A review of portfolio planning: Models and systems

In this chapter, we first provide an overview of a number of portfolio planning models which have been proposed and investigated over the last forty years. We revisit the mean-variance (M-V) model of Markowitz and the construction of the risk-return efficient frontier. A piecewise linear approximation of the problem through a reformulation involving diagonalisation of the quadratic form into a variable separable function is also considered. A few other models, such as, the Mean Absolute Deviation (MAD), the Weighted Goal Programming (WGP) and the Minimax (MM) model which use alternative metrics for risk are also introduced, compared and contrasted. Recently asymmetric measures of risk have gained in importance; we consider a generic representation and a number of alternative symmetric and asymmetric measures of risk which find use in the evaluation of portfolios. There are a number of modelling and computational considerations which have been introduced into practical portfolio planning problems. These include: (a) buy-in thresholds for assets, (b) restriction on the number of assets (cardinality constraints), (c) transaction roundlot restrictions. Practical portfolio models may also include (d) dedication of cashflow streams, and, (e) immunization which involves duration matching and convexity constraints. The modelling issues in respect of these features are discussed. Many of these features lead to discrete restrictions involving zero-one and general integer variables which make the resulting model a quadratic mixed-integer programming model (QMIP). The QMIP is a NP-hard problem; the algorithms and solution methods for this class of problems are also discussed. The issues of preparing the analytic data (financial datamarts) for this family of portfolio planning problems are examined. We finally present computational results which provide some indication of the state-of-the-art in the solution of portfolio optimisation problems

Use of cohesive elements in fatigue analysis

Cohesive laws describe the resistance to incipient separation of material surfaces. A cohesive finite element is formulated on the basis of a particular cohesive law. Cohesive elements are placed at the boundary between adjacent standard volume finite elements to model fatigue damage that leads to fracture at the separation of the element boundaries per the cohesive law. In this work, a cohesive model for fatigue crack initiation is taken to be the irreversible loadingunloading hysteresis that represents fatigue damage occuring due to cyclic loads leading to the initiation of small cracks. Various cohesive laws are reviewed and one is selected that incorporates a hysteretic cyclic loading that accounts for energetic dissipative mechanisms. A mathematical representation is developed based on an exponential effective load-separation cohesive relationship. A three-dimensional cohesive element is defined using this compliance relationship integrated at four points on the mid-surface of the area element. Implementation into finite element software is discussed and particular attention is applied to numerical convergence issues as the inflection point between loading and 'unloading in the cohesive law is encountered. A simple example of a displacementcontrolled fatigue test is presented in a finite element simulation. Comments are made on applications of the method to prediction of fatigue life for engineering structures such as pressure vessels and piping

High-fidelity quantum logic gates using trapped-ion hyperfine qubits

We demonstrate laser-driven two-qubit and single-qubit logic gates with fidelities 99.9(1)% and 99.9934(3)% respectively, significantly above the approximately 99% minimum threshold level required for fault-tolerant quantum computation, using qubits stored in hyperfine ground states of calcium-43 ions held in a room-temperature trap. We study the speed/fidelity trade-off for the two-qubit gate, for gate times between 3.8$\mu$s and 520$\mu$s, and develop a theoretical error model which is consistent with the data and which allows us to identify the principal technical sources of infidelity.Comment: 1 trap, 2 ions, 3 nines. Detailed write-up of arXiv:1406.5473 including single-qubit gate data als

A Submillimeter HCN Laser in IRC+10216

We report the detection of a strong submillimeter wavelength HCN laser line at a frequency near 805 GHz toward the carbon star IRC+10216. This line, the J=9-8 rotational transition within the (04(0)0) vibrationally excited state, is one of a series of HCN laser lines that were first detected in the laboratory in the early days of laser spectroscopy. Since its lower energy level is 4200 K above the ground state, the laser emission must arise from the inner part of IRC+10216's circumstellar envelope. To better characterize this environment, we observed other, thermally emitting, vibrationally excited HCN lines and find that they, like the laser line, arise in a region of temperature approximately 1000 K that is located within the dust formation radius; this conclusion is supported by the linewidth of the laser. The (04(0)0), J=9-8 laser might be chemically pumped and may be the only known laser (or maser) that is excited both in the laboratory and in space by a similar mechanism.Comment: 11 pages, 3 figure

Solar radiation force modeling for TDRS orbit determination

The relative orbit determination accuracies resulting from several TDRS models are evaluated. These models include spherical, single-plate, and restricted two-plate models. The plate models can be adjusted in both area and reflectivity through differential correction. The restricted two-plate model has an Earth-pointing plate and a solar plate; the orientation of the solar plate is restricted to rotation about an axis perpendicular to the satellite's orbital plane

Consistent Gravitationally-Coupled Spin-2 Field Theory

Inspired by the translational gauge structure of teleparallel gravity, the theory for a fundamental massless spin-2 field is constructed. Accordingly, instead of being represented by a symmetric second-rank tensor, the fundamental spin-2 field is assumed to be represented by a spacetime (world) vector field assuming values in the Lie algebra of the translation group. The flat-space theory naturally emerges in the Fierz formalism and is found to be equivalent to the usual metric-based theory. However, the gravitationally coupled theory, with gravitation itself described by teleparallel gravity, is shown not to present the consistency problems of the spin-2 theory constructed on the basis of general relativity.Comment: 16 pages, no figures. V2: Presentation changes, including addition of a new sub-section, aiming at clarifying the text; version accepted for publication in Class. Quantum Grav

High-fidelity trapped-ion quantum logic using near-field microwaves

We demonstrate a two-qubit logic gate driven by near-field microwaves in a room-temperature microfabricated ion trap. We measure a gate fidelity of 99.7(1)\%, which is above the minimum threshold required for fault-tolerant quantum computing. The gate is applied directly to $^{43}$Ca$^+$ "atomic clock" qubits (coherence time $T_2^*\approx 50\,\mathrm{s}$) using the microwave magnetic field gradient produced by a trap electrode. We introduce a dynamically-decoupled gate method, which stabilizes the qubits against fluctuating a.c.\ Zeeman shifts and avoids the need to null the microwave field

Revisiting the effect of external fields in Axelrod's model of social dynamics

The study of the effects of spatially uniform fields on the steady-state properties of Axelrod's model has yielded plenty of controversial results. Here we re-examine the impact of this type of field for a selection of parameters such that the field-free steady state of the model is heterogeneous or multicultural. Analyses of both one and two-dimensional versions of Axelrod's model indicate that, contrary to previous claims in the literature, the steady state remains heterogeneous regardless of the value of the field strength. Turning on the field leads to a discontinuous decrease on the number of cultural domains, which we argue is due to the instability of zero-field heterogeneous absorbing configurations. We find, however, that spatially nonuniform fields that implement a consensus rule among the neighborhood of the agents enforces homogenization. Although the overall effects of the fields are essentially the same irrespective of the dimensionality of the model, we argue that the dimensionality has a significant impact on the stability of the field-free homogeneous steady state