arXiv research

Study shows dense roots of Yamada polynomial for certain graphs.

Study on Jones polynomials and their roots in the unit circle and complex plane.

Study non-semisimple TQFT for Burau representation density and unitarity.

Introduces new geometric framework for probability densities on manifolds.

We prove that the density of a topologically nontrivial, area-minimizing hypercone with an isolated singularity must be greater than the square root of 2. The Simons' cones show that this is the best possible constant. If one of the components of the complement of the cone has nontrivial kth homotopy group, we prove a …

New PL invariant classifies K3 surface degenerations.

The Volterra square-root process shows non-uniqueness of limiting distributions and regularity of its law.

Improved MLMC method for robust and efficient probability and density estimation.

Introduces a new geometric framework for probability distributions.

We show that for an odd prime r > 3 and an integer g > 1, in the projective representation given by the SO(3) Witten-Chern-Simons theory at an rth root of unity, the image of the mapping class group of a surface of genus g is dense.

We investigate the position of the Buchen-Kelly density in a family of entropy maximising densities which all match European call option prices for a given maturity observed in the market. Using the Legendre transform which links the entropy function and the cumulant generating function, we show that it is both the uni…

Paper tackles anomaly detection with missing causal knowledge.

Efficient neural networks compute various differential operators cheaply.

We identify the leading order term of the asymptotic expansion of the Witten-Reshetikhin-Turaev invariants for finite order mapping tori with classical invariants for all simple and simply-connected compact Lie groups. The square root of the Reidemeister torsion is used as a density on the moduli space of flat connecti…

The MoN loss fails to accurately represent ground truth probability density functions in probabilistic trajectory prediction.

OPAA estimates probability densities using functional analysis.

New properties established for SO(3) quantum representations, showing density and surjectivity.

We compute the noncommutative de Rham cohomology for the finite-dimensional q-deformed coordinate ring $C_q[SL_2]$ at odd roots of unity and with its standard 4-dimensional differential structure. We find that $H^1$ and $H^3$ have three additional modes beyond the generic $q$-case where they are 1-dimensional, while $H…

We show that the topological modular functor from Witten-Chern-Simons theory is universal for quantum computation in the sense a quantum circuit computation can be efficiently approximated by an intertwining action of a braid on the functor's state space. A computational model based on Chern-Simons theory at a fifth ro…

Unified kernel density and empirical Bayes for unsupervised learning.

Bayesian neural networks are shown to be minimax and admissible under certain conditions.

Constructs Dirac generating operators for split Courant algebroids.

A new sampling method, RC-LMC, reduces computational cost for high-dimensional log-concave distributions.

We consider Feller mean-reverting square-root diffusion, which has been applied to model a wide variety of processes with linearly state-dependent diffusion, such as stochastic volatility and interest rates in finance, and neuronal and populations dynamics in natural sciences. We focus on the statistical mixing (or sup…

Smooth flows for physical systems with smooth energies and forces.

Two-root Riemannian manifolds have no odd-dimensional examples.

Kernel ridge regression imputation with consistent variance estimation for handling missing data.

In this paper, we characterize locally dually flat generalized m-th root Finsler metrics. Then we find a condition under which a generalized m-th root metric is projectively related to a m-th root metric. Finally, we prove that if a generalized m-th root metric is conformal to a m-th root metric, then both of them redu…

New definition of patient-specific root causes of disease using counterfactuals.

A conservative drifting method improves generative modeling by using KDE gradients, proving convergence rates.

Uniqueness of quasi-roots explored in right-angled Artin groups.

New matching estimators correct bias in multivariate settings without smoothing parameters.

Study differential properties of matrix square roots in specific cases.

Identifies root causes of outliers in unknown cyclic graphs.

D. Margalit and S. Schleimer found examples of roots of the Dehn twist about a nonseparating curve in a closed orientable surface, that is, homeomorphisms whose nth power is isotopic to the Dehn twist. Our main theorem gives elementary number-theoretic conditions that describe the values of n for which an nth root exis…

Root Laplacian Eigenmaps help in spectral embedding of graphs.

CROC identifies the earliest-changing stream as the root cause in multi-stream data.

Margalit and Schleimer observed that Dehn twists on orientable surfaces have nontrivial roots. We investigate the problem of roots of a Dehn twist t_c about a nonseparating circle c in the mapping class group M(N_g) of a nonorientable surface N_g of genus g. We explore the existence of roots and, following the work of …

New model identifies patient-specific disease root causes.

A new method simulates square-root processes efficiently.

Enhanced ROOT-SGD optimizes stochastic optimization with diminishing stepsizes.

The study of random positive 3-strand braids reveals patterns in the roots of their Alexander polynomials.

GT is a new method for denoising and enhancing datasets using Gaussian density estimates.

In this paper, we prove that every m-th root metric with isotropic mean Berwald curvature reduces to a weakly Berwald metric. Then we show that an m-th root metric with isotropic mean Landsberg curvature is a weakly Landsberg metric. We find necessary and sufficient condition under which conformal $β$-change of an m-th…

Automorphisms of Lie algebras and their root systems are fully lifted.

Margalit and Schleimer constructed nontrivial roots of the Dehn twist about a nonseparating curve. We prove that the conjugacy classes of roots of the Dehn twist about a nonseparating curve correspond to the conjugacy classes of periodic maps with certain conditions. Futhermore, we give data set which determine the con…

Root's barrier is continuous and finite under certain conditions.

In this paper, we find a condition under which a Finsler space with Kropina change of mth-root metric is projectively related to a mth-root metric and also we find a condition under which this Kropina transformed mth-root metric is locally dually flat. Moreover we find the condition for its Projective flatness.