arXiv research

Fiber simplifies RL and population-based methods for distributed training.

Study variations of Riemannian submersions to maintain geodesic fibers and positive curvatures.

DUPLE tackles cross-deployment recognition in fiber-optic perimeter security with meta-learning.

Machine learning is used to compute achievable information rates (AIRs) for a simplified fiber channel. The approach jointly optimizes the input distribution (constellation shaping) and the auxiliary channel distribution to compute AIRs without explicit channel knowledge in an end-to-end fashion.

Defines Wodzicki residue using groupoids and fibered distributions.

The horizontal Laplacian of a Riemannian submersion with totally geodesic fibers and an integrable horizontal distribution.

This paper presents an investigation of the relation between some positivity of the curvature and the finiteness of fundamental groups in semi-Riemannian geometry. We consider semi-Riemannian submersions $π: (E, g) \rightarrow (B, -g_{B})$ under the condition with $(B, g_{B})$ Riemannian, the fiber closed Riemannian, …

Given a fibered link, consider the characteristic polynomial of the monodromy restricted to first homology. This generalizes the notion of the Alexander polynomial of a knot. We define a construction, called iterated plumbing, to create a sequence of fibered links from a given one. The resulting sequence of characteris…

We show that on a closed smooth manifold $M$ equipped with $k$ fiber bundle structures whose vertical distributions span the tangent bundle, every smooth diffeomorphism $f$ of $M$ sufficiently close to the identity can be written as a product $f=f_1... f_k$, where $f_i$ preserves the $i^{\text{th}}$-fiber. The factors …

Modeling aortic wall inhomogeneities to predict dissection risks.

In 1910 E. Cartan constructed a canonical frame and found the most symmetric case for maximally nonholonomic rank 2 distributions in $\mathbb R^5$. We solve the analogous problem for germs of generic rank 2 distributions in ${\mathbb R}^n$ for n>5. We use a completely different approach based on the symplectification o…

Diffusion-weighted MR imaging (DWI) is the only method we currently have to measure connections between different parts of the human brain in vivo. To elucidate the structure of these connections, algorithms for tracking bundles of axonal fibers through the subcortical white matter rely on local estimates of the fiber …

Base of fibered correspondence is arbitrary correspondence. Fibered correspondence is interesting when we consider relationship between different bundles. However composition of fibered correspondences may not always be defined. Reduced fibered correspondence is defined only between fibers over the same point of base. …

Extends Frohman and Rannard's result to Seifert fiber spaces with singular surfaces.

Investigates conditions for GKM fiber bundles and realizability of fiber bundles of GKM graphs.

Study fiber-preserving, orientation-reversing involutions on Seifert fibered 3-manifolds.

We study the relationship between fibered ribbon 1-knots and fibered ribbon 2-knots by studying fibered slice disks with handlebody fibers. We give a characterization of fibered homotopy-ribbon disks and give analogues of the Stallings twist for fibered disks and 2-knots. As an application, we produce infinite families…

Introduces Darboux-Lie derivative for fiber bundles.

The paper proves non-existence of positive scalar curvature on certain fiber bundles.

New examples show not all homology fiber bundles are topological.

New exotic 4-manifolds found with fiber bundles.

Study shows simplicial volume of certain fiber bundles is zero.

In this paper, we show an approach to build deep learning algorithms for recognizing signals in distributed fiber optic monitoring and security systems for long perimeters. Synthesizing such detection algorithms poses a non-trivial research and development challenge, because these systems face stringent error (type I a…

We construct two infinite families of knots each of which admits a Seifert fibered surgery with none of these surgeries coming from Dean's primitive/Seifert-fibered construction. This disproves a conjecture that all Seifert fibered surgeries arise from Dean's primitive/Seifert-fibered construction. The (-3,3,5)-pretzel…

We show that a compact complex surface which fibers smoothly over a curve of genus >1 with fibers of genus >1 fibers holomorphically. We deduce an improvement of a result in [D Kotschick, Math. Research Letters, 5 (1998) 227-234], and a characterisation of fibered surfaces with zero signature.

Constructs a family to handle unstable fibers on complex surfaces.

The concept of F-algebra and its representation can be extended to an arbitrary bundle. We define operations of fibered F-algebra in fiber. The paper presents the representation theory of of fibered F-algebra as well as a comparison of representation of F-algebra and of representation of fibered F-algebra.

Groups with Property (T) have fiber products with Property (T).

Boundary of fiber convex domains is a cohomological sphere.

Study complex surfaces fibered over Teichmüller curves with Veech fibers.

In this paper, we define the primitive/Seifert-fibered property for a knot in S^3. If satisfied, the property ensures that the knot has a Dehn surgery that yields a small Seifert-fibered space (i.e. base S^2 and three or fewer critical fibers). Next we describe the twisted torus knots, which provide an abundance of exa…

Describes 3-manifolds by families of singularly fibered surfaces.

A fibered concordance of knots, introduced by Harer, is a concordance between fibered knots that is well-behaved with respect to the fibrations. We consider semi-fibered concordance of two component ordered links $L=J \sqcup K$ with $J$ fibered. These are concordances that restrict to fibered concordances on the first …

Study Veech groups in fibered 3-manifolds, proving no parabolics for fibers.

Paper connects homologically fibered links to solutions of equations.

Defines products for fibered corners manifolds, generalizing resolutions.

Study simplicial volume in fiber bundles with connected groups.

New research finds infinitely many hyperbolic knots not almost-fibered.

The paper constructs trisections for fiber bundles over a circle.

Simpler proof for Kielak's virtual fibering criterion.

We characterize cutting arcs on fiber surfaces that produce new fiber surfaces, and the changes in monodromy resulting from such cuts. As a corollary, we characterize band surgeries between fibered links and introduce an operation called Generalized Hopf banding. We further characterize generalized crossing changes bet…

Study non-fibered links' relation to tight contact structures.

Around 1960, R. Palais and J. Cerf proved a fundamental result relating spaces of diffeomorphisms and imbeddings of manifolds: If V is a submanifold of M, then the map from Diff(M) to Imb(V,M) that takes f to its restriction to V is locally trivial. We extend this and related results into the context of fibered manifol…

The notion of a (stably) decomposable fiber bundle is introduced. In low dimensions, for torus fiber bundles over a circle the notion translates into a property of elements of the special linear group of integral matrices. We give a complete characterization of the stably decomposable torus fiber bundle of fiber-dimens…

We study the connections between subsurface projections in curve and arc complexes in fibered 3-manifolds and Agol's veering triangulation. The main theme is that large-distance subsurfaces in fibers are associated to large simplicial regions in the veering triangulation, and this correspondence holds uniformly for all…

New bases found for Kauffman bracket skein module of fibered torus.

Extends fibering theorems for 3-manifolds.

We construct an explicit topological model (similar to the topological Springer fibers appearing in work of Khovanov and Russell) for every two-row Springer fiber associated with the even orthogonal group and prove that the respective topological model is homeomorphic to its corresponding Springer fiber. This confirms …