Dimensional Metrics Research Articles

Morphology of Barchan Dunes on Earth and Mars: Classification and Scale‐Invariance

AbstractMorphological characteristics were measured for barchan dunes on Earth (2,686 dunes in 30 barchan fields) and Mars (720 dunes in 10 barchan fields) using satellite images. The data were used to (a) develop a new barchan classification system; (b) compare characteristics of barchans on Earth and Mars; and (c) assess whether barchans, in bulk, display allometric or scale‐invariant characteristics. Dimensional metrics were obtained for the width and length of barchan bodies, the width and length of barchans including the horns, and the length of each horn. Dimensionless metrics were derived for the ratios of the body width to the width between the tips of the horns (width ratio), the length of the entire barchan to the length of the body (length ratio), and the length of the longer horn to the shorter horn (symmetry ratio). The width, length, and symmetry ratios were used to classify barchans into eight types and compare the characteristics of their distributions on the two planets. From this analysis, it was established that, statistically, barchans on Earth are distinctive from those on Mars based on the morphometrics, with terrestrial barchans being, on average, of smaller size and more often symmetrical, while Martian barchans more often have convergent horns that are short relative to the central dune body and are more often asymmetrical. The analysis further reveals that barchan planform morphology can be considered scale‐invariant, and we argue that body width is the most appropriate measure representing barchan size.

Approximation schemes for Min-Sum [formula omitted]-Clustering

We consider the Min-Sum k-Clustering (k-MSC) problem. Given a set of points in a metric which is represented by an edge-weighted graph G=(V,E) and a parameter k, the goal is to partition the points V into k clusters such that the sum of distances between all pairs of the points within the same cluster is minimized.The k-MSC problem is known to be APX-hard on general metrics. The best known approximation algorithms for the problem obtained by Behsaz et al. (2019) achieve an approximation ratio of O(log|V|) in polynomial time for general metrics and an approximation ratio 2+ϵ in quasi-polynomial time for metrics with bounded doubling dimension. No approximation schemes for k-MSC (when k is part of the input) is known for any non-trivial metrics prior to our work. In fact, most of the previous works rely on the simple fact that there is a 2-approximate reduction from k-MSC to the balanced k-median problem and design approximation algorithms for the latter to obtain an approximation for k-MSC.In this paper, we obtain the first Quasi-Polynomial Time Approximation Schemes (QPTAS) for the problem on metrics induced by graphs of bounded treewidth, graphs of bounded highway dimension, graphs of bounded doubling dimensions (including fixed dimensional Euclidean metrics), and planar and minor-free graphs. We bypass the barrier of 2 for k-MSC by introducing a new clustering problem, which we call min-hub clustering, which is a generalization of balanced k-median and is a trade off between center-based clustering problems (such as balanced k-median) and pair-wise clustering (such as Min-Sum k-clustering). We then show how one can find approximation schemes for Min-hub clustering on certain classes of metrics.

Mapping neural correlates of biological motion perception in autistic children using high-density diffuse optical tomography

BackgroundAutism spectrum disorder (ASD), a neurodevelopmental disorder defined by social communication deficits plus repetitive behaviors and restricted interests, currently affects 1/36 children in the general population. Recent advances in functional brain imaging show promise to provide useful biomarkers of ASD diagnostic likelihood, behavioral trait severity, and even response to therapeutic intervention. However, current gold-standard neuroimaging methods (e.g., functional magnetic resonance imaging, fMRI) are limited in naturalistic studies of brain function underlying ASD-associated behaviors due to the constrained imaging environment. Compared to fMRI, high-density diffuse optical tomography (HD-DOT), a non-invasive and minimally constraining optical neuroimaging modality, can overcome these limitations. Herein, we aimed to establish HD-DOT to evaluate brain function in autistic and non-autistic school-age children as they performed a biological motion perception task previously shown to yield results related to both ASD diagnosis and behavioral traits.MethodsWe used HD-DOT to image brain function in 46 ASD school-age participants and 49 non-autistic individuals (NAI) as they viewed dynamic point-light displays of coherent biological and scrambled motion. We assessed group-level cortical brain function with statistical parametric mapping. Additionally, we tested for brain-behavior associations with dimensional metrics of autism traits, as measured with the Social Responsiveness Scale-2, with hierarchical regression models.ResultsWe found that NAI participants presented stronger brain activity contrast (coherent > scrambled) than ASD children in cortical regions related to visual, motor, and social processing. Additionally, regression models revealed multiple cortical regions in autistic participants where brain function is significantly associated with dimensional measures of ASD traits.LimitationsOptical imaging methods are limited in depth sensitivity and so cannot measure brain activity within deep subcortical regions. However, the field of view of this HD-DOT system includes multiple brain regions previously implicated in both task-based and task-free studies on autism.ConclusionsThis study demonstrates that HD-DOT is sensitive to brain function that both differentiates between NAI and ASD groups and correlates with dimensional measures of ASD traits. These findings establish HD-DOT as an effective tool for investigating brain function in autistic and non-autistic children. Moreover, this study established neural correlates related to biological motion perception and its association with dimensional measures of ASD traits.

Polynomial Equivalence of Complexity Geometries

This paper proves the polynomial equivalence of a broad class of definitions of quantum computational complexity. We study right-invariant metrics on the unitary group—often called `complexity geometries' following the definition of quantum complexity proposed by Nielsen—and delineate the equivalence class of metrics that have the same computational power as quantum circuits. Within this universality class, any unitary that can be reached in one metric can be approximated in any other metric in the class with a slowdown that is at-worst polynomial in the length and number of qubits and inverse-polynomial in the permitted error. We describe the equivalence classes for two different kinds of error we might tolerate: Killing-distance error, and operator-norm error. All metrics in both equivalence classes are shown to have exponential diameter; all metrics in the operator-norm equivalence class are also shown to give an alternative definition of the quantum complexity class BQP. My results extend those of Nielsen et al., who in 2006 proved that one particular metric is polynomially equivalent to quantum circuits. The Nielsen et al. metric is incredibly highly curved. I show that the greatly enlarged equivalence class established in this paper also includes metrics that have modest curvature. I argue that the modest curvature makes these metrics more amenable to the tools of differential geometry, and therefore makes them more promising starting points for Nielsen's program of using differential geometry to prove complexity lowerbounds. In a previous paper my collaborators and I—inspired by the UV/IR decoupling that happens in the phenomenon of renormalization—conjectured that high- dimensional metrics that look very different at short scales will often nevertheless give rise at long scales to the same emergent effective geometry. The results of this paper provide evidence for those conjectures, since many complexity metrics that have radically different penalty factors and therefore radically different short- distance properties are shown to belong to the same long-distance equivalence class.

ADQE: Obtain Better Deep Learning Models by Evaluating the Augmented Data Quality Using Information Entropy

Data augmentation, as a common technique in deep learning training, is primarily used to mitigate overfitting problems, especially with small-scale datasets. However, it is difficult for us to evaluate whether the augmented dataset truly benefits the performance of the model. If the training model is relied upon in each case to validate the quality of the data augmentation and the dataset, it will take a lot of time and resources. This article proposes a simple and practical approach to evaluate the quality of data augmentation for image classification tasks, enriching the theoretical research on data augmentation quality evaluation. Based on the information entropy, multiple dimensional metrics for data quality augmentation are established, including diversity, class balance, and task relevance. Additionally, a comprehensive data augmentation quality fusion metric is proposed. Experimental results on the CIFAR-10 and CUB-200 datasets show that our method maintains optimal performance in a variety of scenarios. The cosine similarity between the score of our method and the precision of model is up to 99.9%. A rigorous evaluation of data augmentation quality is necessary to guide the improvement of DL model performance. The quality standards and evaluation defined in this article can be utilized by researchers to train high-performance DL models in situations where data are limited.

Simple Rules for Parachute Inflation Testing at Underscale and Performance Extrapolation to Full-Scale

Testing smaller-sized parachutes in the hopes of extrapolating inflation performance to large-scale parachutes () has been a long-sought goal in decelerator systems research and development. Using a new approach based on the momentum-impulse theorem, this paper discusses how the nondimensional and dimensional metrics of peak drag are related to several dimensionless inputs driving the relevant physics at any scale, namely, the mass ratio, the Froude number, and the Reynolds number. This input list is further expanded to probe the size scaling of inflation duration, another important driver of peak drag. The result is the inclusion of the canopy stiffness index to the list, as well as of a new so-called volume-surface-diameter ratio, a parametrization of the filled canopy volume (postinflation) per unit of initial skirt cross-section area and canopy diameter. The dynamical relationships that result yield so-called “underscale” construction dimensions and deployment conditions that inform inflation performance at the larger scale. Interestingly, not all small-scale parachute systems can achieve this, unless dropped at impractical speeds and altitudes. Finally, it is shown how these rules differ, depending on what to match at both scales: that is, matching to get the same nondimensional peak drag or the same (dimensional) peak drag per canopy area.

Deep-learned generators of porosity distributions produced during metal Additive Manufacturing

Laser Powder Bed Fusion has become a widely adopted method for metal Additive Manufacturing (AM) due to its ability to mass produce complex parts with increased local control. However, AM produced parts can be subject to undesirable porosity, negatively influencing the properties of printed components. Thus, controlling porosity is integral for creating effective parts. A precise understanding of the porosity distribution is crucial for accurately simulating potential fatigue and failure zones. Previous research on generating synthetic porous microstructures have succeeded in generating parts with high density, isotropic porosity distributions but are often inapplicable to cases with sparser, boundary-dependent pore distributions. Our work bridges this gap by providing a method that considers these constraints by deconstructing the generation problem into its constitutive parts. A framework is introduced that combines Generative Adversarial Networks with Mallat Scattering Transform-based autocorrelation methods to construct novel realizations of the individual pore geometries and surface roughness, then stochastically reconstruct them to form realizations of a porous printed part. The generated parts are compared to the existing experimental porosity distributions based on statistical and dimensional metrics, such as nearest neighbor distances, pore volumes, pore anisotropies and scattering transform based auto-correlations.

Tumor Size Measurements for Predicting Hodgkin's and Non-Hodgkin's Lymphoma Response to Treatment.

The purpose of this study was to investigate the value of tumor size measurements as prognostic indicators of treatment outcome of Hodgkin’s and Non-Hodgkin’s lymphomas. 18F-FDG PET/CT exams before and after treatment were analyzed and metabolic and anatomic parameters—tumor maximum diameter, tumor maximum area, tumor volume, and maximum standardized uptake value (SUVmax)—were determined manually by an expert and automatically by a computer algorithm on PET and CT images. Results showed that the computer algorithm measurements did not correlate well with the expert’s standard maximum tumor diameter measurements but yielded better three dimensional metrics that could have clinical value. SUVmax was the strongest prognostic indicator of the clinical outcome after treatment, followed by the automated metabolic tumor volume measurements and the expert’s metabolic maximum diameter measurements. Anatomic tumor measurements had poor prognostic value. Metabolic volume measurements, although promising, did not significantly surpass current standard of practice, but automated measurements offered a significant advantage in terms of time and effort and minimized biases and variances in the PET measurements. Overall, considering the limited value of tumor size in predicting response to treatment, a paradigm shift seems necessary in order to identify robust prognostic markers in PET/CT; radiomics, namely combinations of anatomy, metabolism, and imaging, may be an option.

γ-Metrics in higher dimensions

We introduce five and higher dimensional γ-metrics. The higher dimensional metrics are exact solutions of the vacuum field equations and represent new types of singularities. For dimensions d>5 we have obtained γ-metrics in flat coordinates. We obtain singularities of metrics and for a better understanding of geometrical and physical properties of the five dimensional metric, stable circular orbits are determined by means of the effective potential. Effect of the deformed parameter (γ) on redshift of the γ-metrics are calculated. Interior solution for the five-dimensional γ-metric is also obtained.

T-copula and Wasserstein distance-based stochastic neighbor embedding

The aim of dimensionality reduction is to obtain the faithful low-dimensional representations of high-dimensional data by preserving the data quality. It is beneficial to better visualize the high-dimensional data and improve the classification or clustering performance. Many dimensionality reduction methods based on the framework of stochastic neighbor embedding have been developed. However, most of them use the Euclidean distance to describe the dissimilarity of data points in high-dimensional space, which is not suitable for high-dimensional data with non-linear manifold structure. In addition, they usually use the family of normal distributions as their embedding distributions in low-dimensional space. This will incur that they are only suitable to deal with the spherical data. In order to deal with these issues, we present a novel dimensionality reduction method by integrating the Wasserstein distance and t-copula function into the stochastic neighbor embedding model. We first employ the Gaussian distribution equipped with the Wasserstein distance to describe the pairwise similarity in the high-dimensional space. Then, the t-copula function is used to generate a general heavy-tailed distribution for the description of low-dimensional pairwise similarity, which can process different shapes of data and avoid the crowding problem. Furthermore, Kullback–Leibler divergence is employed to measure the difference between the high-dimensional and low-dimensional similarities. Finally, a gradient descent algorithm with adaptive moment estimation is developed to solve the proposed objective function. Extensive experiments are conducted on eight real-world datasets to demonstrate the effectiveness of the proposed method in terms of the dimensional reduction quality, classification and clustering evaluation metrics.

Free data at spacelike {mathscr {I}} and characterization of Kerr-de Sitter in all dimensions

We study the free data in the Fefferman–Graham expansion of asymptotically Einstein (n+1)-dimensional metrics with non-zero cosmological constant. We analyze the relation between the electric part of the rescaled Weyl tensor at {mathscr {I}}, D, and the free data at {mathscr {I}}, namely a certain traceless and transverse part of the n-th order coefficient of the expansion mathring{g}_{(n)}. In the case Lambda <0 and Lorentzian signature, it was known [23] that conformal flatness at {mathscr {I}} is sufficient for D and mathring{g}_{(n)} to agree up to a universal constant. We recover and extend this result to general signature and any sign of non-zero Lambda . We then explore whether conformal flatness of {mathscr {I}} is also neceesary and link this to the validity of long-standing open conjecture that no non-trivial purely magnetic Lambda -vacuum spacetimes exist. In the case of {mathscr {I}} non-conformally flat we determine a quantity constructed from an auxiliary metric which can be used to retrieve mathring{g}_{(n)} from the (now singular) electric part of the Weyl tensor. We then concentrate in the Lambda >0 case where the Cauchy problem at {mathscr {I}} of the Einstein vacuum field equations is known to be well-posed when the data at {mathscr {I}} are analytic or when the spacetime has even dimension. We establish a necessary and sufficient condition for analytic data at {mathscr {I}} to generate spacetimes with symmetries in all dimensions. These results are used to find a geometric characterization of the Kerr-de Sitter metrics in all dimensions in terms of its geometric data at null infinity.

Identification of influencers in online social networks: measuring influence considering multidimensional factors exploration

Online Social networks exhibit heterogeneous nature with nodes playing far different roles in structure and function. To identify influencers is thus very significant, allowing us to control the outbreak of public negative opinion, to conduct advertisements for e-commercial products, to predict popular scientific publications, and so on. The identification of influencers attracts increasing attentions from both computer science and communication science, with multiple dimensional metrics ranging from structure-based to information-based and action-based. However, most work simply rely on one dimensional metrics. Therefore, in this paper, we analyze three dimensional characteristics (structure-based, information-based, and action-based factors) to develop the multidimensional social influence (MSI) measurement approach. With topic distillation and conditional expectation, the MSI approach can not only measure users topic-level influence, but also measure users global-level influence. Based on data collected from SinaWeibo.com, the experimental results show that the proposed framework outperforms two traditional methods (LeaderRank and FBI) both on the topic-level and the global-level. The proposed framework can be effectively applied to promote word-of-mouth marketing, and to steer public opinion in certain directions, even to support decisions during a negotiation process.

Configurational-based institutional analysis: Unbundling the multi-dimensional state fragility construct

To guide researchers interested in replicating our configurational approach to comparative institutional analysis, we report on a methodology that builds from existing state fragility indices to differentiate between types of state fragility in 189 countries across the world. We first present the steps we used to identify three constituent dimensions of state fragility. We then report how we configured these first-order institutional measures to build a large-N, fuzzy set qualitative set analysis (fs/QCA) of variation in the degree and type of informal economic sectors found across the world. Our discussion of the methodology shows that:•Configurational-based analysis requires unbundling aggregate measures into constituent dimensions as a first step to analyzing possible systemic interactions.•Configurational-based analysis recognizes sources of cross-national diversity that aggregated or single dimensional metrics are unable to fully capture.

Perfect fluid filled universe in odd dimensional pure Lovelock gravity

It is well known that d = 2 N + 1 dimensional pure Lovelock metrics do not describe bounded distributions neither do they admit nontrivial vacuum solutions. On this basis it has been variously claimed that matter fields should be nondynamical. However, from earlier work it has long been demonstrated fairly generally that 2 N + 1 pure Lovelock solutions are not kinematic. In this work we find perfect fluid filled universes with d = 2 N + 1 that exhibit curvature of spacetime. New classes of exact solutions for pure Gauss–Bonnet gravity ( N = 2 ) are generated by integrating the pressure isotropy condition with suitable metric potential choices for the critical spacetime dimension 5. Amongst the physically important cases we study are the Vaidya–Tikekar superdense star ansatz, the Finch–Skea model as well as isothermal fluids. The physical properties are analysed with the aid of graphical plots and the model is found to be causal and stable in the sense of Chandrasekhar and satisfies the energy conditions. Finally we examine the most general Lovelock polynomials for all N and d = 2 N + 1 . In particular the special case N = 3 , d = 7 has not been considered previously in the literature and we discover a number of classes of exact solutions for this case.

Insomnia, Alcohol Consumption and ADHD Symptoms in Adults.

IntroductionSubstance use disorders and insomnia are common in the general population, and particularly among adults with attention-deficit/hyperactivity disorder (ADHD). Here we investigated the relationship between insomnia, alcohol consumption and ADHD symptoms.MethodsAdults with an ADHD diagnosis (n = 235, 41.3% males) and controls (n = 184, 38% males) completed a questionnaire assessing insomnia (Bergen Insomnia Scale), alcohol consumption (Alcohol Use Disorders Identification Test), and current ADHD symptoms (Adult ADHD Self-report Scale). The majority of the sample (95%) gave additional information about childhood ADHD symptoms (Wender Utah Rating Scale), and information about lifetime occurrence of an internalizing disorder was included as part of background information.ResultsCompared to controls, the ADHD group reported a higher frequency of insomnia, a higher quantity of consumed alcohol and a higher frequency of internalizing disorders. Current and childhood ADHD symptoms were more severe in those with than without insomnia. Scores on ADHD symptom scales were explained by the presence of insomnia and internalizing disorders, while the contribution from alcohol consumption was restricted to the control group.DiscussionThe high functional impact of insomnia, alcohol misuse and internalizing disorders is well known. The present study contributed by focusing on their relations to ADHD symptoms, and by showing that strong relations were not restricted to adults with a clinical ADHD diagnosis. By this, the results put a critical light on a categorical delineation between adults with an ADHD diagnosis and population selected controls, and call for further studies including dimensional metrics of ADHD symptoms and co-occurring problems.

The Value of Alpha SPF Roofing: An Alpha Case Study at William Lipscomb Elementary School

An Alpha roof is a type of Spray Polyurethane Foam (SPF) roofing system that has been documented to be one of the highest performing roofs in the industry. Despite the high level of performance of the Alpha SPF roofs, owners still try to protect themselves by purchasing warranties. When the Dallas Independent School District (DISD) did not receive enough funding to purchase the Alpha roofs for their school buildings, general contractors started shopping the Alpha contractors. The demand for Alpha roofs during DISD bond programs exceeded the supply of Alpha vendors. DISD lowered the requirements and the contractors and manufacturers delivered lower quality roofs. DISD still required the performance of the Alpha roofing system, even though they bought lower performing systems without the quality control requirements of the higher performing Alpha roofs. DISD was not happy with the lower performance on some of the inexpensive roofs. This paper describes a case study that proposes that high roof performance is a result of expert contractors proving their past performance, detailed preplanning, manufacturers doing quality control, contractors tracking their time and cost deviations and independent third party inspections. The expert Alpha contractor completed the project with the best dimensional stability metrics (dimensional stability is a metric of long lasting roofs). The roof installation was completed in 20 days and saved DISD over 20% of the cost of the roof, despite an increase in the scope of work. It was the first DISD project that had no punch-list items after the final walkthrough. DISD was extremely satisfied with the roof and the Alpha program demonstrated its effectiveness in the installation of roofs.

All the three dimensional Lorentzian metrics admitting three Killing vectors

We obtain all the three-dimensional Lorentzian metrics which admit three Killing vectors. The classification has been made with the aid of the formalism which exploits the obstruction criteria for the Killing equations recently developed by the present authors. The current classification method does not rely on the transitivity property of the isometry group. It turns out that the Lorentzian manifold harbors a much richer spectrum of metrics with various Segre types, compared to the Riemannian case.

Hierarchically measuring urban expansion in fast urbanizing regions using multi-dimensional metrics: A case of Wuhan metropolis, China

Measuring urban expansion is essential for sustainable growth management. However, many widely adopted methods are not suitable for measuring hierarchical urban expansion, particularly in rapidly growing regions. This study provides a framework for hierarchically measuring urban expansion using sub-dimensional, dimensional, and comprehensive metrics. The framework was applied in the Wuhan metropolis (WHM), China, during two 5-year periods from 2005 to 2015. The results show generally improved urban functions and land use conditions in the WHM during the time periods analyzed. However, single period-based sprawl and multi-temporal sprawling patterns remain evident in the WHM as evidenced by decreased accessibility to work opportunities, ecosystem services and natural landscapes, and land use density, as well as disorderly and unplanned land use in certain local areas. Findings derived from the empirical analyses in WHM indicate that the provided framework can demonstrate how gains in certain urban functionality may still occur in regions that have not experienced additional urban land expansion in the WHM. The framework is suitable for hierarchically measuring urban expansion in rapidly urbanizing areas exhibiting multi-temporal, mixed expansion patterns. The hierarchical framework and findings provided in the study contribute to urban expansion measurement and management in the WHM as well as other rapidly urbanizing regions around the world.

Three dimensional (3D) spatial metrics for objects

The increasing availability of lidar data and structure from motion processing techniques is moving pattern metric research toward the development of three-dimensional (3D) analysis. There is a need to develop spatial pattern metrics that leverage 3D datasets, such as those derived from lidar or unmanned aircraft systems technology, that are meaningful and interpretable across landscape contexts. We introduce a suite of 3D spatial pattern metrics that can be computed on gradient surfaces such as digital surface models, but are rooted in traditional, patch-based landscape metrics that are familiar and interpretable across landscape contexts. We compute a suite of 3D metrics and demonstrate their use by analyzing a landscape pattern in the built environment of New Orleans in 2002 and 2008—pre- and post- Hurricane Katrina. Lidar data are used to segment individual buildings and calculate 3D patterns at the equivalent of the patch-, class- and landscape-levels for traditional landscape metrics. 3D spatial metrics can characterize landscape patterns at multiple spatial scales. These metrics capture aspect of pattern that traditional patch-mosaic and surface metrics cannot. Future research can build from these measures to develop other measures of 3D spatial patterns that are applicable for different ecological contexts. Continuing advances in full waveform lidar may contribute to the development of more complex metrics.

A systematic literature review on social media metrics

When conducting activities on social media (SM), with strategies related to business aims, it is necessary to monitor the activity over time in order to improve the actions taken. This paper aims to provide a theoretical proposal of measurement framework, based on those analyzed through a literature review. The paper also proposes a classification of the SM performance control metrics, from which emerge five different categories of metrics: business activity, brand sharing, dimensional, engagement and business performance metrics. The research highlights: 1) the agreement among experts regarding the need to constantly measure the activity of SM marketing; 2) the need to have a measurement framework to base the control of the strategy; 3) the need to systematize measurement metrics.