Explicit Estimates Research Articles

Sources and sinks of greenhouse gases in the landscape: Approach for spatially explicit estimates

Climate change mitigation is a global response that requires actions at the local level. Quantifying local sources and sinks of greenhouse gases (GHG) facilitate evaluating mitigation options. We present an approach to collate spatially explicit estimated fluxes of GHGs (carbon dioxide, methane and nitrous oxide) for main land use sectors in the landscape, to aggregate, and to calculate the net emissions of an entire region. Our procedure was developed and tested in a large river basin in Finland, providing information from intensively studied eLTER research sites. To evaluate the full GHG balance, fluxes from natural ecosystems (lakes, rivers, and undrained mires) were included together with fluxes from anthropogenic activities, agriculture and forestry. We quantified the fluxes based on calculations with an anthropogenic emissions model (FRES) and a forest growth and carbon balance model (PREBAS), as well as on emission coefficients from the literature regarding emissions from lakes, rivers, undrained mires, peat extraction sites and cropland. Spatial data sources included CORINE land use data, soil map, lake and river shorelines, national forest inventory data, and statistical data on anthropogenic activities. Emission uncertainties were evaluated with Monte Carlo simulations. Artificial surfaces were the most emission intensive land-cover class. Lakes and rivers were about as emission intensive as arable land. Forests were the dominant land cover in the region (66%), and the C sink of the forests decreased the total emissions of the region by 72%. The region's net emissions amounted to 4.37 ± 1.43 Tg CO2-eq yr−1, corresponding to a net emission intensity 0.16 Gg CO2-eq km−2 yr−1, and estimated per capita net emissions of 5.6 Mg CO2-eq yr−1. Our landscape approach opens opportunities to examine the sensitivities of important GHG fluxes to changes in land use and climate, management actions, and mitigation of anthropogenic emissions.

A nonlinear Korn inequality on a surface with an explicit estimate of the constant

A nonlinear Korn inequality on a surface with an explicit estimate of the constant

Computable Interpolation Error Constants for the Geometric Simplex Finite Elements

In this paper, a novel high accuracy computation method for interpolation error constants is proposed over the geometric simplex finite elements. Firstly, the expansions of bounded linear operators are employed to derive the explicit estimate of interpolation error constants, which depend only on the shape of the geometric simplex finite elements and the definition of interpolation functions. Then, this method is applied to the linear interpolation function, and the results are consistent with our analysis. Finally, some numerical examples are given to validate our analysis. Such high accuracy computation method for interpolation error constants are beneficial attempts to accelerate the adaptive computation and verification of finite element solutions.

A fractional degenerate parabolic-hyperbolic Cauchy problem with noise

We consider the Cauchy problem for a stochastic scalar parabolic-hyperbolic equation in any space dimension with nonlocal, nonlinear, and possibly degenerate diffusion terms. The equations are nonlocal because they involve fractional diffusion operators. We adapt the notion of stochastic entropy solution and provide a new technical framework to prove the uniqueness. The existence proof relies on the vanishing viscosity method. Moreover, using bounded variation (BV) estimates for vanishing viscosity approximations, we derive an explicit continuous dependence estimate on the nonlinearities and derive error estimate for the stochastic vanishing viscosity method. In addition, we develop uniqueness method “à la Kružkov” for more general equations where the noise coefficient may depend explicitly on the spatial variable.

Tempered D-modules and Borel\u2013Moore homology vanishing

We characterize the tempered part of the automorphic Langlands category mathfrak {D}({text {Bun}}_G) using the geometry of the big cell in the affine Grassmannian. We deduce that, for G non-abelian, tempered D-modules have no de Rham cohomology with compact support. The latter fact boils down to a concrete statement, which we prove using the Ran space and some explicit t-structure estimates: for G non-abelian and Sigma a smooth affine curve, the Borel–Moore homology of the indscheme {text {Maps}}(Sigma ,G) vanishes.

Inference and preference in intertemporal choice

AbstractWhen choosing between immediate and future rewards, how do people deal with uncertainty about the value of the future outcome or the delay until its occurrence? Skylark et al. (2020) suggested that people employ a delay-reward heuristic: the inferred value of an ambiguous future reward is a function of the stated delay, and vice-versa. The present paper investigates the role of this heuristic in choice behaviour. In Studies 1a–2b, participants inferred the value of an ambiguous future reward or delay before the true value was revealed and a choice made. Preference for the future option was predicted by the discrepancy between the estimated and true values: the more pleasantly surprising the delayed option, the greater the willingness to choose it. Studies 3a–3c examined the association between inference and preference when the ambiguous values remained unknown. As predicted by the use of a delay-reward heuristic, inferred delays and rewards were positively related to stated rewards and delays, respectively. More importantly, choices were associated with inferred rewards and, in some circumstances, delays. Critically, estimates and choices were both order-dependent: when estimates preceded choices, estimates were more optimistic (people inferred smaller delays and larger rewards) and were subsequently more likely to choose the delayed option than when choices were made before estimates. These order effects argue against a simple model in which people deal with ambiguity by first estimating the unknown value and then using their estimate as the basis for decision. Rather, it seems that inferences are partly constructed from choices, and the role of inference in choice depends on whether an explicit estimate is made prior to choosing. Finally, we also find that inferences about ambiguous delays depend on whether the estimate has to be made in “days” or in a self-selected temporal unit, and replicate previous findings that older participants make more pessimistic inferences than younger ones. We discuss the implications and possible mechanisms for these findings.

New general and explicit stability result for a thermoelastic Timoshenko system

The goal of this article is to study a thermoelastic Timoshenko system with viscoelastic law acting on the shear force and thermoelastic dissipation acting on the bending moment. We prove a general decay as well as an explicit decay estimate for solution energy, from which the exponential and polynomial decay results are only special cases. The result is obtained without imposing equal-wave-speed condition, this is achieved by considering the Neumann–Dirichlet–Neumann boundary conditions . This result is therefore of great interest compared to majority of results in the literature that often time impose the equal-wave-speed condition.

Variance Propagation for Density Surface Models

Spatially explicit estimates of population density, together with appropriate estimates of uncertainty, are required in many management contexts. Density surface models (DSMs) are a two-stage approach for estimating spatially varying density from distance sampling data. First, detection probabilities—perhaps depending on covariates—are estimated based on details of individual encounters; next, local densities are estimated using a GAM, by fitting local encounter rates to location and/or spatially varying covariates while allowing for the estimated detectabilities. One criticism of DSMs has been that uncertainty from the two stages is not usually propagated correctly into the final variance estimates. We show how to reformulate a DSM so that the uncertainty in detection probability from the distance sampling stage (regardless of its complexity) is captured as an extra random effect in the GAM stage. In effect, we refit an approximation to the detection function model at the same time as fitting the spatial model. This allows straightforward computation of the overall variance via exactly the same software already needed to fit the GAM. A further extension allows for spatial variation in group size, which can be an important covariate for detectability as well as directly affecting abundance. We illustrate these models using point transect survey data of Island Scrub-Jays on Santa Cruz Island, CA, and harbour porpoise from the SCANS-II line transect survey of European waters. Supplementary materials accompanying this paper appear on-line.

Simultaneous multi-slice image reconstruction using regularized image domain split slice-GRAPPA for diffusion MRI.

The main goal of this work is to improve the quality of simultaneous multi-slice (SMS) reconstruction for diffusion MRI. We accomplish this by developing an image domain method that reaps the benefits of both SENSE and GRAPPA-type approaches and enables image regularization in an optimization framework. We propose a new approach termed regularized image domain split slice-GRAPPA (RI-SSG), which establishes an optimization framework for SMS reconstruction. Within this framework, we use a robust forward model to take advantage of both the SENSE model with explicit sensitivity estimations and the SSG model with implicit kernel relationship among coil images. The proposed approach also allows combining of coil images to increase the SNR and enables image domain regularization on estimated coil-combined single slices. We compare the performance of RI-SSG with that of SENSE and SSG using in-vivo diffusion EPI datasets with simulated and actual SMS acquisitions collected on a 3T MR scanner. Reconstructed diffusion-weighted images (DWIs) and the resulting diffusion tensor imaging (DTI) and neurite orientation dispersion and density imaging (NODDI) maps are analyzed to evaluate the quantitative and qualitative performance of the three methods. The DWIs reconstructed by RI-SSG are closer to the single-band ground truth images than SENSE and SSG. Specifically, the proposed RI-SSG reduces the normalized root-mean-square-error (nRMSE) against ground truth images by ∼5% and increases the structural similarity index (SSIM) by ∼4% compared to SSG. All three methods produce similar fractional anisotropy (FA) maps using DTI representation, but mean diffusivity (MD) and fiber orientation estimates using RI-SSG are closer to the reference than SENSE and SSG. RI-SSG results in NODDI maps with noticeably smaller errors than those of SENSE and SSG and improves the accuracy of the mean value of orientation dispersion index (ODI) by ∼5% and the mean value of intracellular volume fraction by ∼7% in regions of interest in brain white matter compared to SSG.

Predictive models of distribution and abundance of a threatened mountain species show that impacts of climate change overrule those of land use change

AbstractAimClimate is often the sole focus of global change research in mountain ecosystems although concomitant changes in land use might represent an equally important threat. As mountain species typically depend on fine‐scale environmental characteristics, integrating land use change in predictive models is crucial to properly assess their vulnerability. Here, we present a modelling framework that aims at providing more comprehensive projections of both species’ distribution and abundance under realistic scenarios of land use and climate change, and at disentangling their relative effects.LocationSwitzerland.MethodsWe used the ring ouzel (Turdus torquatus), a red‐listed and declining mountain bird species, as a study model. Based on standardized monitoring data collected across the whole country, we fitted high‐resolution ensemble species distribution models to predict current occurrence probability, while spatially explicit density estimates were obtained from N‐mixture models. We then tested for the effects of realistic scenarios of land use (land abandonment versus farming intensification) and climate change on future species distribution and abundance.ResultsOccurrence probability was mostly explained by climatic conditions, so that climate change was predicted to have larger impacts on distribution and abundance than any scenarios of land use change. In the mid‐term (2030–2050), predicted effects of environmental change show a high spatial heterogeneity due to regional differences in climate and dominant land use, with farming intensification identified as an important threat locally. In the long term (2080–2100), climate models forecast a marked upward range shift (up to +560 m) and further population decline (up to −35%).Main conclusionsOur innovative approach highlights the spatio‐temporal heterogeneity in the relative effects of different environmental drivers on species distribution and abundance. The proposed framework thus provides a useful tool not only for better assessing species’ vulnerability in the face of global change, but also for identifying key areas for conservation interventions at a meaningful scale.

Viscosity explicit analysis for finite element methods of time-dependent Navier–Stokes equations

In this paper, the viscosity explicit stability and error estimate for the finite element method of the time-dependent Navier–Stokes equations are deduced. Firstly, the viscosity explicit analysis is derived for a linearized auxiliary problem. Then, by introducing an iterative procedure and investigating its convergence, the results are extended to the time-dependent Navier–Stokes equations. The new error estimate for the finite element method is also derived. The analysis shows that, under some assumptions on the given data, both the stability and the error for the finite element approximation of the time-dependent Navier–Stokes equations depend on the viscosity coefficient with algebraic orders, which is different from the exponential dependence in the literature. Moreover, the relationship between the body force’s regularity and the stability is also analyzed in detail.

General stochastic separation theorems with optimal bounds

Phenomenon of stochastic separability was revealed and used in machine learning to correct errors of Artificial Intelligence (AI) systems and analyze AI instabilities. In high-dimensional datasets under broad assumptions each point can be separated from the rest of the set by simple and robust Fisher’s discriminant (is Fisher separable). Errors or clusters of errors can be separated from the rest of the data. The ability to correct an AI system also opens up the possibility of an attack on it, and the high dimensionality induces vulnerabilities caused by the same stochastic separability that holds the keys to understanding the fundamentals of robustness and adaptivity in high-dimensional data-driven AI. To manage errors and analyze vulnerabilities, the stochastic separation theorems should evaluate the probability that the dataset will be Fisher separable in given dimensionality and for a given class of distributions. Explicit and optimal estimates of these separation probabilities are required, and this problem is solved in the present work. The general stochastic separation theorems with optimal probability estimates are obtained for important classes of distributions: log-concave distribution, their convex combinations and product distributions. The standard i.i.d. assumption was significantly relaxed. These theorems and estimates can be used both for correction of high-dimensional data driven AI systems and for analysis of their vulnerabilities. The third area of application is the emergence of memories in ensembles of neurons, the phenomena of grandmother’s cells and sparse coding in the brain, and explanation of unexpected effectiveness of small neural ensembles in high-dimensional brain.

Sampling the Flow of a Bandlimited Function

We analyze the problem of reconstruction of a bandlimited function f from the space–time samples of its states f_t=phi _t*f resulting from the convolution with a kernel phi _t. It is well-known that, in natural phenomena, uniform space–time samples of f are not sufficient to reconstruct f in a stable way. To enable stable reconstruction, a space–time sampling with periodic nonuniformly spaced samples must be used as was shown by Lu and Vetterli. We show that the stability of reconstruction, as measured by a condition number, controls the maximal gap between the spacial samples. We provide a quantitative statement of this result. In addition, instead of irregular space–time samples, we show that uniform dynamical samples at sub-Nyquist spatial rate allow one to stably reconstruct the function widehat{f} away from certain, explicitly described blind spots. We also consider several classes of finite dimensional subsets of bandlimited functions in which the stable reconstruction is possible, even inside the blind spots. We obtain quantitative estimates for it using Remez-Turán type inequalities. En route, we obtain Remez-Turán inequality for prolate spheroidal wave functions. To illustrate our results, we present some numerics and explicit estimates for the heat flow problem.

Birational geometry of singular Fano double spaces of index two

We describe the birational geometry of Fano double spaces of index 2 and dimension with at most quadratic singularities of rank , satisfying certain additional conditions of general position: we prove that these varieties have no structures of a rationally connected fibre space over a base of dimension , that every birational map onto the total space of a Mori fibre space induces an isomorphism of the blow-up of along , where is a linear subspace of codimension 2, and that every birational map of onto a Fano variety with -factorial terminal singularities and Picard number 1 is an isomorphism. We give an explicit lower estimate, quadratic in , for the codimension of the set of varieties that have worse singularities or do not satisfy the conditions of general position. The proof makes use of the method of maximal singularities and the improved -inequality for the self-intersection of a mobile linear system. Bibliography: 20 titles.

Remaining Useful Life Prediction of IIoT-Enabled Complex Industrial Systems With Hybrid Fusion of Multiple Information Sources

Industrial Internet of Things has significantly boosted predictive maintenance for complex industrial systems, where the accurate prediction of remaining useful life (RUL) with high-level confidence is challenging. By aggregating multiple informative sources of system degradation, information fusion can be applied to improve the prediction accuracy and reduce the uncertainty. It can be performed on the data-level, feature-level, and decision-level. To fully exploit the available degradation information, this article proposes a hybrid fusion method on both the data level and decision level to predict the RUL. On the data level, genetic programming (GP) is adopted to integrate physical sensor sources into a composite health indicator (HI), resulting in an explicit nonlinear data-level fusion model. Subsequently, the predictions of the RUL based on each physical sensor and the developed composite HI are synthesized in the framework of belief functions theory, as the decision-level fusion method. Moreover, the decision-level method is flexible for incorporating other statistical data-driven methods with explicit estimations of the RUL. The proposed method is verified via a case study on NASA's C-MAPSS data set. Compared to the single-level fusion methods, the results confirm the superiority of the proposed method for higher accuracy and certainty of predicting the RUL.

Quantifying the hydrodynamic limit of Vlasov-type equations with alignment and nonlocal forces

In this paper, we quantify the asymptotic limit of collective behavior kinetic equations arising in mathematical biology modeled by Vlasov-type equations with nonlocal interaction forces and alignment. More precisely, we investigate the hydrodynamic limit of a kinetic Cucker–Smale flocking model with confinement, nonlocal interaction, and local alignment forces, linear damping and diffusion in velocity. We first discuss the hydrodynamic limit of our main equation under strong local alignment and diffusion regime, and we rigorously derive the isothermal Euler equations with nonlocal forces. We also analyze the hydrodynamic limit corresponding to strong local alignment without diffusion. In this case, the limiting system is pressureless Euler-type equations. Our analysis includes the Coulomb interaction potential for both cases and explicit estimates on the distance towards the limiting hydrodynamic equations. The relative entropy method is the crucial technology in our main results, however, for the case without diffusion, we combine a modulated macroscopic kinetic energy with the bounded Lipschitz distance to deal with the nonlocality in the interaction forces. The existence of weak and strong solutions to the kinetic and fluid equations is also obtained. We emphasize that the existence of global weak solution with the needed free energy dissipation for the kinetic model is established.

Mesoscale Approximation of the Electromagnetic Fields

The point-interaction approximation (or the Foldy–Lax approximation) of the electromagnetic fields generated by a cluster of small-scaled inhomogeneities is derived in the mesoscale (i.e., mesoscopic scale) regime, that is, when the minimum distance $$\varvec{\delta }$$ between the particles is proportional to their maximum diameter $${\varvec{a}}$$ in the form $$\varvec{\delta }={\varvec{c}}_r \, {\varvec{a}}$$ with a positive constant $${\varvec{c}}_r$$ that we call the dilution parameter. The small particles are modeled by anisotropic and variable electric permittivities and/or magnetic permeabilities with possibly complex values. We provide the dominating field (the so-called Foldy–Lax field) with explicit error estimates in terms of the dilution parameter $${\varvec{c}}_r$$ uniformly in terms of the distribution of these inhomogeneities. Such approximations are key steps in different research areas as imaging and material sciences.

Feedback Stabilization of Delayed Bilinear Systems

In this paper, we discuss the problem of feedback stabilization for distributed bilinear systems with discrete delay evolving on a Hilbert state space. Firstly, we prove the existence and uniqueness of the mild solution of system at hand. Secondly, we study the weak and strong stabilization. More precisely, we provide some sufficient conditions to ensure the weak and strong stabilization for the delayed bilinear system. Moreover, in the case of the strong stabilization, an explicit decay estimate is established. Applications to wave and heat equations with delayed bilinear parts are considered.

Robust point-process Granger causality analysis in presence of exogenous temporal modulations and trial-by-trial variability in spike trains.

Assessing directional influences between neurons is instrumental to understand how brain circuits process information. To this end, Granger causality, a technique originally developed for time-continuous signals, has been extended to discrete spike trains. A fundamental assumption of this technique is that the temporal evolution of neuronal responses must be due only to endogenous interactions between recorded units, including self-interactions. This assumption is however rarely met in neurophysiological studies, where the response of each neuron is modulated by other exogenous causes such as, for example, other unobserved units or slow adaptation processes. Here, we propose a novel point-process Granger causality technique that is robust with respect to the two most common exogenous modulations observed in real neuronal responses: within-trial temporal variations in spiking rate and between-trial variability in their magnitudes. This novel method works by explicitly including both types of modulations into the generalized linear model of the neuronal conditional intensity function (CIF). We then assess the causal influence of neuron i onto neuron j by measuring the relative reduction of neuron j's point process likelihood obtained considering or removing neuron i. CIF's hyper-parameters are set on a per-neuron basis by minimizing Akaike's information criterion. In synthetic data sets, generated by means of random processes or networks of integrate-and-fire units, the proposed method recovered with high accuracy, sensitivity and robustness the underlying ground-truth connectivity pattern. Application of presently available point-process Granger causality techniques produced instead a significant number of false positive connections. In real spiking responses recorded from neurons in the monkey pre-motor cortex (area F5), our method revealed many causal relationships between neurons as well as the temporal structure of their interactions. Given its robustness our method can be effectively applied to real neuronal data. Furthermore, its explicit estimate of the effects of unobserved causes on the recorded neuronal firing patterns can help decomposing their temporal variations into endogenous and exogenous components.

The role of the power law exponent in wind energy assessment: A global analysis

The power law is most often applied to extrapolate the near-surface wind speed to the wind turbine hub height. Due to variations of the meteorological conditions, the power law exponent varies over time. Usually, no long-term wind speed measurements from multiple heights are available which would allow time-dependent and spatially explicit power law exponent estimations. Instead, often the mean of the power law exponent or a constant value of 0.14 is assumed. The goal of this study was to quantify the error in wind potential assessments resulting from applying the mean of the power law exponent or a value of 0.14. The data base for this study are the hourly wind speed time series at 10 and 100 m above ground available for the period 2007 to 2018 from the ERA5 reanalysis project at a global 0.25° × 0.25° grid. The errors in the estimation of the wind power density and the capacity factor were calculated. It was found that, onshore, the global median of the absolute percentage error related to the wind power density using the mean of the power law exponent is 7.5%. Assuming a constant value of 0.14, the power law is less accurate (absolute percentage error: 37.1%). For the estimation of the capacity factor the absolute percentage errors are 5.5% and 36.9%. Based on the results of this study, the use of time-dependent and spatially explicit power law exponents is suggested. In the absence of long-term wind speed measurements from multiple heights, the results provide a comprehensive global overview of the errors to be expected from using the mean of the power law exponent or assuming a value of 0.14. In many regions where the wind resource is abundant, using the mean of the power law exponent only leads to minor errors in capacity factor estimation. There, the assessment of wind resources with small errors is possible, even in the absence of long-term wind speed measurements at different heights.