Scalar Indices Research Articles

Efficacy of PZT Sensors Network Different Configurations in Damage Detection of Fiber-Reinforced Concrete Prisms under Repeated Loading.

Real-time structural health monitoring (SHM) and accurate diagnosis of imminent damage are critical to ensure the structural safety of conventional reinforced concrete (RC) and fiber-reinforced concrete (FRC) structures. Implementations of a piezoelectric lead zirconate titanate (PZT) sensor network in the critical areas of structural members can identify the damage level. This study uses a recently developed PZT-enabled Electro-Mechanical Impedance (EMI)-based, real-time, wireless, and portable SHM and damage detection system in prismatic specimens subjected to flexural repeated loading plain concrete (PC) and FRC. Furthermore, this research examined the efficacy of the proposed SHM methodology for FRC cracking identification of the specimens at various loading levels with different sensor layouts. Additionally, damage quantification using values of statistical damage indices is included. For this reason, the well-known conventional static metric of the Root Mean Square Deviation (RMSD) and the Mean Absolute Percentage Deviation (MAPD) were used and compared. This paper addresses a reliable monitoring experimental methodology in FRC to diagnose damage and predict the forthcoming flexural failure at early damage stages, such as at the onset of cracking. Test results indicated that damage assessment is successfully achieved using RMSD and MAPD indices of a strategically placed network of PZT sensors. Furthermore, the Upper Control Limit (UCL) index was adopted as a threshold for further sifting the scalar damage indices. Additionally, the proposed PZT-enable SHM method for prompt damage level is first established, providing the relationship between the voltage frequency response of the 32 PZT sensors and the crack propagation of the FRC prisms due to the step-by-step increased imposed load. In conclusion, damage diagnosis through continuous monitoring of PZTs responses of FRC due to flexural loading is a quantitative, reliable, and promising application.

Entanglement and Generalized Berry Geometrical Phases in Quantum Gravity

A new formalism is introduced that makes it possible to elucidate the physical and geometric content of quantum space–time. It is based on the Minimum Group Representation Principle (MGRP). Within this framework, new results for entanglement and geometrical/topological phases are found and implemented in cosmological and black hole space–times. Our main results here are as follows: (i) We find the Berry phases for inflation and for the cosmological perturbations and express them in terms of the observables, such as the spectral scalar and tensor indices, nS and nT, and the tensor-to-scalar ratio r. The Berry phase for de Sitter inflation is imaginary with the sign describing the exponential acceleration. (ii) The pure entangled states in the minimum group (metaplectic) Mp(n) representation for quantum de Sitter space–time and black holes are found. (iii) For entanglement, the relation between the Schmidt type representation and the physical states of the Mp(n) group is found: This is a new non-diagonal coherent state representation complementary to the known Sudarshan diagonal one. (iv) Mean value generators of Mp(2) are related to the adiabatic invariant and topological charge of the space–time, (matrix element of the transition −∞<t<∞). (v) The basic even and odd n-sectors of the Hilbert space are intrinsic to the quantum space–time and its discrete levels (in particular, continuum for n→∞), they do not require any extrinsic generation process such as the standard Schrodinger cat states, and are entangled. (vi) The gravity or cosmological on one side and another of the Planck scale are entangled. Examples: The quantum primordial trans-Planckian de Sitter vacuum and the classical late de Sitter vacuum today; the central quantum gravity region and the external classical gravity region of black holes. The classical and quantum dual gravity regions of the space–time are entangled. (vii) The general classical-quantum gravity duality is associated with the Metaplectic Mp(n) group symmetry which provides the complete full covering of the phase space and of the quantum space–time mapped from it.

Transformer Outage Contingency in the Southern Interconnected Grid of Cameroon Based on Dynamic Power Flow Simulation

The power system is a network of components having specific operational limits such that any violation of these limits during their operation could lead to more damage in the grid. The grid in Cameroon has been facing several undesired loading events at some sections of the network and the utility company has over the years, employed measures to mitigate these issues. This study has used the ETAP software to conduct a contingency analysis on the largest independent grid in Cameroon, supplying 6 regions in Cameroon. Seventeen transformer outage events in the network were used to conduct the N‐1 scenario‐based contingency, so that the vulnerability of the network can be evaluated. The fast decoupled power flow method was continuously applied on the network, and the different contingency scenarios were ranked using a combination of 4 performance indices. These four performance indices gave information on the impact of the various transformer outage scenarios on the grid. The four indices were added to give a combined value, and the outages were ranked in order of severity based on this combined index. A major contribution of this paper is the use of four scalar indices to classify the critical elements in the grid of a developing country. The initial load flow simulation of the network showed that 12 nodes had under voltages, while 3 transformers and one transmission line were overloaded. The Ngousso corridor suffered one of the worst under voltage situation during the initial power flow study. This is an indication that the utility company needs to undertake intensive network upgrade and implore measures to increase power generation to support the growing loads. It was observed that all the contingency scenarios experienced convergence. The Oyomabang transformer 1 had the highest combined index of 71.20, showing a huge negative impact on the network as a result of the outage of the transformer. This was followed by the Oyomabang transformer 2 with a combined index of 48.63. The results will be very useful to utility operators in prioritizing transformers in the network with high risk of causing huge impact on the network in case of an outage.

Domino: A new framework for the automated identification of weather event precursors, demonstrated for European extreme rainfall

AbstractA number of studies have investigated the large‐scale drivers and upstream precursors of extreme weather events, making it clear that the earliest warning signs of extreme events can be remote from the impacted region in both time and space. Integrating and leveraging our understanding of dynamical precursors provides a new perspective on ensemble forecasting for extreme events, focused on building storylines of possible event evolution. This then acts as a tool for raising awareness of the conditions conducive to high‐impact weather and providing early warning of their possible development. However, operational applications of this developing knowledge base are limited, perhaps for want of a clear framework for doing so. Here, we present such a framework, supported by open software tools, designed for identifying large‐scale precursors of categorical weather events in an automated fashion and reducing them to scalar indices suitable for statistical prediction, forecast interpretation, and model validation. We demonstrate this framework by systematically analysing the precursor circulations of daily rainfall extremes across 18 regional‐ to national‐scale European domains. We discuss the precursor rainfall dynamics for three disparate regions, and show our findings are consistent with, and extend, previous work. We provide an estimate of the predictive utility of these precursors across Europe based on logistic regression, and show that large‐scale precursors can usefully predict heavy rainfall between two and six days ahead, depending on region and season. We further show how, for more continental‐scale applications, the regionally specific precursors can be synthesised into a minimal set of indices that drive heavy precipitation. We then provide comments and guidance for generalisation and application of our demonstrated approach to new variables, timescales, and regions.

Full-Season Crop Phenology Monitoring Using Two-Dimensional Normalized Difference Pairs

The monitoring of crop phenology informs decisions in environmental and agricultural management at both global and farm scales. Current methodologies for crop monitoring using remote sensing data track crop growth stages over time based on single, scalar vegetative indices (e.g., NDVI). Crop growth and senescence are indistinguishable when using scalar indices without additional information (e.g., planting date). By using a pair of normalized difference (ND) metrics derived from hyperspectral data—one primarily sensitive to chlorophyll concentration and the other primarily sensitive to water content—it is possible to track crop characteristics based on the spectral changes only. In a two-dimensional plot of the metrics (ND-space), bare soil, full canopy, and senesced vegetation data all plot in separate, distinct locations regardless of the year. The path traced in the ND-space over the growing season repeats from year to year, with variations that can be related to weather patterns. Senescence follows a return path that is distinct from the growth path.

Mapping the individual human cortex using multidimensional MRI and unsupervised learning.

Human evolution has seen the development of higher-order cognitive and social capabilities in conjunction with the unique laminar cytoarchitecture of the human cortex. Moreover, early-life cortical maldevelopment has been associated with various neurodevelopmental diseases. Despite these connections, there is currently no noninvasive technique available for imaging the detailed cortical laminar structure. This study aims to address this scientific and clinical gap by introducing an approach for imaging human cortical lamina. This method combines diffusion-relaxation multidimensional MRI with a tailored unsupervised machine learning approach that introduces enhanced microstructural sensitivity. This new imaging method simultaneously encodes the microstructure, the local chemical composition and importantly their correlation within complex and heterogenous tissue. To validate our approach, we compared the intra-cortical layers obtained using our ex vivo MRI-based method with those derived from Nissl staining of postmortem human brain specimens. The integration of unsupervised learning with diffusion-relaxation correlation MRI generated maps that demonstrate sensitivity to areal differences in cytoarchitectonic features observed in histology. Significantly, our observations revealed layer-specific diffusion-relaxation signatures, showing reductions in both relaxation times and diffusivities at the deeper cortical levels. These findings suggest a radial decrease in myelin content and changes in cell size and anisotropy, reflecting variations in both cytoarchitecture and myeloarchitecture. Additionally, we demonstrated that 1D relaxation and high-order diffusion MRI scalar indices, even when aggregated and used jointly in a multimodal fashion, cannot disentangle the cortical layers. Looking ahead, our technique holds the potential to open new avenues of research in human neurodevelopment and the vast array of disorders caused by disruptions in neurodevelopment.

Exact expressions and numerical evaluation of average evolvability measures for characterizing and comparing textbf{G} matrices

Theory predicts that the additive genetic covariance (textbf{G}) matrix determines a population’s short-term (in)ability to respond to directional selection—evolvability in the Hansen–Houle sense—which is typically quantified and compared via certain scalar indices called evolvability measures. Often, interest is in obtaining the averages of these measures across all possible selection gradients, but explicit formulae for most of these average measures have not been known. Previous authors relied either on approximations by the delta method, whose accuracy is generally unknown, or Monte Carlo evaluations (including the random skewers analysis), which necessarily involve random fluctuations. This study presents new, exact expressions for the average conditional evolvability, average autonomy, average respondability, average flexibility, average response difference, and average response correlation, utilizing their mathematical structures as ratios of quadratic forms. The new expressions are infinite series involving top-order zonal and invariant polynomials of matrix arguments, and can be numerically evaluated as their partial sums with, for some measures, known error bounds. Whenever these partial sums numerically converge within reasonable computational time and memory, they will replace the previous approximate methods. In addition, new expressions are derived for the average measures under a general normal distribution for the selection gradient, extending the applicability of these measures into a substantially broader class of selection regimes.

Acquisition and Analysis of Excised Neocortex from Pediatric Patients with Focal Cortical Dysplasia Using Mesoscale Diffusion MRI.

Non-invasive classification of focal cortical dysplasia (FCD) subtypes remains challenging from a radiology perspective. Quantitative imaging biomarkers (QIBs) have the potential to distinguish subtypes that lack pathognomonic features and might help in defining the extent of abnormal connectivity associated with each FCD subtype. A key motivation of diagnostic imaging is to improve the localization of a "lesion" that can guide the surgical resection of affected tissue, which is thought to cause seizures. Conversely, surgical resections to eliminate or reduce seizures provided unique opportunities to develop magnetic resonance imaging (MRI)-based QIBs by affording long scan times to evaluate multiple contrast mechanisms at the mesoscale (0.5 mm isotropic voxel dimensions). Using ex vivo hybrid diffusion tensor imaging on a 9.4 T MRI scanner, the grey to white matter ratio of scalar indices was lower in the resected middle temporal gyrus (MTG) of two neuropathologically confirmed cases of FCD compared to non-diseased control postmortem fixed temporal lobes. In contrast, fractional anisotropy was increased within FCD and also adjacent white matter tracts. Connectivity (streamlines/mm3) in the MTG was higher in FCD, suggesting that an altered connectivity at the lesion locus can potentially provide a tangible QIB to distinguish and characterize FCD abnormalities. However, as illustrated here, a major challenge for a robust tractographical comparison lies in the considerable differences in the ex vivo processing of bioptic and postmortem samples. Mesoscale diffusion MRI has the potential to better define and characterize epileptic tissues obtained from surgical resection to advance our understanding of disease etiology and treatment.

Renormalization of the Standard Model Effective Field Theory from geometry

S-matrix elements are invariant under field redefinitions of the Lagrangian. They are determined by geometric quantities such as the curvature of the field-space manifold of scalar and gauge fields. We present a formalism where scalar and gauge fields are treated together, with a metric on the combined space of both types of fields. Scalar and gauge scattering amplitudes are given by the Riemann curvature Rijkl of this combined space, with indices i, j, k, l chosen to be scalar or gauge indices depending on the type of external particle. One-loop divergences can also be computed in terms of geometric invariants of the combined space, which greatly simplifies the computation of renormalization group equations. We apply our formalism to the Standard Model Effective Field Theory (SMEFT), and compute the renormalization group equations for even-parity bosonic operators to mass dimension eight.

Moment-based representation of the diffusion inside the brain from reduced DMRI acquisitions: Generalized AMURA.

AMURA (Apparent Measures Using Reduced Acquisitions) was originally proposed as a method to infer micro-structural information from single-shell acquisitions in diffusion MRI. It reduces the number of samples needed and the computational complexity of the estimation of diffusion properties of tissues by assuming the diffusion anisotropy is roughly independent on the b-value. This simplification allows the computation of simplified expressions and makes it compatible with standard acquisition protocols commonly used even in clinical practice. The present work proposes an extension of AMURA that allows the calculation of general moments of the diffusion signals that can be applied to describe the diffusion process with higher accuracy. We provide simplified expressions to analytically compute a set of scalar indices as moments of arbitrary orders over either the whole 3-D space, particular directions, or particular planes. The existing metrics previously proposed for AMURA (RTOP, RTPP and RTAP) are now special cases of this generalization. An extensive set of experiments is performed on public data and a clinical clase acquired with a standard type acquisition. The new metrics provide additional information about the diffusion processes inside the brain.

The Worker-Job Surplus

The worker-job surplus — the sum of the worker's and the employer's net values of an employment relationship — is the object that drives decisions in most matching models of the labor market. In this paper, we develop a theory-based empirical method to determine which of the observable worker and job characteristics impact the worker-job surplus in the data. To do so, we exploit the mobility choices of employed workers. Our method further indicates whether workers sort along those surplus-relevant attributes when searching for jobs. It also provides a test of the commonly used single-index assumption, according to which worker and job heterogeneity can each be summarized by scalar indices. We implement our method on US data using the Survey of Income and Program Participation and the O*NET. The results suggest that a relatively sparse model underlies the data. On the job side, a cognitive and an interpersonal skill requirement impact the surplus along with the (dis)amenity of work duration as well as the workplace size. On the worker side, we find that most of the relevant characteristics are symmetric to the selected job requirements. We reject the existence of a single-index representation of these relevant multi-dimensional worker and job attributes. We then use our results in a new approach to defining the economy's labor submarkets, highlighting a potentially important application of our methodology.

Q-space Conditioned Translation Networks for Directional Synthesis of Diffusion Weighted Images from Multi-modal Structural MRI.

Current deep learning approaches for diffusion MRI modeling circumvent the need for densely-sampled diffusion-weighted images (DWIs) by directly predicting microstructural indices from sparsely-sampled DWIs. However, they implicitly make unrealistic assumptions of static q-space sampling during training and reconstruction. Further, such approaches can restrict downstream usage of variably sampled DWIs for usages including the estimation of microstructural indices or tractography. We propose a generative adversarial translation framework for high-quality DWI synthesis with arbitrary q-space sampling given commonly acquired structural images (e.g., B0, T1, T2). Our translation network linearly modulates its internal representations conditioned on continuous q-space information, thus removing the need for fixed sampling schemes. Moreover, this approach enables downstream estimation of high-quality microstructural maps from arbitrarily subsampled DWIs, which may be particularly important in cases with sparsely sampled DWIs. Across several recent methodologies, the proposed approach yields improved DWI synthesis accuracy and fidelity with enhanced downstream utility as quantified by the accuracy of scalar microstructure indices estimated from the synthesized images. Code is available at https://github.com/mengweiren/q-space-conditioned-dwi-synthesis.

Efficient and accurate EAP imaging from multi-shell dMRI with micro-structure adaptive convolution kernels and dual Fourier Integral Transforms (MiSFIT)

A number of computational techniques have been lately devised to image the Ensemble Average Propagator (EAP) within the white matter of the brain, propelled by the deployment of multi-shell acquisition protocols and databases: approaches like Mean Apparent Propagator Imaging (MAP-MRI) and its Laplacian-regularized version (MAPL) aim at describing the low frequency spectrum of the EAP (limited by the maximum b-value acquired) and afterwards computing scalar indices that embed useful descriptions of the white matter, e. g. the Return-to-Origin, Plane, or Axis Probabilities (RTOP, RTPP, RTAP). These methods resort to a non-parametric, bandwidth limited representation of the EAP that implies fitting a set of 3-D basis functions in a large-scale optimization problem. We propose a semi-parametric approach inspired by signal theory: the EAP is approximated as the spherical convolution of a Micro-Structure adaptive Gaussian kernel with a non-parametric orientation histogram, which aims at representing the low-frequency response of an ensemble of coherent sets of fiber bundles at the white matter. This way, the optimization involves just the 2 to 3 parameters that describe the kernel, making our approach far more efficient than the related state of the art. We devise dual Fourier domains Integral Transforms to analytically compute RTxP-like scalar indices as moments of arbitrary orders over either the whole 3-D space, particular directions, or particular planes. The so-called MiSFIT is both time efficient (a typical multi-shell data set can be processed in roughly one minute) and accurate: it provides estimates of widely validated indices like RTOP, RTPP, and RTAP comparable to MAPL for a wide variety of white matter configurations.

Competencia espacial y calidad personal de los candidatos. Elecciones presidenciales entre 2006 y 2018 en México

This research project presents a spatial competition model for Mexican presidential elections based on the effective number of parties and weighted and scalar polarization indices. The model makes it possible to construct a classification of candidates influences based on personality as an remainder unexplained by spatial ideological competition. In addition to classifying the candidates in the last three presidential elections by their personal influence, the authors offer predictions for future balloting based on change in ideological distribution. Suppositions of symmetrical ideological votes and a single dimension were used to build the model.

Mesoscale diffusion magnetic resonance imaging of the ex vivo human hippocampus.

Mesoscale diffusion magnetic resonance imaging (MRI) endeavors to bridge the gap between macroscopic white matter tractography and microscopic studies investigating the cytoarchitecture of human brain tissue. To ensure a robust measurement of diffusion at the mesoscale, acquisition parameters were arrayed to investigate their effects on scalar indices (mean, radial, axial diffusivity, and fractional anisotropy) and streamlines (i.e., graphical representation of axonal tracts) in hippocampal layers. A mesoscale resolution afforded segementation of the pyramidal cell layer (CA1‐4), the dentate gyrus, as well as stratum moleculare, radiatum, and oriens. Using ex vivo samples, surgically excised from patients with intractable epilepsy (n = 3), we found that shorter diffusion times (23.7 ms) with a b‐value of 4,000 s/mm2 were advantageous at the mesoscale, providing a compromise between mean diffusivity and fractional anisotropy measurements. Spatial resolution and sample orientation exerted a major effect on tractography, whereas the number of diffusion gradient encoding directions minimally affected scalar indices and streamline density. A sample temperature of 15°C provided a compromise between increasing signal‐to‐noise ratio and increasing the diffusion properties of the tissue. Optimization of the acquisition afforded a system's view of intra‐ and extra‐hippocampal connections. Tractography reflected histological boundaries of hippocampal layers. Individual layer connectivity was visualized, as well as streamlines emanating from individual sub‐fields. The perforant path, subiculum and angular bundle demonstrated extra‐hippocampal connections. Histology of the samples confirmed individual cell layers corresponding to ROIs defined on MR images. We anticipate that this ex vivo mesoscale imaging will yield novel insights into human hippocampal connectivity.

Torsional irregularity indices for the seismic demand assessment of RC moment resisting frame buildings

Design standards across the world use different parameters to quantify degree of torsional irregularity of buildings. Popular among such descriptors are the normalized static eccentricity ratio, torsional radius to mass radius of gyration ratio, maximum to minimum (or average) elastic floor displacement ratio, etc. However prior research, particularly on idealized single storey systems have indicated that these parameters do not correlate well with the seismic demands at all stages of structural behaviour (i.e. elastic and inelastic). The present study aims to identify a robust torsional irregularity index that captures the susceptibility of a structure to torsional effects at all ground motion intensity levels. To this end, the correlation between the maximum interstorey drift demands and popular torsional irregularity descriptors is first examined under different intensities of ground shaking using an approach that integrates multiple stripe analysis and statistical regression analysis. The numerical study is based on the nonlinear seismic assessment of thirteen three-storey gravity designed RC moment frame buildings subjected to bidirectional seismic excitation. The results indicate that none of the scalar indices considered correlate well with the drift demands at all intensities of ground shaking. A vector comprising of the normalized static eccentricity ratio and the torsional radius to mass radius of gyration ratio is found to perform well at low shaking intensity levels, where the structure responds in an elastic manner. However, at high intensity levels where the structure undergoes significant excursions into the inelastic range of behaviour, the strength eccentricity is observed to be a better descriptor of torsional irregularity. A three-element vector comprising of the above indices is found to capture the maximum interstorey drifts accurately at all ground motion intensity levels. A seismic demand model for maximum interstorey drift, sensitive to the above torsional irregularity descriptors, is also defined.

Micro-structure diffusion scalar measures from reduced MRI acquisitions.

In diffusion MRI, the Ensemble Average diffusion Propagator (EAP) provides relevant micro-structural information and meaningful descriptive maps of the white matter previously obscured by traditional techniques like Diffusion Tensor Imaging (DTI). The direct estimation of the EAP, however, requires a dense sampling of the Cartesian q-space involving a huge amount of samples (diffusion gradients) for proper reconstruction. A collection of more efficient techniques have been proposed in the last decade based on parametric representations of the EAP, but they still imply acquiring a large number of diffusion gradients with different b-values (shells). Paradoxically, this has come together with an effort to find scalar measures gathering all the q-space micro-structural information probed in one single index or set of indices. Among them, the return-to-origin (RTOP), return-to-plane (RTPP), and return-to-axis (RTAP) probabilities have rapidly gained popularity. In this work, we propose the so-called "Apparent Measures Using Reduced Acquisitions" (AMURA) aimed at computing scalar indices that can mimic the sensitivity of state of the art EAP-based measures to micro-structural changes. AMURA drastically reduces both the number of samples needed and the computational complexity of the estimation of diffusion properties by assuming the diffusion anisotropy is roughly independent from the radial direction. This simplification allows us to compute closed-form expressions from single-shell information, so that AMURA remains compatible with standard acquisition protocols commonly used even in clinical practice. Additionally, the analytical form of AMURA-based measures, as opposed to the iterative, non-linear reconstruction ubiquitous to full EAP techniques, turns the newly introduced apparent RTOP, RTPP, and RTAP both robust and efficient to compute.

A framework to construct a longitudinal DW-MRI infant atlas based on mixed effects modeling of dODF coefficients.

Building of atlases plays a crucial role in the analysis of brain images. In scenarios where early growth, aging or disease trajectories are of key importance, longitudinal atlases become necessary as references, most often created from cross-sectional data. New opportunities will be offered by creating longitudinal brain atlases from longitudinal subject-specific image data, where explicit modeling of subject's variability in slope and intercept leads to a more robust estimation of average trajectories but also to estimates of confidence bounds. This work focuses on a framework to build a continuous 4D atlas from longitudinal high angular resolution diffusion images (HARDI) where, unlike atlases of derived scalar diffusion indices such as FA, statistics on dODFs is preserved. Multi-scalar images obtained from DW images are used for geometric alignment, and linear mixed-effects modeling from longitudinal diffusion orientation distribution functions (dODF) leads to estimation of continuous dODF changes. The proposed method is applied to a longitudinal dataset of HARDI images from healthy developing infants in the age range of 3 to 36 months. Verification of mixed-effects modeling is obtained by voxel-wise goodness of fit calculations. To demonstrate the potential of our method, we display changes of longitudinal atlas using dODF and derived generalized fractional anisotropy (GFA) of dODF. We also investigate white matter maturation patterns in genu, body, and splenium of the corpus callosum. The framework can be used to build an average dODF atlas from HARDI data and to derive subject-specific and population-based longitudinal change trajectories.

Linear Inverse Modeling for Coupled Atmosphere‐Ocean Ensemble Climate Prediction

AbstractPaleoclimate data assimilation (PDA) experiments reconstruct climate fields by objectively blending information from climate models and proxy observations. Due to high computational cost and relatively low forecast skill, most reconstruction experiments omit the prediction step, where a forecast is made from the previously reconstructed state to the next time proxy data is available. In order to enable this critical aspect of PDA, we propose an efficient method of generating forecast ensembles of coupled climate fields using a linear inverse model (LIM). We describe the general calibration of a LIM on multiple fields using a two‐step empirical orthogonal function field compression to efficiently represent the state. We find that a LIM calibrated on global climate model (GCM) data yields skillful forecasts, including for out‐of‐sample tests on data from a different GCM. The deterministic forecast skill tests for scalar indices show that the LIM outperforms damped persistence at leads up to 3 years and has skill up to 10 years for global average sea surface temperature. Analysis of 1‐year forecasts reveals that the LIM captures dynamic climate features with local and remote predictability related to teleconnections. The forecast ensemble characteristics of the LIM, which in part determine the weighting of information for PDA experiments, show that the LIM generally produces ensemble forecast errors that are 10% to 70% larger than ensemble variance for 1‐year forecasts on data representative of the last millennium. These results show that the LIM produces ensembles with reasonable calibration but also that LIMs for PDA may require some variance tuning to work optimally for data assimilation experiments.

Probabilistic Assessment of Nerve Regeneration with Diffusion MRI in Rat Models of Peripheral Nerve Trauma

Nerve regeneration after injury must occur in a timely fashion to restore function. Unfortunately, current methods (e.g., electrophysiology) provide limited information following trauma, resulting in delayed management and suboptimal outcomes. Herein, we evaluated the ability of diffusion MRI to monitor nerve regeneration after injury/repair. Sprague-Dawley rats were divided into three treatment groups (sham = 21, crush = 23, cut/repair = 19) and ex vivo diffusion tensor imaging (DTI) and diffusion kurtosis imaging (DKI) was performed 1–12 weeks post-surgery. Behavioral data showed a distinction between crush and cut/repair nerves at 4 weeks. This was consistent with DTI, which found that thresholds based on the ratio of radial and axial diffusivities (RD/AD = 0.40 ± 0.02) and fractional anisotropy (FA = 0.53 ± 0.01) differentiated crush from cut/repair injuries. By the 12th week, cut/repair nerves whose behavioral data indicated a partial recovery were below the RD/AD threshold (and above the FA threshold), while nerves that did not recover were on the opposite side of each threshold. Additional morphometric analysis indicated that DTI-derived normalized scalar indices report on axon density (RD/AD: r = −0.54, p < 1e-3; FA: r = 0.56, p < 1e-3). Interestingly, higher-order DKI analyses did not improve our ability classify recovery. These findings suggest that DTI may provide promising biomarkers for distinguishing successful/unsuccessful nerve repairs and potentially identify cases that require reoperation.