arXiv research

This study addresses transitions in conically singular associative submanifolds and their desingularizations.

We consider minimal immersions in MxR. We study existence and uniqueness of associate and conjugate isometric immersions to a given minimal surface. We use the theory of univalent harmonic map between surfaces. Then we study the geometry of associate minimal vertical graphs. We prove that an associate surface of a vert…

Study of associative submanifolds in Berger space SO(5)/SO(3).

The study shows acylindrical hyperbolicity for Artin groups not associated with joins or cones.

This paper studies the associativity of gluing of trajectories in Morse theory. We show that the associativity of gluing follows from of the existence of compatible manifold with face structures on the compactified moduli spaces. Using our previous work, we obtain the associativity of gluing in certain cases. In partic…

Homology theories for associative algebraic structures are well established and have been studied for a long time. More recently, homology theories for self-distributive algebraic structures motivated by knot theory, such as quandles and their relatives, have been developed and investigated. In this paper, we study ass…

We study deformations of associative submanifolds $Y^3\subset M^7$ of a $G_2$ manifold $M^7$. We show that the deformation space can be perturbed to be smooth, and it can be made compact and zero dimensional by constraining it with an additional equation. This allows us to associate local invariants to associative subm…

Study explores associated groups of symmetric quandles and their properties.

The paper studies scaling laws for associative memory mechanisms.

Genome-wide association studies (GWASs) aim to detect genetic risk factors for complex human diseases by identifying disease-associated single-nucleotide polymorphisms (SNPs). The traditional SNP-wise approach along with multiple testing adjustment is over-conservative and lack of power in many GWASs. In this article, …

Study constructs associative submanifolds in $G_2$-manifolds from orbifolds.

LLMs can be tricked into recalling facts based on context clues.

In this paper we study a functional equation associated to the Kummer's equation (K) of the trilogarithm. Then we apply our results to web geometry and to characterize the functions solution of (K).

Study Legendrian graph invariants via augmentation and ruling polynomials.

In this paper we study two types of fibrations associated with a 3-dimensional unital associative irreducible algebra and their basic properties. We investigate trivial principal fibrations of degenerate semi-Euclidean sphere and their semi-conformal and projective models. We use Norden normalization method for constru…

Deep models improve GWAS by identifying genetic interactions.

Poisson algebra is usually defined to be a commutative algebra together with a Lie bracket, and these operations are required to satisfy the Leibniz rule. We describe Poisson structures in terms of a single bilinear operation. This enables us to explore Poisson algebras in the realm of non-associative algebras. We stud…

Paper studies non-associativity in quantum systems with magnetic fields.

Second generation sequencing technologies are being increasingly used for genetic association studies, where the main research interest is to identify sets of genetic variants that contribute to various phenotype. The phenotype can be univariate disease status, multivariate responses and even high-dimensional outcomes.…

Genome-wide association studies have proven to be essential for understanding the genetic basis of disease. However, many complex traits---personality traits, facial features, disease subtyping---are inherently high-dimensional, impeding simple approaches to association mapping. We developed a nonparametric Bayesian re…

We study Lie algebras endowed with an abelian complex structure which admit a symplectic form compatible with the complex structure. We prove that each of those Lie algebras is completely determined by a pair (U,H) where U is a complex commutative associative algebra and H is a sesquilinear hermitian form on U which ve…

For six dimensional nilmanifolds we build a module $\mathcal{H}$ of an affine Kac Moody vertex algebras. Then, we associate some logarithmic fields for the module $\mathcal{H}$ and we study their singularities. We also presented a physics motivation behind this construction. We study a particular case, we show that whe…

Study compatible and associated metrics for contact-symplectic structures, showing geodesic integral curves and minimal leaf properties.

A test for neural networks identifies genetic associations.

Common complex diseases are likely influenced by the interplay of hundreds, or even thousands, of genetic variants. Converging evidence shows that genetic variants with low marginal effects (LME) play an important role in disease development. Despite their potential significance, discovering LME genetic variants and as…

In a noncommutative torus, effect of perturbation by inner derivation on the associated quantum stochastic process and geometric parameters like volume and scalar curvature have been studied. Cohomological calculations show that the above perturbation produces new spectral triples. Also for the Weyl C^*-algebra, the La…

New connections defined for a specific geometric structure.

The object of study is almost paracomplex pseudo-Riemannian manifolds with a pair of metrics associated each other by the almost paracomplex structure. A torsion-free connection and tensors with geometric interpretation are found which are invariant under the twin interchange, i.e. the swap of the counterparts of the p…

The purpose of the article is to study a foliation associated to a lattice-equivariant harmonic map of small rank from a complex ball to another. The result is related to rigidity of some complex ball quotients.

We study co-associative fibrations of G_{2}-manifolds. We propose that the adiabatic limit of this structure should be given locally by a maximal submanifold in a space of indefinite signature and set up global versions of the constructions.

OMBA learns product and user representations for better online market basket analysis.

Study improves scalability of cell-free massive MIMO networks by optimizing UE-AP association.

Vassiliev invariants can be studied by studying the spaces of chord diagrams associated with singular knots. To these chord diagrams are associated the intersection graphs of the chords. We extend results of Chmutov, Duzhin and Lando to show that these graphs determine the chord diagram if the graph has at most one loo…

The monodromy conjecture states that every pole of the topological (or related) zeta function induces an eigenvalue of monodromy. This conjecture has already been studied a lot; however, in full generality it is proven only for zeta functions associated to a polynomial in two variables. In this article we consider zeta…

The article develops deformation theory for ACyl associative submanifolds in ACyl G2-manifolds.

Given genetic variations and various phenotypical traits, such as Magnetic Resonance Imaging (MRI) features, we consider two important and related tasks in biomedical research: i)to select genetic and phenotypical markers for disease diagnosis and ii) to identify associations between genetic and phenotypical data. Thes…

The study compares feed-forward and attention layers in language models.

There are introduced and studied a pair of associated Schouten-van Kampen affine connections adapted to the contact distribution and an almost contact B-metric structure generated by the pair of associated B-metrics and their Levi-Civita connections. By means of the constructed non-symmetric connections, the basic clas…

Study on new Monge-Ampère functionals and their variational problems.

One primary task of population health analysis is the identification of risk factors that, for some subpopulation, have a significant association with some health condition. Examples include finding lifestyle factors associated with chronic diseases and finding genetic mutations associated with diseases in precision he…

Study approximates sub-Riemannian structures with Riemannian metrics and analyzes spectral convergence.

New BDEs reveal singular surfaces from line congruences.

The study classifies special flows on specific geometric groups.

In this work we study the geodesic flow on nilmanifolds associated to graphs. We are interested in the construction of first integrals to show complete integrability on some compact quotients. Also examples of integrable geodesic flows and of non-integrable ones are shown.

In this paper we study the cobordism of algebraic knots associated with weighted homogeneous polynomials, and in particular Brieskorn polynomials. Under some assumptions we prove that the associated algebraic knots are cobordant if and only if the Brieskorn polynomials have the same exponents.

The spaces of Riemannian metrics on a closed manifold $M$ are studied. On the space ${\mathcal M}$ of all Riemannian metrics on $M$ the various weak Riemannian structures are defined and the corresponding connections are studied. The space ${\mathcal AM}$ of associated metrics on a symplectic manifold $M,ω$ is consider…

Associative submanifolds of the 7-sphere S^7 are 3-dimensional minimal submanifolds which are the links of calibrated 4-dimensional cones in R^8 called Cayley cones. Examples of associative 3-folds are thus given by the links of complex and special Lagrangian cones in C^4, as well as Lagrangian submanifolds of the near…

Discovering causal genetic variants from large genetic association studies poses many difficult challenges. Assessing which genetic markers are involved in determining trait status is a computationally demanding task, especially in the presence of gene-gene interactions. A non-parametric Bayesian approach in the form o…