A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
Filters
A point calculus for interlevel set homology
2012
Pattern Recognition Letters
Preserved Fulltext
We refer to this new angle at a classical subject within algebraic topology as a point calculus, which we present for the family of interlevel sets of a real-valued function. ...
The theory of persistent homology opens up the possibility to reason about topological features of a space or a function quantitatively and in combinatorial terms. ...
In particular, the persistence diagram of a function forms a comprehensive book-keeping tool on which we build our point calculus. ...
doi:10.1016/j.patrec.2011.10.007
fatcat:mrpoq4hixvfazfqebtbj44q6ne
Homology and Robustness of Level and Interlevel Sets
[article]
2011
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
Given a function f: → on a topological space, we consider the preimages of intervals and their homology groups and show how to read the ranks of these groups from the extended persistence diagram of f. ...
In addition, we quantify the robustness of the homology classes under perturbations of f using well groups, and we show how to read the ranks of these groups from the same extended persistence diagram. ...
Acknowledgements The authors thank Vin de Silva for many helpful technical discussions leading to a strengthening of this paper. ...
arXiv:1102.3389v1
fatcat:bynpnks7afaqtdref5v52lfifi
Homology and robustness of level and interlevel sets
2013
Homology, Homotopy and Applications
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2015; you can also visit the original URL.
The file type is application/pdf.
Given a continuous function f : X → R on a topological space, we consider the preimages of intervals and their homology groups and show how to read the ranks of these groups from the extended persistence ...
In addition, we quantify the robustness of the homology classes under perturbations of f using well groups, and we show how to read the ranks of these groups from the same extended persistence diagram. ...
Acknowledgements The authors thank Vin de Silva for many helpful technical discussions leading to a strengthening of this paper. ...
doi:10.4310/hha.2013.v15.n1.a3
fatcat:pmuum364krhtjfp3fvgnycjgoq
Climbing Brain Levels of Organisation from Genes to Consciousness
2017
Trends in Cognitive Sciences
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Interlevel bridging mechanisms include intrinsic variation-selection mechanisms, which offer a community of bottom-up and top-down models linking genes to consciousness in a stepwise manner. ...
for drug design. ...
It is no more than a method of calculus. ...
doi:10.1016/j.tics.2017.01.004
pmid:28161289
fatcat:o2yu6o3sjjdptiruymbmfhhxra
Theories, models, and equations in systems biology
[chapter]
2007
Systems Biology
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
I disagree with that view, and describe an alternative framework for biological theories as collections of prototypical interlevel largely qualitative causal models that can be extrapolated by analogy ...
I look at two cases in particular in this intersection area: the development of the Hodgkin-Huxley giant squid model for action potentials, and at a more recent model of Ferrée and Lockery for worm (Caenorhabditis ...
On this point Hille writes: 'The Na, Ca, and K families of voltage-gated channels form a homologous gene superfamily, as may be expected from their broad apparent functional similarity. ...
doi:10.1016/b978-044452085-2/50009-7
fatcat:52hexbvjr5eddkoropinza47ti
Bigraded Betti numbers and Generalized Persistence Diagrams
[article]
2024
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is application/pdf.
Note that this fulltext copy is not of the "primary" version of this work. The version it corresponds to is:
2022 pre-print arXiv:2111.02551v3 fatcat:ni3zp6ozjfajpdb4haoralhjmmOther Versions
In this paper we show that the bigraded Betti numbers of M, a classical algebraic invariant of M, are obtained by counting the corner points of these subsets Is. ...
We also show that the aforementioned results are optimal in the sense that they cannot be extended to d-parameter persistence modules for d ≥ 3. ...
By Int(P), we denote the set of all intervals of P. For example, any interval of a zigzag poset in (1) is a set of consecutive points in {• 1 , • 2 , . . . , • n }. ...
arXiv:2111.02551v4
fatcat:zmejbnbcdvb5remocmvhhmbvyy
A Lattice for Persistence
[article]
2014
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Other Versions
Its algorithmic construction leads to two operations on homology groups which describe a diagram of spaces as a complete Heyting algebra, which is a generalization of a Boolean algebra. ...
The intrinsic connection between lattice theory and topology is fairly well established, For instance, the collection of open subsets of a topological subspace always forms a distributive lattice. ...
A point calculus for interlevel set homology. Pattern Recognition
572
Letters, 33(11):1436{1444, 2012.
573
[30] A. Polishchuk and L. Positselski. ...
arXiv:1307.4192v4
fatcat:2b5sg7isbjf5rduy5prob73x44
Analysis of meeting protocols by formalisation, simulation, and verification
2006
Computational and mathematical organization theory
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
This generic protocol is used as a starting point to study real-life meetings. Next, an example meeting is simulated using the generic meeting protocol. ...
When carried out successfully, meetings offer a common medium for participants to exchange ideas and make decisions. However, many meetings suffer from unfocused discussions or irrelevant dialogues. ...
Acknowledgments The authors are grateful to the editor and anonymous reviewers who gave a number of constructive suggestions on how to improve the paper and its readabilty, and to the participants in the ...
doi:10.1007/s10588-006-9001-8
fatcat:vnkxs5bpvnearb3l4hdgv65plq
Co-evolution in Epistemic Networks -- Reconstructing Social Complex Systems
2005
Structure and Dynamics : e-Journal of Anthropological and Related Sciences
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL.
The file type is application/pdf.
; for instance Lane (1993) proposed λ-calculus as a way to generate truly novel objects, generally thanks to a chaotic process -such generative processes however could hardly be considered realistic, ...
This yields a generic method for producing a comprehensive taxonomy of any field where categories can be described as a set of items sharing equivalently some property set. ...
The second point alone, because it assumes the existence of cultural attractors for mankind, lacks credibility: here, cultural diversity confronts cultural similarity. ...
doi:10.5070/sd913003280
fatcat:wgj4moto5fdktjarp2v7idpucu
Can the East Help the West to Value Nature?
1987
Philosophy East & West
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2018; you can also visit the original URL.
The file type is application/pdf.
At this point a nondual, inarticulate mystic union has got to go further. ...
either policy regulations or the moral calculus, nothing comes of it. ...
doi:10.2307/1398737
fatcat:mho2jhbsevbgzorfmsrg7i6vhu
On the representation theory of persistence modules
2023
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2024; you can also visit the original URL.
The file type is application/pdf.
Both of this is complemented by a discussion of the representation theoretic foundations of persistence modules in terms of functor categories, reviewing their calculus, decomposition theory and homological ...
The first subject is an investigation of the spectrum of the category of vector space representations of a totally ordered set $T$: We show the existence of and determine the spectrum of this category ...
Then for different choices of I and C one can obtain all pairs which are involved in the relative interlevel set persistent (co)homology, confer [CSM09; BBF22] . ...
doi:10.4119/unibi/2985257
fatcat:2lihzo5yorddtdm35veqnttjcq
Diachronic metaphysical building relations: towards the metaphysics of extended cognition
2022
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is application/pdf.
First, that a metaphysical building relation - such as composition, constitution, realization, supervenience or emergence - is a relation of ontological dependence, because if a metaphysical building relation ...
To my knowledge there has been no attempt to establish a robust diachronic account of metaphysical building (or, dependence) relations such as, e.g., composition and constitution. ...
In doing so, I will argue for two points. ...
doi:10.25949/19437911.v1
fatcat:gmaicmd4sfgsdlj4mev2hsfa3u
UC Irvine Structure and Dynamics Title Co-evolution in Epistemic Networks-Reconstructing Social Complex Systems Publication Date
2005
unpublished
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2018; you can also visit the original URL.
The file type is application/pdf.
; for instance Lane (1993) proposed λ-calculus as a way to generate truly novel objects, generally thanks to a chaotic process -such generative processes however could hardly be considered realistic, ...
This yields a generic method for producing a comprehensive taxonomy of any field where categories can be described as a set of items sharing equivalently some property set. ...
The second point alone, because it assumes the existence of cultural attractors for mankind, lacks credibility: here, cultural diversity confronts cultural similarity. ...
fatcat:g7u7k6w23ngqfh26g73j7ahi2i