Covariant Formulation Research Articles

Residuals-based distributionally robust optimization with covariate information

Residuals-based distributionally robust optimization with covariate information

Device and method for low-uncertainty and high-efficiency neutron time-of-flight spectrometry

Neutron detection systems demand precise knowledge of detection efficiency. The goal of this work is to assess the suitability of a neutron detection concept to perform neutron spectrometry by time-of-flight with low systematic uncertainty while attaining high detection efficiency. The device is based on a neutron-to-gamma converter, made of a highly pure 10B disk, coupled to a gamma detector. The behavior of the whole detection system, using the neutron field generated by the 7Li(p,n)7Be reaction at near-threshold energies is studied. Neutron energies ranging from 1 keV up to 250 keV were used. The distribution of TOF events at proton energy equal to 2018 keV was measured and the conversion to neutron spectrum is reported. At around 30 keV of neutron energy, a comparison to a commercially available 6Li-glass scintillator is performed in terms of detection efficiency. An almost three times higher count rate was observed in our detector compared to the commercial one. Using the covariance information on neutron cross section to generate a set of perturbed cross section data, detection efficiency uncertainty ranging from 0.8% to 2.3% was estimated.

Distribution-free algorithms for predictive stochastic programming in the presence of streaming data

This paper studies a fusion of concepts from stochastic programming and non-parametric statistical learning in which data is available in the form of covariates interpreted as predictors and responses. Such models are designed to impart greater agility, allowing decisions under uncertainty to adapt to the knowledge of predictors (leading indicators). This paper studies two classes of methods for such joint prediction-optimization models. One of the methods may be classified as a first-order method, whereas the other studies piecewise linear approximations. Both of these methods are based on coupling non-parametric estimation for predictive purposes, and optimization for decision-making within one unified framework. In addition, our study incorporates several non-parametric estimation schemes, including k nearest neighbors (kNN) and other standard kernel estimators. Our computational results demonstrate that the new algorithms proposed in this paper outperform traditional approaches which were not designed for streaming data applications requiring simultaneous estimation and optimization as important design features for such algorithms. For instance, coupling kNN with Stochastic Decomposition (SD) turns out to be over 40 times faster than an online version of Benders Decomposition while finding decisions of similar quality. Such computational results motivate a paradigm shift in optimization algorithms that are intended for modern streaming applications.

Derivation of MOND from Hossenfelder–Verlinde gravity

Verlinde proposed emergent gravity, which naturally explains the Tully–Fisher relation, an empirical relation in galaxy rotation curves. Inspired by this theory, Hossenfelder constructed a covariant formulation of Verlinde’s emergent gravity. In this work, we show that the equation of motion gains an extra acceleration in addition to the usual geodesic equation, according to Hossenfelder’s theory. Moreover, we show that the extra acceleration is precisely the square root of the Newtonian gravitational acceleration if the mass of the imposter field is negligible, thus completing the proof that Hossenfelder’s theory reduces to modified Newtonian dynamics (MOND) and determining which version of MOND it reduces to. We also obtain the value of L in Hossenfelder–Verlinde gravity theory, which is a constant, contrary to what Hossenfelder claimed. Finally, we suggest how the Newtonian limit that suitably describes our observations in Solar System is recovered in Hossenfelder’s theory, by considering the mass of the imposter field.

Relativistic dynamical friction in stellar systems

Aims.We extend the classical formulation of the dynamical friction effect on a test star by Chandrasekhar to the case of relativistic velocities and velocity distributions, also accounting for post-Newtonian corrections to the gravitational force.Methods.The original kinetic framework was revised and used to construct a special-relativistic dynamical friction formula where the relative velocity changes in subsequent encounters are added up with Lorentz transformation, and the velocity distribution of the field stars accounts for relativistic velocities. Furthermore, a simple expression is obtained for systems where the post-Newtonian correction on the gravitational forces become relevant even at non-relativistic particle velocities. Finally, using a linearized Lagrangian we derived another expression for the dynamical friction expression in a more compact form than previously used.Results.Comparing our formulation with the classical one, we observe that a given test particle undergoes a slightly stronger drag when moving through a distribution of field stars with relativistic velocity distribution. Vice versa, a purely classical treatment of a system where post-Newtonian (PN) corrections should be included, overestimates the effect of dynamical friction at low test particle velocity, regardless of the form of velocity distribution. Finally, a first-order PN dynamical friction covariant formulation is weaker its classical counterpart at small velocities, but much higher for large velocities over a broad range of mass ratios.

A dynamic prediction model supporting individual life expectancy prediction based on longitudinal time-dependent covariates.

In the field of clinical chronic diseases, common prediction results (such as survival rate) and effect size hazard ratio (HR) are relative indicators, resulting in more abstract information. However, clinicians and patients are more interested in simple and intuitive concepts of (survival) time, such as how long a patient may live or how much longer a patient in a treatment group will live. In addition, due to the long follow-up time, resulting in generation of longitudinal time-dependent covariate information, patients are interested in how long they will survive at each follow-up visit. In this study, based on a time scale indicator-restricted mean survival time (RMST)-we proposed a dynamic RMST prediction model by considering longitudinal time-dependent covariates and utilizing joint model techniques. The model can describe the change trajectory of longitudinal time-dependent covariates and predict the average survival times of patients at different time points (such as follow-up visits). Simulation studies through Monte Carlo cross-validation showed that the dynamic RMST prediction model was superior to the static RMST model. In addition, the dynamic RMST prediction model was applied to a primary biliary cirrhosis (PBC) population to dynamically predict the average survival times of the patients, and the average C-index of the internal validation of the model reached 0.81, which was better than that of the static RMST regression. Therefore, the proposed dynamic RMST prediction model has better performance in prediction and can provide a scientific basis for clinicians and patients to make clinical decisions.

Accessibility of covariance information creates vulnerability in Federated Learning frameworks.

Federated Learning (FL) is gaining traction in various fields as it enables integrative data analysis without sharing sensitive data, such as in healthcare. However, the risk of data leakage caused by malicious attacks must be considered. In this study, we introduce a novel attack algorithm that relies on being able to compute sample means, sample covariances, and construct known linearly independent vectors on the data owner side. We show that these basic functionalities, which are available in several established FL frameworks, are sufficient to reconstruct privacy-protected data. Additionally, the attack algorithm is robust to defense strategies that involve adding random noise. We demonstrate the limitations of existing frameworks and propose potential defense strategies analyzing the implications of using differential privacy. The novel insights presented in this study will aid in the improvement of FL frameworks. The code examples are provided at GitHub (https://github.com/manuhuth/Data-Leakage-From-Covariances.git). The CNSIM1 dataset, which we used in the manuscript, is available within the DSData R package (https://github.com/datashield/DSData/tree/main/data).

Quadratic gravity potentials in de Sitter spacetime from Feynman diagrams

We employ a manifestly covariant formalism to compute the tree-level amputated Green’s function of non-minimally coupled scalar fields in quadratic gravity in a de Sitter background. We study this Green’s function in the adiabatic limit, and construct the classical Newtonian potential. At short distances, the flat-spacetime Yukawa potential is reproduced, while the curvature gives rise to corrections to the potential at large distances. Beyond the Hubble radius, the potential vanishes identically, in agreement with the causal structure of de Sitter spacetime. For sub-Hubble distances, we investigate whether the modifications to the potential reproduce Modified Newtonian Dynamics.

Space–time-range clutter suppression via tensor-based STAP for airborne FDA-MIMO radar

Frequency diverse array (FDA) multiple-input multiple-out (MIMO) radar has an inherent higher-dimensional data structure that can be exploited in temporal, spatial, and range-dependent dimensions for space–time-range adaptive processing (STRAP). This paper addresses the problem of tensor filters in application to space–time-range clutter suppression for FDA-MIMO radar. The characteristics of space–time-range clutter are discussed to establish the multidimensional signal models. FDA-MIMO radar can divide the secondary range cell within the range resolution cell of MIMO radar when they have the same matching filter bandwidth in the receive channel. Specifically, the target-free covariance information can be estimated from more secondary training cells for FDA-MIMO radar. According to the discussed properties of space–time-range clutter, namely secondary clutter rings, clutter degrees of freedom (DOFs), and the range-dimensional non-stationary characteristic, a tensor-based STRAP approach with range compensation is proposed to suppress clutter for FDA-MIMO radar. Numerical results verify the mentioned clutter characteristics and illustrate the importance of the samples number and range compensation operation for the proposed tensor filter. Finally, the STRAP performance benefits of FDA-MIMO radar over MIMO radar are discussed by simulations.

Quadratic estimation for stochastic systems in the presence of random parameter matrices, time-correlated additive noise and deception attacks

Networked systems usually face different random uncertainties that make the performance of the least-squares (LS) linear filter decline significantly. For this reason, great attention has been paid to the search for other kinds of suboptimal estimators. Among them, the LS quadratic estimation approach has attracted considerable interest in the scientific community for its balance between computational complexity and estimation accuracy. When it comes to stochastic systems subject to different random uncertainties and deception attacks, the quadratic estimator design has not been deeply studied. In this paper, using covariance information, the LS quadratic filtering and fixed-point smoothing problems are addressed under the assumption that the measurements are perturbed by a time-correlated additive noise, as well as affected by random parameter matrices and exposed to random deception attacks. The use of random parameter matrices covers a wide range of common uncertainties and random failures, thus better reflecting the engineering reality. The signal and observation vectors are augmented by stacking the original vectors with their second-order Kronecker powers; then, the linear estimator of the original signal based on the augmented observations provides the required quadratic estimator. A simulation example illustrates the superiority of the proposed quadratic estimators over the conventional linear ones and the effect of the deception attacks on the estimation performance.

Finite charges from the bulk action

Constructing charges in the covariant phase space formalism often leads to formally divergent expressions, even when the fields satisfy physically acceptable fall-off conditions. These expressions can be rendered finite by corner ambiguities in the definition of the presymplectic potential, which in some cases may be motivated by arguments involving boundary Lagrangians. We show that the necessary corner terms are already present in the variation of the bulk action and can be extracted in a straightforward way. Once these corner terms are included in the presymplectic potential, charges derived from an associated codimension-2 form are automatically finite. We illustrate the procedure with examples in two and three dimensions, working in Bondi gauge and obtaining integrable charges. As a by-product, actions are derived for these theories that admit a well-defined variational principle when the fields satisfy boundary conditions on a timelike surface with corners. An interesting feature of our analysis is that the fields are not required to be fully on-shell.

Modernizing the design and analysis of prevalence surveys for neglected tropical diseases.

Current WHO guidelines set prevalence thresholds below which a neglected tropical disease can be considered to have been eliminated as a public health problem, and specify how surveys to assess whether elimination has been achieved should be designed and analysed, based on classical survey sampling methods. In this paper, we describe an alternative approach based on geospatial statistical modelling. We first show the gains in efficiency that can be obtained by exploiting any spatial correlation in the underlying prevalence. We then suggest that the current guidelines' implicit use of a significance testing argument is not appropriate; instead, we argue for a predictive inferential framework, leading to design criteria based on controlling the rates at which areas whose true prevalence lies above and below the elimination threshold are incorrectly classified. We describe how this approach naturally accommodates context-specific information in the form of georeferenced covariates that have been shown to be predictive of disease prevalence. Finally, we give a progress report of an ongoing collaboration with the Guyana Ministry of Health Neglected Tropical Disease programme on the design of an IDA (ivermectin, diethylcarbamazine and albendazole) Impact Survey of lymphatic filariasis to be conducted in Guyana in early 2023. This article is part of the theme issue 'Challenges and opportunities in the fight against neglected tropical diseases: a decade from the London Declaration on NTDs'.

A modified stochastic model for LS+AR hybrid method and its application in polar motion short-term prediction

Short-term (up to 30 days) predictions of Earth Rotation Parameters (ERPs) such as Polar Motion (PM: PMX and PMY) play an essential role in real-time applications related to high-precision reference frame conversion. Currently, least squares (LS) + auto-regressive (AR) hybrid method is one of the main techniques of PM prediction. Besides, the weighted LS + AR hybrid method performs well for PM short-term prediction. However, the corresponding covariance information of LS fitting residuals deserves further exploration in the AR model. In this study, we have derived a modified stochastic model for the LS + AR hybrid method, namely the weighted LS + weighted AR hybrid method. By using the PM data products of IERS EOP 14 C04, the numerical results indicate that for PM short-term forecasting, the proposed weighted LS + weighted AR hybrid method shows an advantage over both the LS + AR hybrid method and the weighted LS + AR hybrid method. Compared to the mean absolute errors (MAEs) of PMX/PMY short-term prediction of the LS + AR hybrid method and the weighted LS + AR hybrid method, the weighted LS + weighted AR hybrid method shows average improvements of 6.61%/12.08% and 0.24%/11.65%, respectively. Besides, for the slopes of the linear regression lines fitted to the errors of each method, the growth of the prediction error of the proposed method is slower than that of the other two methods.

Noether Currents and Generators of Local Gauge Transformations in the Covariant Canonical Formalism

Noether Currents and Generators of Local Gauge Transformations in the Covariant Canonical Formalism

Competing risks analysis for neutrophil to lymphocyte ratio as a predictor of diabetic retinopathy incidence in the Scottish population

BackgroundDiabetic retinopathy (DR) is a major sight-threatening microvascular complication in individuals with diabetes. Systemic inflammation combined with oxidative stress is thought to capture most of the complexities involved in the pathology of diabetic retinopathy. A high level of neutrophil–lymphocyte ratio (NLR) is an indicator of abnormal immune system activity. Current estimates of the association of NLR with diabetes and its complications are almost entirely derived from cross-sectional studies, suggesting that the nature of the reported association may be more diagnostic than prognostic. Therefore, in the present study, we examined the utility of NLR as a biomarker to predict the incidence of DR in the Scottish population.MethodsThe incidence of DR was defined as the time to the first diagnosis of R1 or above grade in the Scottish retinopathy grading scheme from type 2 diabetes diagnosis. The effect of NLR and its interactions were explored using a competing risks survival model adjusting for other risk factors and accounting for deaths. The Fine and Gray subdistribution hazard model (FGR) was used to predict the effect of NLR on the incidence of DR.ResultsWe analysed data from 23,531 individuals with complete covariate information. At 10 years, 8416 (35.8%) had developed DR and 2989 (12.7%) were lost to competing events (death) without developing DR and 12,126 individuals did not have DR. The median (interquartile range) level of NLR was 2.04 (1.5 to 2.7). The optimal NLR cut-off value to predict retinopathy incidence was 3.04. After accounting for competing risks at 10 years, the cumulative incidence of DR and deaths without DR were 50.7% and 21.9%, respectively. NLR was associated with incident DR in both Cause-specific hazard (CSH = 1.63; 95% CI: 1.28–2.07) and FGR models the subdistribution hazard (sHR = 2.24; 95% CI: 1.70–2.94). Both age and HbA1c were found to modulate the association between NLR and the risk of DR.ConclusionsThe current study suggests that NLR has a promising potential to predict DR incidence in the Scottish population, especially in individuals less than 65 years and in those with well-controlled glycaemic status.

Combining aggregate and individual-level data to estimate individual-level associations between air pollution and COVID-19 mortality in the United States.

Imposing stricter regulations for PM2.5 has the potential to mitigate damaging health and climate change effects. Recent evidence establishing a link between exposure to air pollution and COVID-19 outcomes is one of many arguments for the need to reduce the National Ambient Air Quality Standards (NAAQS) for PM2.5. However, many studies reporting a relationship between COVID-19 outcomes and PM2.5 have been criticized because they are based on ecological regression analyses, where area-level counts of COVID-19 outcomes are regressed on area-level exposure to air pollution and other covariates. It is well known that regression models solely based on area-level data are subject to ecological bias, i.e., they may provide a biased estimate of the association at the individual-level, due to within-area variability of the data. In this paper, we augment county-level COVID-19 mortality data with a nationally representative sample of individual-level covariate information from the American Community Survey along with high-resolution estimates of PM2.5 concentrations obtained from a validated model and aggregated to the census tract for the contiguous United States. We apply a Bayesian hierarchical modeling approach to combine county-, census tract-, and individual-level data to ultimately draw inference about individual-level associations between long-term exposure to PM2.5 and mortality for COVID-19. By analyzing data prior to the Emergency Use Authorization for the COVID-19 vaccines we found that an increase of 1 μg/m3 in long-term PM2.5 exposure, averaged over the 17-year period 2000-2016, is associated with a 3.3% (95% credible interval, 2.8 to 3.8%) increase in an individual's odds of COVID-19 mortality. Code to reproduce our study is publicly available at https://github.com/NSAPH/PM_COVID_ecoinference. The results confirm previous evidence of an association between long-term exposure to PM2.5 and COVID-19 mortality and strengthen the case for tighter regulations on harmful air pollution and greenhouse gas emissions.

BRST cohomology is Lie algebroid cohomology

In this paper we demonstrate that the exterior algebra of an Atiyah Lie algebroid generalizes the familiar notions of the physicist's BRST complex. To reach this conclusion, we develop a general picture of Lie algebroid isomorphisms as commutative diagrams between algebroids preserving the geometric structure encoded in their brackets. We illustrate that a necessary and sufficient condition for such a diagram to define a morphism of Lie algebroid brackets is that the two algebroids possess gauge-equivalent connections. This observation indicates that the aforementioned set of Lie algebroid isomorphisms should be regarded as equivalent to the set of local diffeomorphisms and gauge transformations. Moreover, a Lie algebroid isomorphism being a chain map in the exterior algebra sense ensures that isomorphic algebroids are cohomologically equivalent. The Atiyah Lie algebroids derived from principal bundles with common base manifolds and structure groups may therefore be divided into equivalence classes of isomorphic algebroids. Each equivalence class possesses a local representative which we refer to as the trivialized Lie algebroid, and we show that the exterior algebra of the trivialized algebroid gives rise to the BRST complex. We conclude by illustrating the usefulness of Lie algebroid cohomology in computing quantum anomalies, including applications to the chiral and Lorentz-Weyl (LW) anomalies. In particular, we pay close attention to the fact that the geometric intuition afforded by the Lie algebroid (which was absent in the naive BRST complex) provides hints of a deeper picture that simultaneously geometrizes the consistent and covariant forms of the anomaly. In the algebroid construction, the difference between the consistent and covariant anomalies is simply a different choice of basis.

Multi-scale adaptive multivariate state estimation fault detection enhancement for time-varying industrial system based on multi-output Gaussian process autoregression

Most chemical processes are time-varying and nonlinear due to load changes, product demand transitions or other causes, causing unsatisfactory performance of conventional non-parametric multivariate statistical fault detection method. In this work, a probabilistic multivariate state estimation fault detection method based on multi-output Gaussian process autoregression is first developed to overcome the linear limitation and noise information ignorance of multivariate state estimation technology-based fault detection methods. In multi-output Gaussian process regression framework, the Leave-One-Sample-Out strategy is developed to construct the dataset by leaving each historical sample from the memory matrix out as one training output in turn while regarding the corresponding remaining historical samples as one training input. Then, we design the multi-output Gaussian process autoregression model to estimate the current state of the system. Utilizing the estimation covariance information, a probabilistic index based on multivariate Kullback-Leibler divergence is developed for fault detection. Moreover, a multi-scale adaptive fault detection enhancement based on discrete multi-objective Archimedes optimization and just-in-time learning is further proposed to handle the time-varying problem. In this scheme, the memory matrix is batch-adaptively updated at monthly intervals based on discrete multi-objective Archimedes optimization to handle the slow change of system characteristics caused by equipment degradation. On the other hand, to cope with the rapid change of system characteristics caused by operation transition, the just-in-time learning is employed to select samples from the memory matrix that best match to the current system state for sample-adaptive updating. Finally, two industrial cases are used to verify the performance of the proposed method.

Modified Strong Tracking Slide Window Variational Adaptive Kalman Filter With Unknown Noise Statistics

The filter performance will be degraded in the measurements with time-varying and unknown noise statistics. To combat the above challenges, a modified strong tracking slide window variational adaptive Kalman filter algorithm is proposed in this article. Firstly, the multiple fading factors are integrated into the proposed algorithm to adjust the error covariance. Next, an improved adaptive slide window method is designed for variational Bayesian Kalman filtering by adaptively adjusting the slide window size and correcting the previous state according to the later state, which improves the estimation accuracy and computational efficiency. Finally, the inverse Wishart distribution is considered for modeling process and measurement noise, and the state vector, as well as noise statistics, are inferred via the variational Bayesian technique without prior noise covariance information. Simulation results demonstrate that the proposed filter algorithm is more robust than existing filters in counteracting measurement and process noise uncertainties.

Smoothed model-assisted small area estimation of proportions.

In countries where population census data are limited, generating accurate subnational estimates of health and demographic indicators is challenging. Existing model-based geostatistical methods leverage covariate information and spatial smoothing to reduce the variability of estimates but often ignore the survey design, while traditional small area estimation approaches may not incorporate both unit-level covariate information and spatial smoothing in a design consistent way. We propose a smoothed model-assisted estimator that accounts for survey design and leverages both unit-level covariates and spatial smoothing. Under certain regularity assumptions, this estimator is both design consistent and model consistent. We compare it with existing design-based and model-based estimators using real and simulated data.