arXiv research

The study proves poor ideal three-edge triangulations are minimal for certain 3-manifolds.

SAM improves generalization by operating near the edge of stability.

STORM enables edge computing for empirical risk minimization.

We show that the 20 graph Heawood family, obtained by a combination of triangle-Y and Y-triangle moves on $K_7$, is precisely the set of graphs of at most 21 edges that are minor minimal for the property not $2$--apex. As a corollary, this gives a new proof that the 14 graphs obtained by triangle-Y moves on $K_7$ are t…

Given a 2-crossing minimal chart $Γ$, a minimal chart with two crossings, set $α=\min\{~i~|~$there exists an edge of label $i$ containing a white vertex$\}$, and $β=\max\{~i~|~$there exists an edge of label $i$ containing a white vertex$\}$. In this paper we study the structure of a neighbourhood of $Γ_α\cupΓ_β$, and p…

New research finds six bipartite intrinsically knotted graphs with 23 edges.

Timelike minimal surfaces in Lorentzian Heisenberg group have singular points.

No minimal chart of type (7) exists.

We show that if X is a minimal length carrier graph in a hyperbolic 3-manifold, M, then if X contains a sufficiently short edge, it must contain a short circuit, as well. The meaning of "short" depends only on the rank of the fundamental group of M. We also expand the class of manifolds which are known to have minimal …

A new method finds DAG models without ground truth.

The paper studies singularities in discrete indefinite affine minimal surfaces.

Soft cells fill space without gaps, derived from minimal surfaces and deformed using edge bending.

A hybrid neural network optimizes AI deployment on edge and cloud for energy efficiency.

Paper studies singularities of timelike minimal surfaces in Minkowski 3-space.

No minimal chart of type (2,3,2) exists.

We show that the 14 graphs obtained by $\nabla\mathrm{Y}$ moves on K_7 constitute a complete list of the minor minimal intrinsically knotted graphs on 21 edges. We also present evidence in support of a conjecture that the 20 graph Heawood family, obtained by a combination of $\nabla\mathrm{Y}$ and $\mathrm{Y}\nabla$ mo…

This paper considers the problem of clustering a partially observed unweighted graph---i.e., one where for some node pairs we know there is an edge between them, for some others we know there is no edge, and for the remaining we do not know whether or not there is an edge. We want to organize the nodes into disjoint cl…

A pseudo-edge graph of a convex polyhedron K is a 3-connected embedded graph in K whose vertices coincide with those of K, whose edges are distance minimizing geodesics, and whose faces are convex. We construct a convex polyhedron K in Euclidean 3-space with a pseudo-edge graph with respect to which K is not unfoldable…

A graph is 2-apex if it is planar after the deletion of at most two vertices. Such graphs are not intrinsically knotted, IK. We investigate the converse, does not IK imply 2-apex? We determine the simplest possible counterexample, a graph on nine vertices and 21 edges that is neither IK nor 2-apex. In the process, we s…

We introduce a principled method for the signed clustering problem, where the goal is to partition a graph whose edge weights take both positive and negative values, such that edges within the same cluster are mostly positive, while edges spanning across clusters are mostly negative. Our method relies on a graph-based …

Optimal discrete harmonic maps between hyperbolic surfaces are found via minimizing energy.

Given a tiling $\mathcal{T}$ of the plane by straight edge polygons, which is invariant by two independent translations, we construct a family of embedded triply periodic minimal surfaces which desingularizes $\mathcal{T}\times\mathbb{R}$. For this purpose, inspired by the work of Martin Traizet, we open the nodes of s…

We investigate minimal charts with loops, a simple closed curve consisting of edges of label $m$ containing exactly one white vertex. We shall show that there does not exist any loop in a minimal chart with exactly seven white vertices in this paper.

A graph is intrinsically knotted if every embedding contains a knotted cycle. It is known that intrinsically knotted graphs have at least 21 edges and that the KS graphs, $K_7$ and the 13 graphs obtained from $K_7$ by $\nabla Y$ moves, are the only minor minimal intrinsically knotted graphs with 21 edges. This set incl…

Flat minimal hypersurfaces found in wedge-shaped domains.

New superbridge index calculations for knots with odd edges.

Efficiently matches random graphs with inhomogeneous edge probabilities.

Minimal charts of specific type contain unique subgraphs.

Proves minimal crossing diagrams for specific spatial graphs.

GD at EoS edge minimizes logistic loss without monotonic convergence.

Previous work of the authors studies minimal triangulations of closed 3-manifolds using a characterisation of low degree edges, embedded layered solid torus subcomplexes and 1-dimensional $\mathbb{Z}_2$-cohomology. The underlying blueprint is now used in the study of minimal ideal triangulations. As an application, it …

The study finds an upper limit for the number of minimal origami pairs on a surface.

Paper proposes efficient weight updates for edge nodes with minimal communication.

The study finds minimal hypersurfaces in wedge-shaped manifolds with boundary.

The paper proves stability and convergence of minimal networks under curvature motion.

Origami edge-paths connect coherent curves on surfaces.

Mobile edge learning is an emerging technique that enables distributed edge devices to collaborate in training shared machine learning models by exploiting their local data samples and communication and computation resources. To deal with the straggler dilemma issue faced in this technique, this paper proposes a new de…

We present a graph-based semi-supervised learning (SSL) method for learning edge flows defined on a graph. Specifically, given flow measurements on a subset of edges, we want to predict the flows on the remaining edges. To this end, we develop a computational framework that imposes certain constraints on the overall fl…

We describe the family of minimal graphs on strips with boundary values $\pm\infty$ disposed alternately on edges of length one, and whose conjugate graphs are contained in horizontal slabs of width one in $\mathbb{R}^3$. We can obtain as limits of such graphs the helicoid, all the doubly periodic Scherk minimal surfac…

We consider the task of causal structure learning over measurement dependence inducing latent (MeDIL) causal models. We show that this task can be framed in terms of the graph theoretic problem of finding edge clique covers,resulting in an algorithm for returning minimal MeDIL causal models (minMCMs). This algorithm is…

Orpheus simplifies deep learning deployment on edge devices.

We describe a new algorithm to compute the geometric intersection number between two curves, given as edge vectors on an ideal triangulation. Most importantly, this algorithm runs in polynomial time in the bit-size of the two edge vectors. In its simplest instances, this algorithm works by finding the minimal position …

Consider a group G and a family $\mathcal{A}$ of subgroups of G. We say that vertex finiteness holds for splittings of G over $\mathcal{A}$ if, up to isomorphism, there are only finitely many possibilities for vertex stabilizers of minimal G-trees with edge stabilizers in $\mathcal{A}$. We show vertex finiteness when G…

Data de-duplication is the task of detecting multiple records that correspond to the same real-world entity in a database. In this work, we view de-duplication as a clustering problem where the goal is to put records corresponding to the same physical entity in the same cluster and putting records corresponding to diff…

Federated edge learning improves with CSIT-free model aggregation using RIS.

Optimal Euclidean structure minimizes energy in weighted toroidal graphs.

New method improves grouped convolutions on edge devices.

Let $Γ$ be a chart. For each label $m$, we denote by $Γ_m$ the "subgraph" of $Γ$ consisting of all the edges of label $m$ and their vertices. Let $Γ$ be a minimal chart of type $(m;3,3)$. That is, a minimal chart $Γ$ has six white vertices, and both of $Γ_m\capΓ_{m+1}$ and $Γ_{m+1}\capΓ_{m+2}$ consist of three white ve…