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Yoav Segev

Publications and source records attributed to Yoav Segev.

29 records · Page 2Linked to original sources
arXiv2015

MetroViz: Visual Analysis of Public Transportation Data

Understanding the quality and usage of public transportation resources is important for schedule optimization and resource allocation. Ridership and adherence are the two main dimensions for evaluating the quality of service. Using Automatic Vehicle Location (AVL), Automatic Passenger Count (APC), and Global Positioning System (GPS) data, ridership data and adherence data of public transportation can be collected. In this paper, we discuss the development of a visualization tool for exploring public transportation data. We introduce "map view" and "route view" to help users locate stops in the context of geography and route information. To visualize ridership and adherence information over several years, we introduce "calendar view" - a miniaturized calendar that provides an overview of data where users can interactively select specific days to explore individual trips and stops ("trip subview" and "stop subview"). MetroViz was evaluated via a series of usability tests that included researchers from the Center for Advanced Transportation Technology (CATT) and students from the University of Maryland - College Park in which test participants used the tool to explore three years of bus transit data from Blacksburg, Virginia.

cs.HC↗
arXiv2014

Normal closure and injective normalizer of a group homomorphism

Let $φ\colonΓ\to G$ be a homomorphism of groups. We consider factorizations $Γ\xrightarrow{f} M\xrightarrow{g} G$ of $φ$ such that either $g$ or $f$ are universal normal maps (namely, crossed modules). These two factorizations are natural generalizations of the usual normal closure and normalizer of a subgroup. Iterating these universal factorizations yield towers related, on the one hand, to hypercentral group extensions, Bousfield's localizations, and relative Schur multipliers. Dually, they extend to a relative situation, the automorphisms tower of a centerless group. Our constructions have strong ties to topological constructions.

math.GR↗
arXiv2014

Relative Schur multipliers and universal extensions of group homomorphisms

In this note, starting with any group homomorphism $f\colonΓ\to G$, which is surjective upon abelianization, we construct a universal central extension $u\colon U\twoheadrightarrow G,$ UNDER $Γ$ with the same surjective property, such that for any central extension $m\colon M\twoheadrightarrow G,$ under $f,$ there is a unique homomorphism $U\to M$ with the obvious commutation condition. The kernel of $u$ is the relative Schur multiplier group $H_2(G,Γ;\mathbb{Z})$ as defined in the paper. The case where $G$ is perfect corresponds to $Γ=1$. This yields homological obstructions to lifting solution of equations in $G.$ Upon repetition, for finite groups, this gives a universal hypercentral factorization of the map $f\colonΓ\to G$.

math.GR↗
arXiv2014

On graphs and valuations

In the last two decades new techniques emerged to construct valuations on an infinite division ring $D,$ given a normal subgroup $N\subseteq D$ of finite index. These techniques were based on the commuting graph of $D^{\times}/N$ in the case where $D$ is non-commutative, and on the Milnor K-graph on $D^{\times}/N,$ in the case where $D$ is commutative. In this paper we unify these two approaches and consider V-graphs on $D^{\times}/N$ and how they lead to valuations. We furthermore generalize previous results to situations of finitely many valuations.

math.RA↗
arXiv2014

Subnormal closure of a homomorphism

Let $φ\colonΓ\to G$ be a homomorphism of groups. In this paper we introduce the notion of a subnormal map (the inclusion of a subnormal subgroup into a group being a basic prototype). We then consider factorizations $Γ\xrightarrowψ M\xrightarrow{n} G$ of $φ,$ with $n$ a subnormal map. We search for a universal such factorization. When $Γ$ and $G$ are finite we show that such universal factorization exists: $Γ\toΓ_{\infty}\to G,$ where $Γ_{\infty}$ is a hypercentral extension of the subnormal closure $\mathcal{C}$ of $φ(Γ)$ in $G$ (i.e.~the kernel of the extension $Γ_{\infty}\to {\mathcal C}$ is contained in the hypercenter of $Γ_{\infty}$). This is closely related to the a relative version of the Bousfield-Kan $\mathbb{Z}$-completion tower of a space. The group $Γ_{\infty}$ is the inverse limit of the normal closures tower of $φ$ introduced by us in a recent paper. We prove several stability and finiteness properties of the tower and its inverse limit $Γ_{\infty}$.

math.GR↗
arXiv2012

Idempotent deformations of finite groups

The action of the idempotent deformations on finite groups is discussed. This action is described in terms of the homological properties of groups. The orbits of finite simple groups are determined.

math.GR↗
arXiv2007

On kernels of cellular covers

In the present paper we continue to examine cellular covers of groups, focusing on the cardinality and the structure of the kernel K of the cellular map G-> M . We show that in general a torsion free reduced abelian group M may have a proper class of non-isomorphic cellular covers. In other words, the cardinality of the kernels is unbounded. In the opposite direction we show that if the kernel of a cellular cover of any group M has certain ``freeness'' properties, then its cardinality must be bounded.

math.GR↗