Smooth Metrics Research Articles

Third-order smoothness metric to characterize progressive addition lenses

Although second-order surface analyses, mainly mean power and cylinder maps, are commonly used to characterize the progressive addition lens (PAL) surface, recently it has been suggested that third-order variations may also have relevancy in PAL optical and visual performance. This paper proposes a third-order smoothness metric, and its associated Riemannian distance, to further characterize PAL’s surface optical performance. These metrics can provide a complementary scoring tool to those classical ones, particularly, to analyze the transition zones between far, near, intermediate, and blending zones. A method to compute these metrics is provided. This third-order smoothness metric also enables a formal definition of the PAL principal curve, namely, the curve embedded in the PAL surface, that minimizes the line path integral joining the far and near reference points weighted by the third-order smoothness metric. Finally, the paper describes a comprehensive methodology to compute such principal curves using a level-set geodesic procedure. All these ideas are put into practice with several real PAL surfaces.

Measurement properties of movement smoothness metrics for upper limb reaching movements in people with moderate to severe subacute stroke

BackgroundMovement smoothness is a potential kinematic biomarker of upper extremity (UE) movement quality and recovery after stroke; however, the measurement properties of available smoothness metrics have been poorly assessed in this group. We aimed to measure the reliability, responsiveness and construct validity of several smoothness metrics.MethodsThis ancillary study of the REM-AVC trial included 31 participants with hemiparesis in the subacute phase of stroke (median time since stroke: 38 days). Assessments performed at inclusion (Day 0, D0) and at the end of a rehabilitation program (Day 30, D30) included the UE Fugl Meyer Assessment (UE-FMA), the Action Research Arm Test (ARAT), and 3D motion analysis of the UE during three reach-to-point movements at a self-selected speed to a target located in front at shoulder height and at 90% of arm length. Four smoothness metrics were computed: a frequency domain smoothness metric, spectral arc length metric (SPARC); and three temporal domain smoothness metrics (TDSM): log dimensionless jerk (LDLJ); number of submovements (nSUB); and normalized average rectified jerk (NARJ).ResultsAt D30, large clinical and kinematic improvements were observed. Only SPARC and LDLJ had an excellent reliability (intra-class correlation > 0.9) and a low measurement error (coefficient of variation < 10%). SPARC was responsive to changes in movement straightness (rSpearman=0.64) and to a lesser extent to changes in movement duration (rSpearman=0.51) while TDSM were very responsive to changes in movement duration (rSpearman>0.8) and not to changes in movement straightness (non-significant correlations). Most construct validity hypotheses tested were verified except for TDSM with low correlations with clinical metrics at D0 (rSpearman<0.5), ensuing low predictive validity with clinical metrics at D30 (non-significant correlations).ConclusionsResponsiveness and construct validity of TDSM were hindered by movement duration and/or noise-sensitivity. Based on the present results and concordant literature, we recommend using SPARC rather than TDSM in reaching movements of uncontrolled duration in individuals with spastic paresis after stroke.Trial RegistrationNCT01383512, https://clinicaltrials.gov/, June 27, 2011.

Weighted Sobolev Type Inequalities in a Smooth Metric Measure Space

In this paper, we obtain weighted Sobolev type inequalities with explicit constants that extend the inequalities obtained by Guo et al. (Math Res Lett 28(5):1419–1439, 2021) in the Riemannian setting. As an application, we prove some new logarithmic Sobolev type inequalities in some smooth metric measure spaces.

Comparison of Gait Smoothness Metrics in Healthy Elderly and Young People

The goal of this study is to compare gait smoothness using different metrics. Methodologically, harmonic ratio (HR), spectral arc length (SPARC) and log dimensionless jerk (LDLJ) metrics were applied to acceleration and angular velocity data collected during gait using a wearable inertial sensor placed on the trunk. Sixteen healthy elderly (68.3 ± 4.4 years) and sixteen young (22.6 ± 1.1 years) participants volunteered for the analysis. They were requested to walk at self-selected normal and fast velocities. The results obtained with the three metrics showed variations in smoothness within and between groups. Notably, the older group exhibited contradictory smoothness trends compared to prior studies, presenting a smoother gait than the younger cohort, except for specific directional accelerations. Contradictory outcomes arose between metrics, challenging the influence of age on gait smoothness. Despite concerns about LDLJ’s susceptibility to disturbances, it emerged as the most robust metric. Conversely, HR exhibited alignment with the existing literature on specific acceleration directions. The differences observed in gait smoothness between the two age groups while walking at different speeds suggest that pace might affect smoothness evaluation. The study posits that aging may have a less pronounced impact on gait smoothness compared to cognitive impairment, implying potential clinical utility in discerning age-related gait changes. These findings highlighted the importance of a comprehensive approach to estimating gait smoothness, integrating different metrics and considering several walking speeds, crucial for understanding age-related gait alterations and their clinical implications.

Netrin 1 directs vascular patterning and maturity in the developing kidney.

The intricate vascular system of the kidneys supports body fluid and organ homeostasis. However, little is known about how vascular architecture is established during kidney development. More specifically, how signals from the kidney influence vessel maturity and patterning remains poorly understood. Netrin 1 (Ntn1) is a secreted ligand that is crucial for vessel and neuronal guidance. Here, we demonstrate that Ntn1 is expressed by Foxd1+ stromal progenitors in the developing mouse kidney and conditional deletion (Foxd1GC/+;Ntn1fl/fl) results in hypoplastic kidneys with extended nephrogenesis. Wholemount 3D analyses additionally revealed the loss of a predictable vascular pattern in Foxd1GC/+;Ntn1fl/fl kidneys. As vascular patterning has been linked to vessel maturity, we investigated arterialization. Quantification of the CD31+ endothelium at E15.5 revealed no differences in metrics such as the number of branches or branch points, whereas the arterial vascular smooth muscle metrics were significantly reduced at both E15.5 and P0. In support of our observed phenotypes, whole kidney RNA-seq revealed disruptions to genes and programs associated with stromal cells, vasculature and differentiating nephrons. Together, our findings highlight the significance of Ntn1 to proper vascularization and kidney development.

Differential inclusions for the Schouten tensor and nonlinear eigenvalue problems in conformal geometry

Let g0 be a smooth Riemannian metric on a closed manifold Mn of dimension n≥3. We study the existence of a smooth metric g conformal to g0 whose Schouten tensor Ag satisfies the differential inclusion λ(g−1Ag)∈Γ on Mn, where Γ⊂Rn is a cone satisfying standard assumptions. Inclusions of this type are often assumed in the existence theory for fully nonlinear elliptic equations in conformal geometry. We assume the existence of a continuous metric g1 conformal to g0 satisfying λ(g1−1Ag1)∈Γ′‾ in the viscosity sense on Mn, together with a nondegenerate ellipticity condition, where Γ′=Γ or Γ′ is a cone slightly smaller than Γ. In fact, we prove not only the existence of metrics satisfying such differential inclusions, but also existence and uniqueness results for fully nonlinear eigenvalue problems for the Schouten tensor. We also give a number of geometric applications of our results. We show that the sign of a nonlinear eigenvalue for the σ2 operator is a conformal invariant in three dimensions. We also give a generalisation of a theorem of Aubin & Ehrlick on pinching of the Ricci curvature, and an application in the study of Green's functions for fully nonlinear Yamabe problems.

Robot trajectory planning for autonomous 3D reconstruction of cockpit in aircraft final assembly testing

The trend towards automation and intelligence in aircraft final assembly testing has led to a new demand for autonomous perception of unknown cockpit operation scenes in robotic collaborative airborne system testing. To address this demand, a robotic automated 3D reconstruction cell which enables to autonomously plan the robot end-camera's trajectory is developed for image acquisition and 3D modeling of the cockpit operation scene. A continuous viewpoint path planning algorithm is proposed that incorporates both 3D reconstruction quality and robot path quality into optimization process. Smoothness metrics for viewpoint position paths and orientation paths are introduced together for the first time in 3D reconstruction. To ensure safe and effective movement, two spatial constraints, Domain of View Admissible Position (DVAP) and Domain of View Admissible Orientation (DVAO), are implemented to account for robot reachability and collision avoidance. By using diffeomorphism mapping, the orientation path is transformed into 3D, consistent with the position path. Both orientation and position paths can be optimized in a unified framework to maximize the gain of reconstruction quality and path smoothness within DVAP and DVAO. The reconstruction cell is capable of automatic data acquisition and fine scene modeling, using the generated robot C-space trajectory. Simulation and physical scene experiments have confirmed the effectiveness of the proposed method to achieve high-precision 3D reconstruction while optimizing robot motion quality.

Quantifying Path Smoothness in Video Object Tracking by Detection

Object detection and tracking are important areas of research in computer vision. Computer vision solutions to object detection are typically single-frame solutions. To perform tracking by detection, these solutions typically do object detection on a perframe basis, thus losing any temporal information from previous frames. Many multiobject tracking solutions report the average precision performance on video datasets, but they do not evaluate the temporal qualities of these solutions. In video, not only the detection of objects is important but the temporal motion attributes of an object’s path, such as its velocity, acceleration, and jerk, are important as well. Many implementations of Object Tracking by Detection systems have run into the problem of motion smoothing for bounding box paths. This paper focuses on quantifying the smoothness of detected object paths within some temporal window. We propose using two smoothness metrics from the field of biokinematics and adapt them for use with detections. Finally, using these metrics, we evaluate the ground truth and two popular object detectors, at the time of experimentation (YOLOv3 and Retinanet), on the entire MOT17 dataset. The results show that the metrics are useful in determining object smoothness, and provide us with an additional approach to evaluate an algorithm’s performance in object tracking. The experiments also demonstrate that YOLOv3 produces smoother bounding boxes than Retinanet. All supplemental graphs and data are shown in our appendix

D3-brane supergravity solutions from Ricci-flat metrics on canonical bundles of Kähler–Einstein surfaces

D3 brane solutions of type IIB supergravity can be obtained by means of a classical Ansatz involving a harmonic warp factor, H(textbf{y},bar{textbf{y}}) multiplying at power -1/2 the first summand, i.e., the Minkowski metric of the D3 brane world-sheet, and at power 1/2 the second summand, i.e., the Ricci-flat metric on a six-dimensional transverse space mathcal {M}_6, whose complex coordinates y are the arguments of the warp factor. Of particular interest is the case where mathcal {M}_6={text {tot}}[ Kleft[ left( mathcal {M}_Bright) right] is the total space of the canonical bundle over a complex Kähler surface mathcal {M}_B. This situation emerges in many cases while considering the resolution à la Kronheimer of singular manifolds of type mathcal {M}_6=mathbb {C}^3/Gamma , where Gamma subset mathrm {SU(3)} is a discrete subgroup. When Gamma = mathbb {Z}_4, the surface mathcal {M}_B is the second Hirzebruch surface endowed with a Kähler metric having mathrm {SU(2)times U(1)} isometry. There is an entire class {text {Met}}(mathcal{F}mathcal{V}) of such cohomogeneity one Kähler metrics parameterized by a single function mathcal{F}mathcal{K}(mathfrak {v}) that are best described in the Abreu–Martelli–Sparks–Yau (AMSY) symplectic formalism. We study in detail a two-parameter subclass {text {Met}}(mathcal{F}mathcal{V})_{textrm{KE}}subset {text {Met}}(mathcal{F}mathcal{V}) of Kähler–Einstein metrics of the aforementioned class, defined on manifolds that are homeomorphic to S^2times S^2, but are singular as complex manifolds. Actually, {text {Met}}(mathcal{F}mathcal{V})_{textrm{KE}}subset {text {Met}}(mathcal{F}mathcal{V})_{textrm{ext}}subset {text {Met}}(mathcal{F}mathcal{V}) is a subset of a four parameter subclass {text {Met}}(mathcal{F}mathcal{V})_{textrm{ext}} of cohomogeneity one extremal Kähler metrics originally introduced by Calabi in 1983 and translated by Abreu into the AMSY action-angle formalism.{text {Met}}(mathcal{F}mathcal{V})_{textrm{ext}} contains also a two-parameter subclass {text {Met}}(mathcal{F}mathcal{V})_{textrm{ext}mathbb {F}_2} disjoint from {text {Met}}(mathcal{F}mathcal{V})_{textrm{KE}} of extremal smooth metrics on the second Hirzebruch surface that we rederive using constraints on period integrals of the Ricci 2-form. The Kähler–Einstein nature of the metrics in {text {Met}}(mathcal{F}mathcal{V})_{textrm{KE}} allows the construction of the Ricci-flat metric on their canonical bundle via the Calabi Ansatz, which we recast in the AMSY formalism deriving some new elegant formulae. The metrics in {text {Met}}(mathcal{F}mathcal{V})_{textrm{KE}} are defined on the base manifolds of U(1) fibrations supporting the family of Sasaki–Einstein metrics textrm{SEmet}_5 introduced by Gauntlett et al. (Adv Theor Math Phys 8:711–734, 2004), and already appeared in Gibbons and Pope (Commun Math Phys 66:267–290, 1979). However, as we show in detail using Weyl tensor polynomial invariants, the six-dimensional Ricci-flat metric on the metric cone of {mathcal M}_5 in {text {Met}}(textrm{SE})_5 is different from the Ricci-flat metric on {text {tot}}[ Kleft[ left( mathcal {M}_{textrm{KE}}right) right] constructed via Calabi Ansatz. This opens new research perspectives. We also show the full integrability of the differential system of geodesics equations on mathcal {M}_B thanks to a certain conserved quantity which is similar to the Carter constant in the case of the Kerr metric.

Smoothness and Efficiency Metrics Behavior after an Upper Extremity Training with Robic Humanoid Robot in Paediatric Spinal Cord Injured Patients

The upper extremity behavior in smoothness and efficiency metrics should be different between paraplegic and tetraplegic patients. The aim of this article was to analyze the behavior of these metrics after receiving upper extremity training with the humanoid robot Robic as a treatment. Ten pediatric patients participated in the study and completed ten experimental sessions with Robic. Patients were assessed at baseline and at ending the training using the Box and Block test and a non-immersive virtual application based on the Leap Motion Controller available in the RehabHand software. From this application, the smoothness metric was calculated as the number of peaks or units of movement detected in the velocity profile of the hand during the execution of the task, and the efficiency metric was assessed by calculating the length of the hand trajectory. Patients with tetraplegia had a significantly longer trajectory (286.01 ± 59.87 mm) than paraplegics (123.61 ± 17.14 mm) in the baseline situation. However, at the end of the training, there were no differences between them. In the Box and Block test, the paraplegic group passed more cubes than tetraplegics. In conclusion, the first experience with a Robic robot in SCI was very positive, with observed improvements in upper extremity dexterity in trained patients.

Path Planning for Unmanned Delivery Robots Based on EWB-GWO Algorithm.

With the rise of robotics within various fields, there has been a significant development in the use of mobile robots. For mobile robots performing unmanned delivery tasks, autonomous robot navigation based on complex environments is particularly important. In this paper, an improved Gray Wolf Optimization (GWO)-based algorithm is proposed to realize the autonomous path planning of mobile robots in complex scenarios. First, the strategy for generating the initial wolf pack of the GWO algorithm is modified by introducing a two-dimensional Tent-Sine coupled chaotic mapping in this paper. This guarantees that the GWO algorithm generates the initial population diversity while improving the randomness between the two-dimensional state variables of the path nodes. Second, by introducing the opposition-based learning method based on the elite strategy, the adaptive nonlinear inertia weight strategy and random wandering law of the Butterfly Optimization Algorithm (BOA), this paper improves the defects of slow convergence speed, low accuracy, and imbalance between global exploration and local mining functions of the GWO algorithm in dealing with high-dimensional complex problems. In this paper, the improved algorithm is named as an EWB-GWO algorithm, where EWB is the abbreviation of three strategies. Finally, this paper enhances the rationalization of the initial population generation of the EWB-GWO algorithm based on the visual-field line detection technique of Bresenham's line algorithm, reduces the number of iterations of the EWB-GWO algorithm, and decreases the time complexity of the algorithm in dealing with the path planning problem. The simulation results show that the EWB-GWO algorithm is very competitive among metaheuristics of the same type. It also achieves optimal path length measures and smoothness metrics in the path planning experiments.

Quantification of Cycling Smoothness in Children with Cerebral Palsy

Smoothness is a hallmark of skilled, coordinated movement, however, mathematically quantifying movement smoothness is nuanced. Several smoothness metrics exist, each having its own limitations and may be specific to a particular motion such as upper limb reaching. To date, there is no consensus on which smoothness metric is the most appropriate for assessing cycling motion in children with cerebral palsy (CP). We evaluated the ability of four preexisting metrics, dimensionless jerk, spectral arc length measure, roughness index, and cross-correlation; and two new metrics, arc length and root mean square error, to quantify the smoothness of cycling in a preexisting dataset from children with CP (mean age 13.7 ± 2.6 years). First, to measure the repeatability of each measure in distinguishing between different levels of un-smoothness, we applied each metric to a set of simulated crank motion signals with a known number of aberrant revolutions using subjects’ actual crank angle data. Second, we used discriminant function analysis to statistically compare the strength of the six metrics, relative to each other, to discriminate between a smooth cycling motion obtained from a dataset of typically developed children (TD), the control group (mean age 14.9 ± 1.4 years), and a less smooth, halted cycling motion obtained from children with CP. Our results show that (1) ArcL showed the highest repeatability in accurately quantifying an unsmooth motion when the same cycling revolutions were presented in a different order, and (2) ArcL and DJ had the highest discriminatory ability to differentiate between an unsmooth and smooth cycling motion. Combining the results from the repeatability and discriminatory analysis, ArcL was the most repeatable and sensitive metric in identifying unsmooth, halted cycling motion from smooth motion. ArcL can hence be used as a metric in future studies to quantify changes in the smoothness of cycling motion pre- vs. post-interventions. Further, this metric may serve as a tool to track motor recovery not just in individuals with CP but in other patient populations with similar neurological deficits that may present with halted, unsmooth cycling motion.

Opus on conformal symmetry of the Nambu–Goto versus Polyakov strings

I investigate the Nambu–Goto and Polyakov strings, accounting for higher-derivative terms in the emergent action for the metric tensor which are classically negligible for smooth metrics but revive quantumly. Using the conformal field theory technique by KPZ-DDK, I compute in the one-loop approximation the conformal dimension and the central charge which differs in the two cases, telling the Nambu–Goto and Polyakov strings apart. I confirm the results by explicit quantum field theory computations of the propagator and the energy–momentum tensor at one loop, using the Pauli–Villars regularization.

Comparison of Various Smoothness Metrics for Upper Limb Movements in Middle-Aged Healthy Subjects.

Metrics for movement smoothness include the number of zero-crossings on the acceleration profile (N0C), the log dimensionless jerk (LDLJ), the normalized averaged rectified jerk (NARJ) and the spectral arc length (SPARC). Sensitivity to the handedness and movement type of these four metrics was compared and correlations with other kinematic parameters were explored in healthy subjects. Thirty-two healthy participants underwent 3D upper limb motion analysis during two sets of pointing movements on each side. They performed forward- and backward-pointing movements at a self-selected speed to a target located ahead at shoulder height and at 90% arm length, with and without a three-second pause between forward and backward movements. Kinematics were collected, and smoothness metrics were computed. LDLJ, NARJ and N0C found backward movements to be smoother, while SPARC found the opposite. Inter- and intra-subject coefficients of variation were lowest for SPARC. LDLJ, NARJ and N0C were correlated with each other and with movement time, unlike SPARC. There are major differences between smoothness metrics measured in the temporal domain (N0C, LDLJ, NARJ), which depend on movement time, and those measured in the frequency domain, the SPARC, which gave results opposite to the other metrics when comparing backward and forward movements.

Bounding Kolmogorov distances through Wasserstein and related integral probability metrics

We establish general upper bounds on the Kolmogorov distance between two probability distributions in terms of the distance between these distributions as measured with respect to the Wasserstein or smooth Wasserstein metrics. These bounds generalise existing results from the literature. To illustrate the broad applicability of our general bounds, we apply them to extract Kolmogorov distance bounds from multivariate normal, beta and variance-gamma approximations that have been established in the Stein's method literature.

The theorems about traces and extensions for functions from Nikolsky-Besov spaces with generalized mixed smoothness

The theory of embedding of spaces of differentiable functions studies important relations of differential (smoothness) properties of functions in various metrics and has wide application in the theory of boundary value problems of mathematical physics, approximation theory and other fields of mathematics. In this article, we prove the theorems about traces and extensions for functions from Nikolsky-Besov spaces with generalized mixed smoothness and mixed metrics. The proofs of the obtained results is based on the inequality of different dimensions for trigonometric polynomials in Lebesgue spaces with mixed metrics and the embedding theorem of classical Nikolsky-Besov spaces in the space of continuous functions.

Hodge modules and singular hermitian metrics

The purpose of this paper is to study certain notions of metric positivity called “minimal extension property” for the lowest nonzero piece in the Hodge filtration of a Hodge module. Let X be a complex manifold and let \(\mathcal {M}\) be a polarized pure Hodge module on X with strict support X. Let \(F_p\mathcal {M}\) be the smallest nonzero piece in the Hodge filtration. Assume that \(\mathcal {M}\) is smooth outside a closed analytic subset Z and let \(j:X\setminus Z \hookrightarrow X\) be the open embedding. Let h be the smooth hermitian metric on \(F_p\mathcal {M}|_{X\setminus Z}\) induced by the polarization. We show that the canonical morphism of \(\mathcal {O}_X\)-modules $$\begin{aligned} F_p\mathcal {M}\rightarrow j_{*}(F_p\mathcal {M}|_{X\setminus Z}) \end{aligned}$$induces an isomorphism between \(F_p\mathcal {M}\) and the subsheaf of \(j_{*}(F_p\mathcal {M}|_{X\setminus Z})\) consisting of sections which are locally \(L^2\) near Z with respect to h and the standard Lebesgue measure on X. In particular, h extends to a singular hermitian metric on \(F_p\mathcal {M}\) with minimal extension property.

Mapping of the Upper Limb Work-Space: Benchmarking Four Wrist Smoothness Metrics

Smoothness is a commonly used measure of motion control. Physiological motion is characterized by high smoothness in the upper limb workspace. Moreover, there is evidence that smoothness-based models describe effectively skilled motion planning. Typical smoothness measures are based on wrist kinematics. Despite smoothness being often used as a measure of motor control and to evaluate clinical pathologies, so far, a smoothness map is not available for the whole workspace of the upper limb. In this work, we provide a map of the upper limb workspace comparing four smoothness metrics: the normalized jerk, the speed metric, the spectral arc length, and the number of speed peaks. Fifteen subjects were enrolled, performing several reaching movements in the upper limb workspace in multiple directions in five planes (frontal, left, right, horizontal and up). Smoothness of the wrist of each movement was computed and a 3D workspace map was reconstructed. The four smoothness metrics were in general accordance. Lower smoothness was found in the less dexterous sectors (up and left sectors), with respect to the frontal, horizontal, and right sectors. The number of speed peaks, frequently used for evaluating motion in neurological diseases, was instead not suitable for assessing movements of healthy subjects. Lastly, strong correlation was found especially between the normalized jerk and speed metric. These results can be used as a benchmark for motor control studies in various fields as well as clinical studies.

Some Inequalities of Hardy Type Related to Witten–Laplace Operator on Smooth Metric Measure Spaces

A complete Riemannian manifold equipped with some potential function and an invariant conformal measure is referred to as a complete smooth metric measure space. This paper generalizes some integral inequalities of the Hardy type to the setting of a complete non-compact smooth metric measure space without any geometric constraint on the potential function. The adopted approach highlights some criteria for a smooth metric measure space to admit Hardy inequalities related to Witten and Witten p-Laplace operators. The results in this paper complement in several aspect to those obtained recently in the non-compact setting.

Noncollapsed degeneration of Einstein 4–manifolds, I

A theorem of Anderson and Bando-Kasue-Nakajima from 1989 states that to compactify the set of normalized Einstein metrics with a lower bound on the volume and an upper bound on the diameter in the Gromov-Hausdorff sense, one has to add singular spaces called Einstein orbifolds, and the singularities form as blow-downs of Ricci-flat ALE spaces. This raises some natural issues, in particular: can all Einstein orbifolds be Gromov-Hausdorff limits of smooth Einstein manifolds? Can we describe more precisely the smooth Einstein metrics close to a given singular one? In this first paper, we prove that Einstein manifolds sufficiently close, in the Gromov-Hausdorff sense, to an orbifold are actually close to a gluing of model spaces in suitable weighted H\"older spaces. The proof consists in controlling the metric in the neck regions thanks to the construction of optimal coordinates. This refined convergence is the cornerstone of our subsequent work on the degeneration of Einstein metrics or, equivalently, on the desingularization of Einstein orbifolds in which we show that all Einstein metrics Gromov-Hausdorff close to an Einstein orbifold are the result of a gluing-perturbation procedure. This procedure turns out to be generally obstructed, and this provides the first obstructions to a Gromov-Hausdorff desingularization of Einstein orbifolds.