Hopf algebras: motivations and examples

This paper provides motivation as well as a method of construction for Hopf algebras, starting from an associative algebra. The dualization technique involved relies heavily on the use of Sweedler's dual

On stoichiometry and intermixing at the spinel/perovskite interface in CoFe2O4/BaTiO3 thin films

The performance of complex oxide heterostructures depends primarily on the interfacial coupling of the two component structures. This interface character inherently varies with the synthesis method and conditions used since even small composition variations can alter the electronic, ferroelectric, or magnetic functional properties of the system. The focus of this article is placed on the interface character of a pulsed laser deposited CoFe2O4/BaTiO3 thin film. Using a range of state-of-the-art transmission electron microscopy methodologies, the roles of substrate morphology, interface stoichiometry, and cation intermixing are determined on the atomic level. The results reveal a surprisingly uneven BaTiO3 substrate surface formed after the film deposition and Fe atom incorporation in the top few monolayers inside the unit cell of the BaTiO3 crystal. Towards the CoFe2O4 side, a disordered region extending several nanometers from the interface was revealed and both Ba and Ti from the substrate were found to diffuse into the spinel layer. The analysis also shows that within this somehow incompatible composite interface, a different phase is formed corresponding to the compound Ba2Fe3Ti5O15, which belongs to the ilmenite crystal structure of FeTiO3 type. The results suggest a chemical activity between these two oxides, which could lead to the synthesis of complex engineered interfaces

Environments for sonic ecologies

This paper outlines a current lack of consideration for the environmental context of Evolutionary Algorithms used for the generation of music. We attempt to readdress this balance by outlining the benefits of developing strong coupling strategies between agent and en- vironment. It goes on to discuss the relationship between artistic process and the viewer and suggests a placement of the viewer and agent in a shared environmental context to facilitate understanding of the artistic process and a feeling of participation in the work. The paper then goes on to outline the installation ‘Excuse Me and how it attempts to achieve a level of Sonic Ecology through the use of a shared environmental context

A/r/cography: art, research and communication

This article aims at establishing the foundations for a/r/cography as an “art and communication”-based research methodology, inspired by a/r/tography yet more encompassing, and particularly suitable for the digital art world. As part of the larger family of practice-based research methodologies, a/r/tography presents various ways through which it can be explored, but since it is aimed at the arts and education, its scope is forcibly hampered by the fact that not all researchers and art practitioners are necessarily teachers. However, since most of its underlying principles can be extended for non-teachers, thus arose the idea to propose a methodology that would retain ontological, epistemological and methodological assumptions, but would expand beyond the limitations imposed by the role of the teacher. This extension is called a/r/cography and is structured upon the interchangeable roles of artist, researcher and communicator, as being intrinsic to the underlying living inquiry processes. Furthermore, this proposal is supported by the author’s own experience from a/r/cographic processes in the creation, exhibition and communication of digital artworks.info:eu-repo/semantics/publishedVersio

From Quantum Mechanics to Quantum Field Theory: The Hopf route

We show that the combinatorial numbers known as {\em Bell numbers} are generic in quantum physics. This is because they arise in the procedure known as {\em Normal ordering} of bosons, a procedure which is involved in the evaluation of quantum functions such as the canonical partition function of quantum statistical physics, {\it inter alia}. In fact, we shall show that an evaluation of the non-interacting partition function for a single boson system is identical to integrating the {\em exponential generating function} of the Bell numbers, which is a device for encapsulating a combinatorial sequence in a single function. We then introduce a remarkable equality, the Dobinski relation, and use it to indicate why renormalisation is necessary in even the simplest of perturbation expansions for a partition function. Finally we introduce a global algebraic description of this simple model, giving a Hopf algebra, which provides a starting point for extensions to more complex physical systems

A generic Hopf algebra for quantum statistical mechanics

In this paper, we present a Hopf algebra description of a bosonic quantum model, using the elementary combinatorial elements of Bell and Stirling numbers. Our objective in doing this is as follows. Recent studies have revealed that perturbative quantum field theory (pQFT) displays an astonishing interplay between analysis (Riemann zeta functions), topology (Knot theory), combinatorial graph theory (Feynman diagrams) and algebra (Hopf structure). Since pQFT is an inherently complicated study, so far not exactly solvable and replete with divergences, the essential simplicity of the relationships between these areas can be somewhat obscured. The intention here is to display some of the above-mentioned structures in the context of a simple bosonic quantum theory, i.e. a quantum theory of non-commuting operators that do not depend on space-time. The combinatorial properties of these boson creation and annihilation operators, which is our chosen example, may be described by graphs, analogous to the Feynman diagrams of pQFT, which we show possess a Hopf algebra structure. Our approach is based on the quantum canonical partition function for a boson gas.Comment: 8 pages/(4 pages published version), 1 Figure. arXiv admin note: text overlap with arXiv:1011.052

Analysis of Transaction Management Performance

There is currently much interest in incorporating transactions into both operating systems and general purpose programming languages. This paper provides a detailed examination of the design and performance of the“¢ transaction manager of the Camelot system. Camelot is a transaction facility that provides a rich model of transactions intended to support a wide variety of general-purpose applications. The transaction manager's principal function is to execute the protocols that ensure atomicity. The conclusions of this study are: a simple optimization to two-phase commit reduces logging activity of distributed transactions; non-blocking commit is practical for some applications; multithreaded design improves throughput provided that log batching is used; multi-casting reduces the variance of distributed commit protocols in a LAN environment; and the performance of transaction mechanisms such as Camelot depend heavily upon kernel performance

Eigenmode Tomography of Surface Charge Oscillations of Plasmonic Nanoparticles by Electron Energy Loss Spectroscopy

Plasmonic devices designed in three dimensions enable careful tuning of optical responses for control of complex electromagnetic interactions on the nanoscale. Probing the fundamental characteristics of the constituent nanoparticle building blocks is, however, often constrained by diffraction-limited spatial resolution in optical spectroscopy. Electron microscopy techniques, including electron energy loss spectroscopy (EELS), have recently been developed to image surface plasmon resonances qualitatively at the nanoscale in three dimensions using tomographic reconstruction techniques. Here, we present an experimental realization of a distinct method that uses direct analysis of modal surface charge distributions to reconstruct quantitatively the three-dimensional eigenmodes of a silver right bipyramid on a metal oxide substrate. This eigenmode tomography removes ambiguity in two-dimensional imaging of spatially-localized plasmonic resonances, reveals substrate-induced mode degeneracy breaking in the bipyramid, and enables EELS for the analysis not of a particular electron-induced response but of the underlying geometric modes characteristic of particle surface plasmons.S.M.C. acknowledges support of a Gates Cambridge Scholarship. E.R. acknowledges support from the Royal Society's Newton International Fellowship scheme and a Trinity Hall Research Fellowship. We thank Ben Knappet for assistance with the synthesis of the silver bipyramids. We thank F.J. de la Peña for helpful discussions on the use of HYPERSPY. The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Program (No. FP7/2007-2013)/ERC Grant Agreement No. 291522-3DIMAGE and the European Union's Seventh Framework Program under a contract for an Integrated Infrastructure Initiative (Reference No. 312483-ESTEEM2)This is the final version of the article. It was first available from ACS via http://dx.doi.org/10.1021/acsphotonics.5b0042

In situ transmission electron microscopy of resistive switching in thin silicon oxide layers

Silicon oxide-based resistive switching devices show great potential for applications in nonvolatile random access memories. We expose a device to voltages above hard breakdown and show that hard oxide breakdown results in mixing of the SiOx layer and the TiN lower contact layers. We switch a similar device at sub-breakdown fields in situ in the transmission electron microscope (TEM) using a movable probe and study the diffusion mechanism that leads to resistance switching. By recording bright-field (BF) TEM movies while switching the device, we observe the creation of a filament that is correlated with a change in conductivity of the SiOx layer. We also examine a device prepared on a microfabricated chip and show that variations in electrostatic potential in the SiOx layer can be recorded using off-axis electron holography as the sample is switched in situ in the TEM. Taken together, the visualization of compositional changes in ex situ stressed samples and the simultaneous observation of BF TEM contrast variations, a conductivity increase, and a potential drop across the dielectric layer in in situ switched devices allow us to conclude that nucleation of the electroforming—switching process starts at the interface between the SiOx layer and the lower contact