Computing and deflating eigenvalues while solving multiple right hand side linear systems in Quantum Chromodynamics

We present a new algorithm that computes eigenvalues and eigenvectors of a Hermitian positive definite matrix while solving a linear system of equations with Conjugate Gradient (CG). Traditionally, all the CG iteration vectors could be saved and recombined through the eigenvectors of the tridiagonal projection matrix, which is equivalent theoretically to unrestarted Lanczos. Our algorithm capitalizes on the iteration vectors produced by CG to update only a small window of vectors that approximate the eigenvectors. While this window is restarted in a locally optimal way, the CG algorithm for the linear system is unaffected. Yet, in all our experiments, this small window converges to the required eigenvectors at a rate identical to unrestarted Lanczos. After the solution of the linear system, eigenvectors that have not accurately converged can be improved in an incremental fashion by solving additional linear systems. In this case, eigenvectors identified in earlier systems can be used to deflate, and thus accelerate, the convergence of subsequent systems. We have used this algorithm with excellent results in lattice QCD applications, where hundreds of right hand sides may be needed. Specifically, about 70 eigenvectors are obtained to full accuracy after solving 24 right hand sides. Deflating these from the large number of subsequent right hand sides removes the dreaded critical slowdown, where the conditioning of the matrix increases as the quark mass reaches a critical value. Our experiments show almost a constant number of iterations for our method, regardless of quark mass, and speedups of 8 over original CG for light quark masses.Comment: 22 pages, 26 eps figure

MCMC inference for Markov Jump Processes via the Linear Noise Approximation

Bayesian analysis for Markov jump processes is a non-trivial and challenging problem. Although exact inference is theoretically possible, it is computationally demanding thus its applicability is limited to a small class of problems. In this paper we describe the application of Riemann manifold MCMC methods using an approximation to the likelihood of the Markov jump process which is valid when the system modelled is near its thermodynamic limit. The proposed approach is both statistically and computationally efficient while the convergence rate and mixing of the chains allows for fast MCMC inference. The methodology is evaluated using numerical simulations on two problems from chemical kinetics and one from systems biology

DESIGN OF A STATED RANKING EXPERIMENT TO STUDY INTERACTIVE FREIGHT BEHAVIOUR: AN APPLICATION TO ROME'S LTZ

City logistics policies require an understanding of several issues (e.g. freight distribution context, preferences and relationship among agents) seldom accounted for in current research. Policies run the risk of producing unsatisfactory results because behavioural and contextual aspects are not considered. The acquisition of relevant data is crucial to test hypothesis and forecast agents' reactions to policy changes. Despite recent methodological advances in modelling interactive behaviour the development of apt survey instruments is still lacking to test innovative policies acceptability. This paper expands and innovate the methodological literature by describing a stated ranking experiment to study freight agent interactive behaviour and discusses the experimental design implemented to incorporate agent-specific priors when efficient design techniques are employed.urban freight distribution, group decision making, agent-specific interaction, stated preference, stated ranking experiments

Evaluation of the optical switching characteristics of erbium-doped fibres for the development of a fibre Bragg grating sensor interrogator

A polling topology that employs optical switching based on the properties of erbium-doped fibres (EDFs) is used to interrogate an array of FBGs. The properties of the EDF are investigated in its pumped and un-pumped states and the EDFs’ switching properties are evaluated by comparing them with a high performance electronically controlled MEM optical switch. Potential advantages of the proposed technique are discussed. © (2014) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only

Algebraic-matrix calculation of vibrational levels of triatomic molecules

We introduce an accurate and efficient algebraic technique for the computation of the vibrational spectra of triatomic molecules, of both linear and bent equilibrium geometry. The full three-dimensional potential energy surface (PES), which can be based on entirely {\it ab initio} data, is parameterized as a product Morse-cosine expansion, expressed in bond-angle internal coordinates, and includes explicit interactions among the local modes. We describe the stretching degrees of freedom in the framework of a Morse-type expansion on a suitable algebraic basis, which provides exact analytical expressions for the elements of a sparse Hamiltonian matrix. Likewise, we use a cosine power expansion on a spherical harmonics basis for the bending degree of freedom. The resulting matrix representation in the product space is very sparse and vibrational levels and eigenfunctions can be obtained by efficient diagonalization techniques. We apply this method to carbonyl sulfide OCS, hydrogen cyanide HCN, water H$_2$O, and nitrogen dioxide NO$_2$. When we base our calculations on high-quality PESs tuned to the experimental data, the computed spectra are in very good agreement with the observed band origins.Comment: 11 pages, 2 figures, containg additional supporting information in epaps.ps (results in tables, which are useful but not too important for the paper

Lateral Gene Expression in Drosophila Early Embryos Is Supported by Grainyhead-Mediated Activation and Tiers of Dorsally-Localized Repression

The general consensus in the field is that limiting amounts of the transcription factor Dorsal establish dorsal boundaries of genes expressed along the dorsal-ventral (DV) axis of early Drosophila embryos, while repressors establish ventral boundaries. Yet recent studies have provided evidence that repressors act to specify the dorsal boundary of intermediate neuroblasts defective (ind), a gene expressed in a stripe along the DV axis in lateral regions of the embryo. Here we show that a short 12 base pair sequence (“the A-box”) present twice within the ind CRM is both necessary and sufficient to support transcriptional repression in dorsal regions of embryos. To identify binding factors, we conducted affinity chromatography using the A-box element and found a number of DNA-binding proteins and chromatin-associated factors using mass spectroscopy. Only Grainyhead (Grh), a CP2 transcription factor with a unique DNA-binding domain, was found to bind the A-box sequence. Our results suggest that Grh acts as an activator to support expression of ind, which was surprising as we identified this factor using an element that mediates dorsally-localized repression. Grh and Dorsal both contribute to ind transcriptional activation. However, another recent study found that the repressor Capicua (Cic) also binds to the A-box sequence. While Cic was not identified through our A-box affinity chromatography, utilization of the same site, the A-box, by both factors Grh (activator) and Cic (repressor) may also support a “switch-like” response that helps to sharpen the ind dorsal boundary. Furthermore, our results also demonstrate that TGF-β signaling acts to refine ind CRM expression in an A-box independent manner in dorsal-most regions, suggesting that tiers of repression act in dorsal regions of the embryo

Effect of Randomness on Quantum Data Buses of Heisenberg Spin Chains

A strongly coupled spin chain can mediate long-distance effective couplings or entanglement between remote qubits, and can be used as a quantum data bus. We study how the fidelity of a spin-1/2 Heisenberg chain as a spin bus is affected by static random exchange couplings and magnetic fields. We find that, while non-uniform exchange couplings preserve the isotropy of the qubit effective couplings, they cause the energy levels, the eigenstates, and the magnitude of the couplings to vary locally. On the other hand, random local magnetic fields lead to an avoided level crossing for the bus ground state manifold, and cause the effective qubit couplings to be anisotropic. Interestingly, the total magnetic moment of the ground state of an odd-size bus may not be parallel to the average magnetic field. Its alignment depends on both the direction of the average field and the field distribution, in contrast with the ground state of a single spin which always aligns with the applied magnetic field to minimize the Zeeman energy. Lastly, we calculate sensitivities of the spin bus to such local variations, which are potentially useful for evaluating decoherence when dynamical fluctuations in the exchange coupling or magnetic field are considered

Unraveling the molecular basis of subunit specificity in P pilus assembly by mass spectrometry

P pili are multisubunit fibers essential for the attachment of uropathogenic Escherichia coli to the kidney. These fibers are formed by the noncovalent assembly of six different homologous subunit types in an array that is strictly defined in terms of both the number and order of each subunit type. Assembly occurs through a mechanism termed “donor-strand exchange (DSE)” in which an N-terminal extension (Nte) of one subunit donates a β-strand to an adjacent subunit, completing its Ig fold. Despite structural determination of the different subunits, the mechanism determining specificity of subunit ordering in pilus assembly remained unclear. Here, we have used noncovalent mass spectrometry to monitor DSE between all 30 possible pairs of P pilus subunits and their Ntes. We demonstrate a striking correlation between the natural order of subunits in pili and their ability to undergo DSE in vitro. The results reveal insights into the molecular mechanism by which subunit ordering during the assembly of this complex is achieved

Augmenting forearm crutches with wireless sensors for lower limb rehabilitation

Forearm crutches are frequently used in the rehabilitation of an injury to the lower limb. The recovery rate is improved if the patient correctly applies a certain fraction of their body weight (specified by a clinician) through the axis of the crutch, referred to as partial weight bearing (PWB). Incorrect weight bearing has been shown to result in an extended recovery period or even cause further damage to the limb. There is currently no minimally invasive tool for long-term monitoring of a patient's PWB in a home environment. This paper describes the research and development of an instrumented forearm crutch that has been developed to wirelessly and autonomously monitor a patient's weight bearing over the full period of their recovery, including its potential use in a home environment. A pair of standard forearm crutches are augmented with low-cost off-the-shelf wireless sensor nodes and electronic components to provide indicative measurements of the applied weight, crutch tilt and hand position on the grip. Data are wirelessly transmitted between crutches and to a remote computer (where they are processed and visualized in LabVIEW), and the patient receives biofeedback by means of an audible signal when they put too much or too little weight through the crutch. The initial results obtained highlight the capability of the instrumented crutch to support physiotherapists and patients in monitoring usage