arXiv research

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

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.

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

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.

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.

Identifies patient-specific root causes of disease using structural equation models.

In this paper, we consider Kropina change of $m$-th root Finsler metrics. We find necessary and sufficient condition under which the Kropina change of an $m$-th root Finsler metric be locally dually flat. Then we prove that the Kropina change of an $m$-th root Finsler metric is locally projectively flat if and only if …

Defines a generalized string concept for abstract root systems.

Continuity of roots of hyperbolic polynomials with smooth coefficients.

Polynomials' roots count tied to surface umbilics.

In this paper, we characterize locally dually flat and Antonelli $m$-th root Finsler metrics. Then, we show that every $m$-th root Finsler metric of isotropic mean Berwald curvature reduces to a weakly Berwald metric.

Improved root-finding method for smooth functions.

The study explores knot invariants using roots of unity.

Jones polynomials have infinitely many roots of unity as zeros.

The notion of limit roots of a Coxeter group W was recently introduced (see arXiv:1112.5415 and arXiv:1303.6710): they are the accumulation points of directions of roots of a root system for W. In the case where the root system lives in a Lorentzian space W admits a faithful representation as a discrete reflection grou…

In this paper we give a sufficient and necessary condition for two rooted trees with the same plucking polynomial. Furthermore, we give a criteria for a sequence of non-negative integers to be realized as a rooted tree.

We construct nontrivial roots of Dehn twists about nonseparating curves.

In this Note, we prove that every m-th root Finsler metric with isotropic Landsberg curvature reduces to a Landsberg metric. Then, we show that every m-th root metric with almost vanishing H-curvature has vanishing H-curvature.

Let $C$ be a curve in a closed orientable surface $F$ of genus $g \geq 2$ that separates $F$ into subsurfaces $\widetilde {F_i}$ of genera $g_i$, for $i = 1,2$. We study the set of roots in $\Mod(F)$ of the Dehn twist $t_C$ about $C$. All roots arise from pairs of $C_{n_i}$-actions on the $\widetilde{F_i}$, where $n=\l…

In this paper, we define some non-Riemannian curvature properties for Cartan spaces. We consider Cartan space with the m-th root metric. We prove that every m-th root Cartan space of isotropic Landsberg curvature, or isotropic mean Landsberg curvature, or isotropic mean Berwald curvature reduces to a Landsberg, weakly …

Guarantees uniform convergence for square-root Lipschitz losses.

We study simple root flows and Liouville currents for Hitchin representations. We show that the Liouville current is associated to the measure of maximal entropy for a simple root flow, derive a Liouville volume rigidity result, and construct a Liouville pressure metric on the Hitchin component.

Study finds price impact follows a 'double' square-root law, suggesting mechanical origin.

Study finds root vertex in large networks with high probability.

Paper simplifies calculating causation probabilities and ranks root causes.

Algorithm removes leaves to find root in uniform trees.

For Finsler spaces (M,F) endowed with m-th root metrics, we provide necessary and sufficient conditions in which they are projectively flat, or projectively related to Berwald/Riemann spaces. We also give a specific characterization for m-th root metrics spaces of Landsberg and of Berwald type.

The paper extends ternary algebra concepts using cube roots of unity.

For an arbitrary positive integer n, we construct infinitely many one-cusped hyperbolic 3-manifolds where each manifold's A-polynomial detects every n-th root of unity. This answers a question of Cooper, Culler, Gillet, Long, and Shalen as to which roots of unity arise in this manner.

We construct an invariant J_M of integral homology spheres M with values in a completion \hat{Z[q]} of the polynomial ring Z[q] such that the evaluation at each root of unity ζgives the the SU(2) Witten-Reshetikhin-Turaev invariant τ_ζ(M) of M at ζ. Thus J_M unifies all the SU(2) Witten-Reshetikhin-Turaev invariants of…

Study centers of quantum tori and skein algebras for even roots of unity.

The paper characterizes roots of pseudo-periodic mapping classes in surface groups.

New method identifies root causes in presence of latent confounding.

Study equigeodesics on $G_2$-type flag manifolds, splitting tangent spaces.