arXiv research

For harmonic maps of degree 2, a similar quantitative stability estimate does not hold uniformly.

Alexander polynomial degree correlates with knot defect, proving conjecture for defect zero.

Biharmonic maps are generalizations of harmonic maps. A well-known result of Eells and Wood on harmonic maps between surfaces shows that there exists no harmonic map from a torus into a sphere (whatever the metrics chosen) in the homotopy class of maps of Brower degree $\pm 1$. It would be interesting to know if there …

New bound on Jones polynomial for specific positive links.

New bounds on Jones polynomial positivity for specific links.

We show that the superconformal symmetries of the (1,1) sigma model decompose into a set of more refined symmetries when the target space admits projectors $P_{\pm}$, and the orthogonal complements $Q_{\pm}$, covariantly constant with respect to the two natural torsionful connections $\nabla^{(\pm)}$ that arise in the …

The study finds obstructions for certain Weyl curvature tensors on manifolds.

Study on stability of half-harmonic maps from R to S, proving non-degeneracy and quantitative stability.

New $\varepsilon$-harmonic maps of low degree are rigid under certain energy bounds.

For a projective algebraic variety $V$ with isolated singularities, endowed with a metric induced from an embedding, we consider the analysis of the natural partial differential operators on the regular part of $V$. We show that, in the complex case, the Laplacians of the de Rham and Dolbeault complexes are discrete op…

New techniques reveal tight contact manifolds with vanishing contact homology.

Investigates polynomial solutions to minimal surface equation, proving constraints and structure theorems.

The paper introduces discrete Dirac structures for mechanics, simplifying dynamics.

P. M. Akhmetiev used a controlled version of the stable Hopf invariant to show that any (continuous) map N -> M between stably parallelizable compact n-manifolds, n\ne 1,2,3,7, is realizable in R^{2n}, i.e. the composition of f with an embedding M\subset R^{2n} is C^0-approximable by embeddings. It has been long believ…

A protocol reduces transaction costs for portfolio managers.

Rationality proved for curvature invariants of 2-complexes.

Although a key driver of Earth's climate system, global land-atmosphere energy fluxes are poorly constrained. Here we use machine learning to merge energy flux measurements from FLUXNET eddy covariance towers with remote sensing and meteorological data to estimate net radiation, latent and sensible heat and their uncer…

High-dimensional neural network manifolds misalign with human perception, causing adversarial examples.

We employ a 2x3 factorial experiment to study two central factors in the design of prediction markets (PMs) for idea evaluation: the overall design of the PM, and the elasticity of market prices set by a market maker. The results show that 'multi-market designs' on which each contract is traded on a separate PM lead to…

We describe a new method to automatically discriminate between patients with Alzheimer's disease (AD) or mild cognitive impairment (MCI) and elderly controls, based on multidimensional classification of hippocampal shape features. This approach uses spherical harmonics (SPHARM) coefficients to model the shape of the hi…

Fine particulate matter (PM$_{2.5}$) is one of the criteria air pollutants regulated by the Environmental Protection Agency in the United States. There is strong evidence that ambient exposure to (PM$_{2.5}$) increases risk of mortality and hospitalization. Large scale epidemiological studies on the health effects of P…

In this paper, we study distance one surgeries between lens spaces $L(p,1)$ with $p \geq 5$ prime and lens spaces $L(n,1)$ for $n \in \mathbb{Z}$ and band surgeries from $T(2,p)$ to $T(2,n)$. In particular, we prove that $L(n,1)$ is obtained by a distance one surgery from $L(5,1)$ only if $n=\pm 1$, $4$, $\pm 5$, $6$ o…

Acute Kidney Injury (AKI) is a common clinical syndrome characterized by the rapid loss of kidney excretory function, which aggravates the clinical severity of other diseases in a large number of hospitalized patients. Accurate early prediction of AKI can enable in-time interventions and treatments. However, AKI is hig…

Research develops a generic method for evaluating trading platform components.

A criterion ensures double sliceness for certain knots and satellite knots.

In this paper, we introduce the notions of $α$-Hermitian-Einstein metric and $α$-stability for $I_\pm$-holomorphic vector bundles on bi-Hermitian manifolds. Moreover, we establish a Kobayashi-Hitchin correspondence for $I_\pm$-holomorphic vector bundles on bi-Hermitian manifolds. Examples of such vector bundles include…

The paper studies $ext{Pin}^{\pm}$-structures on non-oriented 4-manifolds via Lefschetz fibrations.

Partial monitoring is a general model for sequential learning with limited feedback formalized as a game between two players. In this game, the learner chooses an action and at the same time the opponent chooses an outcome, then the learner suffers a loss and receives a feedback signal. The goal of the learner is to mi…

CONDA-PM framework helps analyze concept drift in business processes.

The conjecture of Kosniowski asserts that if the circle acts on a compact unitary manifold $M$ with a non-empty fixed point set and $M$ does not bound a unitary manifold equivariantly, then the dimension of the manifold is bounded above by a linear function on the number of fixed points. We confirm the conjecture for a…

We use conformal, but ghostful, Weyl gravity to study its ghost-free, second derivative, partially massless (PM) spin 2 component in presence of Einstein gravity with positive cosmological constant. Specifically, we consider both gravitational- and self- interactions of PM via the fully non-linear factorization of conf…

For a compact almost complex 4-manifold $(M,J)$, we study the subgroups $H^{\pm}_J$ of $H^2(M, \mathbb{R})$ consisting of cohomology classes representable by $J$-invariant, respectively, $J$-anti-invariant 2-forms. If $b^+ =1$, we show that for generic almost complex structures on $M$, the subgroup $H^-_J$ is trivial. …

In this note we prove that for any finite quandle $X$ and any 2-cocycle $φ\in Z^2_{Q\pm}(X; \mathds{Z})$, the cocycle invariant $Φ^{\pm}_φ(K)$ is trivial for all knots $K$.

Deep neural networks with specific parameter sets can approximate smooth functions efficiently.

We study finite type invariants of nullhomologous knots in a closed 3-manifold $M$ defined in terms of certain descending filtration $\{\mathscr{K}_n(M)\}_{n\geq 0}$ of the vector space $\mathscr{K}(M)$ spanned by isotopy classes of nullhomologous knots in $M$. The filtration $\{\mathscr{K}_n(M)\}_{n \geq 0}$ is define…

Automated segmentation of anatomical structures is a crucial step in image analysis. For lung segmentation in computed tomography, a variety of approaches exist, involving sophisticated pipelines trained and validated on different datasets. However, the clinical applicability of these approaches across diseases remains…

The study explores psc-metrics on non-spin manifolds with pin^\pm or spin^c structures.

The paper proves conditions under which certain geometric structures are rigid.

The paper localizes an index and provides a condition for the orientability of a monopole moduli space.

New method proves cosmetic surgery conjecture for certain knots.

Following Vinberg, we find the criterions for a subgroup generated by reflections $Γ\subset \SL^{\pm}(n+1,\mathbb{R})$ and its finite-index subgroups to be definable over $\mathbb{A}$ where $\mathbb{A}$ is an integrally closed Noetherian ring in the field $\mathbb{R}$. We apply the criterions for groups generated by re…

Let $M$ be any $n$ dimensional smooth manifold and $PM$ be the space of all smooth paths, then we showed that $PM$ is a smooth manifold modelled over a complete normable space. We discussed many geometric structure on Path spaces and its relation to ambient space.

CTRNNs improve blood glucose forecasting in ICU, outperforming traditional models.

In the present paper, we will show that a $(p,q,r)$-pretzel knot has the representativity 3 if and only if $(p,q,r)$ is either $\pm(-2,3,3)$ or $\pm(-2,3,5)$. We also show that a large algebraic knot has the representativity less than or equal to 3.

We prove that for genus $g=3,4$, the extended mapping class group $\text{Mod}^{\pm}(S_g)$ can be generated by two elements of finite orders. But for $g=1$, $\text{Mod}^{\pm}(S_1)$ cannot be generated by two elements of finite orders.

Portfolio management (PM) is a fundamental financial planning task that aims to achieve investment goals such as maximal profits or minimal risks. Its decision process involves continuous derivation of valuable information from various data sources and sequential decision optimization, which is a prospective research d…

We develop Hodge theory for a Riemannian manifold $(M,g)$ with a background closed 3-form, H. Precisely, we prove that if the metric connections with torsion $\pm H$ have holonomy groups $G_\pm$, then the $d^H$-Laplacian preserves the irreducible representations of the Lie algebras of the holonomy groups on the space o…

The paper defines a new algebra structure on skein modules of 3-manifolds and shows it's isomorphic to a known algebra.