#topology — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #topology, aggregated by home.social.
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A Topological Picture Book, Rendered
https://e-infinity.space/picture-book/
Comments: https://news.ycombinator.com/item?id=49618050
#HackerNews #topology #picturebook #rendering #mathematics #education #visualart
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The nuclear pore complex (7R5J & 7R5K) – one of the largest molecular machines in biology.
The nuclear pore complex is the gatekeeper of the cell nucleus – controlling everything that enters or leaves. We captured it in two states: open (dilated) and closed (constricted).
961665 quantum records
#StructuralBiology #Biophysics #Bioinformatics #Topology #InformationTheory #DNAFolding #ComputationalBiology #ComplexSystems #Genomics #OpenScience #EXXOGEN
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While teaching a course on algebraic theories last semester I mentioned at some point that the familiar bicomplete categories Top and Poset were not algebraic, but were topological. A student asked about this later on and I found that the #Wikipedia page on «topological category» pointed to categories enriched in Top, not categories with a forgetful functor to Set which is topological. While I have lost a lot of faith in Wikipedia recently, I am pleased to report that https://en.wikipedia.org/wiki/Topological_category is now a disambiguation page.
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Differential Propositional Calculus • 10
Special Classes of Propositions (cont.)
Let’s pause at this point and get a better sense of how our special classes of propositions are structured and how they relate to propositions in general. We can do this by recruiting our visual imaginations and drawing up a sufficient budget of venn diagrams for each family of propositions. The case for 3 variables is exemplary enough for a start.
Linear Propositions
The linear propositions, may be written as sums:
One thing to keep in mind about these sums is that the values in are added “modulo 2”, that is, in such a way that
In a universe of discourse based on three boolean variables, the linear propositions take the shapes shown in Figure 8.
At the top is the venn diagram for the linear proposition of rank 3, which may be expressed by any one of the following three forms.
Next are the venn diagrams for the three linear propositions of rank 2, which may be expressed by the following three forms, respectively.
Next are the three linear propositions of rank 1, which are none other than the three basic propositions,
At the bottom is the linear proposition of rank 0, the everywhere false proposition or the constant function, which may be expressed by the form or by a simple
Resources
cc: Academia.edu • Cybernetics • Structural Modeling • Systems Science
cc: Conceptual Graphs • Laws of Form • Mathstodon • Research Gate#Amphecks #Animata #BooleanAlgebra #BooleanFunctions #CSPeirce #CactusGraphs #CategoryTheory #Change #Cybernetics #DifferentialAnalyticTuringAutomata #DifferentialCalculus #DifferentialLogic #DiscreteDynamics #EquationalInference #FunctionalLogic #GraphTheory #Hologrammautomaton #IndicatorFunctions #InquiryDrivenSystems #Leibniz #Logic #LogicalGraphs #Mathematics #MinimalNegationOperators #PropositionalCalculus #Time #Topology #Visualization
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Christian Pfleiderer, Professor of #Topology of Correlated Systems, is the new Scientific Director of Research Neutron Source Heinz Maier-Leibnitz (FRM II) from January 1, 2024. 👏 He aims to make the research accessible to the entire #scientificcommunity: http://go.tum.de/509989
📷A.Eckert
