Family Of Metrics Research Articles

HDR Display Quality Evaluation by incorporating Perceptual Component Models into a Machine Learning framework

We present an approach to predict overall high dynamic range (HDR) display quality as a function of key HDR display parameters. Subjective experiments on a high quality HDR display tested five key HDR display parameters: (maximum luminance, minimum luminance, color gamut, bit-depth and local contrast).Two models were explored– a physical model solely based on physically measured display characteristics and a perceptual model that transforms physical parameters using human vision system (HVS) models. For the perceptual model, we used a family of metrics based on a recently published color space (ICTCP), as well as an estimate of the display point spread function. To predict the overall visual quality ratings, we compared linear regression and various machine learning (ML) techniques.We find that the perceptual model is better at predicting subjective quality than the physical model and that ML techniques are better at prediction than linear regression. We also investigate the significance and contribution of each display parameter for the combined model. Further, we explore how well these models perform when applied to display capabilities outside of the training data set, both in terms of extrapolation and interpolation. The use of the perceptual transforms particularly helps with extrapolation, and without their tempering effects, the ML-based models can produce wildly unrealistic quality predictions.

Definitions, formulas, and simulated examples for plagiarism detection with FAIR metrics

ABSTRACTIn prior work, we proposed a family of metrics as a tool to quantify adherence to or deviation from good citation practices in scholarly research and publishing. We called this family of metrics FAIR as an acronym for Fair Attribution to Indexed Reports and Fair Acknowledgment of Information Records, and introduced definitions for these metrics with counts of instances of correct or incorrect attribution or nonattribution in primary research articles with citations for previously published references. In the present work, we extend our FAIR family of metrics by introducing a collection of ratio‐based metrics to accompany the count‐based metrics described previously. We illustrate the mathematical properties of the ratio‐based metrics with various simulated examples in order to assess their suitability as a means of identifying papers under peer review as more or less likely to be suspicious for plagiarism. These FAIR metrics would alert peer reviewers to prioritize low‐scoring manuscripts for closer scrutiny. Finally, we outline our planned strategy for future validation of the FAIR metrics with an approach using both expert human analysts and automated algorithms for computerized analysis.

Virtual Reality as a New Approach for Risk Taking Assessment.

Understanding how people behave when facing hazardous situations, how intrinsic and extrinsic factors influence the risk taking (RT) decision making process and to what extent it is possible to modify their reactions externally, are questions that have long interested academics and society in general. In the spheres, among others, of Occupational Safety and Health (OSH), the military, finance and sociology, this topic has multidisciplinary implications because we all constantly face RT situations. Researchers have hitherto assessed RT profiles by conducting questionnaires prior to and after the presentation of stimuli; however, this can lead to the production of biased, non-realistic, RT profiles. This is due to the reflexive nature of choosing an answer in a questionnaire, which is remote from the reactive, emotional and impulsive decision making processes inherent to real, risky situations. One way to address this question is to exploit VR capabilities to generate immersive environments that recreate realistic seeming but simulated hazardous situations. We propose VR as the next-generation tool to study RT processes, taking advantage of the big four families of metrics which can provide objective assessment methods with high ecological validity: the real-world risks approach (high presence VR environments triggering real-world reactions), embodied interactions (more natural interactions eliciting more natural behaviors), stealth assessment (unnoticed real-time assessments offering efficient behavioral metrics) and physiological real-time measurement (physiological signals avoiding subjective bias). Additionally, VR can provide an invaluable tool, after the assessment phase, to train in skills related to RT due to its transferability to real-world situations.

A new family of dissimilarity metrics for discrete character matrices that include inapplicable characters and its importance for disparity studies.

The use of discrete character data for disparity analyses has become more popular, partially due to the recognition that character data describe variation at large taxonomic scales, as well as the increasing availability of both character matrices co-opted from phylogenetic analysis and software tools. As taxonomic scope increases, the need to describe variation leads to some characters that may describe traits not found across all the taxa. In such situations, it is common practice to treat inapplicable characters as missing data when calculating dissimilarity matrices for disparity studies. For commonly used dissimilarity metrics like Wills's GED and Gower's coefficient, this can lead to the reranking of pairwise dissimilarities, resulting in taxa that share more primary character states being assigned larger dissimilarity values than taxa that share fewer. We introduce a family of metrics that proportionally weight primary characters according to the secondary characters that describe them, effectively eliminating this problem, and compare their performance to common dissimilarity metrics and previously proposed weighting schemes. When applied to empirical datasets, we confirm that choice of dissimilarity metric frequently affects the rank order of pairwise distances, differentially influencing downstream macroevolutionary inferences.

Exploiting recommendation confidence in decision-aware recommender systems

The main goal of a Recommender System is to suggest relevant items to users, although other utility dimensions – such as diversity, novelty, confidence, possibility of providing explanations – are often considered. In this work, we investigate about confidence but from the perspective of the system: what is the confidence a system has on its own recommendations; more specifically, we focus on different methods to embed awareness into the recommendation algorithms about deciding whether an item should be suggested. Sometimes it is better not to recommend than fail because failure can decrease user confidence in the system. In this way, we hypothesise the system should only show the more reliable suggestions, hence, increasing the performance of such recommendations, at the expense of, presumably, reducing the number of potential recommendations. Different from other works in the literature, our approaches do not exploit or analyse the input data but intrinsic aspects of the recommendation algorithms or of the components used during prediction are considered. We propose a taxonomy of techniques that can be applied to some families of recommender systems allowing to include mechanisms to decide if a recommendation should be generated. In particular, we exploit the uncertainty in the prediction score for a probabilistic matrix factorisation algorithm and the family of nearest-neighbour algorithms, the support of the prediction score for nearest-neighbour algorithms, and a method independent of the algorithm. We study how the performance of a recommendation algorithm evolves when it decides not to recommend in some situations. If the decision of avoiding a recommendation is sensible – i.e., not random but related to the information available to the system about the target user or item –, the performance is expected to improve at the expense of other quality dimensions such as coverage, novelty, or diversity. This balance is critical, since it is possible to achieve a very high precision recommending only one item to a unique user, which would not be a very useful recommender. Because of this, on the one hand, we explore some techniques to combine precision and coverage metrics, an open problem in the area. On the other hand, a family of metrics (correctness) based on the assumption that it is better to avoid a recommendation rather than providing a bad recommendation is proposed herein. In summary, the contributions of this paper are twofold: a taxonomy of techniques that can be applied to some families of recommender systems allowing to include mechanisms to decide if a recommendation should be generated, and a first exploration to the combination of evaluation metrics, mostly focused on measures for precision and coverage. Empiric results show that large precision improvements are obtained when using these approaches at the expense of user and item coverage and with varying levels of novelty and diversity.

Cophenetic Median Trees.

Median tree inference under path-difference metrics has shown great promise for large-scale phylogeny estimation. Similar to these metrics is the family of cophenetic metrics that originates from a classic dendrogram comparison method introduced more than 50 years ago. Despite the appeal of this family of metrics, the problem of computing median trees under cophenetic metrics has not been analyzed. Like other standard median tree problems relevant in practice, as we show here, this problem is also NP-hard. NP-hard median tree problems have been successfully addressed by local search heuristics that are solving thousands of instances of a corresponding (local neighborhood) search problem. For the local neighborhood search problem under a cophenetic metric, the best known (naïve) algorithm has a time complexity that is typically prohibitive for effective heuristic searches. Building on the pioneering work on path-difference median trees, we develop efficient algorithms for Manhattan and Euclidean cophenetic search problems that improve on the naïve solution by a linear and a quadratic factor, respectively. We demonstrate the performance and effectiveness of the resulting heuristic methods in a comparative study using benchmark empirical datasets.

Existence and Lipschitz stability for α-dissipative solutions of the two-component Hunter–Saxton system

We establish the concept of [Formula: see text]-dissipative solutions for the two-component Hunter–Saxton system under the assumption that either [Formula: see text] or [Formula: see text] for all [Formula: see text]. Furthermore, we investigate the Lipschitz stability of solutions with respect to time by introducing a suitable parametrized family of metrics in Lagrangian coordinates. This is necessary due to the fact that the solution space is not invariant with respect to time.

Learning shape metrics with Monte Carlo optimization

Quantifying and modeling shape variation within a population, identifying morphological contrasts across groups, and categorizing individuals or objects according to morphological similarity are central problems in numerous domains of science and applications. In this paper, we present an approach to optimal shape categorization through a new family of metrics for shapes presented as a finite collection of labeled landmark points. We develop a technique to learn metrics that optimally differentiate and categorize shapes using Monte Carlo optimization methods. We discuss the theory and the practice of the methods and apply them to the analysis of synthetic data and the classification of multiple species of fruit flies based on the shape of their wings.

Role of evaporation in gravitational collapse

We investigate the consequences of the collapse-induced radiation anticipated before formation of the event horizon. After reviewing the principles underlying semi-classical analysis of black holes we illustrate them by modelling collapse of evaporating massive thin dust shells using two families of metrics for the exterior geometry: the outgoing Vaidya metric and the retarded Schwarzschild metric. We describe how hypothetical pre-Hawking radiation modifies the equation of motion for the shell. Provided that a non-zero radiation flux is perceived by a distant observer, the shell never gets closer than a certain sub-Planckian distance from the Schwarzschild radius. This distance depends only on the shell’s mass and evaporation rate. The stress–energy tensor is everywhere finite, but a comoving observer encounters firewall-like energy density and flux. We emphasize the logical connections between different assumptions within the semi-classical approach and discuss consequences of the apparent contradictions between them.

Expressions for optical scalars and deflection angle at second order in terms of curvature scalars

We present formal expressions for the optical scalars in terms of the curvature scalars in the weak gravitational lensing regime at second order in perturbations of a flat background without mentioning the extension of the lens or their shape. Also, by considering the thin lens approximation for static and axially symmetric configurations we obtain an expression for the second-order deflection angle which generalizes our previous result presented in [Phys.Rev.D 83:083007 (2011)]. As applications of these formulas we compute the optical scalars for some known family of metrics and we recover expressions for the deflection angle. In contrast to other works in the subject, our formalism allows a straightforward identification of how the different components of the curvature tensor contribute to the optical scalars and deflection angle. We also discuss in what sense the Schwarzschild solution can be thought as a true thin lens at second order.

Well-posedness for mutational equations under a general type of dissipativity conditions

This paper is concerned with mutational analysis found by Aubin and developed by Lorenz. To extend their results so that they can be applied to quasi-linear evolution equations initiated by Kato, we focus on a mutational framework where for each r > 0 there exists M ≥ 1 such that d(ϑ(t, x), ϑ(t, y)) ≤ Md(x, y) for t ∈ [0, 1] and x, y ∈ D r (φ), where ϑ is a transition and Dr(φ) is the revel set of a proper lower semicontinuous functional φ. The setting that the constant M may be larger than 1 plays an important role in applying to quasi-linear evolution equations. In that case, it is difficult to estimate the distance between two approximate solutions to mutational equations. Our strategy is to construct a family of metrics depending on both time and state, with respect to which transitions are contractive in some sense.

Gauged supergravities from M-theory reductions

In supergravity compactifications, there is in general no clear prescription on how to select a finite-dimensional family of metrics on the internal space, and a family of forms on which to expand the various potentials, such that the lower-dimensional effective theory is supersymmetric. We propose a finite-dimensional family of deformations for regular Sasaki-Einstein seven-manifolds M7, relevant for M-theory compactifications down to four dimensions. It consists of integrable Cauchy-Riemann structures, corresponding to complex deformations of the Calabi-Yau cone M8 over M7. The non-harmonic forms we propose are the ones contained in one of the Kohn-Rossi cohomology groups, which is finite-dimensional and naturally controls the deformations of Cauchy-Riemann structures. The same family of deformations can be also described in terms of twisted cohomology of the base M6, or in terms of Milnor cycles arising in deformations of M8. Using existing results on SU(3) structure compactifications, we briefly discuss the reduction of M-theory on our class of deformed Sasaki-Einstein manifolds to four-dimensional gauged supergravity.

An Overview of Data Center Metrics and a Novel Approach for a New Family of Metrics

An Overview of Data Center Metrics and a Novel Approach for a New Family of Metrics

Family of boundary overlap metrics for the evaluation of medical image segmentation.

All medical image segmentation algorithms need to be validated and compared, yet no evaluation framework is widely accepted within the imaging community. None of the evaluation metrics that are popular in the literature are consistent in the way they rank segmentation results: they tend to be sensitive to one or another type of segmentation error (size, location, and shape) but no single metric covers all error types. We introduce a family of metrics, with hybrid characteristics. These metrics quantify the similarity or difference of segmented regions by considering their average overlap in fixed-size neighborhoods of points on the boundaries of those regions. Our metrics are more sensitive to combinations of segmentation error types than other metrics in the existing literature. We compare the metric performance on collections of segmentation results sourced from carefully compiled two-dimensional synthetic data and three-dimensional medical images. We show that our metrics: (1)penalize errors successfully, especially those around region boundaries; (2)give a low similarity score when existing metrics disagree, thus avoiding overly inflated scores; and (3)score segmentation results over a wider range of values. We analyze a representative metric from this family and the effect of its free parameter on error sensitivity and running time.

Effect of the scaffold microenvironment on cell polarizability and capacitance determined by probabilistic computations

In living systems, it is frequently stated that form follows function by virtue of evolutionary pressures on organism development, but in the study of how functions emerge at the cellular level, function often follows form. We study this chicken versus egg problem of emergent structure–property relationships in living systems in the context of primary human bone marrow stromal cells cultured in a variety of microenvironments that have been shown to cause distinct patterns of cell function and differentiation. Through analysis of a publicly available catalog of three-dimensional (3D) cell shape data, we introduce a family of metrics to characterize the ‘form’ of the cell populations that emerge from a variety of diverse microenvironments. In particular, measures of form are considered that are expected to have direct significance for cell function, signaling and metabolic activity: dimensionality, polarizability and capacitance. Dimensionality was assessed by an intrinsic measure of cell shape obtained from the polarizability tensor. This tensor defines ellipsoids for arbitrary cell shapes and the thinnest dimension of these ellipsoids, P1, defines a reference minimal scale for cells cultured in a 3D microenvironment. Polarizability governs the electric field generated by a cell, and determines the cell’s ability to detect electric fields. Capacitance controls the shape dependence of the rate at which diffusing molecules contact the surface of the cell, and this has great significance for inter-cellular signaling. These results invite new approaches for designing scaffolds which explicitly direct cell dimensionality, polarizability and capacitance to guide the emergence of new cell functions derived from the acquired form.

Spectral analysis of the Dirac operator on a 3-sphere

We study the (massless) Dirac operator on a 3-sphere equipped with Riemannian metric. For the standard metric the spectrum is known. In particular, the eigenvalues closest to zero are the two double eigenvalues +3/2 and -3/2. Our aim is to analyse the behaviour of eigenvalues when the metric is perturbed in an arbitrary smooth fashion from the standard one. We derive explicit perturbation formulae for the two eigenvalues closest to zero, taking account of the second variations. Note that these eigenvalues remain double eigenvalues under perturbations of the metric: they cannot split because of a particular symmetry of the Dirac operator in dimension three (it commutes with the antilinear operator of charge conjugation). Our perturbation formulae show that in the first approximation our two eigenvalues maintain symmetry about zero and are completely determined by the increment of Riemannian volume. Spectral asymmetry is observed only in the second approximation of the perturbation process. As an example we consider a special family of metrics, the so-called generalized Berger spheres, for which the eigenvalues can be evaluated explicitly.

Monoparametric family of metrics derived from classical Jensen–Shannon divergence

Jensen–Shannon divergence is a well known multi-purpose measure of dissimilarity between probability distributions. It has been proven that the square root of this quantity is a true metric in the sense that, in addition to the basic properties of a distance, it also satisfies the triangle inequality. In this work we extend this last result to prove that in fact it is possible to derive a monoparametric family of metrics from the classical Jensen–Shannon divergence. Motivated by our results, an application into the field of symbolic sequences segmentation is explored. Additionally, we analyze the possibility to extend this result into the quantum realm.

Quarter-pinched Einstein metrics interpolating between real and complex hyperbolic metrics

We show that the one-loop quantum deformation of the universal hypermultiplet provides a family of complete 1 / 4-pinched negatively curved quaternionic Kahler (i.e. half conformally flat Einstein) metrics \(g^c\), \(c\ge 0\), on \(\mathbb {R}^4\). The metric \(g^0\) is the complex hyperbolic metric whereas the family \((g^c)_{c>0}\) is equivalent to a family of metrics \((h^b)_{b>0}\) depending on \(b=1/c\) and smoothly extending to \(b=0\) for which \(h^0\) is the real hyperbolic metric. In this sense the one-loop deformation interpolates between the real and the complex hyperbolic metrics. We also determine the (singular) conformal structure at infinity for the above families.

Asymptotic shapes for ergodic families of metrics on Nilpotent groups

Let \Gamma be a finitely generated virtually nilpotent group. We consider three closely related problems: (i) convergence to a deterministic asymptotic cone for an equivariant ergodic family of inner metrics on \Gamma , generalizing Pansu's theorem; (ii) the asymptotic shape theorem for first passage percolation for general (not necessarily independent) ergodic processes on edges of a Cayley graph of \Gamma ; (iii) the sub-additive ergodic theorem over a general ergodic \Gamma -action. The limiting objects are given in terms of a Carnot–Carathéodory metric on the graded nilpotent group associated to the Mal'cev completion of \Gamma .

A geometric viewpoint on generalized hydrodynamics

Generalized hydrodynamics (GHD) is a large-scale theory for the dynamics of many-body integrable systems. It consists of an infinite set of conservation laws for quasi-particles traveling with effective (“dressed”) velocities that depend on the local state. We show that these equations can be recast into a geometric dynamical problem. They are conservation equations with state-independent quasi-particle velocities, in a space equipped with a family of metrics, parametrized by the quasi-particles' type and speed, that depend on the local state. In the classical hard rod or soliton gas picture, these metrics measure the free length of space as perceived by quasi-particles; in the quantum picture, they weigh space with the density of states available to them. Using this geometric construction, we find a general solution to the initial value problem of GHD, in terms of a set of integral equations where time appears explicitly. These integral equations are solvable by iteration and provide an extremely efficient solution algorithm for GHD.