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Bayesian analysis has emerged as a rapidly expanding frontier in qualitative methods. Recent work in this journal has voiced various doubts regarding how to implement Bayesian process tracing and the costs versus benefits of this approach. In this response, we articulate a very different understanding of the state of the method and a much more positive view of what Bayesian reasoning can do to strengthen qualitative social science. Drawing on forthcoming research as well as our earlier work, we focus on clarifying issues involving mutual exclusivity of hypotheses, evidentiary import, adjudicating among more than two hypotheses, and the logic of iterative research, with the goal of elucidating how Bayesian analysis operates and pushing the field forward.

Fairfield and Charman provide a modern, rigorous and intuitive methodology for case-study research to help social scientists and analysts make better inferences from qualitative evidence. The book develops concrete guidelines for conducting inference to best explanation given incomplete information; no previous exposure to Bayesian analysis or specialized mathematical skills are needed. Topics covered include constructing rival hypotheses that are neither too simple nor overly complex, assessing the inferential weight of evidence, counteracting cognitive biases, selecting cases, and iterating between theory development, data collection, and analysis. Extensive worked examples apply Bayesian guidelines, showcasing both exemplars of intuitive Bayesian reasoning and departures from Bayesian principles in published case studies drawn from process-tracing, comparative, and multimethod research. Beyond improving inference and analytic transparency, an overarching goal of this book is to revalue qualitative research and place it on more equal footing with respect to quantitative and experimental traditions by illustrating that Bayesianism provides a universally applicable inferential framework.

The ALPHA collaboration has successfully demonstrated the production and the confinement of cold antihydrogen, $\overline{\mathrm{H}}$. An analysis of trapping data allowed a stringent limit to be placed on the electric charge of the simplest antiatom. Charge neutrality of matter is known to a very high precision, hence a neutrality limit of $\overline{\mathrm{H}}$ provides a test of CPT invariance. The experimental technique is based on the measurement of the deflection of putatively charged $\overline{\mathrm{H}}$ in an electric field. The tendency for trapped $\overline{\mathrm{H}}$ atoms to be displaced by electrostatic fields is measured and compared to the results of a detailed simulation of $\overline{\mathrm{H}}$ dynamics in the trap. An extensive survey of the systematic errors is performed, with particular attention to those due to the silicon vertex detector, which is the device used to determine the $\overline{\mathrm{H}}$ annihilation position. The limit obtained on the charge of the $\overline{\mathrm{H}}$ atom is \mbox{$ Q = (-1.3\pm1.8\pm0.4)\times10^{-8}$}, representing the first precision measurement with $\overline{\mathrm{H}}$., Comment: 5 pages, 3 figures

We advance efforts to explicate and improve inference in qualitative research that iterates between theory development, data collection, and data analysis, rather than proceeding linearly from hypothesizing to testing. We draw on the school of Bayesian “probability as extended logic,” where probabilities represent rational degrees of belief in propositions given limited information, to provide a solid foundation for iterative research that has been lacking in the qualitative methods literature. We argue that mechanisms for distinguishing exploratory from confirmatory stages of analysis that have been suggested in the context of APSA’s DA-RT transparency initiative are unnecessary for qualitative research that is guided by logical Bayesianism, because new evidence has no special status relative to old evidence for testing hypotheses within this inferential framework. Bayesian probability not only fits naturally with how we intuitively move back and forth between theory and data, but also provides a framework for rational reasoning that mitigates confirmation bias and ad-hoc hypothesizing—two common problems associated with iterative research. Moreover, logical Bayesianism facilitates scrutiny of findings by the academic community for signs of sloppy or motivated reasoning. We illustrate these points with an application to recent research on state building.

Bayesian probability holds the potential to serve as an important bridge between qualitative and quantitative methodology. Yet whereas Bayesian statistical techniques have been successfully elaborated for quantitative research, applying Bayesian probability to qualitative research remains an open frontier. This paper advances the burgeoning literature on Bayesian process tracing by drawing on expositions of Bayesian “probability as extended logic” from the physical sciences, where probabilities represent rational degrees of belief in propositions given the inevitably limited information we possess. We provide step-by-step guidelines for explicit Bayesian process tracing, calling attention to technical points that have been overlooked or inadequately addressed, and we illustrate how to apply this approach with the first systematic application to a case study that draws on multiple pieces of detailed evidence. While we caution that efforts to explicitly apply Bayesian learning in qualitative social science will inevitably run up against the difficulty that probabilities cannot be unambiguously specified, we nevertheless envision important roles for explicit Bayesian analysis in pinpointing the locus of contention when scholars disagree on inferences, and in training intuition to follow Bayesian probability more systematically.

© 2016 Macmillan Publishers Limited. All rights reserved. Antimatter continues to intrigue physicists because of its apparent absence in the observable Universe. Current theory requires that matter and antimatter appeared in equal quantities after the Big Bang, but the Standard Model of particle physics offers no quantitative explanation for the apparent disappearance of half the Universe. It has recently become possible to study trapped atoms - of antihydrogen to search for possible, as yet unobserved, differences in the physical behaviour of matter and antimatter. Here we consider the charge neutrality of the antihydrogen atom. By applying stochastic acceleration to trapped antihydrogen atoms, we determine an experimental bound on the antihydrogen charge, Qe, of |Q| < 0.71 parts per billion (one standard deviation), in which e is the elementary charge. This bound is a factor of 20 less than that determined from the best previous measurement of the antihydrogen charge. The electrical charge of atoms and molecules of normal matter is known to be no greater than about 10-21e for a diverse range of species including H2, He and SF6. Charge-parity-time symmetry and quantum anomaly cancellation demand that the charge of antihydrogen be similarly small. Thus, our measurement constitutes an improved limit and a test of fundamental aspects of the Standard Model. If we assume charge superposition and use the best measured value of the antiproton charge, then we can place a new limit on the positron charge anomaly (the relative difference between the positron and elementary charge) of about one part per billion (one standard deviation), a 25-fold reduction compared to the current best measurement.

Magnetically trapped antihydrogen atoms at low temperatures were used to test the charge neutrality of this antiatomic system, by precisely placing a limit to its electrical charge. A new method for measuring the gravitational interaction of antimatter was also developed, and prospects for making a precise measurement of this interaction are discussed. Finally, progress towards a precise, direct test of CPT symmetry by laser spectroscopy of antihydrogen is presented.

To illustrate how Bayesian logic underpins qualitative research, we provide an application to Fairfield’s (2015) work on tax policy change in Latin America. Fairfield (2013) elaborated a methodological appendix that we believe is the first published account that explicitly applies process-tracing tests to elucidate causal inferences in the author’s case narratives. In the following exercise, which is also the first of its kind, we revise that appendix by replacing the language of process-tracing tests with direct applications of Bayes’ theorem. While we advocate a Bayesian approach to inference over process-tracing tests, we stress the fundamental difficulty of assigning quantitative probabilities in the complex world of social science.

The properties of antihydrogen are expected to be identical to those of hydrogen, and any differences would constitute a profound challenge to the fundamental theories of physics. The most commonly discussed antiatom-based tests of these theories are searches for antihydrogen-hydrogen spectral differences (tests of CPT (charge-parity-time) invariance) or gravitational differences (tests of the weak equivalence principle). Here we, the ALPHA Collaboration, report a different and somewhat unusual test of CPT and of quantum anomaly cancellation. A retrospective analysis of the influence of electric fields on antihydrogen atoms released from the ALPHA trap finds a mean axial deflection of 4.1±3.4 mm for an average axial electric field of 0.51 V mm−1. Combined with extensive numerical modelling, this measurement leads to a bound on the charge Qe of antihydrogen of Q=(−1.3±1.1±0.4) × 10−8. Here, e is the unit charge, and the errors are from statistics and systematic effects., Fundamental theories do not predict a difference between the properties of matter and antimatter, but experimental tests of this are still in their infancy. To this end, this study analyses the effects of electric fields on antihydrogen atoms in the ALPHA trap to place a bound on the charge of antihydrogen.

Assuming hydrogen is charge neutral, CPT invariance demands that antihydrogen also be charge neutral. Quantum anomaly cancellation also demands that antihydrogen be charge neutral. Standard techniques based on measurements of macroscopic quantities of atoms cannot be used to measure the charge of antihydrogen. In this paper, we describe how the application of randomly oscillating electric fields to a sample of trapped antihydrogen atoms, a form of stochastic acceleration, can be used to place experimental limits on this charge. Assuming hydrogen is charge neutral, CPT invariance demands that antihydrogen also be charge neutral. Quantum anomaly cancellation also demands that antihydrogen be charge neutral. Standard techniques based on measurements of macroscopic quantities of atoms cannot be used to measure the charge of antihydrogen. In this paper, we describe how the application of randomly oscillating electric fields to a sample of trapped antihydrogen atoms, a form of stochastic acceleration, can be used to place experimental limits on this charge. Assuming hydrogen is charge neutral, CPT invariance demands that antihydrogen also be charge neutral. Quantum anomaly cancellation also demands that antihydrogen be charge neutral. Standard techniques based on measurements of macroscopic quantities of atoms cannot be used to measure the charge of antihydrogen. In this paper, we describe how the application of randomly oscillating electric fields to a sample of trapped antihydrogen atoms, a form of stochastic acceleration, can be used to place experimental limits on this charge.

Physicists have long wondered whether the gravitational interactions between matter and antimatter might be different from those between matter and itself. Although there are many indirect indications that no such differences exist and that the weak equivalence principle holds, there have been no direct, free-fall style, experimental tests of gravity on antimatter. Here we describe a novel direct test methodology; we search for a propensity for antihydrogen atoms to fall downward when released from the ALPHA antihydrogen trap. In the absence of systematic errors, we can reject ratios of the gravitational to inertial mass of antihydrogen >75 at a statistical significance level of 5%; worst-case systematic errors increase the minimum rejection ratio to 110. A similar search places somewhat tighter bounds on a negative gravitational mass, that is, on antigravity. This methodology, coupled with ongoing experimental improvements, should allow us to bound the ratio within the more interesting near equivalence regime., One intriguing question about antimatter that is yet to be directly answered is whether or not it behaves exactly the same as matter under gravity. Here, a direct experimental method is presented to measure the ratio of inertial to gravitational mass for antihydrogen under free-fall conditions.

CERN currently delivers antiprotons for trapping experiments with the antiproton decelerator (AD), which slows the antiprotons down to about 5 MeV. This energy is currently too high for direct trapping, and thick foils are used to slow down the beam to energies which can be trapped. To allow further deceleration to $\ensuremath{\sim}100\text{ }\text{ }\mathrm{keV}$, CERN is initiating the construction of ELENA, consisting of a ring which will combine rf deceleration and electron cooling capabilities. We describe a simple frictional cooling scheme that can serve to provide significantly improved trapping efficiency, either directly from the AD or first using a standard deceleration mechanism (induction linac or rf quadrupole). This scheme could be implemented in a short time. The device itself is short in length, uses accessible voltages, and at reasonable cost could serve in the interim before ELENA becomes operational, or possibly in lieu of ELENA for some experiments. Simple theory and simulations provide a preliminary assessment of the concept and its strengths and limitations, and highlight important areas for experimental studies, in particular to pin down the level of multiple scattering for low-energy antiprotons. We show that the frictional cooling scheme can provide a similar energy spectrum to that of ELENA, but with higher transverse emittances.

The longitudinal dynamics of a resonantly driven Langmuir wave are analyzed in the limit that the growth of the electrostatic wave is slow compared to the bounce frequency. Using simple physical arguments, the nonlinear distribution function is shown to be nearly gaussian in the canonical particle action, with a slowly evolving mean and fixed variance. Self-consistency with the electrostatic potential provide the basic properties of the nonlinear distribution function including a frequency shift that agrees well with driven, electrostatic particle simulations. This extends earlier work on nonlinear Langmuir waves by Morales and O'Neil [G. J. Morales and T. M. O'Neil, Phys. Rev. Lett. 28, 417 (1972)], and could form the basis of a reduced kinetic treatment of Raman backscatter in a plasma., Comment: 11 pages, 4 figures, submitted to Physics of Plasmas

We present analysis and simulations of electron trapping effect in the Raman pulse amplification in plasma. An ultraintense and ultrashort laser pulse is a very essential part in an advanced acceleration scheme using laser and plasma. Recently many prominent experimental observations and simulations were reported, where laser pulses of a few terawatt in power and less than 100 fs in the duration were used. To make such strong pulses, a novel scheme of using Raman backscatter in plasma was proposed and has been studied intensively. The Raman amplification in plasma does not have a restriction in material damage threshold. However, for the new amplifier to be a promising alternative of the CPA technique, more extensive studies on various issues are required. One of the fundamental issues is the electron kinetic effect such as particle trapping or wavebreaking. We describe averaged-particle-in-cell (aPIC) scheme to simulate the Raman amplification system and discuss the particle trapping effect using the aPIC model.

We augment the usual three-wave cold-fluid equations governing Raman backscatter (RBS) with a new kinetic thermal correction, proportional to an average of particle kinetic energy weighted by the ponderomotive phase. From closed-form analysis within a homogeneous kinetic three-wave model and ponderomotively averaged kinetic simulations in a more realistic pulsed case, the magnitude of these new contributions is shown to be a measure of the dynamical detuning between the pump laser, seed laser, and Langmuir wave. Saturation of RBS is analyzed, and the role of trapped particles illuminated. Simple estimates show that a small fraction of trapped particles (approximately 6%) can significantly suppress backscatter. We discuss the best operating regime of the Raman plasma amplifier to reduce these deleterious kinetic effects.

A modified version of the Plasma Beat-Wave Accelerator scheme is introduced and analyzed, which is based on autoresonant phase-locking of the nonlinear Langmuir wave to the slowly chirped beat frequency of the driving lasers via adiabatic passage through resonance. This new scheme is designed to overcome some of the well-known limitations of previous approaches, namely relativistic detuning and nonlinear modulation or other non-uniformity or non-stationarity in the driven Langmuir wave amplitude, and sensitivity to frequency mismatch due to measurement uncertainties and density fluctuations and inhomogeneities. As in previous schemes, modulational instabilities of the ionic background ultimately limit the useful interaction time, but nevertheless peak electric fields at or approaching the wave-breaking limit seem readily attainable. Compared to traditional approaches, the autoresonant scheme achieves larger accelerating electric fields for given laser intensity, or comparable fields for less laser power; the plasma wave excitation is much more robust to variations or uncertainties in plasma density; it is largely insensitive to the precise choice of chirp rate, provided only that chirping is sufficiently slow; and the quality and uniformity of the resulting plasma wave and its suitability for accelerator applications may be superior. In underdense plasmas, the total frequency shift required is only of the order of a few percent of the laser carrier frequency, and for possible experimental proofs-of-principle, the scheme might be implemented with relatively little additional modification to existing systems based on either solid-state amplifiers and Chirped Pulse Amplification techniques, or, with somewhat greater technological effort, using a CO{sub 2} or other gas laser system.

With the advent of chirped pulse amplification and related technologies, much research been devoted to laser pulse shaping for optimal wake generation in a plasma based accelerator. Also, there has been a recent proposal for a colliding beam accelerator (CBA), which uses a detuned pump laser to enhance a standard LWFA wake. We use analytic scalings and PIC simulations to illustrate optimal wake generation in the LWFA under constraints of maximum laser energy, intensity, and bandwidth. We then compare the optimized LWFA to the CBA, finding that while the addition of a pump will increase the wake of a single pulse, the CBA is inferior to a single‐ or multiple‐pulse LWFA of identical total laser energy.

The influence of gravity on antihydrogen dynamics in magnetic traps is studied. The advantages and disadvantages of various techniques for measuring the ratio of the gravitational mass to the inertial mass of antihydrogen are discussed. Theoretical considerations and numerical simulations indicate that stochasticity may be especially important for some experimental techniques in vertically oriented traps., 12 pages, 9 figures

Results are reported of a one-dimensional simulation study comparing the modeling capability of a recently formulated extended three-wave model [R. R. Lindberg, A. E. Charman, and J. S. Wurtele, Phys. Plasmas 14, 122103 (2007); Phys. Plasmas 15, 055911 (2008)] to that of a particle-in-cell (PIC) code, as well as to a more conventional three-wave model, in the context of the plasma-based backward Raman amplification (PBRA) [G. Shvets, N. J. Fisch, A. Pukhov et al., Phys. Rev. Lett. 81, 4879 (1998); V. M. Malkin, G. Shvets, and N. J. Fisch, Phys. Rev. Lett. 82, 4448 (1999); Phys. Rev. Lett. 84, 1208 (2000)]. The extended three-wave model performs essentially as well as or better than a conventional three-wave description in all temperature regimes tested, and significantly better at the higher temperatures studied, while the computational savings afforded by the extended three-wave model make it a potentially attractive tool that can be used prior to or in conjunction with PIC simulations to model the kinet...

A model of kinetic effects in Langmuir wave dynamics is presented using a nonlinear distribution function that includes particle separatrix crossing and self-consistent electrostatic evolution. This model is based on the adiabatic motion of electrons in the wave to describe Bernstein–Greene–Kruskal-like Langmuir waves over a wide range of temperatures (0.1⩽kλD⩽0.4). The asymptotic distribution function yields a nonlinear frequency shift of the Langmuir wave that agrees well with Vlasov simulations, and can furthermore be used to determine the electrostatic energy required to develop the phase-mixed, asymptotic state. From this incoherent energy, energy conservation is employed to determine a simplified model of nonlinear Landau damping. The resulting nonlinear, dynamic frequency shift and damping are then used in an extended three-wave-type model of driven Langmuir waves and compared to Vlasov simulations in the context of backward Raman scattering.A model of kinetic effects in Langmuir wave dynamics is presented using a nonlinear distribution function that includes particle separatrix crossing and self-consistent electrostatic evolution. This model is based on the adiabatic motion of electrons in the wave to describe Bernstein–Greene–Kruskal-like Langmuir waves over a wide range of temperatures (0.1⩽kλD⩽0.4). The asymptotic distribution function yields a nonlinear frequency shift of the Langmuir wave that agrees well with Vlasov simulations, and can furthermore be used to determine the electrostatic energy required to develop the phase-mixed, asymptotic state. From this incoherent energy, energy conservation is employed to determine a simplified model of nonlinear Landau damping. The resulting nonlinear, dynamic frequency shift and damping are then used in an extended three-wave-type model of driven Langmuir waves and compared to Vlasov simulations in the context of backward Raman scattering.

New solutions to the coupled three-wave equations in a nonuniform plasma medium are presented that include both space and time dependence of the waves. By including the dominant nonlinear frequency shift of the material wave, it is shown that if the driving waves are sufficiently strong in relation to the medium gradient, a nonlinearly phase-locked solution develops that is characteristic of autoresonance. In this case, the material electrostatic wave develops into a front starting at the linear resonance point and moving with the wave group velocity in a manner such that the intensity increases linearly with the propagation distance. The forms of the other two electromagnetic waves follow naturally from the Manley‐Rowe relations. © 2008 American Institute of Physics. DOI: 10.1063/1.2884717

Experiments are described in which a 1mJ, 1ps, 1200nm seed laser beam is amplified by the interaction with an intersecting 350J, 1ns, 1054nm pump beam in a low density (1×1019∕cm3) plasma. The transmission of the seed beam is observed to be enhanced by ≳25× when the plasma is near the resonant density for stimulated Raman scattering, compared to measured transmissions at wavelengths just below the resonant value. The amplification is observed to increase rapidly with increases in both pump intensity and plasma density.

Autoresonance offers an efficient and robust means for the ponderomotive excitation of nonlinear Langmuir waves by phase-locking of the plasma wave to the slowly chirped beat frequency of the driving lasers via adiabatic passage through resonance. This mechanism is analyzed for the case of a cold, relativistic, underdense electron plasma, and its suitability for particle acceleration is discussed. Compared to traditional approaches, this new autoresonant scheme achieves larger accelerating electric fields for given laser intensity; the plasma wave excitation is much more robust to variations in plasma density; it is largely insensitive to the precise choice of chirp rate, provided only that it is sufficiently slow; and the suitability of the resulting plasma wave for accelerator applications is, in some respects, superior. As in previous schemes, modulational instabilities of the ionic background ultimately limit the useful interaction time, but nevertheless peak electric fields approaching the wave-break...

The clinical findings of seven girls and one woman, 2 to 25 years of age, with Rett syndrome are presented. Previous diagnoses included Prader-Willi syndrome, Angleman syndrome, toxic reaction to pertussis vaccine, CNS dysgenesis, and encephalitis. Rett syndrome has a recognizable neurodevelopmental phenotype without a specific biologic marker, which makes the diagnosis difficult at times. Treatment is largely supportive, and an active parents' association has been helpful to many families.

The clinical findings of seven girls and one woman, 2 to 25 years of age, with Rett syndrome are presented. Previous diagnoses included Prader-Willi syndrome, Angleman syndrome, toxic reaction to pertussis vaccine, CNS dysgenesis, and encephalitis. Rett syndrome has a recognizable neurodevelopmental phenotype without a specific biologic marker, which makes the diagnosis difficult at times. Treatment is largely supportive, and an active parents' association has been helpful to many families.

We report 40 cases of postnatal plagiocephaly seen over a 6 yr period (1981-86). Twenty cases had mild to moderate plagiocephaly (10 males, 10 females) due to muscular torticollis and responded to physical therapy and repositioning within the first few months of life. In 3 instances, a head positioning device was helpful; in 2 instances where no consistent therapy was attempted the cranial deformity persisted. An additional 9 cases had severe plagiocephaly due to persistent muscular torticollis (8 males, 1 female). When the above measures failed to correct cranial symmetry by 5 to 6 months, helmet therapy was instituted with excellent results. Another 5 cases (3 males, 2 females), had marked occipital flattening from prolonged use of an Infant Seat; 3 improved with repositioning alone, while 2 with associated muscular torticollis required either head positioning device or helmet. Four children with medical problems resulting in prolonged recumbency (CNS abnormalities, intestinal atresia, TE fistula) and associated mild torticollis, responded to simple repositioning. Two other children with unremitting torticollis due to Klippel-Feil anomaly required helmet therapy. Neck stretching exercises and repositioning were most effective in correcting plagiocephaly when instituted early in the first year of life. When torticollis was severe (more common in males) or due to underlying vertebral anomalies, helmet therapy was effective.

This paper summarizes the clinical findings of 7 girls diagnosed in 1985-86 as having Rett syndrome. Ages ranged from 3.5 to 25 years. Abnormalities of gestation were noted: Neonatal feeding problems (3/7) and positional deformities (3/7)[including hip suppluxation (1), metatarsus adduction (1), “windswept feet” (1)] were identified. Postnatal growth abnormalities included: 7/7 head growth deceleration, 3/7 microcephalic, 7/7 statural growth deceleration, 6/7 short stature. In 6/7 girls, developmental delays were noted prior to true psychomotor regression. In only one girl was there clear documentation of normal development followed by marked deterioration. Age at onset of delays ranged from 6-12 months, with psychomotor regression noted from 10-34 months. Typical hand stereotypy started between 2-3 years in all. Other findings: 6/7 trunk ataxia, 1/7 ambulatory (with gait apraxia), 6/7 seizures, 5/7 strabismus, 4/7 scoliosis, 6/7 had irritability and/or self-injury with music or motion helpful in 2 girls. These gestational abnormalities, neonatal findings and early psychomotor delays prior to regression are important additional phenotypic findings. Until a reliable genetic or biochemical marker is available, the diagnosis of this syndrome rests on the recognizable neurodevelopmental pheno type.