Tootfinder

“He's waiting for me” 🦆👀
https://theblast.com/687811/rogue-florida-duck-reigns-terror-on-the-elderly-in-quiet-neighborhood/

Florida Duck On A Rampage, Injures Seniors & Evades Law
A furious Florida duck is ambushing seniors on porches, sending one to the ER. Locals are shaken, and no one’s stepping in to help.

topology: Internet AS graph (2004)
An integrated snapshot of the structure of the Internet at the level of Autonomous Systems (ASs), reconstructed from multiple sources, including the RouteViews and RIPE BGP trace collectors, route servers, looking glasses, and the Internet Routing Registry databases. This snapshot was created around October 2004.
This network has 34761 nodes and 171403 edges.
Tags: Technological, Communication, Unweighted, Multigraph, Timestamps

A canonical Makanin-Razborov diagram and a pseudo topology for sets of tuples in free groups, semigroups, associative algebras and Lie algebras I
Z. Sela
https://arxiv.org/abs/2505.22755

A canonical Makanin-Razborov diagram and a pseudo topology for sets of tuples in free groups, semigroups, associative algebras and Lie algebras I
The JSJ decomposition and the Makanin-Razborov diagram were proved to be essential in studying varieties over free groups, semigroups and associative algebras. In this paper we suggest a unified conceptual approach to the applicability of these structures over all these algebraic categories. With a variety over each of these algebraic categories we naturally associate a set of tuples in a free group. Then we show how to associate a Makanin-Razborov diagram with any set of tuples over a free gro…

🇺🇦 Auf radioeins läuft...
The Black Seeds:
🎵 Better Days
#NowPlaying #TheBlackSeeds
https://theblackseeds.bandcamp.com/track/better-days-single
https://open.spotify.com/track/1kzl7hqWC0ZJr366DDbmjs

Add richer tooltips to ggiraph with kableExtra and friends: #dataviz …

Measuring topological invariants of even-dimensional non-Hermitian systems through quench dynamics
Xiao-Dong Lin, Long Zhang
https://arxiv.org/abs/2505.23633

Measuring topological invariants of even-dimensional non-Hermitian systems through quench dynamics
The accurate determination of non-Hermitian (NH) topological invariants plays a central role in the study of NH topological phases. In this work, we propose a general framework for directly measuring NH topological invariants in even-dimensional systems through quench dynamics. Our approach hinges on constructing an auxiliary Hermitian matrix topologically equivalent to the original NH Hamiltonian, enabling topological characterization via reduced-dimensional momentum subspaces called band inve…

Topological Machine Learning for Protein-Nucleic Acid Binding Affinity Changes Upon Mutation
Xiang Liu, Junjie Wee, Guo-Wei Wei
https://arxiv.org/abs/2505.22786

Topological Machine Learning for Protein-Nucleic Acid Binding Affinity Changes Upon Mutation
Understanding how protein mutations affect protein-nucleic acid binding is critical for unraveling disease mechanisms and advancing therapies. Current experimental approaches are laborious, and computational methods remain limited in accuracy. To address this challenge, we propose a novel topological machine learning model (TopoML) combining persistent Laplacian (from topological data analysis) with multi-perspective features: physicochemical properties, topological structures, and protein Tran…

This https://arxiv.org/abs/2412.12921 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Equivariant and Invariant Parametrized Topological Complexity
For a $G$-equivariant fibration $p \colon E\to B$, we introduce and study the invariant analogue of Cohen, Farber and Weinberger's parametrized topological complexity, called the invariant parametrized topological complexity. This notion generalizes the invariant topological complexity introduced by Lubawski and Marzantowicz. We establish the equivariant fibrewise homotopy invariance of this notion and derive several bounds, including a cohomological lower bound and a dimensional upper bound. A…

Topological Adaptive Least Mean Squares Algorithms over Simplicial Complexes
Lorenzo Marinucci, Claudio Battiloro, Paolo Di Lorenzo
https://arxiv.org/abs/2505.23160

Topological Adaptive Least Mean Squares Algorithms over Simplicial Complexes
This paper introduces a novel adaptive framework for processing dynamic flow signals over simplicial complexes, extending classical least-mean-squares (LMS) methods to high-order topological domains. Building on discrete Hodge theory, we present a topological LMS algorithm that efficiently processes streaming signals observed over time-varying edge subsets. We provide a detailed stochastic analysis of the algorithm, deriving its stability conditions, steady-state mean-square-error, and converge…

internet_top_pop: Internet topology (PoP level) (1969-2012)
Assorted snapshots of internet graph at the Point of Presence (PoP) level (which lies between the IP and AS levels), collected from around the world and at various times. The earliest snapshots are for ARPANET (1969-1972), with a few more from pre-2000. Most are from 2006 onward. Metadata include link type or speed, longitudes, and latitudes of nodes, URL, and date of record.
This network has 19 nodes and 24 edges.