Relevant bibliographies by topics / Other homology theories

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Academic literature on the topic 'Other homology theories'

Author: Grafiati
Published: 4 June 2021
Last updated: 18 February 2022

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Journal articles on the topic "Other homology theories"

1

Aguilar, Marcelo A., and Carlos Prieto. "Transfers for ramified covering maps in homology and cohomology." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–28. http://dx.doi.org/10.1155/ijmms/2006/94651.

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Making use of a modified version, due to McCord, of the Dold-Thom construction of ordinary homology, we give a simple topological definition of a transfer for ramified covering maps in homology with arbitrary coefficients. The transfer is induced by a suitable map between topological groups. We also define a new cohomology transfer which is dual to the homology transfer. This duality allows us to show that our homology transfer coincides with the one given by L. Smith. With our definition of the homology transfer we can give simpler proofs of the properties of the known transfer and of some new ones. Our transfers can also be defined in Karoubi's approach to homology and cohomology. Furthermore, we show that one can define mixed transfers from other homology or cohomology theories to the ordinary ones.
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Hedley, Jonathan G., Vladimir B. Teif, and Alexei A. Kornyshev. "Nucleosome-induced homology recognition in chromatin." Journal of The Royal Society Interface 18, no. 179 (June 2021): 20210147. http://dx.doi.org/10.1098/rsif.2021.0147.

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One of the least understood properties of chromatin is the ability of its similar regions to recognize each other through weak interactions. Theories based on electrostatic interactions between helical macromolecules suggest that the ability to recognize sequence homology is an innate property of the non-ideal helical structure of DNA. However, this theory does not account for the nucleosomal packing of DNA. Can homologous DNA sequences recognize each other while wrapped up in the nucleosomes? Can structural homology arise at the level of nucleosome arrays? Here, we present a theoretical model for the recognition potential well between chromatin fibres sliding against each other. This well is different from the one predicted for bare DNA; the minima in energy do not correspond to literal juxtaposition, but are shifted by approximately half the nucleosome repeat length. The presence of this potential well suggests that nucleosome positioning may induce mutual sequence recognition between chromatin fibres and facilitate the formation of chromatin nanodomains. This has implications for nucleosome arrays enclosed between CTCF–cohesin boundaries, which may form stiffer stem-like structures instead of flexible entropically favourable loops. We also consider switches between chromatin states, e.g. through acetylation/deacetylation of histones, and discuss nucleosome-induced recognition as a precursory stage of genetic recombination.
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Albin, Pierre, Markus Banagl, Eric Leichtnam, Rafe Mazzeo, and Paolo Piazza. "Refined intersection homology on non-Witt spaces." Journal of Topology and Analysis 07, no. 01 (December 2, 2014): 105–33. http://dx.doi.org/10.1142/s1793525315500065.

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We investigate a generalization to non-Witt stratified spaces of the intersection homology theory of Goresky–MacPherson. The second-named author has described the self-dual sheaves compatible with intersection homology, and the other authors have described a generalization of Cheeger's L2 de Rham cohomology. In this paper we first extend both of these cohomology theories by describing all sheaf complexes in the derived category of constructible sheaves that are compatible with middle perversity intersection cohomology, though not necessarily self-dual. Our main result is that this refined intersection cohomology theory coincides with the analytic de Rham theory on Thom–Mather stratified spaces. The word "refined" is motivated by the fact that the definition of this cohomology theory depends on the choice of an additional structure (mezzo-perversity) which is automatically zero in the case of a Witt space.
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Loday, Jean-Louis. "Algebraic K-theory and cyclic homology." Journal of K-theory 11, no. 3 (April 30, 2013): 553–57. http://dx.doi.org/10.1017/is012011006jkt200.

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The following are personal reminiscences of my research years in algebraic K-theory and cyclic homology during which Dan Quillen was everyday present in my professional life.In the late sixties (of the twentieth century) the groups K0;K1;K2 were known and well-studied. The group K0 had been introduced by Alexander Grothendieck, then came K1 by Hyman Bass [2] (as a variation of the Whitehead group), permitting one to generalize the notion of determinant, and finally K2 by John Milnor [9] and Michel Kervaire. The big problem was: how about Kn? Having in mind topological K-theory and all the other generalized (co)homological theories, one was expecting higher K-groups which satisfy similar axioms, in particular the Mayer-Vietoris exact sequence. The discovery by Richard Swan of the existence of an obstruction for this property to hold shed some embarrassment. What kind of properties should we ask of Kn? There were various attempts, for instance by Max Karoubi and Orlando Villamayor [4]. And suddenly Dan Quillen came with a candidate sharing a lot of nice properties. He had even two different constructions of the same object: the “+” construction and the “Q” construction [14, 15]. Not only did he propose a candidate but he already got a computation: the higher K-theory of finite fields. This was a fantastic step forward and Hyman Bass organized a two week conference at the Battelle Institute in Seattle during the summer of 1972, which was attended by Bass, Borel, Husemoller, Karoubi, Priddy, Quillen, Segal, Stasheff, Tate, Waldhausen, Wall and sixty other mathematicians. The Proceedings appeared as Springer Lecture Notes 341, 342 and 343. I met Quillen for the first time on this occasion.
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Kerler, Thomas. "Homology TQFT's and the Alexander–Reidemeister Invariant of 3-Manifolds via Hopf Algebras and Skein Theory." Canadian Journal of Mathematics 55, no. 4 (August 1, 2003): 766–821. http://dx.doi.org/10.4153/cjm-2003-033-5.

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AbstractWe develop an explicit skein-theoretical algorithm to compute the Alexander polynomial of a 3-manifold from a surgery presentation employing the methods used in the construction of quantum invariants of 3-manifolds. As a prerequisite we establish and prove a rather unexpected equivalence between the topological quantum field theory constructed by Frohman and Nicas using the homology ofU(1)-representation varieties on the one side and the combinatorially constructed Hennings TQFT based on the quasitriangular Hopf algebra= ℤ/2 n ⋊ Λ* ℝ2on the other side. We find that both TQFT's are SL(2; ℝ)-equivariant functors and, as such, are isomorphic. The SL(2; ℝ)-action in the Hennings construction comes from the natural action onand in the case of the Frohman–Nicas theory from the Hard–Lefschetz decomposition of theU(1)-moduli spaces given that they are naturally Kähler. The irreducible components of this TQFT, corresponding to simple representations of SL(2; ℤ) and Sp(2g; ℤ), thus yield a large family of homological TQFT's by taking sums and products. We give several examples of TQFT's and invariants that appear to fit into this family, such as Milnor and Reidemeister Torsion, Seiberg–Witten theories, Casson type theories for homology circlesà laDonaldson, higher rank gauge theories following Frohman and Nicas, and the ℤ=pℤ reductions of Reshetikhin.Turaev theories over the cyclotomic integers ℤ[ζp]. We also conjecture that the Hennings TQFT for quantum-sl2is the product of the Reshetikhin–Turaev TQFT and such a homological TQFT.
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Blunden, Richard, Timothy J. Wilkes, John W. Forster, Mar M. Jimenez, Michael J. Sandery, Angela Karp, and R. Neil Jones. "Identification of the E3900 family, a second family of rye B chromosome specific repeated sequences." Genome 36, no. 4 (August 1, 1993): 706–11. http://dx.doi.org/10.1139/g93-095.

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A second family of highly repeated sequences has been identified on the B chromosome of rye (Secale cereale). The E3900 family was detected as a variant band in EcoRI digests of +B DNA. A clone of the basic repeat of the family was obtained, and the organization of the family was investigated by genomic hybridization. The E3900 family has no apparent homology to the A chromosome sequences of rye or other members of the Gramineae. The family has been localized by in situ hybridization to the end of the long arm of the rye B chromosome. The previously characterized E1100 sequence shows in situ hybridization to the same location as the E3900 family. These results are discussed in light of current theories of the origin of B chromosomes.Key words: B chromosome, Secale cereale, repeated sequence, cloning, in situ hybridization.
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7

Gerhards, Jürgen, Silke Hans, and Michael Mutz. "Social Class and Cultural Consumption: The Impact of Modernisation in a Comparative European Perspective." Comparative Sociology 12, no. 2 (2013): 160–83. http://dx.doi.org/10.1163/15691330-12341258.

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Abstract Pierre Bourdieu’s work has argued that there is a homology of social classes on the one hand and cultural consumption on the other. In contrast, theories of individualisation posit that social class plays only a minor role in shaping lifestyle in contemporary societies. In this paper we examine a) how much contemporary highbrow lifestyles in 27 European countries are structured by class membership, b) the extent to which highbrow consumption varies according to the level of modernisation of a society and c) whether the explanatory power of social class in relation to highbrow consumption decreases in more modernised European countries. The findings show that highbrow lifestyles are strongly influenced by social class, and that highbrow consumption is more common in more modernised societies. Moreover, the findings confirm the hypothesis that the formative power of social class on lifestyle decreases in highly modernised societies, albeit without disappearing completely.
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Zapata, José A. "Gauge from Holography and Holographic Gravitational Observables." Advances in High Energy Physics 2019 (February 7, 2019): 1–14. http://dx.doi.org/10.1155/2019/9781620.

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In a spacetime divided into two regions U1 and U2 by a hypersurface Σ, a perturbation of the field in U1 is coupled to perturbations in U2 by means of the holographic imprint that it leaves on Σ. The linearized gluing field equation constrains perturbations on the two sides of a dividing hypersurface, and this linear operator may have a nontrivial null space. A nontrivial perturbation of the field leaving a holographic imprint on a dividing hypersurface which does not affect perturbations on the other side should be considered physically irrelevant. This consideration, together with a locality requirement, leads to the notion of gauge equivalence in Lagrangian field theory over confined spacetime domains. Physical observables in a spacetime domain U can be calculated integrating (possibly nonlocal) gauge invariant conserved currents on hypersurfaces such that ∂Σ⊂∂U. The set of observables of this type is sufficient to distinguish gauge inequivalent solutions. The integral of a conserved current on a hypersurface is sensitive only to its homology class [Σ], and if U is homeomorphic to a four ball the homology class is determined by its boundary S=∂Σ. We will see that a result of Anderson and Torre implies that for a class of theories including vacuum general relativity all local observables are holographic in the sense that they can be written as integrals of over the two-dimensional surface S. However, nonholographic observables are needed to distinguish between gauge inequivalent solutions.
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Fogassi, Leonardo, and Pier Francesco Ferrari. "Mirror neurons, gestures and language evolution." Interaction Studies 5, no. 3 (April 18, 2005): 345–63. http://dx.doi.org/10.1075/is.5.3.03fog.

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Different theories have been proposed for explaining the evolution of language. One of this maintains that gestural communication has been the precursor of human speech. Here we present a series of neurophysiological evidences that support this hypothesis. Communication by gestures, defined as the capacity to emit and recognize meaningful actions, may have originated in the monkey motor cortex from a neural system whose basic function was action understanding. This system is made by neurons of monkey’s area F5, named mirror neurons, activated by both execution and observation of goal-related actions. Recently, two new categories of mirror neurons have been described. Neurons of one category respond to the sound of an action, neurons of the other category respond to the observation of mouth ingestive and communicative actions. The properties of these neurons indicate that monkey’s area F5 possesses the basic neural mechanisms for associating gestures and meaningful sounds as a pre-adaptation for the later emergence of articulated speech. The homology and the functional similarities between monkey area F5 and Broca’s area support this evolutionary scenario.
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Mesny, Anne. "What Do ‘We’ Know That ‘They’ Don’t? Sociologists’ versus Non-Sociologists’ Knowledge." Canadian Journal of Sociology 34, no. 3 (May 29, 2009): 671–96. http://dx.doi.org/10.29173/cjs6313.

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This paper attempts to clarify or to reposition some of the controversies generated by Burawoy’s defense of public sociology and by his vision of the mutually stimulating relationship between the different forms of sociology. Before arguing if, why, and how, sociology should or could be more ‘public’, it might be useful to reflect upon what it is we think we, as sociologists, know that ‘lay people’ do not. This paper thus explores the public sociology debate’s epistemological core, namely the issue of the relationship between sociologists’ and non-sociologists’ knowledge of the social world. Four positions regarding the status of sociologists’ knowledge versus lay people’s knowledge are explored: superiority (sociologists’ knowledge of the social world is more accurate, objective and reflexive than lay people’s knowledge, thanks to science’s methods and norms), homology (when they are made explicit, lay theories about the social world often parallel social scientists’ theories), complementarity (lay people’s and social scientists’ knowledge complement one another. The former’s local, embedded knowledge is essential to the latter’s general, disembedded knowledge), and circularity (sociologists’ knowledge continuously infuses commonsensical knowledge, and scientific knowledge about the social world is itself rooted in common sense knowledge. Each form of knowledge feeds the other). For each of these positions, implications are drawn regarding the terms, possibilities and conditions of a dialogue between sociologists and their publics, especially if we are to take the circularity thesis seriously. Conclusions point to the accountability we face towards the people we study, and to the idea that sociology is always performative, a point that has, to some extent, been obscured by Burawoy’s distinctions between professional, critical, policy and public sociologies.
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Dissertations / Theses on the topic "Other homology theories"

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Cho, Karina Elle. "Enhancing the Quandle Coloring Invariant for Knots and Links." Scholarship @ Claremont, 2019. https://scholarship.claremont.edu/hmc_theses/228.

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Quandles, which are algebraic structures related to knots, can be used to color knot diagrams, and the number of these colorings is called the quandle coloring invariant. We strengthen the quandle coloring invariant by considering a graph structure on the space of quandle colorings of a knot, and we call our graph the quandle coloring quiver. This structure is a categorification of the quandle coloring invariant. Then, we strengthen the quiver by decorating it with Boltzmann weights. Explicit examples of links that show that our enhancements are proper are provided, as well as background information in quandle theory.
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Books on the topic "Other homology theories"

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Conference Board of the Mathematical Sciences and NSF-CBMS Regional Conference in the Mathematical Sciences on Deformation Theory of Algebras and Modules (2011 : Raleigh, N.C.), eds. Deformation theory of algebras and their diagrams. Providence, Rhode Island: Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, 2012.

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2

Topological modular forms. Providence, Rhode Island: American Mathematical Society, 2014.

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3

1975-, Panov Taras E., ed. Toric topology. Providence, Rhode Island: American Mathematical Society, 2015.

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1974-, Zomorodian Afra J., ed. Advances in applied and computational topology: American Mathematical Society Short Course on Computational Topology, January 4-5, 2011, New Orleans, Louisiana. Providence, R.I: American Mathematical Society, 2012.

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Basterra, Maria, Kristine Bauer, Kathryn Hess, and Brenda Johnson. Women in topology: Collaborations in homotopy theory : WIT, Women in Topology Workshop, August 18-23, 2013, Banff International Research Station, Banff, Alberta, Canada. Providence, Rhode Island: American Mathematical Society, 2015.

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1974-, Nelson Sam, ed. Quandles: An introduction to the algebra of knots. Providence, Rhode Island: American Mathematical Society, 2015.

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Book chapters on the topic "Other homology theories"

1

West-Eberhard, Mary Jane. "Macroevolution." In Developmental Plasticity and Evolution. Oxford University Press, 2003. http://dx.doi.org/10.1093/oso/9780195122343.003.0037.

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Macroevolution, or trans-specific evolution, refers to two different things in the literature on evolution. In discussions of phylogeny, it means phylogenetic branching pattern, or trends, seen at relatively high taxonomic levels (e.g., Stanley, 1979; Brooks and McLennan, 1991; Sober, 1993)—”any patterns that transcend species boundaries” (Lynch, 1991)—such as births and deaths of species and higher taxa and the shapes and diversity of radiations (Valentine, 1990). In discussions of evolutionary phenotypic transitions like those of part II, it means major phenotypic change (Lincoln et al., 1982). Rensch (1960) defined macroevolution as “evolution above the species level.” Microevolution, by contrast, is evolution below the species level, such as adaptive phenotypic and genetic change within populations, and geographic variation within a species. According to Simpson (1953a), the terms “macroevolution” and “microevolution” were invented by Goldschmidt (1940 [1982]), who also claimed that they involve different kinds of evolution. This problematic idea dates back to antiquity (see Rensch, 1960, for a concise review). The macroevolution problem, with emphasis on phylogenesis, was among other things (see Vuilleumier, 1984) behind the skepticism regarding Darwinism promoted by the enormously respected and influential French zoologist P.-P. Grassé. Grassé was convinced that the neo-Darwinian approach, with its emphasis on microevolution, cannot account for the primary features of evolution, namely, the large-scale diversification of life into major phylogenetic branches separated by unbridged gaps (e.g., see Grassé, 1973). This challenge echoes in the writings of many other critics of neo-Darwinism (e.g., Ho and Saunders, 1984; Gould and Eldredge, 1977; Gould, 1994; see also below), especially those who wish to contrast multilevel selection (including species selection) with microevolutionary theories (see Gould, 1999). The two macroevolution concepts, like the homology concepts discussed in chapter 25, are used interchangeably without sufficient attention to potential confusions. The result is needless controversy. The phylogenetic definition, for example, implies that macroevolution cannot, by definition, occur within species, for it refers exclusively to patterns above the species level. The phenotypic, major-change definition, on the other hand, can include processes within species.
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Brower, Andrew V. Z., and Randall T. Schuh. "Character Polarity and Inferring Homology." In Biological Systematics, 113–41. Cornell University Press, 2021. http://dx.doi.org/10.7591/cornell/9781501752773.003.0004.

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This chapter assesses character polarity and homology. Prior to the advent of computer-based analyses, German entomologist and systematic theorist Willi Hennig and other cladistic pioneers routinely used prepolarized characters to construct their phylogenetic hypotheses and developed a specialized terminology to describe their practices. In Hennig's view, all the states of a character — be they plesiomorphic, apomorphic, or homoplastic — are homologous. He argued that synapomorphies — shared derived characters — provide the only evidence for the existence of natural groups. This is the fundamental aspect of his arguments for the phylogenetic system; all of Hennig's other principles are subsidiary to it. Thus, in the Hennigian view, synapomorphy is the only “kind” of homology that bears upon patterns of relationship, a distinction that has led many cladists to equate the two terms.
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