Critical behavior of one-particle spectral weights in the transverse Ising model

We investigate the critical behavior of the spectral weight of a single quasiparticle, one of the key observables in experiment, for the particular case of the transverse Ising model. Series expansions are calculated for the linear chain and the square and simple cubic lattices. For the chain model, a conjectured exact result is discovered. For the square and simple cubic lattices, series analyses are used to estimate the critical exponents. The results agree with the general predictions of Sachdev [Quantum Phase Transitions (Cambridge University Press, Cambridge, England, 1999)].

On functionally-fitted Runge-Kutta methods

Functionally-fitted methods are generalizations of collocation techniques to integrate an equation exactly if its solution is a linear combination of a chosen set of basis functions. When these basis functions are chosen as the power functions, we recover classical algebraic collocation methods. This paper shows that functionally-fitted methods can be derived with less restrictive conditions than previously stated in the literature, and that other related results can be derived in a much more elegant way. The novelty in our approach is to fully retain the collocation framework without reverting back into derivations based on cumbersome Taylor series expansions.

Excitation spectra of the spin-1/2 triangular-lattice Heisenberg antiferromagnet

We use series expansion methods to calculate the dispersion relation of the one-magnon excitations for the spin-(1)/(2) triangular-lattice nearest-neighbor Heisenberg antiferromagnet above a three-sublattice ordered ground state. Several striking features are observed compared to the classical (large-S) spin-wave spectra. Whereas, at low energies the dispersion is only weakly renormalized by quantum fluctuations, significant anomalies are observed at high energies. In particular, we find rotonlike minima at special wave vectors and strong downward renormalization in large parts of the Brillouin zone, leading to very flat or dispersionless modes. We present detailed comparison of our calculated excitation energies in the Brillouin zone with the spin-wave dispersion to order 1/S calculated recently by Starykh, Chubukov, and Abanov [Phys. Rev. B74, 180403(R) (2006)]. We find many common features but also some quantitative and qualitative differences. We show that at temperatures as low as 0.1J the thermally excited rotons make a significant contribution to the entropy. Consequently, unlike for the square lattice model, a nonlinear sigma model description of the finite-temperature properties is only applicable at temperatures < 0.1J. Finally, we review recent NMR measurements on the organic compound kappa-(BEDT-TTF)(2)Cu-2(CN)(3). We argue that these are inconsistent with long-range order and a description of the low-energy excitations in terms of interacting magnons, and that therefore a Heisenberg model with only nearest-neighbor exchange does not offer an adequate description of this material.

Accelerated leap methods for simulating discrete stochastic chemical kinetics

Biologists are increasingly conscious of the critical role that noise plays in cellular functions such as genetic regulation, often in connection with fluctuations in small numbers of key regulatory molecules. This has inspired the development of models that capture this fundamentally discrete and stochastic nature of cellular biology - most notably the Gillespie stochastic simulation algorithm (SSA). The SSA simulates a temporally homogeneous, discrete-state, continuous-time Markov process, and of course the corresponding probabilities and numbers of each molecular species must all remain positive. While accurately serving this purpose, the SSA can be computationally inefficient due to very small time stepping so faster approximations such as the Poisson and Binomial τ-leap methods have been suggested. This work places these leap methods in the context of numerical methods for the solution of stochastic differential equations (SDEs) driven by Poisson noise. This allows analogues of Euler-Maruyuma, Milstein and even higher order methods to be developed through the Itô-Taylor expansions as well as similar derivative-free Runge-Kutta approaches. Numerical results demonstrate that these novel methods compare favourably with existing techniques for simulating biochemical reactions by more accurately capturing crucial properties such as the mean and variance than existing methods.

Approximate Bayesian techniques for inference in stochastic dynamical systems

This thesis is concerned with approximate inference in dynamical systems, from a variational Bayesian perspective. When modelling real world dynamical systems, stochastic differential equations appear as a natural choice, mainly because of their ability to model the noise of the system by adding a variant of some stochastic process to the deterministic dynamics. Hence, inference in such processes has drawn much attention. Here two new extended frameworks are derived and presented that are based on basis function expansions and local polynomial approximations of a recently proposed variational Bayesian algorithm. It is shown that the new extensions converge to the original variational algorithm and can be used for state estimation (smoothing). However, the main focus is on estimating the (hyper-) parameters of these systems (i.e. drift parameters and diffusion coefficients). The new methods are numerically validated on a range of different systems which vary in dimensionality and non-linearity. These are the Ornstein-Uhlenbeck process, for which the exact likelihood can be computed analytically, the univariate and highly non-linear, stochastic double well and the multivariate chaotic stochastic Lorenz '63 (3-dimensional model). The algorithms are also applied to the 40 dimensional stochastic Lorenz '96 system. In this investigation these new approaches are compared with a variety of other well known methods such as the ensemble Kalman filter / smoother, a hybrid Monte Carlo sampler, the dual unscented Kalman filter (for jointly estimating the systems states and model parameters) and full weak-constraint 4D-Var. Empirical analysis of their asymptotic behaviour as a function of observation density or length of time window increases is provided.

Foreign direct investment and corruption

In the last few decades, the world has witnessed an enormous growth in the volume of foreign direct investment (FDI). The global stock of FDI reached US$ 7.5 trillion in 2003 and accounted for 11% of world Gross Domestic Product, up from 7% in 1990. The sales of multinational enterprises at around US$ 19 trillion were more than double the level of world exports. Substantial FDI inflows went into transition countries. Inflows into one of the region's largest recipient, the Russian Federation, almost doubled, enabling Russia to become one of the five top FDI destinations in 2005-2006. FDI inflows in Russia have increased almost threefold from 13.6% in 2003 to 35% in 2007. In 2003, these flows were twice greater than those into China; whilst in 2007 they were six times larger. Russia's FDI inflows were also about 2.5 times greater than those of Brazil. Efficient government institutions are argued by many economists to foster FDI and growth as a result. However, the magnitude of this effect has yet to be measured. This thesis takes a Political Economy approach to explore, empirically, the potential impact of malfunctioning governmental institutions, proxied by three indices of perceived corruption, on FDI stocks accumulation/distribution within Russia over the period of 2002-2004. Using a regional data-set it concentrates on three areas relating to FDI. Firstly, it considers the significance, the size and the sign of the impact of perceived corruption on accumulation of FDI stocks within Russia. Secondly, it quantifies the impact of perceived corruption on the volume of FDI stocks simultaneously estimating the impact of the investment in public capital such as telecommunications and transportation networks on FDI in the presence of corruption. In particular, it addresses the question whether more corrupt regions in Russia are also those that could have accumulated more of FDI stocks, and investigates whether those 'more corrupt' regions would have had lower level of public capital investment. Finally, it examines whether decentralisation increases or decreases corruption and whether a larger extent of decentralisation has a positive or negative impact on FDI (stocks). The results of three studies are as follows. Firstly, along with market potential, corruption is found to be one of the key factors in explaining FDI distribution within Russia between 2002 and 2004. Secondly, corruption on average is found to be related to FDI positively suggesting that it may act as speed money: to save their time foreign direct investors might be willing to bribe the regional authorities so to move in front of the bureaucratic lines. Thirdly, although when corruption is controlled for, the impact of the latter on unobservable FDI is found to be on average positive, no association between FDI and public investment is observed with the only exception of transportation infrastructure (i.e., railway). The results might suggest therefore that it is possible that not only regions with high levels of perceived corruption attract more FDI but also that expansions in public capital investments are not accompanied by an increase of the volume of FDI (stocks) in regions with high levels of corruption. This casts some doubt on the productivity of the investment in public capital in these regions as it might be that bureaucrats may prefer to use these infrastructural projects for rent extraction. Finally, we find decentralisation to have a significant and positive impact on both FDI stock accumulation and corruption, suggesting that local governments may spend more on public goods to make the area more attractive to foreign investors but at the same time they may be interested into extracting rents from foreign investors. These results support the idea that the regulation of FDI is associated with and facilitated by a larger public sector, which distorts competition and introduces opportunities for rent-seeking by particular economic and political factors.

Developments in technologies for human-centric mobile computing and applications

With recent expansions in technology, mobile computing continues to play a vital role in all aspects of our lives. Digital technology tools such as Web browsing, media tracking, social media, and emailing have made mobile technology more than just a means of communication but has widespread use in business and social networks. Developments in Technologies for Human-Centric Mobile Computing and Applications is a comprehensive collection of knowledge and practice in the development of technologies in human –centric mobile technology. This book focuses on the developmental aspects of mobile technology; bringing together researchers, educators, and practitioners to encourage readers to think outside of the box.

Algorithms for Evaluation of the Wright Function for the Real Arguments’ Values

2000 Math. Subject Classification: 33E12, 65D20, 33F05, 30E15

A Fast Algorithm for Weber Problem on a Grid

AMS subject classification: 90B80.

On Thom Polynomials for A4(−) via Schur Functions

2000 Mathematics Subject Classification: 05E05, 14N10, 57R45.

Spectral Shift Function for the Perturbations of Schrödinger Operators at High Energy

2000 Mathematics Subject Classification: 35P20, 35J10, 35Q40.

On an ODE Relevant for the General Theory of the Hyperbolic Cauchy Problem

2000 Mathematics Subject Classification: 34E20, 35L80, 35L15.

The Deformed Trigonometric Functions of two Variables

MSC 2010: 33B10, 33E20

Class Number Two for Real Quadratic Fields of Richaud-Degert Type

2000 Mathematics Subject Classification: Primary: 11D09, 11A55, 11C08, 11R11, 11R29; Secondary: 11R65, 11S40; 11R09.

Contemporary aspects of dividends: Before and during the financial crisis

The number of dividend paying firms has been on the decline since the popularity of stock repurchases in the 1980s, and the recent financial crisis has brought about a wave of dividend reductions and omissions. This dissertation examined the U.S. firms and American Depository Receipts that are listed on the U.S. equity exchanges according to their dividend paying history in the previous twelve quarters. While accounting for the state of the economy, the firm’s size, profitability, earned equity, and growth opportunities, it determines whether or not the firm will pay a dividend in the next quarter. It also examined the likelihood of a dividend change. Further, returns of firms were examined according to their dividend paying history and the state of the economy using the Fama-French three-factor model. Using forward, backward, and step-wise selection logistic regressions, the results show that firms with a history of regular and uninterrupted dividend payments are likely to continue to pay dividends, while firms that do not have a history of regular dividend payments are not likely to begin to pay dividends or continue to do so. The results of a set of generalized polytomous logistic regressions imply that dividend paying firms are more likely to reduce dividend payments during economic expansions, as opposed to recessions. Also the analysis of returns using the Fama-French three factor model reveals that dividend paying firms are earning significant abnormal positive returns. As a special case, a similar analysis of dividend payment and dividend change was applied to American Depository Receipts that trade on the NYSE, NASDAQ, and AMEX exchanges and are issued by the Bank of New York Mellon. Returns of American Depository Receipts were examined using the Fama-French two-factor model for international firms. The results of the generalized polytomous logistic regression analyses indicate that dividend paying status and economic conditions are also important for dividend level change of American Depository Receipts, and Fama-French two-factor regressions alone do not adequately explain returns for these securities.