arXiv AI
Aug 10
A Finite E-Group of Nilpotency Class Three
arXiv:2608. 07275v1 Announce Type: cross Abstract: A group is an E-group if every element commutes with each of its endomorphic images.
Computations and ML for surjective rational maps
arXiv:2510. 08093v2 Announce Type: replace-cross Abstract: The present note studies \emph{surjective rational endomorphisms} $f: \mathbb{P}^2 \dashrightarrow \mathbb{P}^2$ with \emph{cubic} terms and the indeterminacy locus $I_f \ne \emptyset$.
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arXiv AI
Jun 12
Real-rootedness of the Poincar\'e polynomials of $\overline{\mathcal M}_{0,n}$: an AI-assisted proof
arXiv:2605. 29151v2 Announce Type: replace-cross Abstract: We prove real-rootedness for the Poincar\'e polynomial \[ P_n(t)=\sum_{i=0}^{n-3} \dim H^{2i}(\overline{\mathcal M}_{0,n};\mathbb{Q})t^i \] of the Deligne--Mumford moduli space $\overline{\mathcal M}_{0,n}$ of stable $n$-pointed rational curves, proving a conjecture of Aluffi--Chen--Marcolli.
arXiv Machine Learning
Aug 4
Polyatomic Complexes: A topologically-informed learning representation for atomistic systems
arXiv:2409. 15600v3 Announce Type: replace Abstract: A representation of a molecule or material should be invariant to the symmetries of physics, unique, continuous, efficient and general.
arXiv Machine Learning
Jul 28
Decision trees, Frobenius traces, and Weierstrass coefficients of elliptic curves
arXiv:2607. 24251v1 Announce Type: cross Abstract: We investigate the extent to which the reduced minimal Weierstrass coefficients of an elliptic curve over $\mathbb{Q}$ may be computed from it's Frobenius traces.
arXiv Machine Learning
1d ago
High-Dimensional Nonparametric Change-Point Detection via Low-Rank Degree-Three Density Projection
arXiv:2608. 15466v1 Announce Type: new Abstract: Distributional changes can be invisible to means and covariances yet appear in skewness, asymmetric interactions, or other third-order structure.
arXiv Machine Learning
Jun 11
Minimal surfaces, Knots, and Neural Networks
arXiv:2605. 26234v2 Announce Type: replace-cross Abstract: A recent conjecture by Joel Fine posits a relationship between the coefficients of the HOMFLY polynomial of a knot $K$ in the 3-sphere $S^3$, and the signed count of minimal surfaces in hyperbolic 4-space $\mathrm{H}^4$ meeting the sphere at infinity at $K$, with prescribed genus and self-intersection number.
arXiv AI
Jul 1
Improved Upper Bounds for Slicing the Hypercube
arXiv:2602. 16807v2 Announce Type: replace Abstract: A collection of hyperplanes $\mathcal{H}$ slices all edges of the $n$-dimensional hypercube $Q_n$ with vertex set $\{-1,1\}^n$ if, for every edge $e$ in the hypercube, there exists a hyperplane in $\mathcal{H}$ intersecting $e$ in its interior.
arXiv Machine Learning
Aug 12
Discrete Coefficients and Open Invariant Covers in the Homology of Ample Groupoids
arXiv:2603. 20861v2 Announce Type: replace-cross Abstract: The homology of an ample groupoid is computed from the complex of compactly supported continuous functions on the nerve.
arXiv AI
Jun 10
Moonshine: An Autonomous Mathematical Research Agent Centered on Conjecture Generation
arXiv:2606. 10806v1 Announce Type: new Abstract: Moonshine is an autonomous agent whose central objective is to generate mathematical conjectures.
arXiv Machine Learning
Aug 4
Detecting Nonproperness of Likelihood Equations
arXiv:2608. 01976v1 Announce Type: cross Abstract: Given an algebraic statistical model, a challenging problem is classifying the data according to the number of positive critical points of the likelihood function.
arXiv AI
Jul 28
An Explicit Counterexample to Stanley's Rankwise Lower-Bound Conjecture for Differential Posets
arXiv:2607. 22988v1 Announce Type: cross Abstract: In Problem~6 of his 1988 paper on differential posets, Stanley asked for the least possible cardinality of a fixed rank of an $r$-differential poset and suggested that the minimum should be attained by $Y^r$, the $r$-fold Cartesian power of Young's lattice.
arXiv Machine Learning
Jun 15
On the Geometry and Optimization of Polynomial Convolutional Networks
arXiv:2410. 00722v3 Announce Type: replace Abstract: We study convolutional neural networks with monomial activation functions.