Autonomous Tracking and State Estimation With Generalized Group Lasso.

We address the problem of autonomous tracking and state estimation for marine vessels, autonomous vehicles, and other dynamic signals under a (structured) sparsity assumption. The aim is to improve the tracking and estimation accuracy with respect to the classical Bayesian filters and smoothers. We formulate the estimation problem as a dynamic generalized group Lasso problem and develop a class of smoothing-and-splitting methods to solve it. The Levenberg-Marquardt iterated extended Kalman smoother-based multiblock alternating direction method of multipliers (LM-IEKS-mADMMs) algorithms are based on the alternating direction method of multipliers (ADMMs) framework. This leads to minimization subproblems with an inherent structure to which three new augmented recursive smoothers are applied. Our methods can deal with large-scale problems without preprocessing for dimensionality reduction. Moreover, the methods allow one to solve nonsmooth nonconvex optimization problems. We then prove that under mild conditions, the proposed methods converge to a stationary point of the optimization problem. By simulated and real-data experiments, including multisensor range measurement problems, marine vessel tracking, autonomous vehicle tracking, and audio signal restoration, we show the practical effectiveness of the proposed methods.

Nationwide infection control strategy lowered seasonal respiratory infection rate: occupational health care perspective during the COVID-19 epidemic in Finland.

BACKGROUND: Respiratory infection is the 4th most common reason for absence from work in Finland. There is limited knowledge of how social distancing affects the spread of respiratory infections during respiratory epidemics. We assessed the effect of nationwide infection control strategies against coronavirus disease in 2020 on various respiratory infections (International Statistical Classification of Diseases and Related Health Problems code J06) in occupational outpatient clinics. METHODS: We used occupational healthcare data of respiratory infection J06 diagnoses from 2017 to 2020 obtained from the largest health service provider in Finland. The data was divided into three 252 day-long pieces and was weekday-matched and smoothed by 7-day-moving average. The difference in the J06 diagnosis rate between the follow-up years was measured using Pearson correlation. Possible confounding by sex, age, and region was investigated in a stratified analysis. Confounding by respiratory syncytial virus was analysed using nationwide data of confirmed cases obtained from the national registry. RESULTS: In the second quarter of 2020, the trend in the daily number of J06 diagnoses was significantly different from the follow-up years 2019 and 2018. The number of J06 diagnoses peaked between March and April 2020 with roughly 2-fold higher count compared to normal. The timing of these peaks matched with the government issued infection control strategies and lockdowns. Based on stratified analysis, the increase in the number of J06 diagnoses was not confounded by region, age, or sex. Moreover, the rapid increase in the number of J06 diagnoses was not governed by the respiratory syncytial virus. CONCLUSION: Nationwide infection control strategies were effective to slow down the spread of common respiratory infectious diseases in the occupational population.

Early oxygen levels contribute to brain injury in extremely preterm infants.

BACKGROUND: Extremely low gestational age newborns (ELGANs) are at risk of neurodevelopmental impairments that may originate in early NICU care. We hypothesized that early oxygen saturations (SpO2), arterial pO2 levels, and supplemental oxygen (FiO2) would associate with later neuroanatomic changes. METHODS: SpO2, arterial blood gases, and FiO2 from 73 ELGANs (GA 26.4 ± 1.2; BW 867 ± 179 g) during the first 3 postnatal days were correlated with later white matter injury (WM, MRI, n = 69), secondary cortical somatosensory processing in magnetoencephalography (MEG-SII, n = 39), Hempel neurological examination (n = 66), and developmental quotients of Griffiths Mental Developmental Scales (GMDS, n = 58). RESULTS: The ELGANs with later WM abnormalities exhibited lower SpO2 and pO2 levels, and higher FiO2 need during the first 3 days than those with normal WM. They also had higher pCO2 values. The infants with abnormal MEG-SII showed opposite findings, i.e., displayed higher SpO2 and pO2 levels and lower FiO2 need, than those with better outcomes. Severe WM changes and abnormal MEG-SII were correlated with adverse neurodevelopment. CONCLUSIONS: Low oxygen levels and high FiO2 need during the NICU care associate with WM abnormalities, whereas higher oxygen levels correlate with abnormal MEG-SII. The results may indicate certain brain structures being more vulnerable to hypoxia and others to hyperoxia, thus emphasizing the role of strict saturation targets. IMPACT: This study indicates that both abnormally low and high oxygen levels during early NICU care are harmful for later neurodevelopmental outcomes in preterm neonates. Specific brain structures seem to be vulnerable to low and others to high oxygen levels. The findings may have clinical implications as oxygen is one of the most common therapies given in NICUs. The results emphasize the role of strict saturation targets during the early postnatal period in preterm infants.

Tracking of dynamic functional connectivity from MEG data with Kalman filtering.

Owing to their millisecond-scale temporal resolution, magnetoencephalography (MEG) and electroencephalography (EEG) are well-suited tools to study dynamic functional connectivity between regions in the human brain. However, current techniques to estimate functional connectivity from MEG/EEG are based on a two-step approach; first, the MEG/EEG inverse problem is solved to estimate the source activity, and second, connectivity is estimated between the sources. In this work, we propose a method for simultaneous estimation of source activities and their dynamic functional connectivity using a Kalman filter. Based on simulations, our approach can reliably estimate source activities and resolve their time-varying interactions even at low SNR (< 1). When applied on empirical MEG responses to simple visual stimuli, our approach could capture the dynamic patterns of the underlying functional connectivity changes between the lower (pericalcarine) and higher (fusiform and parahippocampal) visual areas. In conclusion, we demonstrate that our approach is capable of tracking changes in functional connectivity at the millisecond resolution of MEG/EEG and thus making it suitable for real-time tracking of functional connectivity, which none of the current techniques are capable of.

Statistical analysis of differential equations: introducing probability measures on numerical solutions.

In this paper, we present a formal quantification of uncertainty induced by numerical solutions of ordinary and partial differential equation models. Numerical solutions of differential equations contain inherent uncertainties due to the finite-dimensional approximation of an unknown and implicitly defined function. When statistically analysing models based on differential equations describing physical, or other naturally occurring, phenomena, it can be important to explicitly account for the uncertainty introduced by the numerical method. Doing so enables objective determination of this source of uncertainty, relative to other uncertainties, such as those caused by data contaminated with noise or model error induced by missing physical or inadequate descriptors. As ever larger scale mathematical models are being used in the sciences, often sacrificing complete resolution of the differential equation on the grids used, formally accounting for the uncertainty in the numerical method is becoming increasingly more important. This paper provides the formal means to incorporate this uncertainty in a statistical model and its subsequent analysis. We show that a wide variety of existing solvers can be randomised, inducing a probability measure over the solutions of such differential equations. These measures exhibit contraction to a Dirac measure around the true unknown solution, where the rates of convergence are consistent with the underlying deterministic numerical method. Furthermore, we employ the method of modified equations to demonstrate enhanced rates of convergence to stochastic perturbations of the original deterministic problem. Ordinary differential equations and elliptic partial differential equations are used to illustrate the approach to quantify uncertainty in both the statistical analysis of the forward and inverse problems.

Infinite-dimensional Bayesian filtering for detection of quasiperiodic phenomena in spatiotemporal data.

This paper introduces a spatiotemporal resonator model and an inference method for detection and estimation of nearly periodic temporal phenomena in spatiotemporal data. The model is derived as a spatial extension of a stochastic harmonic resonator model, which can be formulated in terms of a stochastic differential equation. The spatial structure is included by introducing linear operators, which affect both the oscillations and damping, and by choosing the appropriate spatial covariance structure of the driving time-white noise process. With the choice of the linear operators as partial differential operators, the resonator model becomes a stochastic partial differential equation, which is compatible with infinite-dimensional Kalman filtering. The resulting infinite-dimensional Kalman filtering problem allows for a computationally efficient solution as the computational cost scales linearly with measurements in the temporal dimension. This framework is applied to weather prediction and to physiological noise elimination in functional magnetic resonance imaging brain data.

Dynamic retrospective filtering of physiological noise in BOLD fMRI: DRIFTER.

In this article we introduce the DRIFTER algorithm, which is a new model based Bayesian method for retrospective elimination of physiological noise from functional magnetic resonance imaging (fMRI) data. In the method, we first estimate the frequency trajectories of the physiological signals with the interacting multiple models (IMM) filter algorithm. The frequency trajectories can be estimated from external reference signals, or if the temporal resolution is high enough, from the fMRI data. The estimated frequency trajectories are then used in a state space model in combination of a Kalman filter (KF) and Rauch-Tung-Striebel (RTS) smoother, which separates the signal into an activation related cleaned signal, physiological noise, and white measurement noise components. Using experimental data, we show that the method outperforms the RETROICOR algorithm if the shape and amplitude of the physiological signals change over time.