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.
New polynomials link knot homology to Schröder paths.
Direct proof of Alexander polynomial scaling for L-shaped representations.
Tripod spiders' energy control analyzed for Hooke and Coulomb potentials.
Study spider mechanism configuration spaces using squared distance function.
Solves a recursion for Gromov-Witten invariants of the unknot.
Researchers establish a connection between knot homology and Lie algebra actions.
New methods reveal symmetries in Chern-Simons theory.
This paper investigates the classical and quantum elementary systems with Newton-Hoooke symmetry. A complete classification is given by explicit computation. In addition, we present an application example of quantization using the Moyal scheme.
In [ES2], the first and the third authors introduced new classes in the Johnson cokernels of the mapping class groups of surfaces by a representation theoretic approach based on some previous results for the Johnson cokernels of the automorphism groups of free groups. On the other hand, in [KK1], Kawazumi and the secon…
We discuss the relation between knot polynomials and the KP hierarchy. Mainly, we study the scaling 1-hook property of the coloured Alexander polynomial: for all 1-hook Young diagrams . Via the Kontsevich construction, it is reformulated …
Let $ \B^{n+1} \subset \C^{n+1}$ be the unit ball in a complex Euclidean space, and let $ Σ^n = \partial \B^{n+1} = S^{2n+1}$. Let $ f: Σ^n \hook Σ^{N}$ be a local CR immersion.If , the asymptotic vectors of the second fundamental form of at each point form a subspace of the holomorphic tangent space of…
Quasimodular forms were first studied in the context of counting torus coverings. Here we show that a weighted version of these coverings with Siegel-Veech weights also provides quasimodular forms. We apply this to prove conjectures of Eskin and Zorich on the large genus limits of Masur-Veech volumes and of Siegel-Veec…
Next step is reported in the program of Racah matrices extraction from the differential expansion of HOMFLY polynomials for twist knots: from the double-column rectangular representations R=[rr] to a triple-column and triple-hook R=[333]. The main new phenomenon is the deviation of the particular coefficient $f_{[332]}…
Hidden symmetries of the Goryachev-Chaplygin and Kovalevskaya gyrostats spacetimes, as well as the Brdička-Eardley-Nappi-Witten pp-waves are studied. We find out that these spacetimes possess higher rank Stäckel-Killing tensors and that in the case of the pp-wave spacetimes the symmetry group of the Stäckel-Killing ten…
Proof of Tait-Kneser theorem and related variations using Lorentzian geometry.
Novel symmetry found in colored HOMFLY polynomials from superalgebras.
We connect two important conjectures in the theory of knot polynomials. The first one is the property Al_R(q) = Al_{[1]}(q^{|R|}) for all single hook Young diagrams R, which is known to hold for all knots. The second conjecture claims that all the mixing matrices U_{i} in the relation {\cal R}_i = U_i{\cal R}_1U_i^{-1}…
In this paper, we obtain a new abstract formula relating eigenvalues of a self-adjoint operator to two families of symmetric and skew-symmetric operators and their commutators. This formula generalizes earlier ones obtained by Harrell, Stubbe, Hook, Ashbaugh, Hermi, Levitin and Parnovski. We also show how one can use t…
Let $ X: M \hook S^5$ be a compact Legendrian surface in pseudoconformal(CR) 5-sphere. We introduce a pseudoconformally invariant Willmore type second order functional $ \W(X)$, and study its critical points called Willmore Legendrian surfaces. The fifth order structure equations show that Willmore dual can be defined …
From analysis of a big variety of different knots we conclude that at q which is an root of unity, q^{2m}=1, HOMFLY polynomials in symmetric representations [r] satisfy recursion identity: H_{r+m} = H_r H_m for any A, which is a generalization of the property H_r = (H_1)^r for special polynomials at q=1. We conjecture …
The paper computes group factors and properties of Wilson loops in Chern-Simons theory.
The paper tests if LLMs' capabilities are executed by small subnetworks (circuits).
HZ transform applied to knot polynomials reveals hyperbolic knot structures.
The exploration mechanism used by a Deep Reinforcement Learning (RL) agent plays a key role in determining its sample efficiency. Thus, improving over random exploration is crucial to solve long-horizon tasks with sparse rewards. We propose to leverage an ensemble of partial solutions as teachers that guide the agent's…
The thesis explores kinematical symmetries beyond Lorentzian spacetime.
Optimal dynamic fees for AMMs: A stochastic control approach
Independent component analysis (ICA) decomposes multivariate data into mutually independent components (ICs). The ICA model is subject to a constraint that at most one of these components is Gaussian, which is required for model identifiability. Linear non-Gaussian component analysis (LNGCA) generalizes the ICA model t…
In links with two components there are three different types of crossings: self-crossings in the first component, self crossings in the second component, and crossings between components. In this paper we examine the minimum number of crossing changes needed to unlink without changing the crossings between components. …
New phenomenon found in Gothen components' boundary.
Innovates a three-component link homotopy invariant.
This note proves properties of surface-links with trivial components.
A fast method estimates Gaussian mixture components without iterative fitting.
In this paper the exact linear relation between the leading eigenvectors of the modularity matrix and the singular vectors of an uncentered data matrix is developed. Based on this analysis the concept of a modularity component is defined, and its properties are developed. It is shown that modularity component analysis …
The paper shows infinitely many components in Floer Hessians space.
New concept of quasi-ribbon surface-links simplifies complex surface-links.
New simulations advise caution in choosing principal components for multivariate functional data.
Research has shown that widely used deep neural networks are vulnerable to carefully crafted adversarial perturbations. Moreover, these adversarial perturbations often transfer across models. We hypothesize that adversarial weakness is composed of three sources of bias: architecture, dataset, and random initialization.…
We construct links of arbitrarily many components each component of which is slice and yet are not concordant to any link with even one unknotted component. The only tool we use comes from the Alexander modules.
Uniform bounds found for Sierpinski carpet hyperbolic components.
The object of this paper is to study GL(2,R) orbit closures in hyperelliptic components of strata of abelian differentials. The main result is that all higher rank affine invariant submanifolds in hyperelliptic components are branched covering constructions, i.e. every translation surface in the affine invariant subman…
We develop a mean-field theory for multi-component ICA in high dimensions.
Research examines the distribution of curve components in random multicurves.
FMM fails to accurately determine the number of components even with consistent posterior.
msPCA solves sparse PCA for multiple components efficiently.
Principal component regression (PCR) is a two-stage procedure that selects some principal components and then constructs a regression model regarding them as new explanatory variables. Note that the principal components are obtained from only explanatory variables and not considered with the response variable. To addre…
Bayesian approach learns nonparametric mixture components from heterogeneous data.
System learns to combine multiple model components for personalized text generation.
Found a new connected component in symplectic structures.