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Data quality (DQ) has been defined as ‘fitness for use’. In order to measure and improve DQ, various methodologies have been defined. A DQ methodology is a set of guidelines and techniques that define a rational process to measure and improve the quality of data. In order to make DQ measurement and improvement more organised, DQ dimensions have been defined. A dimension is a single aspect of DQ, such as accuracy, completeness, timeliness, and relevancy. In order to measure dimensions, special tools have been developed. These are called metrics. In most organisations, some data are more significant than others. In other words, some data carry more ‘weight’. Hence, they must play a more... 

Data quality (DQ) has been defined as ‘fitness for use’. In order to measure and improve DQ, various methodologies have been defined. A DQ methodology is a set of guidelines and techniques that define a rational process to measure and improve the quality of data. In order to make DQ measurement and improvement more organised, DQ dimensions have been defined. A dimension is a single aspect of DQ, such as accuracy, completeness, timeliness, and relevancy. In order to measure dimensions, special tools have been developed. These are called metrics. In most organisations, some data are more significant than others. In other words, some data carry more ‘weight’. Hence, they must play a more... 

The main purpose of this article is to generalize a characterization of constant functions to the context of metric-measure spaces. In fact, we approximate a measurable function, in terms of a certain integrability condition, by Lipschitz functions. Then, similar to Brezis (2002) [2], we establish a necessary and sufficient condition in order that any measurable function which satisfies an integrability condition to be constant a.e. Also, we provide a different proof for the main result of Pietruska-Pałuba (2004) [7] in the setting of Dirichlet forms  

Metric learning is a powerful approach for semi-supervised clustering. In this paper, a metric learning method considering both pairwise constraints and the geometrical structure of data is introduced for semi-supervised clustering. At first, a smooth metric is found (based on an optimization problem) using positive constraints as supervisory information. Then, an extension of this method employing both positive and negative constraints is introduced. As opposed to the existing methods, the extended method has the capability of considering both positive and negative constraints while considering the topological structure of data. The proposed metric learning method can improve performance of... 

We study the volume averaging of inhomogeneous metrics within GR and discuss its shortcomings, such as gauge dependence, singular behavior as a result of caustics, and causality violations. To remedy these shortcomings, we suggest some modifications to this method. As a case study we focus on the inhomogeneous structured FRW model based on a flat LTB metric. The effect of averaging is then studied in terms of an effective backreaction fluid. It is shown that, contrary to the claims in the literature, the backreaction fluid behaves like a dark matter component, instead of dark energy, having a density of the order of 10-5 times the matter density, and, most importantly, it is gauge-dependent.... 

In this Note, we obtain Einstein solvmanifolds using Abelian extension of two-step nilpotent Lie algebras associated with graphs. To cite this article: H.-R. Fanaï, C. R. Acad. Sci. Paris, Ser. I 344 (2007). © 2006 Académie des sciences  

In this study, we discuss the postural stability of a nonprehensile manipulation problem, which deals with multibody objects. As a metric for postural stability, we define PRI. Then, the system is posturally stable, if PRI is inside the convex hull of the object-manipulator contact surface. We then discuss that dynamic biped locomotion is a special case of dynamic nonprehensile manipulation in all aspects; we prove that ZMP (zero-moment point) and FRI (zoot rotation indicator) are special cases of PRI (palm rotation indicator). Simulations and experiments corresponding to simple examples support the results  

Using a cosmological black hole model proposed recently, we have calculated the quasi-local mass of a collapsing structure within a cosmological setting due to different definitions put forward in the last decades to see how similar or different they are. It has been shown that the mass within the horizon follows the familiar Brown-York behavior. It increases, however, outside the horizon again after a short decrease, in contrast to the Schwarzschild case. Further away, near the void, outside the collapsed region, and where the density reaches the background minimum, all the mass definitions roughly coincide. They differ, however, substantially far from it. Generically, we are faced with... 

A set W ⊆ V (G) is called a resolving set, if for each two distinct vertices u, v ∈ V (G) there exists w ∈ W such that d(u, w) ≠ d(v, w), where d(x, y) is the distance between the vertices x and y. A resolving set for G with minimum cardinality is called a metric basis. The forcing dimension f(G, dim) (or f(G)) of G is the smallest cardinality of a subset S ⊂ V (G) such that there is a unique basis containing S. The forcing dimensions of some well-known graphs are determined. In this paper, among some other results, it is shown that for large enough integer n and all integers a, b with 0 ≤ a ≤ b ≤ n and b ≥ 1, there exists a nontrivial connected graph G of order n with f(G) = a and dim(G) =... 

In Spatial Voting Theory, distortion is a measure of how good the winner is. It has been proved that no deterministic voting mechanism can guarantee a distortion better than 3, even for simple metrics such as a line. In this study, we wish to answer the following question: How does the distortion value change if we allow less motivated agents to abstain from the election? We consider an election with two candidates and suggest an abstention model, which is a general form of the abstention model proposed by Kirchgässner. Our results characterize the distortion value and provide a rather complete picture of the model. ©2021 AI Access Foundation  

In many real-world applications, data contain heterogeneous input modalities (e.g., web pages include images, text, etc.). Moreover, data such as images are usually described using different views (i.e. different sets of features). Learning a distance metric or similarity measure that originates from all input modalities or views is essential for many tasks such as content-based retrieval ones. In these cases, similar and dissimilar pairs of data can be used to find a better representation of data in which similarity and dissimilarity constraints are better satisfied. In this paper, we incorporate supervision in the form of pairwise similarity and/or dissimilarity constraints into... 

This paper presents a new multi-model control scheme which integrates the stability and performance requirements to determine the nominal local models. Gap metric and stability margin concepts are applied to measure the distance between the local models and to grid the operation range of nonlinear system, respectively. The minimization of the integral of time absolute error is included as performance criterion. Furthermore, the multi-model decomposition and local controllers design are integrated in an optimization problem which provides avoidance of the redundancy issue. A fixed PI structure is considered as the local controllers to simplify the global multi-model controller structure.... 

Modeling languages are needed to describe the conceptual construct underlying software. Several modeling languages have been proposed during the last decades. Cognitive complexity is one of the common problems in designing modeling languages. Users have to split their attention and cognitive resources between two different tasks when working with complex language: solving the problem and understanding the elements composing the language. Several researches have been accomplished to evaluate cognitive complexity of modeling languages, among them, metric based and empirical approaches aremore important and convenient than others. In this paper, we compared these two methods. Results show that... 

Embedding metrics into constant-dimensional geometric spaces, such as the Euclidean plane, is relatively poorly understood. Motivated by applications in visualization, ad-hoc networks, and molecular reconstruction, we consider the natural problem of embedding shortest-path metrics of unweighted planar graphs (planar graph metrics) into the Euclidean plane. It is known that, in the special case of shortest-path metrics of trees, embedding into the plane requires Θ(√n) distortion in the worst case [19, 1], and surprisingly, this worst-case upper bound provides the best known approximation algorithm for minimizing distortion. We answer an open question posed in this work and highlighted by... 

Assist-as-needed control is underlain by the aim of replacing skillful therapists with rehabilitation robots. The objective of this research was to introduce a smart assist-as-needed control system for the elderly or partially paralyzed individuals. The main function of the proposed system is to assist the patients just in the required sub phases of the motion. To ensure that a smart and compliant system is developed, the target admittance gains of the controller was adapted according to the concept of energy The admittance gains were modified so that an exoskeleton reduces interaction energy in cases wherein users have sufficient strength for task execution and maximizes the interaction... 

In this paper, the metric theory of Diophantine approximation associated with mixed type small linear forms is investigated. We prove Khintchine–Groshev type theorems for both the real and complex number systems. The motivation for these metrical results comes from their applications in signal processing. One such application is discussed explicitly. © Springer Nature Switzerland AG 2020  

The increasing variability of renewables and volatile chronological net-load in power grids engenders significant risks of an uncertain sufficiency of flexible capacity. Although considerable advances in power grid flexibility assessment have been made, modeling the effect of temporal correlations associated with wind generations on the system flexibility provision capability has remained a challenge. This paper proposes a novel UC-time-scale security-constrained affinely robust formulation for wind-originated uncertainty sets in order to evaluate the system flexibility capacity over time. An efficient model based on duality theorem and affine policy is proposed to assess a secure region in... 

Let P be a set of n points in R3 amid a bounded number of obstacles. Consider the metric space M=(P,dM) where dM(p,q) is the geodesic distance of p and q, i.e., the length of a shortest path from p to q avoiding obstacles. When obstacles are axis-parallel boxes, we prove that M admits an 83-spanner with O(nlog3⁡n) edges. In other words, let S be a complete graph on n vertices where each node corresponds to a point p∈P. For nodes u and v of S corresponding to p,q∈P, the edge (u,v) is associated with the geodesic distance of p and q as its weight. We indeed prove that S admits a near linear-size t-spanner for some constant t. © 2020 Elsevier B.V  

Let P be a set of n points in R3 amid a bounded number of obstacles. Consider the metric space M=(P,dM) where dM(p,q) is the geodesic distance of p and q, i.e., the length of a shortest path from p to q avoiding obstacles. When obstacles are axis-parallel boxes, we prove that M admits an 83-spanner with O(nlog3⁡n) edges. In other words, let S be a complete graph on n vertices where each node corresponds to a point p∈P. For nodes u and v of S corresponding to p,q∈P, the edge (u,v) is associated with the geodesic distance of p and q as its weight. We indeed prove that S admits a near linear-size t-spanner for some constant t. © 2020 Elsevier B.V