Classical Distance Research Articles

A Representation of Cloth States based on a Derivative of the Gauss Linking Integral

Robotic manipulation of cloth is a complex task because of the infinite-dimensional shape-state space of textiles, which makes their state estimation very difficult. In this paper we introduce the dGLI Cloth Coordinates, a finite low-dimensional representation of cloth states that allows us to efficiently distinguish a large variety of different folded states, opening the door to efficient learning methods for cloth manipulation planning and control. Our representation is based on a directional derivative of the Gauss Linking Integral and allows us to represent spatial as well as planar folded configurations in a consistent and unified way. The proposed dGLI Cloth Coordinates are shown to be more accurate in the representation of cloth states and significantly more sensitive to changes in grasping affordances than other classic shape distance methods. Finally, we apply our representation to real images of a cloth, showing that with it we can identify the different states using a distance-based classifier.

MPED: Quantifying Point Cloud Distortion Based on Multiscale Potential Energy Discrepancy.

In this article, we propose a new distortion quantification method for point clouds, the multiscale potential energy discrepancy (MPED). Currently, there is a lack of effective distortion quantification for a variety of point cloud perception tasks. Specifically, in human vision tasks, a distortion quantification method is used to predict human subjective scores and optimize the selection of human perception task parameters, such as dense point cloud compression and enhancement. In machine vision tasks, a distortion quantification method usually serves as loss function to guide the training of deep neural networks for unsupervised learning tasks (e.g., sparse point cloud reconstruction, completion, and upsampling). Therefore, an effective distortion quantification should be differentiable, distortion discriminable, and have low computational complexity. However, current distortion quantification cannot satisfy all three conditions. To fill this gap, we propose a new point cloud feature description method, the point potential energy (PPE), inspired by classical physics. We regard the point clouds are systems that have potential energy and the distortion can change the total potential energy. By evaluating various neighborhood sizes, the proposed MPED achieves global-local tradeoffs, capturing distortion in a multiscale fashion. We further theoretically show that classical Chamfer distance is a special case of our MPED. Extensive experiments show that the proposed MPED is superior to current methods on both human and machine perception tasks. Our code is available at https://github.com/Qi-Yangsjtu/MPED.

Light strings and strong coupling in F-theory

We consider 4d mathcal{N} = 1 theories arising from F-theory compactifications on elliptically-fibered Calabi-Yau four-folds and investigate the non-perturbative structure of their scalar field space beyond the large volume/large complex structure regime. We focus on regimes where the F-theory field space effectively reduces to the deformation space of the worldsheet theory of a critical string obtained from a wrapped D3-brane. In case that this critical string is a heterotic string with a simple GLSM description, we identify new strong coupling singularities in the interior of the F-theory field space. Whereas from the perturbative perspective these singularities manifest themselves through a breakdown of the perturbative α′-expansion, the dual GLSM perspective reveals that at the non-perturbative level these singularities correspond to loci in field space along which the worldsheet theory of the critical D3-brane string breaks down and a 7-brane gauge theory becomes strongly coupled due to quantum effects. Therefore these singularities signal a transition to a strong coupling phase in the F-theory field space which can be shown to arise due to the failure of the F-theory field space to factorize between complex structure and Kähler sector at the quantum level. Such singularities are hence a feature of a genuine mathcal{N} = 1 theory without a direct counterpart in mathcal{N} = 2 theories in 4d. By relating our setup to recent studies of global string solutions associated to axionic strings we argue that the D3-brane string dual to the perturbative heterotic string leaves the spectrum of BPS strings when traversing into the strong coupling phase. The absence of the perturbative, critical heterotic string then provides a physical explanation for the breakdown of the perturbative expansion and the obstruction of certain classical infinite distance limits in accordance with the Emergent String Conjecture.

An exploration, analysis, and correction of the distance effect on terrestrial hyperspectral LiDAR data

Terrestrial hyperspectral light detection and ranging (LiDAR) (HSL), as one novel LiDAR system integrated with more wavelengths, has supplied enhanced possibilities in many fields by delivering the geographic coordinate and the hyperspectral backscattered intensity simultaneously. However, like the traditional single-wavelength LiDAR, it is faced with the distance effect, which restricts the accurate acquisition of the hyperspectral intensities and the quantitative retrieval of characteristics of the targets. The previously reported distance effect correction models mainly concentrated on the distance effect correction for the single-wavelength LiDAR system, and some normalization methods with the standard reflectance panel were also provided to calibrate the data measured by multispectral LiDAR and HSL, producing the reflectance-related value. Nevertheless, it is valuable to systematically explore the distance effect of HSL over long distances and search for the corresponding correction methods. Along these lines, in this study, the homogeneous targets and standard reflectance panels with different reflectance values were employed to participate in the distance experiment to systematically explore and analyze the distance effect phenomenon on terrestrial HSL data. A novel practical piecewise fitting model was proposed to output realistic correction results and it was also compared with the classic inverse distance square law and polynomial fitting model. To further demonstrate the feasibility and good capability, the models were employed in the intensity correction for the various vegetation leaf species. A simple 3-D scene experiment was then carried out to demonstrate the intensity variation before and after the implementation of the distance effect correction. From the acquired result, it suggests that (1) the distance effect on terrestrial HSL data is not related to the wavelength and the scanned target. All the wavelengths share a common distance effect; (2) the concept of the ‘distance effect function’ could represent well the distance effect for the terrestrial HSL; (3) as far as the correction ability is concerned, the proposed piecewise fitting model achieved better performance than the others because it exhibited the smallest standard deviation (σ), coefficient of variation (CV), and the ratio of the coefficient of variation (ε) for the correction results of the homogeneous targets, and the leaf experiments confirmed it again; and (4) the further 3-D experiment result exhibited the intensity variation. It proves that the distance effect does exist in the 3-D scanning results and the correction is necessary. Besides, for small-scanned scenes, the incidence angle effect dominates and largely affects the intensity data instead of the distance effect. This study enriches the study of the distance effect mechanism on the terrestrial HSL data, which facilitates the development of research on the radiative effect correction of the HSL. At the same time, the proposed model can be adopted for the analysis and correction of the distance effect on terrestrial HSL data in actual scanning tasks.

Sliced Wasserstein cycle consistency generative adversarial networks for fault data augmentation of an industrial robot

We investigate the role of the loss function in cycle consistency generative adversarial networks (CycleGANs). Namely, the sliced Wasserstein distance is proposed for this type of generative model. Both the unconditional and the conditional CycleGANs with and without squeeze-and-excitation mechanisms are considered. Two data sets are used in the evaluation of the models, i.e., the well-known MNIST and a real-world in-house data set acquired for an industrial robot fault diagnosis. A comprehensive set of experiments show that, for both the unconditional and the conditional cases, sliced Wasserstein distance outperforms classic Wasserstein distance in CycleGANs. For the robot faulty data augmentation a model compatibility of 99.73% (conditional case) and 99.21% (unconditional case) were observed. In some cases, the improvement in convergence efficiency was higher than 2 (two) orders of magnitude.

The DetectDeviatingCells algorithm was a useful addition to the toolkit for cellwise error detection in observational data

ObjectivesWe evaluated the error detection performance of the DetectDeviatingCells (DDC) algorithm which flags data anomalies at observation (casewise) and variable (cellwise) level in continuous variables. We compared its performance to other approaches in a simulated dataset. Study Design and SettingWe simulated height and weight data for hypothetical individuals aged 2–20 years. We changed a proportion of height values according to predetermined error patterns. We applied the DDC algorithm and other error-detection approaches (descriptive statistics, plots, fixed-threshold rules, classic, and robust Mahalanobis distance) and we compared error detection performance with sensitivity, specificity, likelihood ratios, predictive values, and receiver operating characteristic (ROC) curves. ResultsAt our chosen thresholds error detection specificity was excellent across all scenarios for all methods and sensitivity was higher for multivariable and robust methods. The DDC algorithm performance was similar to other robust multivariable methods. Analysis of ROC curves suggested that all methods had comparable performance for gross errors (e.g., wrong measurement unit), but the DDC algorithm outperformed the others for more complex error patterns (e.g., transcription errors that are still plausible, although extreme). ConclusionsThe DDC algorithm has the potential to improve error detection processes for observational data.

Open-Set Signal Recognition Based on Transformer and Wasserstein Distance

Open-set signal recognition provides a new approach for verifying the robustness of models by introducing novel unknown signal classes into the model testing and breaking the conventional closed-set assumption, which has become very popular in real-world scenarios. In the present work, we propose an efficient open-set signal recognition algorithm, which contains three key sub-modules: the signal representation sub-module based on a vision transformer (ViT) structure, a set distance metric sub-module based on Wasserstein distance, and a class space compression sub-module based on reciprocal point separation and central loss. In this algorithm, the representing features of signals are established based on transformer-based neural networks, i.e., ViT, in order to extract global information about time series-related data. The employed reciprocal point is used in modeling the potential unknown space without using the corresponding samples, while the distance metric between different class spaces is mathematically modeled in terms of the Wasserstein distance instead of the classical Euclidean distance. Numerical experiments on different open-set signal recognition tasks show that the proposed algorithm can significantly improve the recognition efficiency in both known and unknown categories.

Wildlife Population Assessment: Changing Priorities Driven by Technological Advances

Advances in technology are having a large effect on the priorities for innovation in statistical ecology. Collaborations between statisticians and ecologists have always been important in driving methodological development, but increasingly, expertise from computer scientists and engineers is also needed. We discuss changes that are occurring and that may occur in the future in surveys for estimating animal abundance. As technology advances, we expect classical distance sampling and capture-recapture to decrease in importance, as camera (still and video) survey, acoustic survey, spatial capture-recapture and genetic methods continue to develop and find new applications. We explore how these changes are impacting the work of the statistical ecologist.

On the hardness of the minimum distance problem of quantum codes

We study the hardness of the problem of finding the distance of quantum error-correcting codes. The analogous problem for classical codes is known to be NP-hard, even in approximate form. For quantum codes, various problems related to decoding are known to be NP-hard, but the hardness of the distance problem has not been studied before. In this work, we show that finding the minimum distance of stabilizer quantum codes exactly or approximately is NP-hard. This result is obtained by reducing the classical minimum distance problem to the quantum problem, using the CWS framework for quantum codes, which constructs a quantum code using a classical code and a graph. A main technical tool used for our result is a lower bound on the so-called graph state distance of 4-cycle free graphs. In particular, we show that for a 4-cycle free graph <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</i> , its graph state distance is either δ or δ + 1, where δ is the minimum vertex degree of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</i> . Due to a well-known reduction from stabilizer codes to CSS codes, our results also imply that finding the minimum distance of CSS codes is also NP-hard.

A connection between the density and temperature of the Lennard-Jones fluids at equilibrium and the first peak of the radial distribution function

A new method to obtain the density and temperature of the Lennard–Jones fluids at equilibrium from the height and the displacement of the first peak of the radial distribution function (RDF) is presented here. The density range and temperature range covered are 0.5≤ρ*≤1.2, 0.2≤β*≤2.0 with ρ*=ρσ3 andβ*=ϵ/kBT being the reduced density and temperature, respectively. Numerically, 152 state points (ρ*,β*) are obtained with Δρ*=0.1 and Δβ*=0.1 by molecular dynamics (MD) simulations. More than 10000 configurations are output for each state point. The RDFs are then obtained through classical distance histogram method. The stability of the RDF is found to be related to the number of configurations because of ensemble average. Two correlations establishing the relation of the height of the first peak of the RDF versus the density and temperature and the relation of the displacement of the first peak of the RDF versus the density and temperature are empirically constructed by fitting 40 state points out of 152. Other 112 state points are used to estimate the accuracy of the two correlations proposed. It is found that all of the 112 state points can be correctly predicted. These results indicate that the RDF can be conveniently used to assure the state point (ρ*,β*) of the Lennard–Jones fluids at equilibrium. The importance of the present work is that a clear connection between a special point of the RDF, i.e., its first peak, and the state point (ρ*,β*) is firstly empirically built up. Their one to one map is observed.

Dynamic Editing Distance-based Extracting Relevant Information Approach from Social Networks

Online social networks, such as Facebook, Twitter, LinkedIn, etc., have grown exponentially in recent times with a large amount of information. These social networks have huge volumes of data especially in structured, textual, and unstructured forms which have often led to cyber-crimes like cyber terrorism, cyber bullying, etc., and extracting information from these data has now become a serious challenge in order to ensure the data safety. In this work, we propose a new, supervised approach for Information Extraction (IE) from Web resources based on remote dynamic editing, called EIDED. Our approach is part of the family of IE approaches based on masks extraction and is articulated around three algorithms: (i) a labeling algorithm, (ii) a learning and inference algorithm, and (iii) an extended edit distance algorithm. Our proposed approach is able to work even in the presence of anomalies in the tuples such as missing attributes, multivalued attributes, permutation of attributes, and in the structure of web pages. The experimental study, which we conducted, on a standard database of web pages, shows the performance of our EIDED approach compared to approaches based on the classic edit distance, and this with respect to the standard metrics recall coefficient, precision, and F1-measure.

Population Classification Model of Liaoning Province Based on Cluster Analysis

Aiming at the problem of urban shrinkage in Liaoning Province, this paper established a population classification model by systematic clustering method. Based on two indicators of population contraction and GDP contraction, we defined the shrinkage rate, and classified 30 cities in Liaoning Province according to the shrinkage rate. Firstly, the weights of population contraction and GDP contraction were calculated by using the analytic hierarchy process. Secondly, the average annual growth rate of the two is weighted, and the shrinkage rate is defined as the weighted value. Then, based on the systematic clustering method, the population classification model was established by using the classical Euclidean distance, and the 30 cities were classified by SPSS software. The results of this paper on shrinking cities have important reference value for examining the future development trend of a city.

On a Combinatorial Approach to Studying the Steiner Diameter of a Graph and Its Line Graph

In 1989, Chartrand, Oellermann, Tian and Zou introduced the Steiner distance for graphs. This is a natural generalization of the classical graph distance concept. Let Γ be a connected graph of order at least 2, and S\V(Γ). Then, the minimum size among all the connected subgraphs whose vertex sets contain S is the Steiner distancedΓ(S) among the vertices of S. The Steiner k-eccentricity ek(v) of a vertex v of Γ is defined by ek(v)=max{dΓ(S)|S\V(Γ),|S|=k,andv∈S}, where n and k are two integers, with 2≤k≤n, and the Steiner k-diameter of Γ is defined by sdiamk(Γ)=max{ek(v)|v∈V(Γ)}. In this paper, we present an algorithm to derive the Steiner distance of a graph; in addition, we obtain a relationship between the Steiner k-diameter of a graph and its line graph. We study various properties of the Steiner diameter through a combinatorial approach. Moreover, we characterize graph Γ when sdiamk(Γ) is given, and we determine sdiamk(Γ) for some special graphs. We also discuss some of the applications of Steiner diameter, including one in education networks.

Collaborative and individual learning of geography in immersive virtual reality: An effectiveness study.

Many university-taught courses moved to online form since the outbreak of the global pandemic of coronavirus disease (COVID-19). Distance learning has become broadly used as a result of the widely applied lockdowns, however, many students lack personal contact in the learning process. A classical web-based distance learning does not provide means for natural interpersonal interaction. The technology of immersive virtual reality (iVR) may mitigate this problem. Current research has been aimed mainly at specific instances of collaborative immersive virtual environment (CIVE) applications for learning. The fields utilizing iVR for knowledge construction and skills training with the use of spatial visualizations show promising results. The objective of this study was to assess the effectiveness of collaborative and individual use of iVR for learning geography, specifically training in hypsography. Furthermore, the study’s goals were to determine whether collaborative learning would be more effective and to investigate the key elements in which collaborative and individual learning were expected to differ–motivation and use of cognitive resources. The CIVE application developed at Masaryk University was utilized to train 80 participants in inferring conclusions from cartographic visualizations. The collaborative and individual experimental group underwent a research procedure consisting of a pretest, training in iVR, posttest, and questionnaires. A statistical comparison between the geography pretest and posttest for the individual learning showed a significant increase in the score (p = 0.024, ES = 0.128) and speed (p = 0.027, ES = 0.123), while for the collaborative learning, there was a significant increase in the score (p<0.001, ES = 0.333) but not in speed (p = 1.000, ES = 0.000). Thus, iVR as a medium proved to be an effective tool for learning geography. However, comparing the collaborative and individual learning showed no significant difference in the learning gain (p = 0.303, ES = 0.115), speed gain (p = 0.098, ES = 0.185), or performance motivation (p = 0.368, ES = 0.101). Nevertheless, the collaborative learning group had significantly higher use of cognitive resources (p = 0.046, ES = 0.223) than the individual learning group. The results were discussed in relation to the cognitive load theories, and future research directions for iVR learning were proposed.

General eccentric distance sum of graphs with given diameter

For [Formula: see text], the general eccentric distance sum of a connected graph [Formula: see text] is defined as [Formula: see text], where [Formula: see text] is the vertex set of [Formula: see text], [Formula: see text] is the eccentricity of [Formula: see text], [Formula: see text] and [Formula: see text] is the distance between vertices [Formula: see text] and [Formula: see text] in [Formula: see text]. For [Formula: see text] and [Formula: see text], we present the graphs having the smallest general eccentric distance sum among graphs with given order and diameter, and among bipartite graphs with given order and odd diameter. The extremal graphs for the classical eccentric distance sum are corollaries of our results on the general eccentric distance sum.

OUTLIER DETECTION ON HIGH DIMENSIONAL DATA USING MINIMUM VECTOR VARIANCE (MVV)

High-dimensional data can occur in actual cases where the variable p is larger than the number of observations n. The problem that often occurs when adding data dimensions indicates that the data points will approach an outlier. Outliers are part of observations that do not follow the data distribution pattern and are located far from the data center. The existence of outliers needs to be detected because it can lead to deviations from the analysis results. One of the methods used to detect outliers is the Mahalanobis distance. To obtain a robust Mahalanobis distance, the Minimum Vector Variance (MVV) method is used. This study will compare the MVV method with the classical Mahalanobis distance method in detecting outliers in non-invasive blood glucose level data, both at p&gt;n and n&gt;p. The test results show that the MVV method is better for n&gt;p. MVV shows more effective results in identifying the minimum data group and outlier data points than the classical method.

Energy minimizing order picker forklift routing problem

The material handling systems used in warehouses involve important operations such as the usage of order picker forklifts. These order picker forklifts provide efficient utilization of the storage space by their ability in moving in narrow aisles and picking items from high level racks. Routing the order picker forklifts to pick ordered items belongs to the operational decision level and is done in high frequency. Therefore, finding an energy-efficient route for an order picker forklift can yield significant savings in the energy consumption in warehouses and the resulting CO2 emission. In this paper, we introduce and study the energy minimizing order picker forklift routing problem (EMFRP) which aims to find an energy-efficient route for an order picker forklift to pick a given list of items. To our knowledge, this is the first study that considers the order picker forklifts in the context of the order picking problem. We calculate the forklift’s energy consumption in both horizontal and vertical moves considering the effects of friction forces, the acceleration and deceleration of the forklift, and its load. A mixed integer programming formulation and a dynamic programming approach are developed to solve small size instances of the EMFRP exactly. To solve larger instances, we provide tour construction and tour improvement heuristics and integrate them into a single solution approach. Computational results show that the proposed heuristic approach finds high quality solutions. Moreover, it is observed that significant energy savings can be achieved by solving the EMFRP instead of the classical distance minimization problem.

A genetic programming approach to WiFi fingerprint meta-distance learning

Driven by the continuous growth in the number of mobile smart devices, location-based services are becoming a fundamental aspect in the ubiquitous computing domain. In this work, we focus on indoor scenarios, where positioning supports tasks such as navigation, logistics, and access management and control. Most indoor positioning solutions are based on WiFi fingerprinting, thanks to its ease of deployment. Such a technique often requires the adoption of a suitable distance metric to compare the currently observed WiFi access points with those pertaining to fingerprints contained in a database, and whose position is already known. Results from the literature make it evident that classical distance functions among WiFi fingerprints do not preserve spatial information in its entirety. Here, we explore the possibility of addressing such a shortcoming by combining a selection of fingerprint distance functions into a meta-distance, using a genetic programming approach to solve a symbolic regression problem. The outcomes of the investigation, based on 16 publicly available datasets, show that a small, but statistically relevant, improvement can be achieved in preserving spatial information, and that the developed meta-distance has a generalization capability no worse than top-performing classical fingerprint distance functions when trained on a dataset and tested on the others. In addition, when used within a k-nearest-neighbor positioning framework, the meta-distance outperforms all the contenders, despite not being expressly designed to support position estimation. This sheds a light on a significant relationship between preservation of spatial information and localization performance. The achieved results pave the way for the development of more advanced metric learning solutions, that go beyond the limitations of currently-employed fingerprint distance functions.

Quantum chaos in supersymmetric quantum mechanics: An exact diagonalization study

We use exact diagonalization to study energy level statistics and out-of-time-order correlators (OTOCs) for the simplest supersymmetric extension $\hat{H}_S = \hat{H}_B \otimes I + \hat{x}_1 \otimes \sigma_1 + \hat{x}_2 \otimes \sigma_3$ of the bosonic Hamiltonian $\hat{H}_B = \hat{p}_1^2 + \hat{p}_2^2 + \hat{x}_1^2 \, \hat{x}_2^2$. For a long time, this bosonic Hamiltonian was considered one of the simplest systems which exhibit dynamical chaos both classically and quantum-mechanically. Its structure closely resembles that of spatially compactified pure Yang-Mills theory. Correspondingly, the structure of our supersymmetric Hamiltonian is similar to that of spatially compactified supersymmetric Yang-Mills theory, also known as the BFSS model. We present numerical evidence that a continuous energy spectrum of the supersymmetric model leads to monotonous growth of OTOCs down to the lowest temperatures, which is also expected for the BFSS model from holographic duality. This growth is saturated by low-energy eigenstates with effectively one-dimensional wave functions and a completely non-chaotic energy level distribution. We observe a sharp boundary separating these low-energy states from the bulk of chaotic high-energy states. Our data suggests, although with a limited confidence, that at low temperatures the OTOC growth might be exponential over a finite range of time, with the corresponding Lyapunov exponent scaling linearly with temperature. In contrast, the gapped low-energy spectrum of the bosonic Hamiltonian leads to oscillating OTOCs at low temperatures without any signatures of exponential growth. We also find that the OTOCs for the bosonic Hamiltonian are never sufficiently close to the classical Lyapunov distance. On the other hand, the OTOCs for the supersymmetric system agree with the classical limit reasonably well over a finite range of temperatures and evolution times.

Choosing Among Notions of Multivariate Depth Statistics

Classical multivariate statistics measures the outlyingness of a point by its Mahalanobis distance from the mean, which is based on the mean and the covariance matrix of the data. A multivariate depth function is a function which, given a point and a distribution in d-space, measures centrality by a number between 0 and 1, while satisfying certain postulates regarding invariance, monotonicity, convexity and continuity. Accordingly, numerous notions of multivariate depth have been proposed in the literature, some of which are also robust against extremely outlying data. The departure from classical Mahalanobis distance does not come without cost. There is a trade-off between invariance, robustness and computational feasibility. In the last few years, efficient exact algorithms as well as approximate ones have been constructed and made available in R-packages. Consequently, in practical applications the choice of a depth statistic is no more restricted to one or two notions due to computational limits; rather often more notions are feasible, among which the researcher has to decide. The article debates theoretical and practical aspects of this choice, including invariance and uniqueness, robustness and computational feasibility. Complexity and speed of exact algorithms are compared. The accuracy of approximate approaches like the random Tukey depth is discussed as well as the application to large and high-dimensional data. Extensions to local and functional depths and connections to regression depth are shortly addressed.