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A cellular model for multi-objects multi-dimensional homotopic deformations

Yann Cointepas, Isabelle Bloch, Line Garnero
<span title="">2001</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jm6w2xclfzguxnhmnmq5omebpi" style="color: black;">Pattern Recognition</a> </i> &nbsp;
This characterization allows to de"ne homotopic deformations of a complex scene.  ...  We propose a consistent topological modeling of such scenes, based on a cellular model. We introduce a de"nition of simple elements for any adjacency graph-based geometrical structure.  ...  For this purpose we showed that a cellular model can be used as an homotopic deformable model.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0031-3203(00)00106-0">doi:10.1016/s0031-3203(00)00106-0</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/grzgfmqhl5dn3nnszrnl7xuuwy">fatcat:grzgfmqhl5dn3nnszrnl7xuuwy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170706043546/https://perso.telecom-paristech.fr/bloch/papers/prYann01.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/91/1c/911c54062fb258fe671489199233250c16065041.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0031-3203(00)00106-0"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

A Discrete Homotopic Deformable Model Dealing with Objects with Different Local Dimensions [chapter]

Yann Cointepas, Isabelle Bloch, Line Garnero
<span title="">1999</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
In this paper we introduce a deformable model based on cellular complexes. This model allows the representation of objects with different local dimensions, and has good topological properties.  ...  This criterion is used to build an homotopic deformable model that can be used for image processing.  ...  Then, in section 3, we define homotopic deformations for this model.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-49126-0_20">doi:10.1007/3-540-49126-0_20</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kyyirl73abdl7lx532ixbbueqi">fatcat:kyyirl73abdl7lx532ixbbueqi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190503075037/https://link.springer.com/content/pdf/10.1007%2F3-540-49126-0_20.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/04/51/0451a56443f18abf2f04629e9b0056b397a79161.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-49126-0_20"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Segmentation-Less 3D Quantitative Image Analysis of Tissue Architecture with Application to the Localization of Organelles in MDCK Cysts

Khaled Khairy, Uros Krzic, Petra Jakob, Philippe Girard, Ernst H.K. Stelzer, Emmanuel Reynaud
<span title="">2009</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/dez2wau7t5aqvklzwrcsreuwq4" style="color: black;">Biophysical Journal</a> </i> &nbsp;
initiative to develop a primate-based tuberculosis model system.  ...  three dimensional (3D) resolution.  ...  Additionally, these shape changes relate to modifications in stem cell adhesion and mobility, and provide a connection between environmental cues, nuclear deformation, and cellular behavior.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.bpj.2008.12.1477">doi:10.1016/j.bpj.2008.12.1477</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/j4y7p3lekza7lhyzoip2yrxaxi">fatcat:j4y7p3lekza7lhyzoip2yrxaxi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170927010055/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/489/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS9zMDAwNjM0OTUwODAxNjkyNQ%3D%3D.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/4f/8a/4f8aa92045c534596c4bd560dec57229542fdc63.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.bpj.2008.12.1477"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Rf Power Consumption Emulation Optimized With Interval Valued Homotopies

Deogratius Musiige, François Anton, Vital Yatskevich, Laulagnet Vincent, Darka Mioc, Nguyen Pierre
<span title="2011-09-27">2011</span> <i title="Zenodo"> Zenodo </i> &nbsp;
The precisions of the instruments used for the physical measurements have been modeled as intervals.  ...  This paper presents a methodology towards the emulation of the electrical power consumption of the RF device during the cellular phone/handset transmission mode using the LTE technology.  ...  Indeed, homotopies have been used successfully for modeling continuously changing physical phenomena as homotopy is a continuous deformation (see section III) . This paper is organised as follows.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5281/zenodo.1057358">doi:10.5281/zenodo.1057358</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/o3uk7trbnnh2lmsgbteb6fy4vi">fatcat:o3uk7trbnnh2lmsgbteb6fy4vi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200116071117/https://zenodo.org/record/1057359/files/2507.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ac/5c/ac5c755e3fbcd8fcdd4964cbee15ed334b45785c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5281/zenodo.1057358"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> zenodo.org </button> </a>

Resolutions of discriminants and topology of their complements [chapter]

Victor Vassiliev
<span title="">2001</span> <i title="Springer Netherlands"> New Developments in Singularity Theory </i> &nbsp;
We describe the main construction of such classes (based on the conical resolutions of discriminants) and list the results for a number of examples.  ...  discriminant sets of degenerate objects.  ...  The poset is a model example of a poset of multi-configurations in the same way as the ones in subsections 3.1, 4.4 were the typical examples of posets of (mono)configurations.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-94-010-0834-1_4">doi:10.1007/978-94-010-0834-1_4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pi5cthiopjd37ish6gttf74goa">fatcat:pi5cthiopjd37ish6gttf74goa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170921220901/http://www.pdmi.ras.ru/~arnsem/papers/SIERSHOOL.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/20/c5/20c59a6a9a00546467f58501c60ebd66f45f0cfe.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-94-010-0834-1_4"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

2D Topological Map Isomorphism for Multi-Label Simple Transformation Definition [chapter]

Guillaume Damiand, Tristan Roussillon, Christine Solnon
<span title="">2014</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
A 2D topological map allows one to fully describe the topology of a labeled image. In this paper we introduce new tools for comparing the topology of two labeled images.  ...  Then we use this notion to give a generic definition of multi-label simple transformation as a set of transformations of labels of pixels which does not modify the topology of the labeled image.  ...  This second question is interesting to propose a deformable model with a topological control for example. In this paper, these two problems are addressed.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-09955-2_4">doi:10.1007/978-3-319-09955-2_4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/e5e2duqejnbtfo3xhuxctf2uku">fatcat:e5e2duqejnbtfo3xhuxctf2uku</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190219215703/http://pdfs.semanticscholar.org/1b78/aa1db42a3172e989e8a06607576ee3042c70.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/1b/78/1b78aa1db42a3172e989e8a06607576ee3042c70.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-09955-2_4"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

A Cellular Nerve for Higher Categories

Clemens Berger
<span title="">2002</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/37jjomjmvfhrzf3di2gjnrrfuu" style="color: black;">Advances in Mathematics</a> </i> &nbsp;
Cellular sets (like simplicial sets) carry a closed model structure in Quillen's sense with weak equivalences induced by a geometric realisation functor.  ...  More generally, there exists a dense subcategory Y A of the category of % A-algebras for each o-operad A in Batanin's sense.  ...  Y is homotopic to id Y under i: An object X is contractible if there is a cofibration * :X with deformation retraction for a cofibrant terminal object * : Lemma 3.6.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1006/aima.2001.2056">doi:10.1006/aima.2001.2056</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/43sex6xr3je3fkie6ssgpu3nda">fatcat:43sex6xr3je3fkie6ssgpu3nda</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20150326215250/http://math.unice.fr/~cberger/nerve.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/86/9d/869d42fe3bb5d728a51999e3477b7ef030b47da5.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1006/aima.2001.2056"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Systems of Preventive Cardiological Monitoring: Models, Algorithms, First Results, and Perspectives [chapter]

Sergey Kirillov, Aleksandr Kirillov, Vitalii Iakimkin, Michael Pecht, Yuri Kaganovich
<span title="2019-02-27">2019</span> <i title="IntechOpen"> Medical Internet of Things (m-IoT) - Enabling Technologies and Emerging Applications </i> &nbsp;
The estimation of the time for reaching the heart events boundaries is calculated on the basis of the evolution equations for the ECG multi-trajectories determined by recognizing automata.  ...  Evaluation time of heart event (HE) boundaries to achieve is calculated on the basis of the evolution equations for ECG multi-paths defined by recognizing machines.  ...  As a result, the complex task of constructing PHM models for the system "biomechanical object plus implantable device or sensor" is relevant for the further development of preventive cardiac-monitoring  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5772/intechopen.75921">doi:10.5772/intechopen.75921</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/r7lc5juhknbm5i7aqnutt6xfcq">fatcat:r7lc5juhknbm5i7aqnutt6xfcq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190426223206/https://cdn.intechopen.com/pdfs/60420.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/85/05/85053a94f4d17e8ccc2614a725f2aee5897dab1e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5772/intechopen.75921"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

From augmented microscopy to the topological transformer: a new approach in cell image analysis for Alzheimer's research [article]

Wooseok Jung
<span title="2021-08-03">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Training model with data of a specific cell type demonstrates transfer learning applies to some extent.  ...  This feature extraction facilitates studying an image as a collection of one-dimensional data, substantially reducing computational costs.  ...  As the multi-class segmentation, we test the model transferablility.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2108.01625v1">arXiv:2108.01625v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5msycs2bfrfqxnqfu5vqkytvsq">fatcat:5msycs2bfrfqxnqfu5vqkytvsq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210805152223/https://arxiv.org/pdf/2108.01625v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/b3/a0/b3a0f66efa92b4b64cc3af499eebef1a387750e4.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2108.01625v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

A Mechanistic End-to-End Concussion Model That Translates Head Kinematics to Neurologic Injury

Laurel J. Ng, Vladislav Volman, Melissa M. Gibbons, Pi Phohomsiri, Jianxia Cui, Darrell J. Swenson, James H. Stuhmiller
<span title="2017-06-15">2017</span> <i title="Frontiers Media SA"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/4kchoxo3jrfubkck3y7nfncina" style="color: black;">Frontiers in Neurology</a> </i> &nbsp;
This paper describes the development of the first quantitative end-to-end (E2E) multi-scale model that links gross head motion to neurological injury by integrating fundamental elements of tissue and cellular  ...  This comprehensive modeling framework provides a basis for the systematic improvement and expansion of this mechanistic-based understanding, including widening the range of neurological injury estimation  ...  A one-dimensional multi-compartmental cable model with cylindrical geometry was used for describing the myelinated axon.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3389/fneur.2017.00269">doi:10.3389/fneur.2017.00269</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/28663736">pmid:28663736</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC5471336/">pmcid:PMC5471336</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/744xolrhbbhphdcrirlel5g6ti">fatcat:744xolrhbbhphdcrirlel5g6ti</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20191115121148/http://europepmc.org/backend/ptpmcrender.fcgi?accid=PMC5471336&amp;blobtype=pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/8e/5d/8e5d110490703eb01718368dbc86009d8eadb15b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3389/fneur.2017.00269"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> frontiersin.org </button> </a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5471336" title="pubmed link"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> pubmed.gov </button> </a>

The Universal Coefficient Theorem, Wormholes, and the Island [article]

Andrei T. Patrascu
<span title="2021-02-01">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
This phenomenon is not unusual in physics, a simple example for that being the spin structure or even the point particle to string transition.  ...  Looking at the axioms of cohomology, the so called Eilenberg-Steenrod axioms, the third axiom states that the cohomology of a point is trivial in all orders.  ...  No more was a single object the focus of geometry, but the whole class of objects and the ways in which it can be linked to its potential deformations.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2104.14343v1">arXiv:2104.14343v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7sergiwbjvaf3p633enfn4zbvq">fatcat:7sergiwbjvaf3p633enfn4zbvq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210502070616/https://arxiv.org/pdf/2104.14343v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/20/7f/207f8fe2436358a543559227681b8adb99bc99a3.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2104.14343v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Connectivity calculus of fractal polyhedrons

Helena Molina-Abril, Pedro Real, Akira Nakamura, Reinhard Klette
<span title="">2015</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jm6w2xclfzguxnhmnmq5omebpi" style="color: black;">Pattern Recognition</a> </i> &nbsp;
objects.  ...  Nevertheless, the underlying concepts apply to general cell complexes and digital images and are suitable for progressing in the computation of advanced algebraic topological information of 3-dimensional  ...  By generalizing the presented graph-based encoding scheme for elementary recursive patterns, it is possible to handle the complex topological phenomenology of general multi-dimensional fractals.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.patcog.2014.05.016">doi:10.1016/j.patcog.2014.05.016</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yeywk4fya5hzzpnuq3xsmmfpaa">fatcat:yeywk4fya5hzzpnuq3xsmmfpaa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170923020432/https://idus.us.es/xmlui/bitstream/handle/11441/38716/Conecctivity%20calculus.pdf?sequence=1" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/a3/40/a340f5fa913e45474851250e5f9a1bba3fcdb6cc.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.patcog.2014.05.016"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Sheaves, Cosheaves and Applications [article]

Justin Curry
<span title="2014-12-17">2014</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
A foundation for multi-dimensional level-set persistent homology is laid via constructible cosheaves, which are equivalent to representations of MacPherson's entrance path category.  ...  We develop cellular (co)sheaves as a new tool for topological data analysis, network coding and sensor networks.  ...  images, which will be definable, we can try to reduce a multi-dimensional problem to a one-dimensional one.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1303.3255v2">arXiv:1303.3255v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/e56cqoblifbcdlupavsoqyzjdy">fatcat:e56cqoblifbcdlupavsoqyzjdy</a> </span>
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L_∞ and A_∞ structures: then and now [article]

Jim Stasheff
<span title="2018-10-02">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
for fibre bundles, one obtains only that g αβ g βγ is homotopic to g αγ as a map of U α ∩ U β ∩ U γ into Haut(F ).  ...  In some cases almost all points of a parameter space will represent the same rigid object, degenerating in various ways to objects admitting proper deformations.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1809.02526v2">arXiv:1809.02526v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nncfiefisjcdtpbt6efhzsjlsq">fatcat:nncfiefisjcdtpbt6efhzsjlsq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20191017174821/https://arxiv.org/pdf/1809.02526v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/0f/c7/0fc7823fdf34ed7ef2dd04c9d1e9229ad6d14748.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1809.02526v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

A Conceptual Construction of Complexity Levels Theory in Spacetime Categorical Ontology: Non-Abelian Algebraic Topology, Many-Valued Logics and Dynamic Systems

R. Brown, J. F. Glazebrook, I. C. Baianu
<span title="2007-11-22">2007</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/l4xjq5zi6jfsnhdqlsi7lzgddy" style="color: black;">Axiomathes</a> </i> &nbsp;
A novel conceptual framework is introduced for the Complexity Levels Theory in a Categorical Ontology of Space and Time.  ...  as well as to derive novel results for (non-commutative) Quantum Logics.  ...  We note here that an interesting, incomplete but computable, model of multi-cellular organisms was formulated in terms of 'cellular' or 'tessellation' automata simulating cellular growth in planar arrays  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10516-007-9010-3">doi:10.1007/s10516-007-9010-3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/246y6llurzhi5mwyofr373rxvm">fatcat:246y6llurzhi5mwyofr373rxvm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20080424172814/http://www.bangor.ac.uk/~mas010/pdffiles/BBG-157-CCCLST.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/56/b8/56b85ff67abfd4f0125db66ac1328163dd9b4f6a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10516-007-9010-3"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>
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