Definition Of Distance Research Articles

Geodesic distances in Liouville quantum gravity

In order to study the quantum geometry of random surfaces in Liouville gravity, we propose a definition of geodesic distance associated to a Gaussian free field on a regular lattice. This geodesic distance is used to numerically determine the Hausdorff dimension associated to shortest cycles of 2d quantum gravity on the torus coupled to conformal matter fields, showing agreement with a conjectured formula by Y. Watabiki. Finally, the numerical tools are put to test by quantitatively comparing the distribution of lengths of shortest cycles to the corresponding distribution in large random triangulations.

A flexible framework for online document segmentation by pairwise stroke distance learning

A flexible framework for handling a variety of segmentation problems in online handwritten documents is introduced. The strategy relies on single linkage clustering and a pairwise stroke distance that is globally trained for direct optimization of the segmentation. We define a variety of features that can contribute to the pairwise distance definition and show how to select a good combination of features for dealing with a new online handwritten document segmentation task. Our experiments demonstrate the validity of the method on a large range of segmentation tasks over several types of documents from various publicly available databases. HighlightsA flexible framework for handling segmentation of online documents is introduced.The system is based on single linkage clustering with globally trained distance.Absence of external parameters permits flexibility for various segmentation tasks.Results on a variety of segmentation tasks demonstrate the method validity.

Gravity, distance, and traffic flows in Mexico

This paper presents an econometric analysis that compares the performance of different measures of distance in a gravity model using state data for Mexico. The estimation shows that at this geographic scale, the definition of distance does not affect the explanatory power of the model significantly. However, time-based definitions of distance have a marginal improvement on the model fit in comparison to length-based measures. When geographic specific fixed effects are unknown, the model shows that distance measured as road network distance is a better predictor. The paper concludes that time-based definitions of distance present several advantages in comparison to traditional length-based definitions. However, at large geographic scales, where relative distances between every geographic unit are long, the use of length-based distance instead of time-based distance to approximate travel costs generates similar results.

An Attempt to Application of Chain Codes for Design Similarity Evaluation

The need of integration of all engineering activities starting from a designing stage finishing on manufacturing implies the necessity of application of a new software solution. Among them CAPP systems seem to be the best and the most promising integration tool. There are the two basic methods of the computer aided process planning it is the variant and generative methods. These CAPP modelling methods are based on the different principles. The variant method is based, in general, on the ideas of the design similarity and group technology whilst the generative one mainly on the basis of utilization of the manufacturing knowledge store and the automatic process synthesis. It is a well-known fact that the variant process planning approach is based on the hypothesis that similar parts would have similar process plans. In a CAPP variant process planning system it is necessary to look for similarities between parts. Process plans formerly prepared and stored in the CAPP system manufacturing database are used for planning of new manufacturing processes for new parts similar to those recorded in system database. In the variant system working out of the classification schema and similarity measures is essential. In this paper an attempt to application of chain codes for a design similarity evaluation is presented. The proposed procedure is based on application of the chain codes for description of the parts selected longitudinal cross sections. The proposed chain code structure is created in similar way to this used for the Freeman code formation but unlike classic Freeman chain code the parts cross section is discretized in more than the 8 cardinal directions. The characteristic feature of the proposed profile coding method is the approach for the code starting point selection. In each case the part design chain code is created starting from the a priori selected upper left corner of a product. The idea of products similarity evaluation bases on the parts profile codes and application of the minimum edit distance definitions. In the paper the Levenshtein and Hamming distance for code chains similarity comparison are proposed At the current stage of research this method is used for similarity evaluation of rotational symmetric parts. The choice of the minimum edit distance measure in the proposed solution depends on product pins number.

Image super-resolution using windowed ordinary Kriging interpolation

Abstract This paper presents a novel interpolation approach for single image super-resolution based on ordinary Kriging interpolation, which has been widely used in geostatistics. The proposed method simultaneously considers the intensity distances and geometry of the pixel data. We employ a new intensity distance definition and local windows surrounding each unknown high-resolution pixel to implement the algorithm. The proposed approach is able to produce adaptive weights and edge preservation is achieved. Our experimental results show the efficiency of the proposed approach compared to conventional interpolation methods in terms of the peak signal-to-noise (PNSR) and visual perception.

Grey Target Decision Model of Hesitant Three-Parameter Interval Grey Number

A new uncertainty information representation—hesitant three-parameter interval grey number is put forward, and its distance estimation approach of hesitant three-parameter interval grey number and sequence are studied. Based on the distance definition of hesitant three-parameter interval grey number, the paper defines the ideal optimization scheme is the positive clout and the ideal inferior scheme is the negative clout of the grey target and comprehensively considers the optimization and the positive off-target distance, and base on the spatial analysis, defines the comprehensive target distance. In the last, the model validity and practicability is demonstrated by example.

On Stability of Operational Risk Estimates by LDA: From Causes to Approaches

The stability of estimates is critical when applying advanced measurement approaches (AMA) such as loss distribution approach (LDA) for operational risk capital modeling. Recent studies have identified issues associated with capital estimates by applying the maximum likelihood estimation (MLE) method for truncated distributions: significant upward mean-bias, considerable uncertainty about the estimates, and non-robustness to both small and large losses. Although alternative estimation approaches have been proposed, there has not been any comprehensive review of the causes of instability and how the alternative approaches either address the sources of instability or improve estimates compared to the MLE method. In this paper, we systematically review the causes of capital instability. Then we review several approaches (right-truncated distributions, bias-corrected capital estimators and quantile-distance estimation) in addressing each source of instability. First, we analyze the advantages of imposing an upper bound on a single loss in order to address the infinite-mean issue and make the subjective assumptions (if necessary) understandable for risk managers and regulators. We also provide a framework for calculating the expected loss and for approximating capital estimates under the right-truncation formulation. Second, we summarize performance measures for evaluating capital estimates and provide a simulation-based approach to correct the bias of capital estimates when MLE is employed. In doing so, we point out that although the approach may decrease the mean-bias, it introduces more median-bias. Finally, while noting the potential robustness of applying the quantile-distance estimator, we review the factors that affect the capital estimator’s performance, and suggest that this method should be used with caution because of its significant sensitivity to various definitions of quantile distance.

Curvature dark energy reconstruction through different cosmographic distance definitions

In the context of gravity, dark energy is a geometrical fluid with negative equation of state. Since the function is not known a priori, the need of a model independent reconstruction of its shape represents a relevant technique to determine which model is really favored with respect to others. To this aim, cosmography is related to a generic and its derivatives in order to provide a model‐independent investigation at redshift . The analysis is based on the use of three different cosmological distance definitions, in order to alleviate the duality problem, i.e. the problem of which cosmological distance to use with specific cosmic data sets. We therefore consider the luminosity, , flux, , and angular, , distances and we find numerical constraints by the Union 2.1 supernovae compilation and measurement of baryonic acoustic oscillations, at . We notice that all distances reduce to the same expression, i.e. , at first order. Thus, to fix the cosmographic series of observables, we impose the initial value of H0 by fitting through supernovae only, in the redshift regime . We find that the pressure of curvature dark energy fluid is slightly lower than the one related to the cosmological constant. This indicates that a possible evolving curvature dark energy realistically fills the current universe. Moreover, the combined use of and shows that the sign of the acceleration parameter agrees with theoretical bounds, while its variation, namely the jerk parameter, is compatible with . Finally, we infer the functional form of by means of a truncated polynomial approximation, in terms of fourth order scale factor .

Minkowski Generalizations of Ward’s Method in Hierarchical Clustering

In this paper, we consider several generalizations of the popular Ward's method for agglomerative hierarchical clustering. Our work was motivated by clustering software, such as the R function hclust, which accepts a distance matrix as input and applies Ward's definition of inter-cluster distance to produce a clustering. The standard version of Ward's method uses squared Euclidean distance to form the distance matrix. We explore the effect on the clustering of using other definitions of distance, such as the Minkowski distance.

Mapping Large Spatial Flow Data with Hierarchical Clustering

AbstractIt is challenging to map large spatial flow data due to the problem of occlusion and cluttered display, where hundreds of thousands of flows overlap and intersect each other. Existing flow mapping approaches often aggregate flows using predetermined high‐level geographic units (e.g. states) or bundling partial flow lines that are close in space, both of which cause a significant loss or distortion of information and may miss major patterns. In this research, we developed a flow clustering method that extracts clusters of similar flows to avoid the cluttering problem, reveal abstracted flow patterns, and meanwhile preserves data resolution as much as possible. Specifically, our method extends the traditional hierarchical clustering method to aggregate and map large flow data. The new method considers both origins and destinations in determining the similarity of two flows, which ensures that a flow cluster represents flows from similar origins to similar destinations and thus minimizes information loss during aggregation. With the spatial index and search algorithm, the new method is scalable to large flow data sets. As a hierarchical method, it generalizes flows to different hierarchical levels and has the potential to support multi‐resolution flow mapping. Different distance definitions can be incorporated to adapt to uneven spatial distribution of flows and detect flow clusters of different densities. To assess the quality and fidelity of flow clusters and flow maps, we carry out a case study to analyze a data set of 243,850 taxi trips within an urban area.

On Recursive Edit Distance Kernels With Application to Time Series Classification

This paper proposes some extensions to the work on kernels dedicated to string or time series global alignment based on the aggregation of scores obtained by local alignments. The extensions that we propose allow us to construct, from classical recursive definition of elastic distances, recursive edit distance (or time-warp) kernels that are positive definite if some sufficient conditions are satisfied. The sufficient conditions we end up with are original and weaker than those proposed in earlier works, although a recursive regularizing term is required to get proof of the positive definiteness as a direct consequence of the Haussler's convolution theorem. Furthermore, the positive definiteness is maintained when a symmetric corridor is used to reduce the search space, and thus the algorithmic complexity, which is quadratic in the worst case. The classification experiment we conducted on three classical time-warp distances (two of which are metrics), using support vector machine classifier, leads to the conclusion that when the pairwise distance matrix obtained from the training data is far from definiteness, the positive definite recursive elastic kernels outperform in general the distance substituting kernels for several classical elastic distances we have tested.

On cumulative nonlinear acoustic waveform distortions from high-speed jets

AbstractA model is proposed for predicting the presence of cumulative nonlinear distortions in the acoustic waveforms produced by high-speed jet flows. The model relies on the conventional definition of the acoustic shock formation distance and employs an effective Gol’dberg number$\Lambda $for diverging acoustic waves. The latter properly accounts for spherical spreading, whereas the classical Gol’dberg number$\Gamma $is restricted to plane wave applications. Scaling laws are then derived to account for the effects imposed by jet exit conditions of practical interest and includes Mach number, temperature ratio, Strouhal number and an absolute observer distance relative to a broadband Gaussian source. Surveys of the acoustic pressure produced by a laboratory-scale, shock-free and unheated Mach 3 jet are used to support findings of the model. Acoustic waveforms are acquired on a two-dimensional grid extending out to 145 nozzle diameters from the jet exit plane. Various statistical metrics are employed to examine the degree of local and cumulative nonlinearity in the measured waveforms and their temporal derivatives. This includes a wave steepening factor (WSF), skewness, kurtosis and the normalized quadrature spectral density. The analysed data are shown to collapse reasonably well along rays emanating from the post-potential-core region of the jet. An application of the generalized Burgers equation is used to demonstrate the effect of cumulative nonlinear distortion on an arbitrary acoustic waveform produced by a high-convective-Mach-number supersonic jet. It is advocated that cumulative nonlinear distortion effects during far-field sound propagation are too subtle in this range-restricted environment and over the region covered, which may be true for other laboratory-scale jet noise facilities.

Relativistic cosmology number densities in void-Lemaître-Tolman-Bondi models

The goal of this work is to compute the number density of far-IR selected galaxies in the comoving frame and along the past lightcone of observationally constrained LTB models and to compare those results with their standard model counterparts. We derived integral number densities and differential number densities using different cosmological distance definitions in the LTB models. Then, we computed selection functions and consistency functions for the luminosity functions in the combined fields of the Herschel/PACS evolutionary probe (PEP) survey in both standard and void cosmologies, from which we derived the observed values of the above-mentioned densities. We used the Kolmogorov-Smirnov statistics to study both the evolution of the consistency functions and its connection to the evolution of the comoving density of sources. Finally, we fitted the power-law behaviour of the densities along the observer's past lightcone. The analysis of the comoving number density shows that the increased flexibility of the LTB models is not enough to fit the observed redshift evolution of the number counts, if it is specialised to a recent best-fit giant void parametrisation. The results for the power-law fits of the densities along the observer's past lightcone show general agreement across both cosmological models studied here around a slope of -2.5 $\pm$ 0.1 for the integral number density on the luminosity-distance volumes. The differential number densities show much bigger slope discrepancies. We conclude that the differential number densities on the observer's past lightcone were still rendered dependent on the cosmological model by the flux limits of the PEP survey. In addition, we show that an intrinsic evolution of the sources must be assumed to fit the comoving number-density redshift evolution in the giant void parametrisation for the LTB models used in this work.

A Note on Minimax Testing and Confidence Intervals in Moment Inequality Models

This note uses a simple example to show how moment inequality models used in the empirical economics literature lead to general minimax relative efficiency comparisons. The main point is that such models involve inference on a low dimensional parameter, which leads naturally to a definition of “distance” that, in full generality, would be arbitrary in minimax testing problems. This definition of distance is justified by the fact that it leads to a duality between minimaxity of confidence intervals and tests, which does not hold for other definitions of distance. Thus, the use of moment inequalities for inference in a low dimensional parametric model places additional structure on the testing problem, which leads to stronger conclusions regarding minimax relative efficiency than would otherwise be possible.

Formalised definition of communicational spaces

This article deals with the concept of communicational spaces and tries to renew, clarify and formalise it from mathematical, geographical and philosophical standpoints. Starting from the concept that space is constituted by communication, a mathematical formulation of space is sought. In a similar manner to quantum mechanics, the present deliberation attempts to provide more generalised theories of reality than did preceding theories of space. In some approaches, spaces are intrinsically constituted by metrics, mainly by definitions of distance. The triangle inequality seems to be constitutive for space; however, it might no longer be applicable in spaces mediated by internet communication. The recent shift to virtual spaces and recent redefinitions of thirdspaces in human geography lead to a fundamental reconsideration of what space is at all, including drawing on distant philosophies. Concluding, this paper posits not that manifoldness is embedded in space, but conversely, that space is a product of manifoldness.

P7. Experimental investigation of the definition of reference accent distance between speakers toward automatic accent clustering of speakers of World Englishes (Summaries of Presentations at the 28th General Meeting)

P7. Experimental investigation of the definition of reference accent distance between speakers toward automatic accent clustering of speakers of World Englishes (Summaries of Presentations at the 28th General Meeting)

A depth estimation method based on geometric transformation for stereo light microscope.

Stereo light microscopes (SLM) with narrow vision and shallow depth of field are widely used in micro-domain research. In this paper, we propose a depth estimation method of micro objects based on geometric transformation. By analyzing the optical imaging geometry, the definition of geometric transformation distance is given and the depth-distance relation express is obtained. The parameters of geometric transformation and express are calibrated with calibration board images captured in aid of precise motorized stage. The depth of micro object can be estimated by calculating the geometric transformation distance. The proposed depth-distance relation express is verified using an experiment in which the depth map of an Olanzapine tablet surface is reconstructed.

Coming to an Airport Near You

Definition of an effective distance between airports helps to explain the spread of epidemics across the global aviation network. [Also see Report by Brockmann and Helbing ]

Topological contact dynamics II: Topological automorphisms, contact homeomorphisms, and non-smooth contact dynamical systems

This sequel to our previous paper [MS11b] continues the study of topological contact dynamics and applications to contact dynamics and topological dynamics. We provide further evidence that the topological automorphism groups of a contact structure and a contact form are the appropriate transformation groups of contact dynamical systems. The article includes an examination of the groups of time-one maps of topological contact and strictly contact isotopies, and the construction of a bi-invariant metric on the latter. Moreover, every topological contact or strictly contact dynamical system is arbitrarily close to a continuous contact or strictly contact dynamical system with the same end point. In particular, the above groups of time-one maps are independent of the choice of norm in the definition of the contact distance. On every contact manifold we construct topological contact dynamical systems with time-one maps that fail to be Lipschitz continuous, and smooth contact vector fields whose flows are topologically conjugate but not conjugate by a contact C^1-diffeomorphism.

Genetic links among individuals: from genealogies to molecular markers

Genetic links among individuals are widely used to characterize the diversity of domesticated and natural populations and they also provide complementary information for statistical population summaries. We first discuss the measures used by geneticists based on genealogy and DNA data. The choice of metrics of genetic links should be coherent with the objectives: biodiversity or genotype–phenotype relationships. For the last objective, we evaluate by simulation the interest of genetic distances when the objective is the prediction of individual genetic values and phenotypes using kernel regression. A pseudo-distance based on correlations between marker genotypes of pairs of individual yields better predictions than other classical definition of distances.