arXiv research

It is shown that a small cover (resp. real moment-angle manifold) over a simple polytope is an infra-solvmanifold if and only if it is diffeomorphic to a real Bott manifold (resp. flat torus). Moreover, we obtain several equivalent conditions for a small cover being homeomorphic to a real Bott manifold. In addition, we…

Study finds conditions for operator fields to be in strictly upper triangular form in small dimensions.

Generative Latent Implicit Conditional Optimization (GLICO) learns from small samples.

In this note we prove that, under a weak condition, small deformations of a compact balanced manifold are also balanced. This condition is satisfied on the twistor space over a compact self-dual four manifold.

SHADOWCAST generates graphs with user-specified attributes.

New condition ensures submanifolds are skew in small areas.

Small sub-Riemannian balls have diameter close to twice their radius.

A new algorithm for robust causal discovery in small sample sizes.

Local smoothing of metrics with small curvature, removing Ricci curvature condition.

We will consider locally conformally balanced manifolds. We prove that a locally conformally balanced condition is not stable under a small deformation. We prove that locally conformally balanced condition is stable under any proper modification. We prove that symmetric products of the Kodaira surface can be resolve to…

Unique minimal surfaces near quadratic cones are identified.

Analyzes Willmore flow for graphs with boundary data, proving existence and convergence.

Gradient descent benefits from tangent kernel advantages under specific conditions.

For incomplete sub-Riemannian manifolds, and for an associated second-order hypoelliptic operator, which need not be symmetric, we identify two alternative conditions for the validity of Gaussian-type upper bounds on heat kernels and transition probabilities, with optimal constant in the exponent. Under similar conditi…

We show that all the small covers which are infra-nilmanifolds are exactly real Bott manifolds. This implies that any small cover which admits a flat Riemannian metric must be a real Bott manifold. In addition, we will study small covers which admit Riemannian metrics with positive or nonnegative Ricci curvature or sec…

In this paper, we investigate the minimal symplectic fillings of small Seifert 3-manifolds with a canonical contact structure. As a result, we classify all minimal symplectic fillings of small Seifert 3-manifolds satisfying certain conditions. Furthermore, we also demonstrate that every such a minimal symplectic fillin…

We explain and generalise a construction due to Gromov to realise geometric small cancellation groups over graphs of groups as fundamental groups of non-positively curved 2-dimensional complexes of groups. We then give conditions so that the hyperbolicity and some finiteness properties of the small cancellation quotien…

New method improves nonlinear filtering accuracy with reduced computation.

Estimates CATEs for structured treatments using a new decomposition method.

This paper investigates the projectivization of real vector bundles over small covers. We first give a necessary and sufficient condition for such a projectivization to be a small cover. Then associated with moment-angle manifolds, we further study the structure of such a projectivization as a small cover. As an applic…

This paper studies least-square regression penalized with partly smooth convex regularizers. This class of functions is very large and versatile allowing to promote solutions conforming to some notion of low-complexity. Indeed, they force solutions of variational problems to belong to a low-dimensional manifold (the so…

Random branched covers of groups are homotopy equivalent to geometrically small cancellation complexes.

Algorithm recovers large causal tree from small samples.

The small-ball method was introduced as a way of obtaining a high probability, isomorphic lower bound on the quadratic empirical process, under weak assumptions on the indexing class. The key assumption was that class members satisfy a uniform small-ball estimate: that $Pr(|f| \geq κ\|f\|_{L_2}) \geq δ$ for given const…

SFM resolves small-scale physics challenges in weather data.

Proposes a new signal model for high-dimensional, small-sample-size data.

The Willmore conjecture states that any immersion F:T^2 -> R^n of a 2-torus into flat euclidean space satisfies $\int_{T^2} H^2\geq 2π^2$. We prove it under the condition that the L^p-norm of the Gaussian curvature is sufficiently small.

The paper classifies virtual knot polynomials and trivalent graph invariants using skein theory.

YuruGAN generates yuru-chara images using GANs and clustering for small datasets.

Generative models use kernel smoothing for conditioning on small example sets.

We study small Seifert possibly chiral cosmetic surgeries on not necessarily null-homologous knot in rational homology spheres. Using $PSL_2(\mathbb{C})$-character variety theory we give a sharp bound on the number of slopes producing the same small Seifert manifold if the ambient manifold satisfies some representation…

This is the second of a series of two papers where we construct embedded Willmore tori with small area constraint in Riemannian three-manifolds. In both papers the construction relies on a Lyapunov-Schmidt reduction, the difficulty being the Möbius degeneration of the tori. In the first paper the construction was perfo…

Motivated by marginals-mimicking results for Itô processes via SDEs and by their applications to volatility modeling in finance, we discuss the weak convergence of the law of a hypoelliptic diffusions conditioned to belong to a target affine subspace at final time, namely $\mathcal{L}(Z_t|Y_t = y)$ if $X_{\cdot}=(Y_\cd…

Polyhedra can be Rupert if they can be slightly rotated to fit inside each other.

New examples of deformed Hermitian-Yang-Mills connections found.

Generalizes Ricci flow starting from small curvature concentration with a Morrey-type condition.

Consider a generic $r$-dimensional subspace of $\mathbb{R}^d$, $r<d$, and suppose that we are only given projections of this subspace onto small subsets of the canonical coordinates. The paper establishes necessary and sufficient deterministic conditions on the subsets for subspace identifiability.

Geometric framework links clustering accuracy to structural recovery.

Early training of deep neural networks leads to small, directionally converging weights.

In this paper we establish a gap phenomenon for immersed surfaces with arbitrary codimension, topology and boundaries that satisfy one of a family of systems of fourth-order anisotropic geometric partial differential equations. Examples include Willmore surfaces, stationary solitons for the surface diffusion flow, and …

Small bubbles sliding on a boundary maintain half-spherical shape.

We analyze the information-theoretic limits for the recovery of node labels in several network models. This includes the Stochastic Block Model, the Exponential Random Graph Model, the Latent Space Model, the Directed Preferential Attachment Model, and the Directed Small-world Model. For the Stochastic Block Model, the…

Few-Shot Diffusion Models generate new samples from small image sets.

We consider small-time asymptotics for diffusion processes conditioned by their initial and final positions, under the assumption that the diffusivity has a sub-Riemannian structure, not necessarily of constant rank. We show that, if the endpoints are joined by a unique path of minimal energy, and lie outside the sub-R…

The distance function to a generic submanifold behaves well under small perturbations.

Density mode clustering is a nonparametric clustering method. The clusters are the basins of attraction of the modes of a density estimator. We study the risk of mode-based clustering. We show that the clustering risk over the cluster cores --- the regions where the density is high --- is very small even in high dimens…

Quite a number of distinct versions of Bartnik's definition of quasi-local mass appear in the literature, and it is not a priori clear that any of them produce the same value in general. In this paper we make progress on reconciling these definitions. The source of discrepancies is two-fold: the choice of boundary cond…

Algorithm learns causal structures from low-order conditional independencies.