We sat down with the founder and owner of Nicolai Bikes to talk about the past, present, and future.
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Joshua Cape, Minh Tang, Carey E. Priebe.

Source: The Annals of Statistics, Volume 47, Number 5, 2405--2439.

Abstract:
The singular value matrix decomposition plays a ubiquitous role throughout statistics and related fields. Myriad applications including clustering, classification, and dimensionality reduction involve studying and exploiting the geometric structure of singular values and singular vectors. This paper provides a novel collection of technical and theoretical tools for studying the geometry of singular subspaces using the two-to-infinity norm. Motivated by preliminary deterministic Procrustes analysis, we consider a general matrix perturbation setting in which we derive a new Procrustean matrix decomposition. Together with flexible machinery developed for the two-to-infinity norm, this allows us to conduct a refined analysis of the induced perturbation geometry with respect to the underlying singular vectors even in the presence of singular value multiplicity. Our analysis yields singular vector entrywise perturbation bounds for a range of popular matrix noise models, each of which has a meaningful associated statistical inference task. In addition, we demonstrate how the two-to-infinity norm is the preferred norm in certain statistical settings. Specific applications discussed in this paper include covariance estimation, singular subspace recovery, and multiple graph inference. Both our Procrustean matrix decomposition and the technical machinery developed for the two-to-infinity norm may be of independent interest.

Miguel de Carvalho, Garritt L. Page, Bradley J. Barney.

Source: Bayesian Analysis, Volume 14, Number 4, 1013--1036.

Abstract:
We provide a geometric interpretation to Bayesian inference that allows us to introduce a natural measure of the level of agreement between priors, likelihoods, and posteriors. The starting point for the construction of our geometry is the observation that the marginal likelihood can be regarded as an inner product between the prior and the likelihood. A key concept in our geometry is that of compatibility, a measure which is based on the same construction principles as Pearson correlation, but which can be used to assess how much the prior agrees with the likelihood, to gauge the sensitivity of the posterior to the prior, and to quantify the coherency of the opinions of two experts. Estimators for all the quantities involved in our geometric setup are discussed, which can be directly computed from the posterior simulation output. Some examples are used to illustrate our methods, including data related to on-the-job drug usage, midge wing length, and prostate cancer.

Anna L. Smith, Dena M. Asta, Catherine A. Calder.

Source: Statistical Science, Volume 34, Number 3, 428--453.

Abstract:
We review the class of continuous latent space (statistical) models for network data, paying particular attention to the role of the geometry of the latent space. In these models, the presence/absence of network dyadic ties are assumed to be conditionally independent given the dyads’ unobserved positions in a latent space. In this way, these models provide a probabilistic framework for embedding network nodes in a continuous space equipped with a geometry that facilitates the description of dependence between random dyadic ties. Specifically, these models naturally capture homophilous tendencies and triadic clustering, among other common properties of observed networks. In addition to reviewing the literature on continuous latent space models from a geometric perspective, we highlight the important role the geometry of the latent space plays on properties of networks arising from these models via intuition and simulation. Finally, we discuss results from spectral graph theory that allow us to explore the role of the geometry of the latent space, independent of network size. We conclude with conjectures about how these results might be used to infer the appropriate latent space geometry from observed networks.

At Battle High School in Columbia, Mo., students in geometry class have swapped their compasses and protractors for hammers and hard hats. And they're doing it for a good cause.

Geometry Global, WPP group’s shopper marketing and brand activation agency, is working towards devising communication that fits the non-linear, omnichannel shopping behaviour of consumers.

Mathematicians are developing forensics to identify political maps that disenfranchise voters

Featuring eye-catching geometries, local and non-toxic materials, these unique furniture pieces meld a medley of traditional weaving and woodworking techniques.

Cham : Springer, c2019.

Cham, Switzerland : Springer, [2019]

Room, T. G. (Thomas Gerald), author

Algebra, Geometry and Mathematical Physics Conference (2011 : Mulhouse, France), creator

Gorguis, Alice, author

Artin, Emil, 1898-1962, author

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Dewey Library - QA671.A47 2020

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Dewey Library - QA9.S5813 2019

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Dewey Library - QA3.Z56 2020

Barker Library - QA641.W66 2019

Hayden Library - QA564.C8794 2018

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This excerpt from Technical Drawing with Engineering Graphics shows how to identify and specify basic geometric elements and shapes.

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Cham : Springer International Publishing : Imprint: Springer, 2014

Berlin ; Springer ; [2006]

Berlin ; New York : Springer, [2005]

Boston : Birkhäuser, [2006]

Hayden Library - QC174.12.B453 2017