Historic Resources Study of Pullman National Monument, Illinois

This Historic Resource Study is a Baseline Research Report for Pullman National Monument. This HRS summarizes the historical writings about Pullman, provides context for the significant themes identified in its founding document, collates collections of primary documents and historical resources that are important sources of information on those themes, and recommends questions that will require additional study. These cultural resources include primary historical materials in archives and oral history collections, as well as architectural, archaeological, museum collections, or landscape resources. While this report includes new historical narrative based in original archival research, other sections present synthetic reviews of existing publications. National Park Service staff will use this document and included resources as they make management decisions and design interpretive programming. In addition to this report and its appendices—which are only published digitally—the research team deposited its entire library with the monument staff, including nearly 2,000 references and thousands of pages of digitally-imaged archival documents

Some Diophantine equations from finite group theory: Φm(x)=2pn−1\Phi_m(x)=2p^n-1

We show that the equation in the title (with $\Phi_m$ the $m$th cyclotomic polynomial) has no integer solution with $n\ge 1$ in the cases $(m,p)=(15,41), (15,5581),(10,271)$. These equations arise in a recent group theoretical investigation by Z. Akhlaghi, M. Khatami and B. Khosravi.Comment: 17 pages, slightly extended version is available as Max-Planck preprint MPIM 2009-6

Classifying Complexity with the ZX-Calculus: Jones Polynomials and Potts Partition Functions

The ZX-calculus is a graphical language which allows for reasoning about suitably represented tensor networks - namely ZX-diagrams - in terms of rewrite rules. Here, we focus on problems which amount to exactly computing a scalar encoded as a closed tensor network. In general, such problems are #P-hard. However, there are families of such problems which are known to be in P when the dimension is below a certain value. By expressing problem instances from these families as ZX-diagrams, we see that the easy instances belong to the stabilizer fragment of the ZX-calculus. Building on previous work on efficient simplification of qubit stabilizer diagrams, we present simplifying rewrites for the case of qutrits, which are of independent interest in the field of quantum circuit optimisation. Finally, we look at the specific examples of evaluating the Jones polynomial and of counting graph-colourings. Our exposition further champions the ZX-calculus as a suitable and unifying language for studying the complexity of a broad range of classical and quantum problems.Comment: QPL 2021 submissio

A revised look at the effects of the Channel Model on molecular communication system

Molecular communications, where information is passed between the Transmitter (TX) and the Receiver (RX) via molecules is a promising area with vast potential applications. However, the infancy of the topic within the overall taxonomy of communications has meant that to date, several channel models are in press, each of which is applied under various constraints and/or assumptions. Amongst them is that the arrival of molecules in different time slots can be, or is, considered as independent events. In practice, this assumption is not accurate, as the molecules arriving in the previous slot reduce the possible number of molecules in the next slot and hence make them correlated. In this letter, we analyze a more realistic performance of a molecular communication assuming correlated events. The key result shown, is that the widely used model assuming independent events significantly overestimates the error rates in the channel. This result is thus critical to researchers who focus on energy use at the nano-scale, as the new analysis provides a more realistic prediction and therefore, less energy will be needed to attain a desired error rate, increasing system feasibility

Nonequilibrium Green's function method for thermal transport in junctions

We present a detailed treatment of the nonequilibrium Green's function method for thermal transport due to atomic vibrations in nanostructures. Some of the key equations, such as self-energy and conductance with nonlinear effect, are derived. A self-consistent mean-field theory is proposed. Computational procedures are discussed. The method is applied to a number of systems including one-dimensional chains, a benzene ring junction, and carbon nanotubes. Mean-field calculations of the Fermi-Pasta-Ulam model are compared with classical molecular dynamics simulations. We find that nonlinearity suppresses thermal transport even at moderately high temperatures.Comment: 14 pages, 10 figure