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Journal articles on the topic 'Families of metrics'

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Published: 22 October 2022

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1

Kiebusch, Sebastian, Bogdan Franczyk, and Andreas Speck. "Metrics for software system families." ACM SIGSOFT Software Engineering Notes 30, no. 4 (July 2005): 1–5. http://dx.doi.org/10.1145/1082983.1083098.

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2

Gabidulin, E. M., and J. Simonis. "Metrics generated by families of subspaces." IEEE Transactions on Information Theory 44, no. 3 (May 1998): 1336–41. http://dx.doi.org/10.1109/18.669429.

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3

Hall, Stuart James. "Quasi-Einstein metrics on hypersurface families." Journal of Geometry and Physics 64 (February 2013): 83–90. http://dx.doi.org/10.1016/j.geomphys.2012.10.013.

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4

Guenancia, Henri. "Families of conic Kähler–Einstein metrics." Mathematische Annalen 376, no. 1-2 (October 28, 2018): 1–37. http://dx.doi.org/10.1007/s00208-018-1769-6.

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5

CASE, JEFFREY S. "SMOOTH METRIC MEASURE SPACES AND QUASI-EINSTEIN METRICS." International Journal of Mathematics 23, no. 10 (October 2012): 1250110. http://dx.doi.org/10.1142/s0129167x12501108.

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Smooth metric measure spaces have been studied from the two different perspectives of Bakry–Émery and Chang–Gursky–Yang, both of which are closely related to work of Perelman on the Ricci flow. These perspectives include a generalization of the Ricci curvature and the associated quasi-Einstein metrics, which include Einstein metrics, conformally Einstein metrics, gradient Ricci solitons and static metrics. In this paper, we describe a natural perspective on smooth metric measure spaces from the point of view of conformal geometry and show how it unites these earlier perspectives within a unified framework. We offer many results and interpretations which illustrate the unifying nature of this perspective, including a natural variational characterization of quasi-Einstein metrics as well as some interesting families of examples of such metrics.

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6

del Hoyo, Matias, and Rui Loja Fernandes. "Riemannian metrics on Lie groupoids." Journal für die reine und angewandte Mathematik (Crelles Journal) 2018, no. 735 (February 1, 2018): 143–73. http://dx.doi.org/10.1515/crelle-2015-0018.

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AbstractWe introduce a notion of metric on a Lie groupoid, compatible with multiplication, and we study its properties. We show that many families of Lie groupoids admit such metrics, including the important class of proper Lie groupoids. The exponential map of these metrics allows us to establish a linearization theorem for Riemannian groupoids, obtaining both a simpler proof and a stronger version of the Weinstein–Zung linearization theorem for proper Lie groupoids. This new notion of metric has a simplicial nature which will be explored in future papers of this series.

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7

Bēts, Raivis, and Alexander Šostak. "Some Remarks on Strong Fuzzy Metrics and Strong Fuzzy Approximating Metrics with Applications in Word Combinatorics." Mathematics 10, no. 5 (February 25, 2022): 738. http://dx.doi.org/10.3390/math10050738.

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Noticing that ordinary metrics do not present an adequate tool for the study of analytic problems of word combinatorics, as well as in the research of some problems related to theoretical computer science, we propose to use fuzzy metrics in this type of problems. Specifically, the so-called strong fuzzy metric seems to be more appropriate here. In the first part of the paper, we study some special classes of strong fuzzy metrics, topological and lattice properties of certain families of strong fuzzy metrics, and, more generally, strong k-fuzzy metrics. Noticing that one of the standard axioms of a strong fuzzy metric can be easily violated when applied in real situations, in the second part of the paper we introduce more general, approximating fuzzy metrics and illustrate their applicability with some numerical examples.

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8

Brooks, Robert, and Carolyn Gordon. "Isospectral families of conformally equivalent Riemannian metrics." Bulletin of the American Mathematical Society 23, no. 2 (October 1, 1990): 433–37. http://dx.doi.org/10.1090/s0273-0979-1990-15952-x.

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9

Rhodes, Frank. "Digital metrics generated by families of paths." Discrete Mathematics 135, no. 1-3 (December 1994): 265–77. http://dx.doi.org/10.1016/0012-365x(93)e0102-a.

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10

Gilinsky, Norman L., and Richard K. Bambach. "Asymmetrical patterns of origination and extinction in higher taxa." Paleobiology 13, no. 4 (1987): 427–45. http://dx.doi.org/10.1017/s0094837300009027.

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Using Sepkoski's compendium of fossil marine families (1982a, and updates), we have analyzed the changing pace of familial origination and extinction within 55 extinct and 44 extant higher taxa of marine organisms. Eight different metrics were calculated, and least-squares regression analysis was used to identify within-taxon trends in the data. All metrics and analyses gave essentially the same results. Origination metrics decline significantly with time during the histories of higher taxa, while extinction metrics increase significantly. The number of statistically significant declines of origination metric, however, substantially and invariably exceeds the number of statistically significant increases of extinction metric for each pair of corresponding metrics analyzed. It follows, therefore, that temporal trends in the pace of origination and extinction within higher taxa are highly asymmetrical.Further analysis shows that truncating data from temporal endpoints has little effect upon the intensity of origination trends, implying that declining pace of origination is a sustained property of the long term histories of taxa. Such truncation, however, reduces the intensity of extinction trends to statistical insignificance and confirms Van Valen's (1985a) suggestion that extinction behaves largely as a stationary process. If the histories of higher taxa are characterized by substantial declines in the pace of origination while the pace of extinction remains largely stationary, it follows that declining pace of origination is an important controlling factor in long term taxic evolution.

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11

Paredes, Marlio. "Families of(1,2)-symplectic metrics on full flag manifolds." International Journal of Mathematics and Mathematical Sciences 29, no. 11 (2002): 651–64. http://dx.doi.org/10.1155/s0161171202012267.

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We obtain new families of(1,2)-symplectic invariant metrics on the full complex flag manifoldsF(n). Forn≥5, we characterizen−3differentn-dimensional families of(1,2)-symplectic invariant metrics onF(n). Each of these families corresponds to a different class of nonintegrable invariant almost complex structures onF(n).

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12

Donaldson, Simon. "Algebraic families of constant scalar curvature Kähler metrics." Surveys in Differential Geometry 19, no. 1 (2014): 111–37. http://dx.doi.org/10.4310/sdg.2014.v19.n1.a5.

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13

Hall, Stuart J. "Perelman’s Entropy for Some Families of Canonical Metrics." Experimental Mathematics 23, no. 3 (July 3, 2014): 277–84. http://dx.doi.org/10.1080/10586458.2014.898220.

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14

chen, Chao, Zhiqi chen, and Yuwang Hu. "Einstein metrics and Einstein–Randers metrics on a class of homogeneous manifolds." International Journal of Geometric Methods in Modern Physics 15, no. 04 (March 13, 2018): 1850052. http://dx.doi.org/10.1142/s0219887818500524.

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In this paper, we give [Formula: see text]-invariant Einstein metrics on a class of homogeneous manifolds [Formula: see text], and then prove that every homogeneous manifold [Formula: see text] admits at least three families of [Formula: see text]-invariant non-Riemannian Einstein–Randers metrics.

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15

Fiorineschi, Lorenzo, Francesco Saverio Frillici, and Federico Rotini. "Three-Dimensional Approach for Assessing Uncommonness of Ideas." Proceedings of the Design Society: International Conference on Engineering Design 1, no. 1 (July 2019): 229–38. http://dx.doi.org/10.1017/dsi.2019.26.

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AbstractA posteriori novelty metrics are often used in design research, in order to extract important information about creativity. However, different assessment approaches can be found in the literature, each of them with related pros and cons. In particular, weighted uncommonness, overall uncommonness and uncommonness across groups are the three main families of a-posteriori novelty metrics identified in this paper. Each of the considered literature metrics can provide specific types of information about the uncommonness of ideas, but in certain experimental circumstances, it could be difficult to rapidly identify the best-suited approach. This paper proposes an integrated procedure where the advantages offered by the three families of metrics can be applied concurrently. A generic case study is used for a first application of the proposal, and the obtained results show that a more comprehensive set of information about a-posteriori novelty can be extracted. In particular, novelty data from the three families of metrics are extracted in a single assessment process.

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16

Foote, Mike. "Temporal variation in extinction risk and temporal scaling of extinction metrics." Paleobiology 20, no. 4 (1994): 424–44. http://dx.doi.org/10.1017/s0094837300012914.

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Many areas of paleobiological research require reliable extinction metrics. Branching-and-extinction simulations and data on Phanerozoic marine families and genera are used to investigate the relationship between interval length and commonly used extinction metrics. Normalization of extinction metrics for interval length is problematic, even when interval length is known without error, because normalization implicitly assumes some model of variation in extinction risk within an interval. If extinction risk within an interval were constant, or if it varied but played no role in the definition of stratigraphic intervals, then Van Valen's time-normalized extinction metric would provide a measure of average extinction risk that is effectively unbiased by interval length. When extinction risk varies greatly within an interval and interval boundaries are drawn at times of heavy extinction, extinction metrics that normalize for interval length are negatively correlated with interval length. Despite its intuitive appeal, the per-taxon extinction rate (proportional extinction per million years) is biased by interval length under a wide range of extinction models.Empirically, time-normalized extinction metrics for Phanerozoic families and genera are negatively correlated with interval length. This is consistent with an extinction model in which many times of very low risk are punctuated by a few times of very high risk which in turn determine stage boundaries. Origination and extinction patterns are similar, but origination intensity varies less among stages than extinction intensity. This observation has at least two plausible explanations: that origination episodes are more protracted than extinction episodes, and that biologic groups do not respond in unison to origination opportunities the way they seem to respond during extinction events. For families and genera, there is enough variation in extinction intensity among stages that stage length can be ignored when studying certain extinction patterns over the entire Phanerozoic.

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17

Bliemel, Martin, and Elicia Maine. ""Academic and Commercial Patent Families: Same Metrics, Different Story"." Academy of Management Proceedings 2015, no. 1 (January 2015): 16700. http://dx.doi.org/10.5465/ambpp.2015.16700abstract.

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18

Hiai, Fumio, Hideki Kosaki, Dénes Petz, and Mary Beth Ruskai. "Families of completely positive maps associated with monotone metrics." Linear Algebra and its Applications 439, no. 7 (October 2013): 1749–91. http://dx.doi.org/10.1016/j.laa.2013.05.012.

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19

Schueth, Dorothee. "Continuous Families of Isospectral Metrics on Simply Connected Manifolds." Annals of Mathematics 149, no. 1 (January 1999): 287. http://dx.doi.org/10.2307/121026.

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20

Gaburro, Romina, and William R. B. Lionheart. "Recovering Riemannian metrics in monotone families from boundary data." Inverse Problems 25, no. 4 (February 13, 2009): 045004. http://dx.doi.org/10.1088/0266-5611/25/4/045004.

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21

Sabourau, Stéphane, and Zeina Yassine. "Optimal systolic inequalities on Finsler Möbius bands." Journal of Topology and Analysis 08, no. 02 (March 15, 2016): 349–72. http://dx.doi.org/10.1142/s1793525316500138.

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We prove optimal systolic inequalities on Finsler Möbius bands relating the systole and the height of the Möbius band to its Holmes–Thompson volume. We also establish an optimal systolic inequality for Finsler Klein bottles of revolution, which we conjecture to hold true for arbitrary Finsler metrics. Extremal metric families both on the Möbius band and the Klein bottle are also presented.

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22

Cantrell, Michael, and Alex Furman. "Asymptotic shapes for ergodic families of metrics on Nilpotent groups." Groups, Geometry, and Dynamics 11, no. 4 (December 7, 2017): 1307–45. http://dx.doi.org/10.4171/ggd/430.

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23

Chau, H. F. "Metrics on unitary matrices and their application to quantifying the degree of non-commutativity between unitary matrices." Quantum Information and Computation 11, no. 9&10 (September 2011): 721–40. http://dx.doi.org/10.26421/qic11.9-10-1.

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By studying the minimum resources required to perform a unitary transformation, families of metrics and pseudo-metrics on unitary matrices that are closely related to a recently reported quantum speed limit by the author are found. Interestingly, this family of metrics can be naturally converted into useful indicators of the degree of non-commutativity between two unitary matrices.

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24

Yang, Guojun. "On a Class of Two-Dimensional Douglas and Projectively Flat Finsler Metrics." Scientific World Journal 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/291491.

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We study a class of two-dimensional Finsler metrics defined by a Riemannian metricαand a 1-formβ. We characterize those metrics which are Douglasian or locally projectively flat by some equations. In particular, it shows that the known fact thatβis always closed for those metrics in higher dimensions is no longer true in two-dimensional case. Further, we determine the local structures of two-dimensional (α,β)-metrics which are Douglasian, and some families of examples are given for projectively flat classes withβbeing not closed.

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25

To, Wing-Keung, and Lin Weng. "$L^{2}$-metrics, projective flatness and families of polarized abelian varieties." Transactions of the American Mathematical Society 356, no. 7 (December 9, 2003): 2685–707. http://dx.doi.org/10.1090/s0002-9947-03-03488-3.

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26

Gordon, Carolyn S., and Edward N. Wilson. "Continuous families of isospectral Riemannian metrics which are not locally isometric." Journal of Differential Geometry 47, no. 3 (1997): 504–29. http://dx.doi.org/10.4310/jdg/1214460548.

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27

Vasil'ev, A. Yu. "Moduli of families of curves and invariant metrics on Teichmüller space." Siberian Mathematical Journal 37, no. 5 (September 1996): 868–75. http://dx.doi.org/10.1007/bf02110718.

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28

TELEMAN, ANDREI. "FAMILIES OF HOLOMORPHIC BUNDLES." Communications in Contemporary Mathematics 10, no. 04 (August 2008): 523–51. http://dx.doi.org/10.1142/s0219199708002892.

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The first goal of the article is to solve several fundamental problems in the theory of holomorphic bundles over non-algebraic manifolds. For instance, we prove that stability and semi-stability are Zariski open properties in families when the Gauduchon degree map is a topological invariant, or when the parameter manifold is compact. Second, we show that, for a generically stable family of bundles over a Kähler manifold, the Petersson–Weil form extends as a closed positive current on the whole parameter space of the family. This extension theorem uses classical tools from Yang–Mills theory (e.g., the Donaldson functional on the space of Hermitian metrics and its properties). We apply these results to study families of bundles over a Kählerian manifold Y parametrized by a non-Kählerian surface X, proving that such families must satisfy very restrictive conditions. These results play an important role in our program to prove existence of curves on class VII surfaces [22–24].

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29

Chen, Bin, and Lili Zhao. "A Note on Randers Metrics of Scalar Flag Curvature." Canadian Mathematical Bulletin 55, no. 3 (September 1, 2012): 474–86. http://dx.doi.org/10.4153/cmb-2011-092-1.

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AbstractSome families of Randers metrics of scalar flag curvature are studied in this paper. Explicit examples that are neither locally projectively flat nor of isotropic S-curvature are given. Certain Randers metrics with Einstein α are considered and proved to be complex. Three dimensional Randers manifolds, with α having constant scalar curvature, are studied.

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30

Creţu, Georgeta. "New classes of projectively related Finsler metrics of constant flag curvature." International Journal of Geometric Methods in Modern Physics 17, no. 05 (March 20, 2020): 2050068. http://dx.doi.org/10.1142/s0219887820500681.

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We define a Weyl-type curvature tensor of [Formula: see text]-type to provide a characterization for Finsler metrics of constant flag curvature. This Weyl-type curvature tensor is projective invariant only to projective factors that are Hamel functions. Based on this aspect, we construct new families of projectively related Finsler metrics that have constant flag curvature.

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31

Jang, Jae-wook, Jiyoung Woo, Aziz Mohaisen, Jaesung Yun, and Huy Kang Kim. "Mal-Netminer: Malware Classification Approach Based on Social Network Analysis of System Call Graph." Mathematical Problems in Engineering 2015 (2015): 1–20. http://dx.doi.org/10.1155/2015/769624.

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As the security landscape evolves over time, where thousands of species of malicious codes are seen every day, antivirus vendors strive to detect and classify malware families for efficient and effective responses against malware campaigns. To enrich this effort and by capitalizing on ideas from the social network analysis domain, we build a tool that can help classify malware families using features driven from the graph structure of their system calls. To achieve that, we first construct a system call graph that consists of system calls found in the execution of the individual malware families. To explore distinguishing features of various malware species, we study social network properties as applied to the call graph, including the degree distribution, degree centrality, average distance, clustering coefficient, network density, and component ratio. We utilize features driven from those properties to build a classifier for malware families. Our experimental results show that “influence-based” graph metrics such as the degree centrality are effective for classifying malware, whereas the general structural metrics of malware are less effective for classifying malware. Our experiments demonstrate that the proposed system performs well in detecting and classifying malware families within each malware class with accuracy greater than 96%.

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32

CHERIYAN, JO, and G. P. SAJEEV. "m-PageRank: A NOVEL CENTRALITY MEASURE FOR MULTILAYER NETWORKS." Advances in Complex Systems 23, no. 05 (August 2020): 2050012. http://dx.doi.org/10.1142/s0219525920500125.

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A complex network is an explicit model for a real-world system such as technological networks, social networks, business networks, and biological networks. The social network is an Internet-based media for socially relevant activities like stay connected with families and friends, colleagues, and customers, for socializing, business, or both. The key nodes, usually called central nodes, capable of measuring the performance of various social network applications. Identifying influencing nodes is primary research for any network analysis research. Degree centrality, a locally computed metric, is simple to compute but not persuasive. The global metrics like betweenness centrality and PageRank are only useful for the systems with a simple structure, but incur a high computational cost with the addition of layers. This paper proposes a novel metric m-PageRank for ranking nodes in a multi-layer complex network. The m-PageRank is an advancement of PageRank. It integrates the existence of the rank of each layer from where the connection connects. The proposed metric was validated through simulations performed over various multilayer networks. The result shows that m-PageRank computes the rank of each node accurately. We observe that the comparison with state-of-the-art metrics demonstrated the suitability of the proposed metric.

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33

Topalov, Petar. "Families of metrics geodesically equivalent to the analogs of the Poisson sphere." Journal of Mathematical Physics 41, no. 11 (November 2000): 7510–20. http://dx.doi.org/10.1063/1.1310356.

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34

Bismut, Jean-Michel, and Daniel S. Freed. "The analysis of elliptic families. I. Metrics and connections on determinant bundles." Communications in Mathematical Physics 106, no. 1 (March 1986): 159–76. http://dx.doi.org/10.1007/bf01210930.

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35

Passos, Ana Carolina dos, Riguel Feltrin Contente, Felippe Veneziani Abbatepaulo, Henry Louis Spach, Ciro Colodetti Vilar, Jean Christophe Joyeux, Beatriz Fernanda Chinhilla Cartagena, and Luis Fernando Fávaro. "Analysis of fish assemblages in sectors along a salinity gradient based on species, families and functional groups." Brazilian Journal of Oceanography 61, no. 4 (December 2013): 251–64. http://dx.doi.org/10.1590/s1679-87592013000400006.

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Here we test the effects of the east-west salinity gradient in the subtropical Paranaguá Bay Estuarine Complex (PEC) on the structure of shallow water fish fauna, determined according to taxonomic (families and species) and functional composition metrics. A total of 152 species were observed. The families with the largest number of species were the Sciaenidae, Carangidae, Haemulidae and Gobiidae. The most abundant species were Atherinella brasiliensis, Harengula clupeola, Anchoa januaria and Anchoa tricolor. Marine stragglers dominated in number of species, followed by marine migrants and estuarine species. Most species were zoobenthivores, followed by piscivores and zooplanktivores. Families and species more frequently associated with estuarine conditions dominated in the mesohaline sector, and those more frequently associated with marine conditions dominated in the euhaline sector. The fish assemblages along the estuarine salinity gradient were found to be better characterized by taxonomic metrics than by functional ones. This is most likely because individuals of all functional groups inhabit all salinity sectors, and thus these metrics are not useful for differentiating assemblages along salinity gradients. Our results differ from those of other studies in tropical and subtropical estuaries, which have emphasized the importance of functional groups in determining fish assemblages along salinity gradients.

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36

Boyarsky, Abraham, and Pawel Góra. "The Pseudo-Orbit Shadowing Property for Markov Operators in the Space of Probability Density Functions." Canadian Journal of Mathematics 42, no. 6 (December 1, 1990): 1000–1017. http://dx.doi.org/10.4153/cjm-1990-053-2.

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AbstractLet X be a space with two metrics d1 and d2. Let S :(X, d1) → (X, d2) be continuous. We say S has the generalized pseudoorbit shadowing property with respect to the metrics d1 and d2 if for every every δ-pseudo-orbit in d1 can be ∊-shadowed by a true orbit in d2, i.e., if {x0, x1,…} satisfies for all i ≧ 0, then for all i ≧ 0. The main result of this note shows that certain Markov operators P : L1→ L1 have the generalized shadowing property on weakly compact subsets of the space of probability density functions, where d1 is the metric of norm convergence and d2 is the metric of weak convergence. An important class of such operators are the Frobenius-Perron operators induced by certain expanding and nonexpanding maps on the interval. When there is exponential convergence of the iterates to the density, we can express δ in terms of ∊. We also show that, unlike the situation in the space X itself, the generalized shadowing property is valid for all parameters in families of maps and that there is stability of the shadowing property.

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37

Victor, J. D., and K. P. Purpura. "Nature and precision of temporal coding in visual cortex: a metric-space analysis." Journal of Neurophysiology 76, no. 2 (August 1, 1996): 1310–26. http://dx.doi.org/10.1152/jn.1996.76.2.1310.

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1. We recorded single-unit and multi-unit activity in response to transient presentation of texture and grating patterns at 25 sites within the parafoveal representation of V1, V2, and V3 of two awake monkeys trained to perform a fixation task. In grating experiments, stimuli varied in orientation, spatial frequency, or both. In texture experiments, stimuli varied in contrast, check size, texture type, or pairs of these attributes. 2. To examine the nature and precision of temporal coding, we compared individual responses elicited by each set of stimuli in terms of two families of metrics. One family of metrics, D(spike), was sensitive to the absolute spike time (following stimulus onset). The second family of metrics, D(interval), was sensitive to the pattern of interspike intervals. In each family, the metrics depend on a parameter q, which expresses the precision of temporal coding. For q = 0, both metrics collapse into the "spike count" metric D(Count), which is sensitive to the number of impulses but insensitive to their position in time. 3. Each of these metrics, with values of q ranging from 0 to 512/s, was used to calculate the distance between all pairs of spike trains within each dataset. The extent of stimulus-specific clustering manifest in these pairwise distances was quantified by an information measure. Chance clustering was estimated by applying the same procedure to synthetic data sets in which responses were assigned randomly to the input stimuli. 4. Of the 352 data sets, 170 showed evidence of tuning via the spike count (q = 0) metric, 294 showed evidence of tuning via the spike time metric, 272 showed evidence of tuning via the spike interval metric to the stimulus attribute (contrast, check size, orientation, spatial frequency, or texture type) under study. Across the entire dataset, the information not attributable to chance clustering averaged 0.042 bits for the spike count metric, 0.171 bits for the optimal spike time metric, and 0.107 bits for the optimal spike interval metric. 5. The reciprocal of the optimal cost q serves as a measure of the temporal precision of temporal coding. In V1 and V2, with both metrics, temporal precision was highest for contrast (ca. 10-30 ms) and lowest for texture type (ca. 100 ms). This systematic dependence of q on stimulus attribute provides a possible mechanism for the simultaneous representation of multiple stimulus attributes in one spike train. 6. Our findings are inconsistent with Poisson models of spike trains. Synthetic data sets in which firing rate was governed by a time-dependent Poisson process matched to the observed poststimulus time histogram (PSTH) overestimated clustering induced by D(count) and, for low values of q, D(spike)[q] and D(intervals)[q]. Synthetic data sets constructed from a modified Poisson process, which preserved not only the PSTH but also spike count statistics accounted for the clustering induced by D(count) but underestimated the clustering induced by D(spike)[q] and D(interval)[q].

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38

Nakhman, A. D. "Restriction of Families of Conversion Operators in Lp Spaces." Vestnik Tambovskogo gosudarstvennogo tehnicheskogo universiteta 27, no. 3 (2021): 449–60. http://dx.doi.org/10.17277/vestnik.2021.03.pp.449-460.

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We study a one-parameter family of convolutional operators acting in Lebesgue Lp spaces. The case of integral kernels given by the Fourier coefficients is considered. It is established that the condition of the coefficients being quasiconvex ensures the boundedness of the corresponding maximal operators. The limiting behavior of families in the metrics of spaces of continuous functions and Lp, p ≥ 1, classes is studied, and their convergence is obtained almost everywhere. The ways of possible generalizations and distributions are indicated.

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39

Cardona, Sergio A. H., and Claudio Meneses. "On a functional of Kobayashi for Higgs bundles." International Journal of Geometric Methods in Modern Physics 17, no. 13 (October 12, 2020): 2050200. http://dx.doi.org/10.1142/s021988782050200x.

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We define a functional [Formula: see text] for the space of Hermitian metrics on an arbitrary Higgs bundle over a compact Kähler manifold, as a natural generalization of the mean curvature energy functional of Kobayashi for holomorphic vector bundles, and study some of its basic properties. We show that [Formula: see text] is bounded from below by a nonnegative constant depending on invariants of the Higgs bundle and the Kähler manifold, and that when achieved, its absolute minima are Hermite–Yang–Mills metrics. We derive a formula relating [Formula: see text] and another functional [Formula: see text], closely related to the Yang–Mills–Higgs functional, which can be thought of as an extension of a formula of Kobayashi for holomorphic vector bundles to the Higgs bundles setting. Finally, using 1-parameter families in the space of Hermitian metrics on a Higgs bundle, we compute the first variation of [Formula: see text], which is expressed as a certain [Formula: see text]-Hermitian inner product. It follows that a Hermitian metric on a Higgs bundle is a critical point of [Formula: see text] if and only if the corresponding Hitchin–Simpson mean curvature is parallel with respect to the Hitchin–Simpson connection.

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40

To, Wing-Keung, and Lin Weng. "Admissible Hermitian metrics on families of line bundles over certain degenerating Riemann surfaces." Pacific Journal of Mathematics 197, no. 2 (February 1, 2001): 441–89. http://dx.doi.org/10.2140/pjm.2001.197.441.

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MATSUOKA, SATOSHI. "A coding theoretic study of MLL proof nets." Mathematical Structures in Computer Science 22, no. 3 (February 2, 2012): 409–49. http://dx.doi.org/10.1017/s0960129511000582.

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In this paper we propose a novel approach for analysing proof nets of Multiplicative Linear Logic (MLL) using coding theory. We define families of proof structures called PS-families and introduce a metric space for each family. In each family: (1)an MLL proof net is a true code element; and(2)a proof structure that is not an MLL proof net is a false (or corrupted) code element. The definition of our metrics elegantly reflects the duality of the multiplicative connectives. We show that in our framework one-error-detection is always possible but one-error-correction is always impossible. We also demonstrate the importance of our main result by presenting two proof-net enumeration algorithms for a given PS-family: the first searches proof nets naively and exhaustively without help from our main result, while the second uses our main result to carry out an intelligent search. In some cases, the first algorithm visits proof structures exponentially, while the second does so only polynomially.

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Ávila, Milton P., Rafaela Neves Carvalho, Lilian Casatti, Juliana Simião-Ferreira, Lorrane Faria de Morais, and Fabrício B. Teresa. "Metrics derived from fish assemblages as indicators of environmental degradation in Cerrado streams." Zoologia 35 (March 22, 2018): 1–8. http://dx.doi.org/10.3897/zoologia.35.e12895.

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The development of effective monitoring tools depends on finding sensitive metrics that are capable of detecting the most important environmental impacts at a given region. We assessed if metrics derived from stream fish assemblages reflect physical habitat degradation and changes in land cover. We sampled the ichthyofauna and environmental characteristics of 16 stream sites of first and second order in the Upper Tocantins River basin. The streams were classified according to their environmental characteristics into reference (n = 5), intermediate (n = 4), and impacted (n = 7). A total of 4,079 individuals in five orders, 12 families, and 30 species were collected. Of the 20 metrics tested, eight were non-collinear and were tested for their performance in discriminating among groups of streams. Three metrics were sensitive to the gradient of degradation: Berger-Parker dominance index, percentage of characiform fish, and percentage of rheophilic individuals. Some commonly used metrics did not reflect the disturbances and many others were redundant with those that did. These results indicate that the metrics derived from fish assemblages may be informative for identifying the conservation status of streams, with the potential to be used in biomonitoring.

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Bauer, Martin, Martins Bruveris, Nicolas Charon, and Jakob Møller-Andersen. "A relaxed approach for curve matching with elastic metrics." ESAIM: Control, Optimisation and Calculus of Variations 25 (2019): 72. http://dx.doi.org/10.1051/cocv/2018053.

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In this paper, we study a class of Riemannian metrics on the space of unparametrized curves and develop a method to compute geodesics with given boundary conditions. It extends previous works on this topic in several important ways. The model and resulting matching algorithm integrate within one common setting both the family of H2-metrics with constant coefficients and scale-invariant H2-metrics on both open and closed immersed curves. These families include as particular cases the class of first-order elastic metrics. An essential difference with prior approaches is the way that boundary constraints are dealt with. By leveraging varifold-based similarity metrics we propose a relaxed variational formulation for the matching problem that avoids the necessity of optimizing over the reparametrization group. Furthermore, we show that we can also quotient out finite-dimensional similarity groups such as translation, rotation and scaling groups. The different properties and advantages are illustrated through numerical examples in which we also provide a comparison with related diffeomorphic methods used in shape registration.

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Abubakar, Shamsuddeen Muhammad, and Zahraddeen Sufyanu. "Comparisons of Filter, Wrapper and Embedded-Based Feature Selection Techniques for Consistency of Software Metrics Analysis." SLU Journal of Science and Technology 4, no. 1&2 (July 20, 2022): 188–204. http://dx.doi.org/10.56471/slujst.v4i.238.

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Identifying and selecting the most consistent subset of metrics which improves the performance of software defect prediction model is paramount but challenging problem as it receives little attention in literature. The current research aimed at investigating the consistency of subsets of metrics that are produced by embedded feature selection techniques. Ten (10) feature selection techniques used from the families of filter and wrapper-based feature selection techniques commonly used in the defect prediction domain. Ten (10) publicly available defect datasets were studied which span both proprietary and open source domains. SVM-RFE-RF presented 42-93% consistent metrics across datasets. While the prior study on non-Embedded produced 56.5% consistent metrics at median. SVM-RFE-LF approach of Embedded Feature Selection Technique produced 54-80% consistent metrics across datasets and 42.5% at median. To state the purpose of tittle has been achieved Embedded based Feature Selection Techniques produced most efficient consistent subset selection across the entire datasets and amongst the feature selection techniques as compared with counterpart filter and wrapper-based feature selection techniques

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Johnson, Michael DeShawn, and Randolph Kirchain. "Developing and Assessing Commonality Metrics for Product Families: A Process-Based Cost-Modeling Approach." IEEE Transactions on Engineering Management 57, no. 4 (November 2010): 634–48. http://dx.doi.org/10.1109/tem.2009.2034642.

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Ives, Lindsey. "Book Review: Behavior analysis metrics & applications for the preservation & reunification of families." Research on Social Work Practice 30, no. 8 (July 21, 2020): 918–20. http://dx.doi.org/10.1177/1049731520942598.

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Roldán López de Hierro, Antonio Francisco, Erdal Karapınar, and Andreea Fulga. "Multiparametric Contractions and Related Hardy-Roger Type Fixed Point Theorems." Mathematics 8, no. 6 (June 11, 2020): 957. http://dx.doi.org/10.3390/math8060957.

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In this paper we present some novel fixed point theorems for a family of contractions depending on two functions (that are not defined on t = 0 ) and on some parameters that we have called multiparametric contractions. We develop our study in the setting of b-metric spaces because they allow to consider some families of functions endowed with b-metrics deriving from similarity measures that are more general than norms. Taking into account that the contractivity condition we will employ is very general (of Hardy-Rogers type), we will discuss the validation and usage of this novel condition. After that, we introduce the main results of this paper and, finally, we deduce some consequences of them which illustrates the wide applicability of the main results.

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Dexter, Kyle G., Ricardo A. Segovia, and Andy R. Griffiths. "Exploring the Concept of Lineage Diversity across North American Forests." Forests 10, no. 6 (June 22, 2019): 520. http://dx.doi.org/10.3390/f10060520.

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Lineage diversity can refer to the number of genetic lineages within species or to the number of deeper evolutionary lineages, such as genera or families, within a community or assemblage of species. Here, we study the latter, which we refer to as assemblage lineage diversity (ALD), focusing in particular on its richness dimension. ALD is of interest to ecologists, evolutionary biologists, biogeographers, and those setting conservation priorities, but despite its relevance, it is not clear how to best quantify it. With North American tree assemblages as an example, we explore and compare different metrics that can quantify ALD. We show that both taxonomic measures (e.g., family richness) and Faith’s phylogenetic diversity (PD) are strongly correlated with the number of lineages in recent evolutionary time, but have weaker correlations with the number of lineages deeper in the evolutionary history of an assemblage. We develop a new metric, time integrated lineage diversity (TILD), which serves as a useful complement to PD, by giving equal weight to old and recent lineage diversity. In mapping different ALD metrics across the contiguous United States, both PD and TILD reveal high ALD across large areas of the eastern United States, but TILD gives greater value to the southeast Coastal Plain, southern Rocky Mountains and Pacific Northwest, while PD gives relatively greater value to the southern Appalachians and Midwest. Our results demonstrate the value of using multiple metrics to quantify ALD, in order to highlight areas of both recent and older evolutionary diversity.

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Garliauskas, Vidas. "Guidelines for the Research of the Lithuanian Catholic Church Metrics Books." Bibliotheca Lituana 2 (October 25, 2012): 66–105. http://dx.doi.org/10.15388/bibllita.2012.2.15581.

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The metrics books of the Lithuanian Catholic Church are a heritage treasure of the whole nation. Up until the 20th century there were approximately 600 churches in Lithuania and each church had more than a dozen metrics books on average which means there could be up to 10 000–15 000 metrics books remaining in various archives. Due to the soviet occupation the church archives were damaged and metrics books were scattered to various unclear locations. Due to these unfortunate historical situation metrics books research has only begun and the books themselves are not yet fully catalogued. Some research on metrics books has been done by Zigmas Zinkevičius, Vitalija Macijauskienė, Jonas Palionis and others. Historians have shed some light on metrics book archives in various archives. It is clear that individual important research work has been done but an overall targeted research is lacking. A priority objective is to create a state wide data base of all catalogued metrics books. Second steps would be complex research of the metrics books including creation of a theoretical information base, creation of various data bases, use of the metrics books for localized research and etc. Successful research of metrics books is only possible if specific guidelines are followed. That is why this publication includes methodical instructions for researches to use when uncertain situations are encountered. The publication includes two cases of metrics books research. In the first example a couple of unique excerpts are presented with comments. The second one reconstructs the picture of the Suginčiai (Molėtai district) estate and town community during the 17th century. It includes residents of the estate, newlyweds, families and other persons). Philological notes on names are also included.

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Fu, Xin, Bin Guo, and Jian Song. "Geometric estimates for complex Monge–Ampère equations." Journal für die reine und angewandte Mathematik (Crelles Journal) 2020, no. 765 (August 1, 2020): 69–99. http://dx.doi.org/10.1515/crelle-2019-0020.

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AbstractWe prove uniform gradient and diameter estimates for a family of geometric complex Monge–Ampère equations. Such estimates can be applied to study geometric regularity of singular solutions of complex Monge–Ampère equations. We also prove a uniform diameter estimate for collapsing families of twisted Kähler–Einstein metrics on Kähler manifolds of nonnegative Kodaira dimensions.

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