A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Bicycle paths form geodesics in 3D subspaces, related to Kirchhoff rods.
Introduces Lax-Kirchhoff moduli spaces for quivers and Lie groups.
SHAKE-GNN scales GNNs for large graphs with multi-scale representations.
Kirchhoff energy is a classical functional on the space of arclength-parameterized framed curves whose critical points approximate configurations of springy elastic rods. We introduce a generalized functional on the space of framed curves of arbitrary parameterization, which model rods with axial stretch or cross-secti…
Study p-Willmore disks with boundary energies, finding equilibrium configurations.
Develops control and observer methods for complex systems.
Determinants of theta curves and symmetric graphs are studied.
Theory of point vortices extended to closed surfaces.
New approach to electric group for knots and links.
By a theorem of Kirchhoff if the six sphere admits an almost complex structure then the seven sphere is parallelizable, more crucial, he exhibited an explicit global frame constructed out of the given almost complex structure. This result implicitly equips the seven sphere with a definite H-space multiplication. We pro…
The paper explores variational problems on Riemannian manifolds with special foliations, proving existence results.
We discuss several issues regarding material homogeneity and strain compatibility for materially uniform thin elastic shells from the viewpoint of a 3-dimensional theory, with small thickness, as well as a 2-dimensional Cosserat theory. A relationship between inhomogeneity and incompatibility measures under the two des…
We consider a family of compact manifolds which shrinks with respect to an appropriate parameter to a graph. The main result is that the spectrum of the Laplace-Beltrami operator converges to the spectrum of the (differential) Laplacian on the graph with Kirchhoff boundary conditions at the vertices. On the other hand,…
Knot Theory is currently a very broad field. Even a long survey can only cover a narrow area. Here we concentrate on the path from Goeritz matrices to quasi-alternating links. On the way, we often stray from the main road and tell related stories, especially if they allow as to place the main topic in a historical cont…
In this paper, we propose a probabilistic parsing model, which defines a proper conditional probability distribution over non-projective dependency trees for a given sentence, using neural representations as inputs. The neural network architecture is based on bi-directional LSTM-CNNs which benefits from both word- and …
The paper defines surface area for graphs and derives spectral estimates.
We study the stability of symmetric trajectories of a particle on the Lie group whose motion is governed by an invariant metric and an invariant potential. Our method is to reduce the number of degrees of freedom at {\em singular} values of the momentu…
Given a distribution of defects on a structured surface, such as those represented by 2-dimensional crystalline materials, liquid crystalline surfaces, and thin sandwiched shells, what is the resulting stress field and the deformed shape? Motivated by this concern, we first classify, and quantify, the translational, ro…
Paper derives a formula for the determinant of Dirichlet-to-Neumann operator on Riemann surfaces.
The paper compares PINN methods for solving drift-diffusion equations on metric graphs.
The aim of this paper is to give a formulation of the dynamics of nonlinear RLC circuits as a geometric Birkhoffian system and to discuss in this context the concepts of regularity, conservativeness, dissipativeness. An RLC circuit, with no assumptions placed on its topology, will be described by a family of Birkhoffia…
Solving power flow (PF) equations is the basis of power flow analysis, which is important in determining the best operation of existing systems, performing security analysis, etc. However, PF equations can be out-of-date or even unavailable due to system dynamics and uncertainties, making traditional numerical approach…
New approach links 2D fluid dynamics to matrix theory.
This paper explores vortices and harmonic flows on compact surfaces, using Hodge decomposition.
The spectral geometry of mesh matrices of graphs is explored, leading to new formulas and eigenvalue estimates.