Interpolatory methods for H∞\mathcal{H}_\infty model reduction of multi-input/multi-output systems

We develop here a computationally effective approach for producing high-quality $\mathcal{H}_\infty$-approximations to large scale linear dynamical systems having multiple inputs and multiple outputs (MIMO). We extend an approach for $\mathcal{H}_\infty$ model reduction introduced by Flagg, Beattie, and Gugercin for the single-input/single-output (SISO) setting, which combined ideas originating in interpolatory $\mathcal{H}_2$-optimal model reduction with complex Chebyshev approximation. Retaining this framework, our approach to the MIMO problem has its principal computational cost dominated by (sparse) linear solves, and so it can remain an effective strategy in many large-scale settings. We are able to avoid computationally demanding $\mathcal{H}_\infty$ norm calculations that are normally required to monitor progress within each optimization cycle through the use of "data-driven" rational approximations that are built upon previously computed function samples. Numerical examples are included that illustrate our approach. We produce high fidelity reduced models having consistently better $\mathcal{H}_\infty$ performance than models produced via balanced truncation; these models often are as good as (and occasionally better than) models produced using optimal Hankel norm approximation as well. In all cases considered, the method described here produces reduced models at far lower cost than is possible with either balanced truncation or optimal Hankel norm approximation

Two-Loop g -> gg Splitting Amplitudes in QCD

Splitting amplitudes are universal functions governing the collinear behavior of scattering amplitudes for massless particles. We compute the two-loop g -> gg splitting amplitudes in QCD, N=1, and N=4 super-Yang-Mills theories, which describe the limits of two-loop n-point amplitudes where two gluon momenta become parallel. They also represent an ingredient in a direct x-space computation of DGLAP evolution kernels at next-to-next-to-leading order. To obtain the splitting amplitudes, we use the unitarity sewing method. In contrast to the usual light-cone gauge treatment, our calculation does not rely on the principal-value or Mandelstam-Leibbrandt prescriptions, even though the loop integrals contain some of the denominators typically encountered in light-cone gauge. We reduce the integrals to a set of 13 master integrals using integration-by-parts and Lorentz invariance identities. The master integrals are computed with the aid of differential equations in the splitting momentum fraction z. The epsilon-poles of the splitting amplitudes are consistent with a formula due to Catani for the infrared singularities of two-loop scattering amplitudes. This consistency essentially provides an inductive proof of Catani's formula, as well as an ansatz for previously-unknown 1/epsilon pole terms having non-trivial color structure. Finite terms in the splitting amplitudes determine the collinear behavior of finite remainders in this formula.Comment: 100 pages, 33 figures. Added remarks about leading-transcendentality argument of hep-th/0404092, and additional explanation of cut-reconstruction uniquenes

Motion-Compensation Techniques in Neonatal and Fetal MR Imaging

Fetal and neonatal MR imaging is increasingly used as a complementary diagnostic tool to sonography. MR imaging is an ideal technique for imaging fetuses and neonates because of the absence of ionizing radiation, the superior contrast of soft tissues compared with sonography, the availability of different contrast options, and the increased FOV. Motion in the normally mobile fetus and the unsettled, sleeping, or sedated neonate during a long acquisition will decrease image quality in the form of motion artifacts, hamper image interpretation, and often necessitate a repeat MR imaging to establish a diagnosis. This article reviews current techniques of motion compensation in fetal and neonatal MR imaging, including the following: 1) motion-prevention strategies (such as adequate patient preparation, patient coaching, and sedation, when required), 2) motion-artifacts minimization methods (such as fast imaging protocols, data undersampling, and motion-resistant sequences), and 3) motion-detection/correction schemes (such as navigators and self-navigated sequences, external motion-tracking devices, and postprocessing approaches) and their application in fetal and neonatal brain MR imaging. Additionally some background on the repertoire of motion of the fetal and neonatal patient and the resulting artifacts will be presented, as well as insights into future developments and emerging techniques of motion compensation

Development, acceptability and construct validity of the Aboriginal Women's Experiences of Partner Violence Scale (AEPVS): a co-designed, multiphase study nested within an Australian Aboriginal and Torres Strait Islander birth cohort

OBJECTIVE: Few studies employ culturally safe approaches to understanding Indigenous women's experiences of intimate partner violence (IPV). The aim of this study was to develop a brief, culturally safe, self-report measure of Aboriginal and Torres Strait Islander women's experiences of different types of IPV. DESIGN: Multistage process to select, adapt and test a modified version of the Australian Composite Abuse Scale using community discussion groups and pretesting. Revised draft measure tested in Wave 2 follow-up of an existing cohort of Aboriginal families. Psychometric testing and revision included assessment of the factor structure, construct validity, scale reliability and acceptability to create the Aboriginal Women's Experiences of Partner Violence Scale (AEPVS). SETTING: South Australia, Australia. PARTICIPANTS: 14 Aboriginal women participated in discussion groups, 58 women participated in pretesting of the draft version of the AEPVS and 216 women participating in the Aboriginal Families Study completed the revised draft version of the adapted measure. RESULTS: The initial version of the AEPVS based on item review and adaptation by the study's Aboriginal Advisory Group comprised 31 items measuring physical, emotional and financial IPV. After feedback from community discussion groups and two rounds of testing, the 18-item AEPVS consists of three subscales representing physical, emotional and financial IPV. All subscales had excellent construct validity and internal consistency. The AEPVS had high acceptability among Aboriginal women participating in the Aboriginal Families Study. CONCLUSIONS: The AEPVS is the first co-designed, multidimensional measure of Aboriginal women's experience of physical, emotional and financial IPV. The measure demonstrated cultural acceptability and construct validity within the setting of an Aboriginal-led, community-based research project. Validation in other settings (eg, primary care) and populations (eg, other Indigenous populations) will need to incorporate processes for community governance and tailoring of research processes to local community contexts.Karen Glover, Deirdre Gartland, Cathy Leane, Arwen Nikolof, Donna Weetra, Yvonne Clark, Rebecca Giallo, Stephanie J Brow

A guanosine 5′-triphosphate-dependent protein kinase is localized in the outer envelope membrane of pea chloroplasts

A guanosine 5-triphosphate (GTP)-dependent protein kinase was detected in preparations of outer chloroplast envelope membranes of pea (Pisum sativum L.) chloroplasts. The protein-kinase activity was capable of phosphorylating several envelope-membrane proteins. The major phosphorylated products were 23- and 32.5-kilo-dalton proteins of the outer envelope membrane. Several other envelope proteins were labeled to a lesser extent. Following acid hydrolysis of the labeled proteins, most of the label was detected as phosphoserine with only minor amounts detected as phosphothreonine. Several criteria were used to distinguish the GTP-dependent protein kinase from an ATP-dependent kinase also present in the outer envelope membrane. The ATP-dependent kinase phosphorylated a very different set of envelope-membrane proteins. Heparin inhibited the GTP-dependent kinase but had little effect upon the ATP-dependent enzyme. The GTP-dependent enzyme accepted phosvitin as an external protein substrate whereas the ATP-dependent enzyme did not. The outer membrane of the chloroplast envelope also contained a phosphotransferase capable of transferring labeled phosphate from [-32P]GTP to ADP to yield (-32P]ATP. Consequently, addition of ADP to a GTP-dependent protein-kinase assay resulted in a switch in the pattern of labeled products from that seen with GTP to that typically seen with ATP

MHV Rules for Higgs Plus Multi-Gluon Amplitudes

We use tree-level perturbation theory to show how non-supersymmetric one-loop scattering amplitudes for a Higgs boson plus an arbitrary number of partons can be constructed, in the limit of a heavy top quark, from a generalization of the scalar graph approach of Cachazo, Svrcek and Witten. The Higgs boson couples to gluons through a top quark loop which generates, for large top mass, a dimension-5 operator H tr G^2. This effective interaction leads to amplitudes which cannot be described by the standard MHV rules; for example, amplitudes where all of the gluons have positive helicity. We split the effective interaction into the sum of two terms, one holomorphic (selfdual) and one anti-holomorphic (anti-selfdual). The holomorphic interactions give a new set of MHV vertices -- identical in form to those of pure gauge theory, except for momentum conservation -- that can be combined with pure gauge theory MHV vertices to produce a tower of amplitudes with more than two negative helicities. Similarly, the anti-holomorphic interactions give anti-MHV vertices that can be combined with pure gauge theory anti-MHV vertices to produce a tower of amplitudes with more than two positive helicities. A Higgs boson amplitude is the sum of one MHV-tower amplitude and one anti-MHV-tower amplitude. We present all MHV-tower amplitudes with up to four negative-helicity gluons and any number of positive-helicity gluons (NNMHV). These rules reproduce all of the available analytic formulae for Higgs + n-gluon scattering (n<=5) at tree level, in some cases yielding considerably shorter expressions.Comment: 34 pages, 8 figures; v2, references correcte

Two-Loop Helicity Amplitudes for Quark-Gluon Scattering in QCD and Gluino-Gluon Scattering in Supersymmetric Yang-Mills Theory

We present the two-loop QCD helicity amplitudes for quark-gluon scattering, and for quark-antiquark annihilation into two gluons. These amplitudes are relevant for next-to-next-to-leading order corrections to (polarized) jet production at hadron colliders. We give the results in the `t Hooft-Veltman and four-dimensional helicity (FDH) variants of dimensional regularization. The transition rules for converting the amplitudes between the different variants are much more intricate than for the previously discussed case of gluon-gluon scattering. Summing our two-loop expressions over helicities and colors, and converting to conventional dimensional regularization, gives results in complete agreement with those of Anastasiou, Glover, Oleari and Tejeda-Yeomans. We describe the amplitudes for 2 to 2 scattering in pure N=1 supersymmetric Yang-Mills theory, obtained from the QCD amplitudes by modifying the color representation and multiplicities, and verify supersymmetry Ward identities in the FDH scheme.Comment: 77 pages. v2: corrected errors in eqs. (3.7) and (3.8) for one-loop assembly; remaining results unaffecte

Supersymmetric Regularization, Two-Loop QCD Amplitudes and Coupling Shifts

We present a definition of the four-dimensional helicity (FDH) regularization scheme valid for two or more loops. This scheme was previously defined and utilized at one loop. It amounts to a variation on the standard 't Hooft-Veltman scheme and is designed to be compatible with the use of helicity states for "observed" particles. It is similar to dimensional reduction in that it maintains an equal number of bosonic and fermionic states, as required for preserving supersymmetry. Supersymmetry Ward identities relate different helicity amplitudes in supersymmetric theories. As a check that the FDH scheme preserves supersymmetry, at least through two loops, we explicitly verify a number of these identities for gluon-gluon scattering (gg to gg) in supersymmetric QCD. These results also cross-check recent non-trivial two-loop calculations in ordinary QCD. Finally, we compute the two-loop shift between the FDH coupling and the standard MS-bar coupling, alpha_s. The FDH shift is identical to the one for dimensional reduction. The two-loop coupling shifts are then used to obtain the three-loop QCD beta function in the FDH and dimensional reduction schemes.Comment: 44 pages, minor corrections and clarifications include

Physics Opportunities of a Fixed-Target Experiment using the LHC Beams

We outline the many physics opportunities offered by a multi-purpose fixed-target experiment using the LHC proton and Pb beams extracted by a bent crystal. In a proton run with the LHC 7-TeV beam, one can analyze pp, pd and pA collisions at sqrt(s_NN)~115 GeV and even higher using the Fermi motion in a nuclear target. In a Pb run with a 2.76 TeV-per-nucleon beam, sqrt(s_NN) is as high as 72 GeV. Bent crystals can be used to extract about 5x10^8 protons/s; the integrated luminosity over a year reaches 0.5fb-1 on a typical 1 cm-long target without species limitation. Such an extraction mode does not alter the performance of the collider experiments at the LHC. By instrumenting the target-rapidity region, gluon and heavy-quark proton and neutron PDFs can be accessed at large x and even at x larger than 1 in the nuclear case. Single diffractive physics and, for the first time, the large negative-xF domain can be accessed. The nuclear target-species versatility provides a unique opportunity to study nuclear matter vs. the features of the hot and dense matter formed in heavy-ion collisions, which can be studied in PbA collisions over the full range of target-rapidity domain with a large variety of nuclei. The polarization of hydrogen and nuclear targets allows an ambitious spin program, including measurements of the QCD lensing effects which underlie the Sivers single-spin asymmetry, the study of transversity distributions and possibly of polarized PDFs. We also emphasize the potential offered by pA ultra-peripheral collisions where the nucleus target A is used as a coherent photon source, mimicking photoproduction processes in ep collisions. Finally, we note that W and Z bosons can be produced and detected in a fixed-target experiment and in their threshold domain for the first time, providing new ways to probe the partonic content of the proton and the nucleus.Comment: 14 pages, 2 figures, 5 tables. Comments are welcom

Regression and the Maternal in the History of Psychoanalysis, 1900-1957

This paper examines the history of the concept of ‘regression’ as it was perceived by Sandor Ferenczi and some of his followers in the first half of the twentieth century. The first part provides a short history of the notion of ‘regression’ from the late nineteenth century to Ferenczi's work in the 1920s and 1930s. The second and third parts of the paper focus on two other thinkers on regression, who worked in Britain, under the influence of the Ferenczian paradigm – the interwar Scottish psychiatrist, Ian D. Suttie; and the British-Hungarian psychoanalyst, and Ferenczi's most important pupil, Michael Balint. Rather than a descriptive term which comes to designate a pathological mental stage, Ferenczi understood ‘regression’ as a much more literal phenomenon. For him, the mental desire to go backwards in time is a universal one, and a consequence of an inevitable traumatic separation from the mother in early childhood, which has some deep personal and cultural implications. The paper aims to show some close affinities between the preoccupation of some psychoanalysts with ‘regression’, and the growing interest in social and cultural aspects of ‘motherhood’ and ‘the maternal role’ in mid-twentieth-century British society