arXiv research

Researchers infer gene activity in dividing cells, accounting for protein inheritance and division history.

A new proof of an extension theorem with bounded generators.

Solves division problem for L. Hörmander's systems.

Proves divisibility relations for symplectic curve polynomials.

Uniform convexity in divisible domains leads to hyperbolic geometry.

Paper tackles division difficulty, proposing new methods to improve accuracy.

In contrast to the many examples of convex divisible domains in real projective space, we prove that up to projective isomorphism there is only one convex divisible domain in the Grassmannian of $p$-planes in $\mathbb{R}^{2p}$ when $p > 1$. Moreover, this convex divisible domain is a model of the symmetric space associ…

Division algorithm for surface group rings yields standard complexes and cohomological dimensions.

Adopting a zonal structure of electricity market requires specification of zones' borders. In this paper we use social welfare as the measure to assess quality of various zonal divisions. The social welfare is calculated by Market Coupling algorithm. The analyzed divisions are found by the usage of extended Locational …

HiPart offers an efficient, interactive tool for hierarchical clustering.

New proof of divisibility property for certain algebraic varieties.

The paper sets lower bounds on envy-free divisions in cake-cutting problems.

The paper revisits Rokhlin's divisibility theorem and its significance.

Proves Skoda's Division Theorem using degeneration and positivity of direct image bundles.

Under certain integrability and geometric conditions, we prove division theorems for the exact sequences of holomorphic vector bundles and improve the results in the case of Koszul complex. By introducing a singular Hermitian structure on the trivial bundle, our results recover Skoda's division theorem for holomorphic …

The paper explains the topological origin of the distinction between incidence theorems over division rings and fields.

A new distributed algorithm for fitting sparse additive models with feature division and decorrelation.

Geodesic connectedness proved for statistical manifolds with divisible cubic forms.

Algorithm learns fair division from noisy feedback in uncertain markets.

Study of characteristic numbers in 24-dimensional String manifolds.

An open convex set in real projective space is called divisible if there exists a discrete group of projective automorphisms which acts co-compactly. There are many examples of such sets and a theorem of Benoist implies that many of these examples are strictly convex, have $C^1$ boundary, and have word hyperbolic divid…

In this note we introduce a construction which assigns to an arbitrary manifold bundle its fiberwise orientation covering. This is used to show that the zeta classes of unoriented surface bundles are not divisible in the stable range.

Study shows non-symmetric convex sets have full boundary limits.

Supersymmetry is deeply related to division algebras. Nonabelian Yang-Mills fields minimally coupled to massless spinors are supersymmetric if and only if the dimension of spacetime is 3, 4, 6 or 10. The same is true for the Green-Schwarz superstring. In both cases, supersymmetry relies on the vanishing of a certain tr…

Study explores efficient data division for ICPs.

Study of congestion in negative curvature manifolds using fair-division algorithms.

Nowadays, data are generated massively and rapidly from scientific fields as bioinformatics, neuroscience and astronomy to business and engineering fields. Cluster analysis, as one of the major data analysis tools, is therefore more significant than ever. We propose in this work an effective Semi-supervised Divisive Cl…

LLMs can collude in market divisions, maximizing profits.

Constructs modular forms and proves divisibility results for odd-dimensional manifolds.

New invariants from divisibility of Lee classes for slice-torus.

This paper introduces a divide-and-conquer inspired adversarial learning (DACAL) approach for photo enhancement. The key idea is to decompose the photo enhancement process into hierarchically multiple sub-problems, which can be better conquered from bottom to up. On the top level, we propose a perception-based division…

In this article we consider a version of the geography question for simply-connected symplectic 4-manifolds that takes into account the divisibility of the canonical class as an additional parameter. We also find new examples of 4-manifolds admitting several symplectic structures, inequivalent under deformation and sel…

In this work, we examine the process of Tropical Polynomial Division, a geometric method which seeks to emulate the division of regular polynomials, when applied to those of the max-plus semiring. This is done via the approximation of the Newton Polytope of the dividend polynomial by that of the divisor. This process i…

funLOCI identifies clusters in functional data.

Lumbermark clusters data robustly, slicing limbs of mutual reachability trees.

In this short article we give a geometric meaning of the divisibility of $KO$-theoretical Euler classes for given two spin modules. We are motivated by Furuta's 10/8-inequality for a closed spin $4$-manifold. The role of the reducibles is clarified in the monopole equations of Seiberg-Witten theory, as done by Donaldso…

Dividing local Gaussian processes improve real-time prediction efficiency.

New algorithms for fair item allocation with limited copies.

A definition for elliptical tempered stable distribution, based on the characteristic function, have been explained which involve a unique spectral measure. This definition provides a framework for creating a connection between infinite divisible distribution, and particularly elliptical tempered stable distribution, w…

Classically, isothermic surfaces are characterized as those surfaces which are "divisible into infinitesimal squares by their curvature lines". This characterization is the direct analogue to the definition of discrete isothermic nets. In order to understand the relations between the discrete and the smooth theory bett…

Is it possible to predict the motivation of players just by observing their gameplay data? Even if so, how should we measure motivation in the first place? To address the above questions, on the one end, we collect a large dataset of gameplay data from players of the popular game Tom Clancy's The Division. On the other…

The paper connects polygon spaces with quotient spaces using spin actions and normed division algebras.

A polynomial counterpart of the Seiberg-Witten invariant associated with a negative definite plumbed 3-manifold has been proposed by earlier work of the authors. It is provided by a special decomposition of the zeta-function defined by the combinatorics of the manifold. In this article we give an algorithm, based on mu…

Properly embedded simplices in a convex divisible domain $Ω\subset \mathbb{R} \textrm{P}^d$ behave somewhat like flats in Riemannian manifolds, so we call them flats. We show that the set of codimension-$1$ flats has image which is a finite collection of disjoint virtual $(d-1)$-tori in the compact quotient manifold. I…

We prove that the signature of an even, symmetric form on a finite rank integral lattice, has signature divisible by 8, provided its associated linking form vanishes in the Witt group of linking forms. Our result generalizes the well know fact that an even, unimodular form has signature divisible by 8. We give applicat…

New framework resolves central limit behavior in differential privacy.

This paper shows that, away from 6, the kernel of the Witten genus is precisely the ideal consisting of (bordism classes of) Cayley plane bundles with connected structure group, but only after restricting the Witten genus to string bordism. It does so by showing that the divisibility properties of Cayley plane bundle c…

The paper provides an algorithm to create curves touching a smooth cubic at specific intersection points.