Relevant bibliographies by topics / Grid homology

Academic literature on the topic 'Grid homology'

Author: Grafiati
Published: 10 March 2023

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Journal articles on the topic "Grid homology"

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Droz, Jean-Marie, and Emmanuel Wagner. "Grid diagrams and Khovanov homology." Algebraic & Geometric Topology 9, no. 3 (July 1, 2009): 1275–97. http://dx.doi.org/10.2140/agt.2009.9.1275.

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Shin, Moon-Kyun, Hyun-Ah Lee, Jae-Jun Lee, Ki-Nam Song, and Gyung-Jin Park. "ICONE15-10366 Optimization of a Nuclear Fuel Spacer Grid Spring Using Homology Constraints." Proceedings of the International Conference on Nuclear Engineering (ICONE) 2007.15 (2007): _ICONE1510. http://dx.doi.org/10.1299/jsmeicone.2007.15._icone1510_186.

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Cavallo, Alberto. "The concordance invariant tau in link grid homology." Algebraic & Geometric Topology 18, no. 4 (April 26, 2018): 1917–51. http://dx.doi.org/10.2140/agt.2018.18.1917.

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Ramyachitra, D., and P. Pradeep Kumar. "Frog leap algorithm for homology modelling in grid environment." International Journal of Grid and Utility Computing 7, no. 1 (2016): 29. http://dx.doi.org/10.1504/ijguc.2016.073775.

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Shin, M. K., H. A. Lee, J. J. Lee, K. N. Song, and G. J. Park. "Optimization of a nuclear fuel spacer grid spring using homology constraints." Nuclear Engineering and Design 238, no. 10 (October 2008): 2624–34. http://dx.doi.org/10.1016/j.nucengdes.2008.04.003.

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Dey, Subhankar, and Hakan Doğa. "A combinatorial description of the knot concordance invariant epsilon." Journal of Knot Theory and Its Ramifications 30, no. 06 (May 2021): 2150036. http://dx.doi.org/10.1142/s021821652150036x.

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In this paper, we give a combinatorial description of the concordance invariant [Formula: see text] defined by Hom, prove some properties of this invariant using grid homology techniques. We compute the value of [Formula: see text] for [Formula: see text] torus knots and prove that [Formula: see text] if [Formula: see text] is a grid diagram for a positive braid. Furthermore, we show how [Formula: see text] behaves under [Formula: see text]-cabling of negative torus knots.
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Wong, Michael. "Grid diagrams and Manolescu’s unoriented skein exact triangle for knot Floer homology." Algebraic & Geometric Topology 17, no. 3 (July 17, 2017): 1283–321. http://dx.doi.org/10.2140/agt.2017.17.1283.

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Kaczynski, Tomasz, Marian Mrozek, and Anik Trahan. "Ideas from Zariski Topology in the Study of Cubical Homology." Canadian Journal of Mathematics 59, no. 5 (October 1, 2007): 1008–28. http://dx.doi.org/10.4153/cjm-2007-043-3.

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AbstractCubical sets and their homology have been used in dynamical systems as well as in digital imaging. We take a fresh look at this topic, following Zariski ideas from algebraic geometry. The cubical topology is defined to be a topology in ℝd in which a set is closed if and only if it is cubical. This concept is a convenient frame for describing a variety of important features of cubical sets. Separation axioms which, in general, are not satisfied here, characterize exactly those pairs of points which we want to distinguish. The noetherian property guarantees the correctness of the algorithms. Moreover, maps between cubical sets which are continuous and closed with respect to the cubical topology are precisely those for whom the homology map can be defined and computed without grid subdivisions. A combinatorial version of the Vietoris–Begle theorem is derived. This theorem plays the central role in an algorithm computing homology of maps which are continuous with respect to the Euclidean topology.
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Naumann, Robert K., Patricia Preston-Ferrer, Michael Brecht, and Andrea Burgalossi. "Structural modularity and grid activity in the medial entorhinal cortex." Journal of Neurophysiology 119, no. 6 (June 1, 2018): 2129–44. http://dx.doi.org/10.1152/jn.00574.2017.

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Following the groundbreaking discovery of grid cells, the medial entorhinal cortex (MEC) has become the focus of intense anatomical, physiological, and computational investigations. Whether and how grid activity maps onto cell types and cortical architecture is still an open question. Fundamental similarities in microcircuits, function, and connectivity suggest a homology between rodent MEC and human posteromedial entorhinal cortex. Both are specialized for spatial processing and display similar cellular organization, consisting of layer 2 pyramidal/calbindin cell patches superimposed on scattered stellate neurons. Recent data indicate the existence of a further nonoverlapping modular system (zinc patches) within the superficial MEC layers. Zinc and calbindin patches have been shown to receive largely segregated inputs from the presubiculum and parasubiculum. Grid cells are also clustered in the MEC, and we discuss possible structure-function schemes on how grid activity could map onto cortical patch systems. We hypothesize that in the superficial layers of the MEC, anatomical location can be predictive of function; thus relating functional properties and neuronal morphologies to the cortical modules will be necessary for resolving how grid activity maps onto cortical architecture. Imaging or cell identification approaches in freely moving animals will be required for testing this hypothesis.
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Maršálek, Roman, Radim Zedka, Erich Zöchmann, Josef Vychodil, Radek Závorka, Golsa Ghiaasi, and Jiří Blumenstein. "Persistent Homology Approach for Human Presence Detection from 60 GHz OTFS Transmissions." Sensors 23, no. 4 (February 16, 2023): 2224. http://dx.doi.org/10.3390/s23042224.

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Orthogonal Time Frequency Space (OTFS) is a new, promising modulation waveform candidate for the next-generation integrated sensing and communication (ISaC) systems, providing environment-awareness capabilities together with high-speed wireless data communications. This paper presents the original results of OTFS-based person monitoring measurements in the 60 GHz millimeter-wave frequency band under realistic conditions, without the assumption of an integer ratio between the actual delays and Doppler shifts of the reflected components and the corresponding resolution of the OTFS grid. As the main contribution of the paper, we propose the use of the persistent homology technique as a method for processing gathered delay-Doppler responses. We highlight the advantages of the persistent homology approach over the standard constant false alarm rate target detector for selected scenarios.
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Dissertations / Theses on the topic "Grid homology"

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Tombari, Francesca. "Deformation of surfaces in 2D persistent homology." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/15809/.

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In the context of 2D persistent homology a new metric has been recently introduced, the coherent matching distance. In order to study this metric, the filtering function is required to present particular “regularity” properties, based on a geometrical construction of the real plane, called extended Pareto grid. This dissertation shows a new result for modifying the extended Pareto grid associated to a filtering function defined on a smooth closed surface, with values in the real plane. In future, the technical result presented here could be used to prove the genericity of the regularity conditions assumed for the filtering function.
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Afzelius, Lovisa. "Computational Modelling of Structures and Ligands of CYP2C9." Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis : Univ-bibl. [distributör], 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-4016.

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CELORIA, DANIELE. "Grid homology in lens spaces." Doctoral thesis, 2016. http://hdl.handle.net/2158/1039024.

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Wong, C. M. Michael. "Unoriented skein relations for grid homology and tangle Floer homology." Thesis, 2017. https://doi.org/10.7916/D8251WN1.

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Grid homology is a combinatorial version of knot Floer homology. In a previous thesis, the author established an unoriented skein exact triangle for grid homology, giving a combinatorial proof of Manolescu’s unoriented skein exact triangle for knot Floer homology, and extending Manolescu’s result from Z/2Z coefficients to coefficients in any commutative ring. In Part II of this dissertation, after recalling the combinatorial proof mentioned above, we track the delta-gradings of the maps involved in the skein exact triangle, and use them to establish the Floer-homological sigma-thinness of quasi-alternating links over any commutative ring. Tangle Floer homology is a combinatorial extension of knot Floer homology to tangles, introduced by Petkova–Vertesi; it assigns an A-infinity-(bi)module to each tangle, so that the knot Floer homology of a link L obtained by gluing together tangles T_1, ..., T_n can be recovered from a tensor product of the A-infinity-(bi)modules assigned to the tangles T_i. Currently, tangle Floer homology has only been defined over Z/2Z. Part III of this dissertation presents a joint result with Ina Petkova, establishing an analogous unoriented skein relation for tangle Floer homology over Z/2Z, and tracking the delta-gradings involved.
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Books on the topic "Grid homology"

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Wong, C. M. Michael. Unoriented skein relations for grid homology and tangle Floer homology. [New York, N.Y.?]: [publisher not identified], 2017.

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2

András, Stipsicz, and Szabó Zoltán 1965-, eds. Grid homology for knots and links. Providence, Rhode Island: American Mathematical Society, 2015.

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3

Ozsváth, Peter S., András I. Stipsicz, and Zoltán Szabó. Grid Homology for Knots and Links. American Mathematical Society, 2015.

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Book chapters on the topic "Grid homology"

1

"Grid homology." In Mathematical Surveys and Monographs, 65–90. Providence, Rhode Island: American Mathematical Society, 2015. http://dx.doi.org/10.1090/surv/208/04.

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"Grid homology for links." In Mathematical Surveys and Monographs, 187–214. Providence, Rhode Island: American Mathematical Society, 2015. http://dx.doi.org/10.1090/surv/208/11.

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"The invariance of grid homology." In Mathematical Surveys and Monographs, 91–112. Providence, Rhode Island: American Mathematical Society, 2015. http://dx.doi.org/10.1090/surv/208/05.

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"Basic properties of grid homology." In Mathematical Surveys and Monographs, 127–34. Providence, Rhode Island: American Mathematical Society, 2015. http://dx.doi.org/10.1090/surv/208/07.

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"Grid homology over the integers." In Mathematical Surveys and Monographs, 291–324. Providence, Rhode Island: American Mathematical Society, 2015. http://dx.doi.org/10.1090/surv/208/15.

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