Functional Methods in Stochastic Systems

Field-theoretic construction of functional representations of solutions of stochastic differential equations and master equations is reviewed. A generic expression for the generating function of Green functions of stochastic systems is put forward. Relation of ambiguities in stochastic differential equations and in the functional representations is discussed. Ordinary differential equations for expectation values and correlation functions are inferred with the aid of a variational approach.Comment: Plenary talk presented at Mathematical Modeling and Computational Science. International Conference, MMCP 2011, Star\'a Lesn\'a, Slovakia, July 4-8, 201

Robustness of Planar Fourier Capture Arrays to Colour Changes and Lost Pixels

Planar Fourier capture arrays (PFCAs) are optical sensors built entirely in standard microchip manufacturing flows. PFCAs are composed of ensembles of angle sensitive pixels (ASPs) that each report a single coefficient of the Fourier transform of the far-away scene. Here we characterize the performance of PFCAs under the following three non-optimal conditions. First, we show that PFCAs can operate while sensing light of a wavelength other than the design point. Second, if only a randomly-selected subset of 10% of the ASPs are functional, we can nonetheless reconstruct the entire far-away scene using compressed sensing. Third, if the wavelength of the imaged light is unknown, it can be inferred by demanding self-consistency of the outputs.Comment: 15 pages including cover page, 12 figures, associated with the 9th International Conference on Position Sensitive Detector

A NOTE ON LEDGARD'S MINILANGUAGE 2 AND A PROPOSAL FOR AN ALTERNATIVE

This note reviews and discusses the concepts of assignment statements which occur within programming languages and as exemplified by Minilanguage 2 by Ledgard [3]. Observing that the description of assignment by Ledgard depends on the existence of a nominative addressing scheme, an alternative vignette of language is proposed which is based on type directed addressing systems

Anomalous Scaling of Structure Functions and Dynamic Constraints on Turbulence Simulations

The connection between anomalous scaling of structure functions (intermittency) and numerical methods for turbulence simulations is discussed. It is argued that the computational work for direct numerical simulations (DNS) of fully developed turbulence increases as $Re^{4}$, and not as $Re^{3}$ expected from Kolmogorov's theory, where $Re$ is a large-scale Reynolds number. Various relations for the moments of acceleration and velocity derivatives are derived. An infinite set of exact constraints on dynamically consistent subgrid models for Large Eddy Simulations (LES) is derived from the Navier-Stokes equations, and some problems of principle associated with existing LES models are highlighted.Comment: 18 page

The creation of large photon-number path entanglement conditioned on photodetection

Large photon-number path entanglement is an important resource for enhanced precision measurements and quantum imaging. We present a general constructive protocol to create any large photon number path-entangled state based on the conditional detection of single photons. The influence of imperfect detectors is considered and an asymptotic scaling law is derived.Comment: 6 pages, 4 figure

Magnetic Structures of Some Multiferroics

We studied crystal and magnetic structures of some composite and single-phase multiferroics: (x)MFe2O4 + (1-x)BaTiO3, Ni3-yCoyV2O8, and Bi0.9Ba0.1Fe0.9Ti0.1O3. Composite multiferroics (x)MFe2O4 + (1-x)BaTiO3 with x = (0.2; 0.3; 0.4) and M = (Ni, Co) have ferrimagnetic structure, which is described by the propagation vector k = 0. Oxides Ni3-yCoyV2O8 with y = (0.1; 0.3; 0.5) possess a modulated magnetic structure, described by the vector k = (δ, 0, 0), where δ = 0.283 and 0.348 at 7.4 K for y = 0.1 and 0.5, respectively. In the Bi0.9Ba0.1Fe0.9Ti0.1O3 multiferroic a magnetic order is destroyed at 600 K and the Fe-ion magnetic moment decreases from µ = 3.46(5) μB at 300 K to zero at 600 K

The effect of Goods and Services Tax (GST) imposition on stock market overreaction and trading volume in Malaysia and Australia

This paper investigates the GST imposition effect on stock overreaction and trading volume in Bursa Malaysia and Australian Securities Exchange (ASX). To evaluate the stock overreaction, t-test, Wilcoxon Signed-Rank Test and MannWhitney U-Test are employed to analyse the market-adjusted abnormal returns. The homogeneity of stock trading volume is assessed by block resampling bootstrapping, t-test and regression. Consistent with the Overreaction Hypothesis, this research reveals that all arbitrage portfolios over one-month interval in Bursa Malaysia are able to generate significant abnormal profits. This infers the profitability of implementing short-term contrarian strategy in the Malaysian stock market. However, the analysis for ASX shows the opposite. Additionally, GST imposition reduces the trading volume in Bursa Malaysia but not in ASX. This empirical result will be of interest to the policymakers who are considering imposing tax on fee-based financial services, as well as the investors and fund managers who are concern about profits maximisation

Ground state of graphite ribbons with zigzag edges

We study the interaction effects on the ground state of nanographite ribbons with zigzag edges. Within the mean-field approximation, we found that there are two possible phases: the superconducting (SC) phase and the excitonic insulator (EI). The two phases are separated by a first-order transition point. After taking into account the low-lying fluctuations around the mean-field solutions, the SC phase becomes a spin liquid phase with one gapless charge mode. On the other hand, all excitations in the EI phase, especially the spin excitations, are gapped.Comment: 6 pages, 3 figure