arXiv research

Study fixed-point sets of $S^{1}$-actions on quaternionic manifolds.

Proposes a method to improve hierarchical clustering using set-level structural priors.

Introduces three types of partial bihamiltonian structures.

Given a linearly ordered set I, every surjective map p: A --> I endows the set A with a structure of set of preferences by "replacing" the elements of I with their inverse images via p considered as "balloons" (sets endowed with an equivalence relation), lifting the linear order on A, and "agglutinating" this structure…

Defines invariants for reflection groups and connects them to Frobenius structures.

Determines higher smooth surgery structure sets of complex projective spaces.

Galois action on manifold structures of complex varieties is abelian.

Paper defines invariants for elliptic Weyl groups and connects them to Frobenius structures.

We present a first attempt to elucidate a theoretical and empirical approach to design the reward provided by a natural language environment to some structure learning agent. To this end, we revisit the Information Theory of unsupervised induction of phrase-structure grammars to characterize the behavior of simulated a…

Study the boundaries of ε-neighborhoods of planar sets, showing their structure and curvature.

Rapid progress in deep learning has spurred its application to bioinformatics problems including protein structure prediction and design. In classic machine learning problems like computer vision, progress has been driven by standardized data sets that facilitate fair assessment of new methods and lower the barrier to …

The paper studies properties of group relations induced by compatible coarse structures.

Researchers found a maximal antipodal set of three elements in a 7x7 sphere space.

We calculate the smooth structure set of $S^p \times S^q$, $S(p, q)$, for $p, q \geq 2$ and $p+q \geq 5$. As a consequence we show that in general $S(4j-1, 4k)$ cannot admit a group structure such that the smooth surgery exact sequence is a long exact sequence of groups. We also show that the image of forgetful map $F:…

Survey on Nambu-Poisson structures in infinite dimensions.

Smooth structures on diffeological spaces and sheaves, resolving conjectures.

This study provides a new mathematical structure for Koopman eigenfunctions.

Proposes a new Bayesian score for learning network structure from related datasets.

The study connects periodic surface homeomorphisms to contact structures using rational open books.

In this paper we systematically describe relations between various structure sets which arise naturally for pairs of compact topological manifolds with boundary. Our consideration is based on a deep analogy between the case of a compact manifold with boundary and the case of a closed manifold pair. This approach also g…

Lipschitz equivalence of self-similar sets is an important area in the study of fractal geometry. It is known that two dust-like self-similar sets with the same contraction ratios are always Lipschitz equivalent. However, when self-similar sets have touching structures the problem of Lipschitz equivalence becomes much …

Novel approach for SEM in small samples with $p>n$.

In this short note we update a result proved in [16]. This will complete our program of [12] showing that the structure set vanishes for compact aspherical 3-manifolds.

Study on geodesics in a specific sub-Riemannian structure with two types of behavior.

This work establishes properties on diffeological structures for set-valued maps and measures.

The paper classifies all tight contact structures on a solid torus.

We prove that a theorem of Pawlucki, showing that Whitney regularity for a subanalytic set with a smooth singular locus of codimension one implies the set is a finite union of differentiable manifolds with boundary, applies to definable sets in polynomially bounded o-minimal structures. We give a refined version of Paw…

Let M be an orientable topological manifold of dimension m, m greater or equal to 5, with fundamental group $Γ$. Let S(M) be the topological structure set, endowed with the group structure induced by its identification with Ranicki's algebraic structure set. We prove that the (rationalized) rho map $ρ_Γ: S(M)\rightarro…

We give a generating set of the generalized Reidemeister moves for oriented singular links. We use it to introduce an algebraic structure arising from the study of oriented singular knots. We give some examples, including some non-isomorphic families of such structures over non-abelian groups. We show that the set of c…

OTSL improves structure learning accuracy with out-of-sample and resampling strategies.

Online learning algorithms update models via one sample per iteration, thus efficient to process large-scale datasets and useful to detect malicious events for social benefits, such as disease outbreak and traffic congestion on the fly. However, existing algorithms for graph-structured models focused on the offline set…

Uniformity and proximity are two different ways for defining small scale structures on a set. Coarse structures are large scale counterparts of uniform structures. In this paper, motivated by the definition of proximity, we develop the concept of asymptotic resemblance as a relation between subsets of a set to define a…

Differential structure on partial isometries over Grassmannian constructed.

Bandit learning algorithms typically involve the balance of exploration and exploitation. However, in many practical applications, worst-case scenarios needing systematic exploration are seldom encountered. In this work, we consider a smoothed setting for structured linear contextual bandits where the adversarial conte…

We present new rectification theorems of degenerate quasi-conformal structures that give a meaning to quotients of Riemann surfaces with empty interior "fundamental domains". These techniques are used to define the unique renormalization of polynomials with Cantor set Julia sets.

We classify $R$-spaces that admit a certain natural $Γ$-symmetric structure. We further determine the maximal antipodal sets of these structures.

Paper improves Bayesian network learning from related data sets.

We prove that certain volume preserving actions of Lie groups and their lattices do not preserve rigid geometric structures in the sense of Gromov. The actions considered are the "exotic" examples obtained by Katok and Lewis and the first author, by blowing up closed orbits in the well known actions on homogeneous spac…

We extend profound results in pluripotential theory on Kahler manifolds to Sasaki setting via its transverse Kahler structure. As in Kahler case, these results form a very important piece to solve the existence of Sasaki metrics with constant scalar curvature (cscs) in terms of properness of K-energy. One main result i…

We consider a quiver structure on the set of quandle colorings of an oriented knot or link diagram. This structure contains a wealth of knot and link invariants and provides a categorification of the quandle counting invariant in the most literal sense, i.e., giving the set of quandle colorings the structure of a small…

Cube category simplifies set modeling.

b-LOAD extends local causal discovery with prior knowledge, improving causal effect estimation.

We describe a diagram containing the zero sets of the moment maps associated to the diagonal U(1) and Sp(1) actions on the quaternionic projective space HP^n. These sets are related both to focal sets of submanifolds and to Sasakian-Einstein structures on induced Hopf bundles. As an application, we construct a complex …

Differential K-theory gets a $λ$-ring structure.

Develops methods for structured variational inference with star-structured models.

Abstract: Bijection strengthened to Morita equivalence integrating Poisson and Cartan-Dirac structures.

New adversarial examples with structured distortion sets improve robustness and perceptibility.

We study natural additional structures on real algebraic surfaces with trivial first homology mod 2 of the complexification. If the set of real points realizes the zero of the second homology mod 2 of the complexification, then the set of real points is equipped with a pair of opposite orientations and a Spin structure…