2,948 research outputs found
The structure theory of Nilspaces III: Inverse limit representations and topological dynamics
This paper forms the third part of a series by the authors [GMV1,GMV2]
concerning the structure theory of nilspaces. A nilspace is a compact space
together with closed collections of cubes ,
, satisfying some natural axioms. Our goal is to extend the
structure theory of nilspaces obtained by Antol\'in Camarena and Szegedy, and
to provide new proofs.
Our main result is that, under the technical assumption that is a
connected space for all , then is isomorphic (in a strong sense) to an
inverse limit of nilmanifolds. This is a direct and slight generalization of
the main result of Antol\'in Camarena and Szegedy.
We also apply our methods to obtain structure theorems in the setting of
topological dynamics. Specifically, if is a group (subject to very mild
topological assumptions) and is a minimal dynamical system, then we
give a simple characterization of the maximal pronilfactor of . This
generalizes the case , which is a theorem of Host, Kra and
Maass, although even in that case we give a significantly different proof.Comment: 48 pages, final accepted version, to appear in Adv. Math., Theorem
4.1 as stated in the previous version is false, see Section 4 for more
details, main results are unchange
Shot noise in Weyl semimetals
We study the effect of inelastic processes on the magneto-transport of a
quasi-one dimensional Weyl semi-metal, using a modified Boltzmann-Langevin
approach. The magnetic field drives a crossover to a ballistic regime in which
the propagation along the wire is dominated by the chiral anomaly, and the role
of fluctuations inside the sample is exponentially suppressed. We show that
inelastic collisions modify the parametric dependence of the current
fluctuations on the magnetic field. By measuring shot noise as a function of a
magnetic field, for different applied voltage, one can estimate the
electron-electron inelastic length .Comment: 7 pages, 1 figur
Fermi Edge Resonances in Non-equilibrium States of Fermi Gases
We formulate the problem of the Fermi Edge Singularity in non-equilibrium
states of a Fermi gas as a matrix Riemann-Hilbert problem with an integrable
kernel. This formulation is the most suitable for studying the singular
behavior at each edge of non-equilibrium Fermi states by means of the method of
steepest descent, and also reveals the integrable structure of the problem. We
supplement this result by extending the familiar approach to the problem of the
Fermi Edge Singularity via the bosonic representation of the electronic
operators to non-equilibrium settings. It provides a compact way to extract the
leading asymptotes.Comment: Accepted for publication, J. Phys.
Generalized Bayesian Record Linkage and Regression with Exact Error Propagation
Record linkage (de-duplication or entity resolution) is the process of
merging noisy databases to remove duplicate entities. While record linkage
removes duplicate entities from such databases, the downstream task is any
inferential, predictive, or post-linkage task on the linked data. One goal of
the downstream task is obtaining a larger reference data set, allowing one to
perform more accurate statistical analyses. In addition, there is inherent
record linkage uncertainty passed to the downstream task. Motivated by the
above, we propose a generalized Bayesian record linkage method and consider
multiple regression analysis as the downstream task. Records are linked via a
random partition model, which allows for a wide class to be considered. In
addition, we jointly model the record linkage and downstream task, which allows
one to account for the record linkage uncertainty exactly. Moreover, one is
able to generate a feedback propagation mechanism of the information from the
proposed Bayesian record linkage model into the downstream task. This feedback
effect is essential to eliminate potential biases that can jeopardize resulting
downstream task. We apply our methodology to multiple linear regression, and
illustrate empirically that the "feedback effect" is able to improve the
performance of record linkage.Comment: 18 pages, 5 figure
Stolen Profits: Civil Shoplifting Demands and the Misuse of Neb. Rev. Stat. § 25–21,194
I. Introduction
II. Background ... A. Civil Shoplifting Statutes Generally ... 1. General Authority and Amount Recoverable ... 2. Civil Demand Letters ... 3. Collection of Damages and Penalties Under Civil Shoplifting Statutes ... B. An Overview of Nebraska’s Civil Shoplifting Statute ... 1. The Origins of Nebraska’s Civil Shoplifting Statute ... 2. The Statute as Amended ... 3. Limits on Pre-Litigation Demands Under Neb. Rev. Stat. § 25–21,194 ... a. General Loss-Prevention Costs ... b. Anticipated Litigation Expenses
III. Advising the Client ... A. Pay the Demand ... B. Ignore the Demand ... 1. Defending a Claim ... 2. Liability for Attorney’s Fees ... 3. Impact on Credit Rating ... C. Affirmative Legal Challenges ... 1. Federal Challenges ... a. Fair Debt Collections Practices Act … b. Racketeering Influenced and Corrupt Organization Act ... 2. Nebraska Consumer Protection Act ... a. Standing to Sue Under the NCPA ... b. Unfair or Deceptive Business Practice ... c. Trade or Commerce ... d. Affecting Public Interest ... 3. Declaratory Judgment
IV. A Call to Action ... A. Legislative Repeal ... B. Legislative Amendment ... C. Education and Enforcement
V. Conclusio
Stolen Profits: Civil Shoplifting Demands and the Misuse of Neb. Rev. Stat. § 25–21,194
I. Introduction
II. Background ... A. Civil Shoplifting Statutes Generally ... 1. General Authority and Amount Recoverable ... 2. Civil Demand Letters ... 3. Collection of Damages and Penalties Under Civil Shoplifting Statutes ... B. An Overview of Nebraska’s Civil Shoplifting Statute ... 1. The Origins of Nebraska’s Civil Shoplifting Statute ... 2. The Statute as Amended ... 3. Limits on Pre-Litigation Demands Under Neb. Rev. Stat. § 25–21,194 ... a. General Loss-Prevention Costs ... b. Anticipated Litigation Expenses
III. Advising the Client ... A. Pay the Demand ... B. Ignore the Demand ... 1. Defending a Claim ... 2. Liability for Attorney’s Fees ... 3. Impact on Credit Rating ... C. Affirmative Legal Challenges ... 1. Federal Challenges ... a. Fair Debt Collections Practices Act … b. Racketeering Influenced and Corrupt Organization Act ... 2. Nebraska Consumer Protection Act ... a. Standing to Sue Under the NCPA ... b. Unfair or Deceptive Business Practice ... c. Trade or Commerce ... d. Affecting Public Interest ... 3. Declaratory Judgment
IV. A Call to Action ... A. Legislative Repeal ... B. Legislative Amendment ... C. Education and Enforcement
V. Conclusio
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