arXiv research

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

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

Polynomial density theorem for specific subgroup orbits in quotient spaces.

Polynomial error equidistribution for SL2 groups.

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,…

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…

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.

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

Automated suggestions help train technicians diagnose incidents faster.

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,…

A ``hyperideal circle pattern'' in $S^2$ is a finite family of oriented circles, similar to the ``usual'' circle patterns but such that the closed disks bounded by the circles do not cover the whole sphere. Hyperideal circle patterns are directly related to hyperideal hyperbolic polyhedra, and also to circle packings. …

This paper addresses questions of quasi-isometric rigidity and classification for fundamental groups of finite graphs of groups, under the assumption that the Bass-Serre tree of the graph of groups has finite depth. The main example of a finite depth graph of groups is one whose vertex and edge groups are coarse Poinca…

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.

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

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.

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 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.

Characterizes groups with specific boundary properties.

Finite rigid sets found in surface curve complexes.

Proves polynomial error rate for equidistribution of unipotent flows.

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 …

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

A {\em good drawing\/} of $K_n$ is a drawing of the complete graph with $n$ vertices in the sphere such that: no two edges with a common end cross; no two edges cross more than once; and no three edges all cross at the same point. Gioan's Theorem asserts that any two good drawings of $K_n$ that have the same rotations …

Generative model for hypergraphs captures complex interactions without pairwise reductions.

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

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…

For an arrangement of $n$ pseudolines in the real projective plane let us denote by $t_i$ the number of vertices incident to $i$ lines. We obtain a linear on $t_i$ inequality similar to the Hirzebruch one, but with an elementary proof. We present an algorithm for producing lower bounds of the number of regions basing o…

Compactifies strata of d-differentials in genus 0.

The intersection pattern of the translates of the limit set of a quasi-convex subgroup of a hyperbolic group can be coded in a natural incidence graph, which suggests connections with the splittings of the ambient group. A similar incidence graph exists for any subgroup of a group. We show that the disconnectedness of …

Let $\mathcal{M}^{\mathrm{st}}$ ($\mathcal{M}^{\mathrm{pst}}$) be a moduli space of stable (polystable) bundles with fixed determinant on a complex surface with $b_1=1$, $p_g=0$, and let $Z\subset \mathcal{M}^{\mathrm{st}}$ be a pure $k$-dimensional analytic set. We prove a general formula for the homological boundary …

The large volume of text in electronic healthcare records often remains underused due to a lack of methodologies to extract interpretable content. Here we present an unsupervised framework for the analysis of free text that combines text-embedding with paragraph vectors and graph-theoretical multiscale community detect…

We investigate triangulations of the two-dimensional sphere and torus with the faces properly colored white and black. We focus on matchings between white triangles and incident vertices. On the torus our objects are perfect pairings, whereas on the sphere this is only true after removing one triangle and its vertices.…

This paper realises the Khovanov homology of a link in the 3-sphere as a Lagrangian Floer cohomology group, establishing a conjecture of Seidel and the second author. The starting point is the previously established formality theorem for the symplectic arc algebra over a field k of characteristic zero. Here we prove th…

The results of this paper concern the Morse theory of the norm-square of the moment map on the space of representations of a quiver. We show that the gradient flow of this function converges, and that the Morse stratification induced by the gradient flow co-incides with the Harder-Narasimhan stratification from algebra…

This expository monograph cuts a short path from the common, elementary background in geometry (linear algebra, vector bundles, and algebraic ideals) to the most advanced theorems about involutive exterior differential systems: (1) The incidence correspondence of the characteristic variety, (2) Guillemin normal form an…