order reliability method is then employed within the control variates framework to approximate the highly correlated limit state function as a quadratic polynomial. Subsequently, the probability of failure is obtained through the estimation of the saddle-point approximation and a small number of samples generated by Latin hypercube sampling. To demonstrate the effectiveness of the proposed method, four examples involving mathematical functions and mechanical problems are solved. The results are compared with those obtained using the second-order reliability method (SORM), control variates based on Monte Carlo simulation (CVMCS) with second-order saddle-point approximation (SOSPA), importance sampling (IS) and Monte Carlo simulation (MCS). The findings demonstrate that, while maintaining high-precision reliability results, the proposed method significantly reduces the number of evaluations of the limit state function through a small number of initial samples. The method is capable of efficiently and accurately solving complex practical engineering reliability problems.

Prediction of postoperative speech comprehension with the transcutaneous partially implantable bone conduction hearing system Osia®.

The active transcutaneous, partially implantable osseointegrated bone conduction system Cochlear™ Osia® (Cochlear, Sydney, Australia) has been approved for use in German-speaking countries since April 2021. The Osia is indicated for patients either having conductive (CHL) or mixed hearing loss (MHL) with an average bone conduction (BC) hearing loss of 55 dB HL or less, or having single-sided deafness (SSD). The aim of this retrospective study was to investigate the prediction of postoperative speech recognition with Osia® and to evaluate the speech recognition of patients with MHL and in particular an aided dynamic range of less than 30 dB with Osia®. Between 2017 and 2022, 29adult patients were fitted with the Osia®, 10patients (11ears) with CHL and 19patients (25ears) with MHL. MHL was subdivided into two groups: MHL‑I with four-frequency pure-tone average in BC (BC-4PTA) ≥ 20 dB HL and < 40 dB HL (n = 15patients; 20ears) vs. MHL-II with BC-4PTA ≥ 40 dB HL (n = 4patients; 5ears). All patients tested abone conduction hearing device on asoftband preoperatively. Speech intelligibility in quiet was assessed preoperatively using the Freiburg monosyllabic test in unaided condition, with the trial BCHD preoperatively and with Osia® postoperatively with Osia®. The maximum word recognition score (mWRS) unaided and the word recognition score (WRS) with the test system at 65 dB SPL were correlated with the postoperative WRS with Osia® at 65 dB SPL. Preoperative prediction of postoperative outcome with Osia® was better using the mWRS than by the WRS at 65 dB SPL with the test device on the softband. Postoperative WRS was most predictive for patients with CHL and less predictable for patients with mixed hearing loss with BC-4PTA ≥ 40 dB HL. For the test device on a softband, the achievable outcome tended to a minimum, with the mWRS tending to predict the realistically achievable outcome. Osia® can be used for the treatment of CHL and MHL within the indication limits. The average preoperative bone conduction hearing threshold also provides an approximate estimate of the postoperative WRS with Osia®, for which the most accurate prediction is obtained using the preoperative mWRS. Prediction accuracy decreases from aBC-4PTA of ≥ 40 dB HL.

INVESTIGATION OF THE DYNAMIC CHARACTERISTICS OF A MULTI-STORY BUILDING WITH A POLYMER CONCRETE FRAME

Formulation of the problem. An urgent problem in construction is the development and introduction of new types of structural materials with improved characteristics: high strength, resistance to aggressive environments, frost resistance, etc. One of these materials is polymer concrete. Polymer concretes can be effectively used in modern construction in the manufacture of monolithic elements of structures, such as wall panels, slabs, columns of frame buildings. The purpose of the work is to study the dynamic characteristics of a multi-story building with a polymer concrete frame under the action of seismic loads. Method. Dynamic calculations were carried out using the finite element method in the LIRA−CAD software complex. Scientific novelty. New analytical formulas have been obtained, which allow an approximate estimation of the dimensions of structural elements of polymer concrete buildings. It was determined how changes in the properties of the frame material affect the weight of the building, the frequency of natural oscillations and displacement under the action of seismic loading. Practical significance. The results of the work make it possible to perform design calculations related to the dynamic properties of multi-story buildings with a polymer concrete frame. Conclusions. The use of polymer concrete for the construction of frames of multi-story buildings allows to reduce the cross-sectional dimensions of structural elements, reduce the weight and material consumption of buildings.