FINDING: The Harborth graph — the smallest known 4-regular planar unit-distance graph on 34 vertices — has an analytical coordinate embedding whose minimal polynomials are now explicitly derived, revealing deep ties to crystallographic symmetry and algebraic number theory. | MATH: Harborth graph: 34 vertices, 68 edges,...
Andrew Stewart Caldin· Zenodo (CERN European Organi...· 0 citations
A C₄-Free Classification of Square Relations on Token Graphs with girth, tree and discretization witnesses Driven by Dean A. Kulik October 2026 Abstract Let FK(X) denote the K-token graph of a finite simple graph X: vertices are the K-subsets of V(X), adjacent when their symmetric difference is an edge. Two families of...
Dean Kulik· Zenodo (CERN European Organi...· 0 citations
This study addresses the challenge of autonomous landing of unmanned aerial vehicles (UAVs) in unknown environments by proposing a vision-based system that utilizes a single RGB-D camera. The core of our approach integrates an enhanced real-time semantic segmentation model based on the DDRNet architecture, incorporatin...
Python code and results accompanying the paper "Operator Choice and Echo Artefacts in Fuzzy Graph Cellular Automata for Cascade Spreading on Networks". The code implements a fuzzy graph cellular automaton: nodes of a graph with fuzzy edge memberships carry states in [0, 1] and update synchronously by combining neighbou...
KRISHNA KUMARI RENGANATHAN· Zenodo (CERN European Organi...· 0 citations
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Python code and results accompanying the paper "Operator Choice and Echo Artefacts in Fuzzy Graph Cellular Automata for Cascade Spreading on Networks". The code implements a fuzzy graph cellular automaton: nodes of a graph with fuzzy edge memberships carry states in [0, 1] and update synchronously by combining neighbou...
KRISHNA KUMARI RENGANATHAN· Zenodo (CERN European Organi...· 0 citations
Rank Access and Closure Depth in the Relation-Layer Cohomology of Token Arenas A refuted conjecture, a refuted mechanism, and two species of invariant harmonic residue Driven by Dean Kulik October 2026 Abstract A Kdisj-type relation layer over a token arena assigns cohomology to a graph by declaring which closed loops...
Dean Kulik· Zenodo (CERN European Organi...· 0 citations
A C₄-Free Classification of Square Relations on Token Graphs with girth, tree and discretization witnesses Driven by Dean A. Kulik October 2026 Abstract Let FK(X) denote the K-token graph of a finite simple graph X: vertices are the K-subsets of V(X), adjacent when their symmetric difference is an edge. Two families of...
Dean Kulik· Zenodo (CERN European Organi...· 0 citations
We give exact results for several observables of Kerr black holes that have so far been computed numerically, by fits, or only at isolated parameter values. (i) The area of the shadow seen by an equatorial observer, for every spin, in complete elliptic integrals, together with its small-spin series and its near-extrema...
Jacob Goodchild· Zenodo (CERN European Organi...· 0 citations
This study addresses the challenge of autonomous landing of unmanned aerial vehicles (UAVs) in unknown environments by proposing a vision-based system that utilizes a single RGB-D camera. The core of our approach integrates an enhanced real-time semantic segmentation model based on the DDRNet architecture, incorporatin...
This study addresses the challenge of autonomous landing of unmanned aerial vehicles (UAVs) in unknown environments by proposing a vision-based system that utilizes a single RGB-D camera. The core of our approach integrates an enhanced real-time semantic segmentation model based on the DDRNet architecture, incorporatin...
Propofol anesthesia disrupts functional connectivity, but the magnitude of whole-brain architectural reorganization has not been calibrated against the variability of repeated measurement within a single state, and it is therefore unclear how much apparent reorganization reflects state change rather than estimation noi...
Readers Are Functionals- Representation Control of the Relation Layer on Token Arenas a multiplicity table, a faithful-reader certificate, and an isotypic correction to the rank budget Driven by Dean A. Kulik October 2026 Abstract Attaching 2-cells to a token graph and computing invariant cohomology under a symmetry gr...
Dean Kulik· Zenodo (CERN European Organi...· 0 citations
For decades, a fundamental question about the difficulty of computing in high-dimensional spaces has resisted proof. New research resolves this question, removing a major theoretical obstacle to understanding the efficiency of randomized algorithms used across science and computing. The Kannan–Lovász–Simonovits (KLS) conjecture was proposed in 1995. It asks whether, for a broad class of high-dimensional […] The post Solving a 31-year-old grand challenge in mathematics – the KLS conjecture appear…
MIT News · Artificial Intelligence· news.mit.eduOct 15, 2026
A new computational approach reveals how cells communicate to assemble into tissues. This could accelerate stem cell engineering, improve disease models, and inform therapies.
Microsoft Research Blog· microsoft.comOct 15, 2026
Zero-knowledge proofs can verify computing results without rerunning workloads or exposing sensitive data. Magnetar helps bring them into the mainstream with support for standard programming languages, major speed gains, and quantum-resistant security. The post Proof-based general-purpose computing with Magnetar appeared first on Microsoft Research.
MIT News · Artificial Intelligence· news.mit.eduOct 8, 2026
