Universal Cycles of Restricted Words

A connected digraph in which the in-degree of any vertex equals its out-degree is Eulerian, this baseline result is used as the basis of existence proofs for universal cycles (also known as generalized deBruijn cycles or U-cycles) of several combinatorial objects. We extend the body of known results by presenting new results on the existence of universal cycles of monotone, "augmented onto", and Lipschitz functions in addition to universal cycles of certain types of lattice paths and random walks.Comment: 21 pages, 4 figure

Optimisations for quadrature representations of finite element tensors through automated code generation

We examine aspects of the computation of finite element matrices and vectors which are made possible by automated code generation. Given a variational form in a syntax which resembles standard mathematical notation, the low-level computer code for building finite element tensors, typically matrices, vectors and scalars, can be generated automatically via a form compiler. In particular, the generation of code for computing finite element matrices using a quadrature approach is addressed. For quadrature representations, a number of optimisation strategies which are made possible by automated code generation are presented. The relative performance of two different automatically generated representations of finite element matrices is examined, with a particular emphasis on complicated variational forms. It is shown that approaches which perform best for simple forms are not tractable for more complicated problems in terms of run time performance, the time required to generate the code or the size of the generated code. The approach and optimisations elaborated here are effective for a range of variational forms

Measurement- and comparison-based sizes of Schrödinger cat states of light

We extend several measurement-based definitions of effective superposition size to coherent state superpositions with branches composed of either single coherent states or tensor products of coherent states. These measures of superposition size depend on determining the maximal quantum distinguishability of certain states associated with the superposition state: e.g., in one measure, the maximal distinguishability of the branches of the superposition is considered as in quantum binary decision theory; in another measure, the maximal distinguishability of the initial superposition and its image after a one-parameter evolution generated by a local Hermitian operator is of interest. The scaling of the size of the superposition with the number of modes and mode intensity (i.e., photon number) is compared to the scaling of certain geometric properties of the Wigner function of the superposition and also to the superposition size estimated experimentally from decoherence. We also apply earlier comparison-based methods for determining macroscopic superposition size that require a reference Greenberger-Horne-Zeilinger (GHZ) state. The case of a hierarchical Schrödinger cat state with branches composed of smaller superpositions is also analyzed from a measurement-based perspective. © 2014 American Physical Society

Photoactivated biological processes as quantum measurements.

We outline a framework for describing photoactivated biological reactions as generalized quantum measurements of external fields, for which the biological system takes on the role of a quantum meter. By using general arguments regarding the Hamiltonian that describes the measurement interaction, we identify the cases where it is essential for a complex chemical or biological system to exhibit nonequilibrium quantum coherent dynamics in order to achieve the requisite functionality. We illustrate the analysis by considering measurement of the solar radiation field in photosynthesis and measurement of the earth's magnetic field in avian magnetoreception

Government solvency: revisiting some EMU countries

Corsetti and Roubini (1991) reported that the government finances of Greece, Ireland, Italy and the Netherlands did not satisfy the intertemporal budget constraint (IBC). We re-examine this issue by utilizing a new empirical approach and extended data set. Structural shifts, an issue which Corsetti and Roubini were unable to address due to the lack of suitable econometric methods, are tackled. We show that: (i) government finances of all four countries satisfy the IBC and this finding is robust to different time horizons; (ii) multiple structural shifts, most of which correspond to important policy changes, did occur in the fiscal path of these countries; and (iii) the overall effect of structural shifts has been to strengthen the evidence supporting IBC. We also find a clear positive Maastricht effect on IBC

Problems with Using Evolutionary Theory in Philosophy

Does science move toward truths? Are present scientific theories (approximately) true? Should we invoke truths to explain the success of science? Do our cognitive faculties track truths? Some philosophers say yes, while others say no, to these questions. Interestingly, both groups use the same scientific theory, viz., evolutionary theory, to defend their positions. I argue that it begs the question for the former group to do so because their positive answers imply that evolutionary theory is warranted, whereas it is self-defeating for the latter group to do so because their negative answers imply that evolutionary theory is unwarranted

Single-molecule microscopy reveals new insights into nucleotide selection by DNA polymerase I.

The mechanism by which DNA polymerases achieve their extraordinary accuracy has been intensely studied because of the linkage between this process and mutagenesis and carcinogenesis. Here, we have used single-molecule fluorescence microscopy to study the process of nucleotide selection and exonuclease action. Our results show that the binding of Escherichia coli DNA polymerase I (Klenow fragment) to a primer-template is stabilized by the presence of the next correct dNTP, even in the presence of a large excess of the other dNTPs and rNTPs. These results are consistent with a model where nucleotide selection occurs in the open complex prior to the formation of a closed ternary complex. Our assay can also distinguish between primer binding to the polymerase or exonuclease domain and, contrary to ensemble-averaged studies, we find that stable exonuclease binding only occurs with a mismatched primer terminus