Modulational instability of two-component Bose-Einstein condensates in an optical lattice

We study modulational instability of two-component Bose-Einstein condensates in an optical lattice, which is modelled as a coupled discrete nonlinear Schr \"{o}dinger equation. The excitation spectrum and the modulational instability condition of the total system are presented analytically. In the long-wavelength limit, our results agree with the homogeneous two-component Bose-Einstein condensates case. The discreteness effects result in the appearance of the modulational instability for the condensates in miscible region. The numerical calculations confirm our analytical results and show that the interspecies coupling can transfer the instability from one component to another.Comment: 4 pages, 3 figures (to be published in Phys. Rev. A

Effective-Range Expansion of the Neutron-Deuteron Scattering Studied by a Quark-Model Nonlocal Gaussian Potential

The S-wave effective range parameters of the neutron-deuteron (nd) scattering are derived in the Faddeev formalism, using a nonlocal Gaussian potential based on the quark-model baryon-baryon interaction fss2. The spin-doublet low-energy eigenphase shift is sufficiently attractive to reproduce predictions by the AV18 plus Urbana three-nucleon force, yielding the observed value of the doublet scattering length and the correct differential cross sections below the deuteron breakup threshold. This conclusion is consistent with the previous result for the triton binding energy, which is nearly reproduced by fss2 without reinforcing it with the three-nucleon force.Comment: 21 pages, 6 figures and 6 tables, submitted to Prog. Theor. Phy

On Turing dynamical systems and the Atiyah problem

Main theorems of the article concern the problem of M. Atiyah on possible values of l^2-Betti numbers. It is shown that all non-negative real numbers are l^2-Betti numbers, and that "many" (for example all non-negative algebraic) real numbers are l^2-Betti numbers of simply connected manifolds with respect to a free cocompact action. Also an explicit example is constructed which leads to a simply connected manifold with a transcendental l^2-Betti number with respect to an action of the threefold direct product of the lamplighter group Z/2 wr Z. The main new idea is embedding Turing machines into integral group rings. The main tool developed generalizes known techniques of spectral computations for certain random walk operators to arbitrary operators in groupoid rings of discrete measured groupoids.Comment: 35 pages; essentially identical to the published versio

Law's Looking Glass: Expert Identification Evidence Derived from Photographic and Video Images

This article offers a critical overview of expert identification evidence based on images. It reviews the Australian case law and then, in an interdisciplinary manner, endeavours to explain methodological, technical and theoretical problems with facial mapping evidence. It suggests that extant admissibility jurisprudence and traditional safeguards associated with expert opinion evidence and the adversarial trial might not adequately protect those accused of committing criminal acts when they are confronted with incriminating expert identification evidence

On the role of specific drug binding in modelling arterial eluting stents

In this paper we consider drug binding in the arterial wall following delivery by a drug-eluting stent. Whilst it is now generally accepted that a non-linear saturable reversible binding model is required to properly describe the binding process, the precise form of the binding model varies between authors. Our particular interest in this manuscript is in assessing to what extent modelling specific and non-specific binding in the arterial wall as separate phases is important. We study this issue by extending a recently developed coupled model of drug release and arterial tissue distribution, and comparing simulated profiles of drug concentration and drug mass in each phase within the arterial tissue

Digital back-propagation for nonlinearity mitigation in distributed Raman amplified links

The performance of digital back-propagation (DBP) for distributed Raman amplified optical communication systems is evaluated through analytical models and numerical simulations, and is compared with conventional lumped amplifier solutions, such as EDFA. The complexity of the DBP algorithm including the characteristic signal power profile of distributed Raman amplifiers is assessed. The use of full-field DBP in distributed Raman amplified systems leads to 1.3 dB additional gain with respect to systems employing lumped amplification, at the cost of only a 25% increase in complexity

A Closed-Form Expression to Evaluate Nonlinear Interference in Raman-Amplified Links

An accurate, closed-form expression to evaluate the nonlinear interference (NLI) noise power in Nyquist-spaced, coherent optical communication systems using backward-pumped Raman amplification is presented. This enables rapid estimation of the signal-to-noise ratio (SNR) and avoids the need of integral evaluations and split-step simulations. The accuracy of the proposed formula is compared to numerical integration of the Gaussian noise (GN) model and split-step simulations over a wide range of parameters, including three different fiber types. Additionally, the impact of pump depletion on the NLI noise power is studied and the formula is applied to a second-order Raman-amplified system. In the case of first-order amplification and negligible pump depletion, a maximum deviation of 0.34 dB in NLI coefficient between the GN model and the closed-form formula is found which corresponds to a maximum deviation of 0.1 dB in optimal SNR or similar figures of merit (e.g., maximum reach). When pump depletion is considered, it is shown that the NLI coefficient becomes a function of launch power and as a result the cubic power dependence of the NLI noise power is no longer valid in such regimes. Finally, for the second-order Raman-amplified system, a maximum deviation of 0.39 dB in NLI coefficient is reported

Extramural venous invasion is a potential imaging predictive biomarker of neoadjuvant treatment in rectal cancer

BACKGROUND: Extramural venous invasion (EMVI) is a poor prognostic factor in rectal cancer and identified on magnetic resonance imaging (MRI) (mrEMVI). The clinical relevance of improvement in mrEMVI following neoadjuvant therapy is unknown. This study aimed to demonstrate that regression of mrEMVI following neoadjuvant chemoradiotherapy (CRT) results in improved outcomes and mrEMVI can be used as an imaging biomarker METHODS: Retrospective analysis of prospectively collected data was conducted examining the staging and post-treatment MRIs of patients who had presented with EMVI-positive rectal cancer. All patients had undergone neoadjuvant CRT and curative surgery. Changes in mrEMVI were graded with a new MRI-based TRG scale–mr-vTRG; and related to disease-free survival (DFS). The study fulfilled Reporting Recommendations for Tumour Marker Prognostic Studies criteria for biomarkers. RESULTS: Sixty-two patients were included. Thirty-five patients showed more than 50% fibrosis of mrEMVI (mr-vTRG 1-3); 3-year DFS 87.8% and 9% recurrence. Twenty-seven patients showed less than 50% fibrosis (mr-vTRG 4-5); 3-year DFS 45.8% with 44% recurrence – P<0.0001. On multivariate Cox-regression, only mr-vTRG 4-5 increased risk of disease recurrence – HR=5.748. CONCLUSION: Patients in whom there has been a significant response of EMVI to CRT show improved DFS. Those patients with poor response should be considered for intensive treatment. As an imaging biomarker in rectal cancer, mrEMVI can be used

Simple and Nearly Optimal Polynomial Root-finding by Means of Root Radii Approximation

We propose a new simple but nearly optimal algorithm for the approximation of all sufficiently well isolated complex roots and root clusters of a univariate polynomial. Quite typically the known root-finders at first compute some crude but reasonably good approximations to well-conditioned roots (that is, those isolated from the other roots) and then refine the approximations very fast, by using Boolean time which is nearly optimal, up to a polylogarithmic factor. By combining and extending some old root-finding techniques, the geometry of the complex plane, and randomized parametrization, we accelerate the initial stage of obtaining crude to all well-conditioned simple and multiple roots as well as isolated root clusters. Our algorithm performs this stage at a Boolean cost dominated by the nearly optimal cost of subsequent refinement of these approximations, which we can perform concurrently, with minimum processor communication and synchronization. Our techniques are quite simple and elementary; their power and application range may increase in their combination with the known efficient root-finding methods.Comment: 12 pages, 1 figur

Analysis of Parametric Oscillatory Instability in Power Recycled LIGO Interferometer

We present the analysis of a nonlinear effect of parametric oscillatory instability in power recycled LIGO interferometer with the Fabry-Perot (FP) cavities in the arms. The basis for this effect is the excitation of the additional (Stokes) optical mode and the mirror elastic mode, when the optical energy stored in the main FP cavity main mode exceeds the certain threshold and the frequencies are related so that sum of frequencies of Stokes and elastic modes are approximately equal to frequencyof main mode. The presence of anti-Stokes modes (with frequency approximately equal to sum of frequencies of main and elastic modes) can depress parametric instability. However, it is very likely that the anti-Stokes modes will not compensate the parametric instability completely.Comment: 9 pages, 2 figures. submitted to Physics Letters