arXiv research

The paper extends group constructions to coset geometries, creating new ways to combine geometries.

A new Euclidean approach reveals the pentagram map's beauty.

Investigates proving geometric theorems over complex and real numbers using tilings.

Polynomial error equidistribution for SL2 groups.

The paper studies how points and lines can move while preserving incidences.

Polynomial density theorem for specific subgroup orbits in quotient spaces.

We study the 3-dimensional combinatorial Yamabe flow in hyperbolic background geometry. For a triangulation of a 3-manifold, we prove that if the number of tetrahedra incident to each vertex is at least 23, then there exist real or virtual ball packings with vanishing (extended) combinatorial scalar curvature, i.e. the…

A lemma of Tits establishes a connection between the simple connectivity of an incidence geometry and the universal completion of an amalgam induced by a sufficiently transitive group of automorphisms of that geometry. In the present paper, we generalize this lemma to intransitive geometries, thus opening the door for …

Detect spacetime curvature without rulers and clocks in 3D.

Motivated by the study of wave fronts in anisotropic media, we propose an incidence geometry of anisotropic spheres in a Finsler-Minkowski space. An anisotropic version of the Laguerre functional is considered. In some circumstances, this functional can be used to determine that two wavefronts observed at distinct time…

Given a bordified space, Karlsson defines an incidence geometry of stars at infinity. These stars and their incidence are closely related to well-understood objects when the space is hyperbolic, CAT(0), or a bounded convex domain with the Hilbert metric. A question stemming from Karlsson's original paper was whether or…

The "dancing metric" is a pseudo-riemannian metric $\pmb{g}$ of signature $(2,2)$ on the space $M^4$ of non-incident point-line pairs in the real projective plane $\mathbb{RP}^2$. The null-curves of $(M^4,\pmb{g})$ are given by the "dancing condition": the point is moving towards a point on the line, about which the li…

We consider congruences of straight lines in a plane with the combinatorics of the square grid, with all elementary quadrilaterals possessing an incircle. It is shown that all the vertices of such nets (we call them incircular or IC-nets) lie on confocal conics. Our main new results are on checkerboard IC-nets in the p…

Accurate traffic speed prediction is an important and challenging topic for transportation planning. Previous studies on traffic speed prediction predominately used spatio-temporal and context features for prediction. However, they have not made good use of the impact of urban traffic incidents. In this work, we aim to…

Critical incident stages identification and reasonable prediction of traffic incident duration are essential in traffic incident management. In this paper, we propose a traffic incident duration prediction model that simultaneously predicts the impact of the traffic incidents and identifies the critical groups of tempo…

Sparse incidence tensors can represent a variety of structured data. For example, we may represent attributed graphs using their node-node, node-edge, or edge-edge incidence matrices. In higher dimensions, incidence tensors can represent simplicial complexes and polytopes. In this paper, we formalize incidence tensors,…

This paper aims to optimize incident-specific cyber insurance design.

Crowdsourced data helps detect incidents faster, balancing accuracy and practicality.

Predicting traffic incident duration is a major challenge for many traffic centres around the world. Most research studies focus on predicting the incident duration on motorways rather than arterial roads, due to a high network complexity and lack of data. In this paper we propose a bi-level framework for predicting th…

Study uses vehicle trajectory data to predict traffic incidents on highways.

HYVINT generates hypergraphs with intensity-driven incidence formation and variational learning.

We study the Dictionary Learning (aka Sparse Coding) problem of obtaining a sparse representation of data points, by learning \emph{dictionary vectors} upon which the data points can be written as sparse linear combinations. We view this problem from a geometry perspective as the spanning set of a subspace arrangement,…

The abstract discusses a new causal structure on manifolds using paths and points.

Study shows data breaches cause significant financial losses for firms, especially in health sector.

Automated suggestions help train technicians diagnose incidents faster.

This paper proposes a real-time signal plan recommendation system for traffic incidents.

We characterize the boundary at infinity of a complex hyperbolic space as a compact Ptolemy space that satisfies four incidence axioms.

Crimes emerge out of complex interactions of human behaviors and situations. Linkages between crime incidents are highly complex. Detecting crime linkage given a set of incidents is a highly challenging task since we only have limited information, including text descriptions, incident times, and locations. In practice,…

Develops regression trees for estimating cumulative incidence curves in competing risks.

The paper explains the topological origin of the distinction between incidence theorems over division rings and fields.

In a recent work of Ayaka Shimizu$^{[5]}$, she defined an operation named region crossing change on link diagrams, and showed that region crossing change is an unknotting operation for knot diagrams. In this paper, we prove that region crossing change on a 2-component link diagram is an unknotting operation if and only…

Enhances cyber risk assessment with entity-specific features.

Study finds companies react negatively to material cybersecurity incident disclosures.

In the spirit of Klein's Erlangen Program, we investigate the geometric and algebraic structure of fundamental line complexes and the underlying privileged discrete integrable system for the minors of a matrix which constitute associated Plücker coordinates. Particular emphasis is put on the restriction to Lie circle g…

In this paper we continue the study of generic properties of the Novikov complex, began in the work "The incidence coefficients in the Novikov complex are generically rational functions" ( dg-ga/9603006). For a Morse map $f:M\to S^1$ there is a refined version of Novikov complex, defined over the Novikov completion of …

QTIP improves traffic prediction in sudden disruptions.

The geometry of cosets in the subgroups H of the two-generator free group G =\textless{} a, b \textgreater{} nicely fits, via Grothendieck's dessins d'enfants, the geometry of commutation for quantum observables. Dessins stabilize point-line incidence geometries that reflect the commutation of (generalized) Pauli opera…

Proves polynomial error rate for equidistribution of unipotent flows.

Characterizes groups with specific boundary properties.

Finite rigid sets found in surface curve complexes.

Statistical models outperform mechanistic models in short-term COVID-19 incidence forecasts.

We estimate treatment cost-savings from early cancer diagnosis. For breast, lung, prostate and colorectal cancers and melanoma, which account for more than 50% of new incidences projected in 2017, we combine published cancer treatment cost estimates by stage with incidence rates by stage at diagnosis. We extrapolate to…

Despite the robust structure of the Internet, it is still susceptible to disruptive routing updates that prevent network traffic from reaching its destination. Our research shows that BGP announcements that are associated with disruptive updates tend to occur in groups of relatively high frequency, followed by periods …

Generative model for hypergraphs captures complex interactions without pairwise reductions.

Although aviation accidents are rare, safety incidents occur more frequently and require a careful analysis to detect and mitigate risks in a timely manner. Analyzing safety incidents using operational data and producing event-based explanations is invaluable to airline companies as well as to governing organizations s…

Understanding the exceptional Lie groups as the symmetry groups of simpler objects is a long-standing program in mathematics. Here, we explore one famous realization of the smallest exceptional Lie group, G2. Its Lie algebra acts locally as the symmetries of a ball rolling on a larger ball, but only when the ratio of r…

The paper develops a comprehensive theory of submanifolds in conformal geometries.

Geometric framework for signed multivariate tail-dependence compatibility at various thresholds.