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

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

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

Mitochondrial genome of an Allegheny Woodrat (\u3ci\u3eNeotoma magister\u3c/i\u3e)

The Allegheny woodrat (Neotoma magister) is endemic to the eastern United States. Population numbers have decreased rapidly over the last four decades due to habitat fragmentation, disease-related mortality, genetic isolation and inbreeding depression; however, effective management is hampered by limited genetic resources. To begin addressing this need, we sequenced and assembled the entire Allegheny woodrat mitochondrial genome. The genome assembly is 16,310 base pairs in length, with an overall base composition of 34% adenine, 27% thymine, 26% cytosine and 13% guanine. This resource will facilitate our understanding of woodrat population genetics and behavioral ecology

Heisenberg-Weyl algebra revisited: Combinatorics of words and paths

The Heisenberg-Weyl algebra, which underlies virtually all physical representations of Quantum Theory, is considered from the combinatorial point of view. We provide a concrete model of the algebra in terms of paths on a lattice with some decomposition rules. We also discuss the rook problem on the associated Ferrers board; this is related to the calculus in the normally ordered basis. From this starting point we explore a combinatorial underpinning of the Heisenberg-Weyl algebra, which offers novel perspectives, methods and applications.Comment: 5 pages, 3 figure

Combinatorics and Boson normal ordering: A gentle introduction

We discuss a general combinatorial framework for operator ordering problems by applying it to the normal ordering of the powers and exponential of the boson number operator. The solution of the problem is given in terms of Bell and Stirling numbers enumerating partitions of a set. This framework reveals several inherent relations between ordering problems and combinatorial objects, and displays the analytical background to Wick's theorem. The methodology can be straightforwardly generalized from the simple example given herein to a wide class of operators.Comment: 8 pages, 1 figur

Role of thyroid hormones in early postnatal development of skeletal muscle and its implications for undernutrition

Published online by Cambridge University Press 09 Mar 2007Energy intake profoundly influences many endocrine axes which in turn play a central role in development. The specific influence of a short period of mild hypothyroidism, similar to that induced by undernutrition, in regulating muscle development has been assessed in a large mammal during early postnatal life. Hypothyroidism was induced by providing methimazole and iopanoic acid in the feed of piglets between 4 and 14 d of age, and controls were pair-fed to the energy intake of their hypothyroid littermates. Thyroid status was evaluated, and myofibre differentiation and cation pump concentrations were then assessed in the following functionally distinct muscles: longissimus dorsi (l. dorsi), soleus and rhomboideus. Reductions in plasma concentrations of thyroxine (T4; 32%, P < O·Ol), triiodothyronine (T3;48%, P < 0·001), free T3, (58%, P < 0·001)and hepatic 5'-monodeiodinase (EC 1.11.1.8) activity (74%, P < 0·001) occurred with treatment. Small, although significant, increases in the proportion of type I slow-twitch oxidative fibres occurred with mild hypothyroidism, in l. dorsi (2%, P < 0·01) and soleus(7%, P < 0·01). Nuclear T3-receptor concentration in l. dorsi of hypothyroid animals compared with controls increased by 46% (P < 0·001), a response that may represent a homeostatic mechanism making muscle more sensitive to low levels of circulating thyroid hormones. Nevertheless, Na+, K+-ATPase (EC 3.6.1.37) concentration was reduced by 15–16% in all muscles (l.dorsi P< 0·05,soleus P < 0·001, rhomboideus P < 0·05), and Ca2+-ATPase (EC 3.6.1.38) concentration was significantly reduced in the two slow-twitch muscles: by 22% in rhomboideus (P < 0·001) and 23% in soleus (P < 0·05). It is concluded that during early postnatal development of large mammals a period of mild hypothyroidism, comparable with that found during undernutrition, induces changes in myofibre differentiation and a down-regulation of cation pumps in skeletal muscle. Such changes would result in slowness of movement and muscle weakness, and also reduce ATP hydrolysis with a concomitant improvement in energetic efficiency.A. P. Harrison, D. R. Tivey, T. Clausen, C. Duchamp and M. J. Daunce

Hierarchical Dobinski-type relations via substitution and the moment problem

We consider the transformation properties of integer sequences arising from the normal ordering of exponentiated boson ([a,a*]=1) monomials of the form exp(x (a*)^r a), r=1,2,..., under the composition of their exponential generating functions (egf). They turn out to be of Sheffer-type. We demonstrate that two key properties of these sequences remain preserved under substitutional composition: (a)the property of being the solution of the Stieltjes moment problem; and (b) the representation of these sequences through infinite series (Dobinski-type relations). We present a number of examples of such composition satisfying properties (a) and (b). We obtain new Dobinski-type formulas and solve the associated moment problem for several hierarchically defined combinatorial families of sequences.Comment: 14 pages, 31 reference