arXiv research

Abstract: Proves no non-trivial normal orbits for specific Hamiltonians.

We obtain sufficient conditions exlcuding the existence of non-trivial distribution sections of bundles over the boundary of symmetric spaces of negative curvature which are invariant with respect to a geometrically finite group of isometries and are supported on the limit set in a strong sense.

We develop a general theory for irreducible homogeneous spaces $M= G/H$, in relation to the nullity $ν$ of their curvature tensor. We construct natural invariant (different and increasing) distributions associated with the nullity, that give a deep insight of such spaces. In particular, there must exist an order-two tr…

Generative models learn to capture target distribution support with extreme value loss.

Algorithm estimates multivariate normal parameters from hidden truncated samples.

Study calculates slope gaps on polygon surfaces, finding non-unimodal distributions.

Over-parameterized models reduce Out-of-Distribution (OOD) generalization loss.

Surveying methods to create spaces with non-trivial self covers.

Study shows non-trivial knot Floer homology for specific knots.

This paper studies quandles with one non-trivial column and their properties.

We give a short proof that if a non-trivial band sum of two knots results in a tight fibered knot, then the band sum is a connected sum. In particular, this means that any prime knot obtained by a non-trivial band sum is not tight fibered. Since a positive L-space knot is tight fibered, a non-trivial band sum never yie…

We say that a graph is intrinsically non-trivial if every spatial embedding of the graph contains a non-trivial spatial subgraph. We prove that an intrinsically non-trivial graph is intrinsically linked, namely every spatial embedding of the graph contains a non-splittable 2-component link. We also show that there exis…

This paper deals with the enumeration of the higher order non-trivial compositions of the differential operations and the directional derivative in the space $R^n$ ($n \geq 3$). We present the recurrences for a counting the higher order non-trivial compositions.

New methods found persistent tangles in knots.

New knots found with non-trivial Steenrod operations on Khovanov homology.

The paper explores non-trivial welded knots and ribbon torus-knots, proving their existence.

Characterizes G2-structures on Lie algebras with non-trivial center.

Non-trivial conservation law found for a specific system.

We prove that the degenerate part of the distributive homology of a multispindle is determined by the normalized homology. In particular, when the multispindle is a quandle $Q$, the degenerate homology of $Q$ is completely determined by the quandle homology of $Q$. For this case (and generally for two term homology of …

Non-trivial action on surface configuration homology.

We prove the Weinstein conjecture for non-trivial contact connected sums under either of two topological conditions: non-trivial fundamental group or torsion-free homology.

We construct a 2-generated 2-related group without non-trivial finite factors. That answers a question of J. Button.

New construction provides non-trivial representations for geometric quantisation.

Every non-trivial knot group is fully residually perfect.

New families of embeddings in 4-manifolds, topologically trivial but smoothly non-trivial.

We show an integrality of the quantum SU(2)-invariant associated with a non-trivial first cohomology class modulo two.

We propose a new approach to the value distribution theory of entire holomorphic curves. We define a ``packing density'' of an entire holomorphic curve, and show that it has various non-trivial properties. We prove a ``gap theorem'' for holomorphic maps from elliptic curves to the complex projective space, and study th…

We solve exactly a simple model of trend following strategy, and obtain the analytical shape of the profit per trade distribution. This distribution is non trivial and has an option like, asymmetric structure. The degree of asymmetry depends continuously on the parameters of the strategy and on the volatility of the tr…

The study finds non-trivial elements in moduli spaces of curvature metrics.

The goal of this note is to construct, on many manifolds, non-trivial concordances from the identity to itself. This produces counterexamples to a recent conjecture by Botvinnik.

Let X be a compact Kahler manifold with a non-trivial holomorphic Poisson structure. Then there exist deformations of non-trivial generalized Kahler structures with one pure spinor on X. We prove that every Poisson submanifold of X is a generalized Kahler submanifold with respect to the deformed generalized Kahler stru…

We prove that if a link admits non-trivial (2k+1)-colorings, with prime 2k+1>7, it also admits non-trivial (2k+1)-colorings not involving colors 2k, 2k-1, nor k.

By 2-twist-spinning the knotted graph that represents the knotted handlebody $5_2$, we obtain a knotted foam in 4-dimensional space with a non-trivial quandle cocycle invariant.

Survey on closed-form Fisher-Rao distance expressions.

Paper proposes a framework to detect distribution shifts using embedding space geometry.

A method for learning distributions on complex manifolds using normalizing flows.

We use a simple geometric argument and small cancellation properties of link groups to prove that alternating links are non-trivial. This proof uses only classic results in topology and combinatorial group theory.

In this paper, we study the colorability of link diagrams by the Alexander quandles. We show that if the reduced Alexander polynomial $Δ_{L}(t)$ is vanishing, then $L$ admits a non-trivial coloring by any non-trivial Alexander quandle $Q$, and that if $Δ_{L}(t)=1$, then $L$ admits only the trivial coloring by any Alexa…

The paper revisits a claim about a principal bundle over a contractible base and finds it non-trivial.

We present some non-trivial calculations of Baldwin-Ozsváth-Szabó cohomology of links, and applications to Heegaard-Floer homology of branched double covers.

This paper highlights the size-dependency of income distributions, i.e. the income distribution curves versus the population of a country systematically. By using the generalized Lotka-Volterra model to fit the empirical income data in the United States during 1996-2007, we found an important parameter $λ$ can scale wi…

New entropy-based objective for sparse coding improves learning.

The paper constructs non-trivial cocycles for long embeddings with more than one loop.

The multivariate normal density is a monotonic function of the distance to the mean, and its ellipsoidal shape is due to the underlying Euclidean metric. We suggest to replace this metric with a locally adaptive, smoothly changing (Riemannian) metric that favors regions of high local density. The resulting locally adap…

A new metric predicts model performance on unseen data.

For each odd prime p, and for each non-split link admitting non-trivial p-colorings, we prove that the maximum number of Fox colors is p. We also prove that we can assemble a non-trivial p-coloring with any number of colors, from the minimum to the maximum number of colors. Furthermore, for any rational link, we prove …

For n at least 3, let SAut(F_n) denote the unique subgroup of index two in the automorphism group of a free group. The standard linear action of SL(n,Z) on R^n induces non-trivial actions of SAut(F_n) on R^n and on S^{n-1}. We prove that SAut(F_n) admits no non-trivial actions by homeomorphisms on acyclic manifolds or …

Some of the well known Fefferman like constructions of parabolic geometries end up with a new structure on the same manifold. In this paper, we classify all such cases with the help of the classical Onishchik's lists \cite{onish1} and we treat in detail the only new series of inclusions providing the spinorial structur…