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

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

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

Optimizing time and space MIMO antenna system for frequency selective fading channels

Smart or adaptive antennas promise to provide significant increases in system capacity and performance in wireless communication systems. In this paper, we investigate the use of adaptive antennas at the base and mobile stations, operating jointly, to maximize the average signal-to-interference and noise ratio (SINR) of each packet in the system for frequency selective channels with prior knowledge of the channel at the transmitter. Our approach is based on deriving an analytic formula for the average packet SINR and using the Lagrange multiplier method to determine an optimum. We derive necessary conditions for an optimum solution and propose an analytical expression for the optimum. Our analytical expression is not guaranteed to be the global optimum but it does satisfy the derived necessary conditions and, in addition for frequency flat channels, our results reduce to expressions for optimal weights previously published. To demonstrate the potential of the proposed system, we provide Monte Carlo simulation results of the system bit-error rates and make comparisons with other adaptive antenna systems. These show that significant improvements in performance are possible in a wireless communications context

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

Performance enhancement of multiuser MIMO wireless communication systems

This paper describes a new approach to the problem of enhancing the performance of a multiuser multiple-input-multiple-output (MIMO) system for communication from one base station to many mobile stations in both frequency-flat and frequency-selective fading channels. This problem arises in space-division multiplexing systems with multiple users where many independent signal streams can be transmitted in the same frequency and time slot through the exploitation of multiple antennas at both the base and mobile stations, Our new approach is based on maximizing a lower bound for the product of signal-to-interference plus noise ratio (SINR) of a multiuser MIMO system. This provides a closed-form (noniterative) solution for the antenna weights for all the users, under the constraint of fixed transmit power. Our solution is shown by simulation to have better performance than previously proposed iterative or noniterative solutions. In addition, our solution requires significantly reduced complexity over a gradient search-based method that directly optimizes the product SINgs while still maintaining similar performance. Our solution assumes channel state information is present at the base station or transmitter