Accurate light-time correction due to a gravitating mass

Path integrals with discarded degrees of freedom

The stroke patient population is heterogeneous, leading to wide variation in outcome caused by differences in age, initial severity, and presence of concomitant disease. Setting an identical recovery target for all patients in intervention trials may conceal individually important therapeutic treatment effects. Instead, a variable end point that takes severity or likely prognosis into account may be more informative. We used data from the Glycine Antagonist in Neuroprotection (GAIN) International trial to assess statistical power of various primary end points for intervention trials. We selected prognosis-adjusted cut points based on Barthel Index (BI) or Rankin Scale (RS) using a prognostic model, or assigned a fixed end point within subgroups of patients defined by their Oxford category or National Institutes of Health Stroke Scale (NIHSS) score. We simulated a treatment effect and estimated statistical power with standard formulae. Assignment of end points using a prognostic model for individual patients increased statistical power, when compared with assigning end points using only the Oxford classification. For the BI, power was increased from 60% to 88% (equivalent to a 49% reduction in sample size if power remains unchanged). With the RS end points, power was increased from 84% to 92% (or a 24% reduction in sample size). Versus a fixed end point for all patients, model-based methods increased power by 22 percentage points for BI> or =95 and 14 percentage points for RS< or =1 (effective sample size reductions 43% and 34%). Prognosis-adjusted end points can increase statistical power compared with fixed end points. Assessment is based on realistic goals for individual patients and yet trial results remain generalizable.

The conductance of graphene nanoribbons and nanoconstrictions under the effect of a scanning gate microscopy tip is systematically studied. Using a scattering approach for noninvasive probes, the first- and second-order conductance corrections caused by the tip potential disturbance are expressed explicitly in terms of the scattering states of the unperturbed structure. Numerical calculations confirm the perturbative results, showing that the second-order term prevails in the conductance plateaus, exhibiting a universal scaling law for armchair graphene strips. For stronger tips, at specific probe potential widths and strengths beyond the perturbative regime, the conductance corrections reveal the appearance of resonances originated from states trapped below the tip. The zero-transverse-energy mode of an armchair metallic strip is shown to be insensitive to the long-range electrostatic potential of the probe. For nanoconstrictions defined on a strip, scanning gate microscopy allows to get insight into the breakdown of conductance quantization. The first-order correction generically dominates at low tip strength, while for Fermi energies associated with faint conductance plateaus, the second-order correction becomes dominant for relatively small potential tip strengths. In accordance with the spatial dependence of the partial local density of states, the largest tip effect occurs in the central part of the constriction, close to the edges. Nanoribbons and nanoconstrictions with zigzag edges exhibit a similar response as in the case of armchair nanostructures, except when the intervalley coupling induced by the tip potential destroys the chiral edge states.

We propose a perturbative method to compute the deflection angle of both null and massive particles for source and detector at finite distance. This method applies universally to the motion of particles with general velocity in the equatorial plane of stationary axisymmetric spacetimes or static spherical symmetric spacetimes that are asymptotically flat. The resultant deflection angle automatically arranges into a quasi-inverse series form of the impact parameter, with coefficients depending on the metric functions, the signal velocity and the source and detector locations through the apparent angles. In the large impact parameter limit, the series coefficients are reduced to rational functions of sine/cosine functions of the zeroth order apparent angle.

We investigate the limitations of the first-order nonlinear Schrödinger equation for describing slow-light enhanced optical nonlinearities in photonic crystal structures. We do this by introducing the concept of generalized Bloch modes to describe light propagation in nonlinear photonic crystal structures. By considering how the nonlinear effects perturb the eigenproblem that describes such generalized Bloch modes, we derive a formalism that allows us to determine the impact of nonlinearities up to an arbitrary order. Based on our formalism, we derive expressions for the first- and second-order nonlinear terms experienced by a single generalized Bloch mode. We then theoretically demonstrate that the second-order terms can in silicon-based slow-light photonic crystal waveguides already become significant at optical powers as small as 100 mW. Additionally, we show that the significance of the second-order term is closely related with the structural group index dispersion or second-order dispersion parameter of the structures considered.

Assessing validity and reliability of end points used in docosahexanoic and arachidonic acids (DHA and ARA) infant formula supplementation trials as an example for addressing the impact of end-point selection and critical need for well-defined, reliable and validated clinical outcome assessments for neurocognitive assessment in neonates and infants. We searched eight electronic databases and reviewed all randomized, controlled human trials using DHA/ARA supplements with neurodevelopment clinical outcomes. We systematically evaluated the validity and reliability of end-point measures based on the criteria for studying nutritional additives recommended by the Institute of Medicine, criteria described in the Food and Drug Administration guidance for clinical outcome assessment, development and literature review. We identified 29 articles that met the selection criteria. The end points that were used for neurodevelopment measures in 23 out of 29 original short-term studies included the Bayley Scale of Infant Development (BSID)-I and -II (n=12), Brunet-Lezine test (n=2), videotape infant's movements (n=1), record time to milestones including sitting, crawling, standing and walking (n=1), problem-solving test (n=2), brainstem auditory-evoked potential (n=1), Touwen examination (n=1), Fagan test of infant intelligence (n=2) and visual habituation protocol (n=1). None of these end points have a long-term predictive property for neurocognitive assessment. Compared with standard infant formula, the beneficial effects of DHA/ARA supplementation on neurodevelopment were reported in 2 out of 12 studies using BSID vs 8 out of 11 studies using other end-point measures. In addition, 6 out of 29 long-term follow-up studies used the end points including Stanford-Binet IQ test (n=1), Wechsler Preschool and Primary Scale of Intelligence (n=4) and Bracken Basic Concept Scale (n=1), which are generally scales of intellectual ability and typically do not change substantively in the short term. None of these long-term follow-up studies demonstrated beneficial effects of DHA/ARA supplementation on neurodevelopment. The choice of end-point measures affects the outcomes of DHA/ARA-supplemented infant formula trials. Available data are currently inadequate to conclude that DHA/ARA supplementation has a clinically meaningful beneficial effect upon neurological development. Although BSID is validated to assess early developmental delays, it is not designed to predict long-term neurocognitive outcome. A well-defined, valid and reliable clinical outcome assessment that measures neurocognitive function in neonates and infants is essential to provide the scientific evidence required for future clinical trials.

There is an increasing interest in the photoinduced dynamics in the low frequency, ω, regime. The multiphoton absorptions by molecules in strong laser fields depend on the polarization of the laser and on the molecular structure. The unique properties of the interaction of atoms and molecules with lasers in the low-frequency regime imply new concepts and directions in strong-field light-matter interactions. Here we represent a perturbational approach for the calculations of the quasi-energy spectrum in the low-frequency regime, which avoids the construction of the Floquet operator with extremely large number of Floquet channels. The zero-order Hamiltonian in our perturbational approach is the adiabatic Hamiltonian where the atoms/molecules are exposed to a dc electric field rather than to ac-field. This is in the spirit of the first step in the Corkum three-step model. The second-order perturbation correction terms are obtained when iℏω∂∂τ serves as a perturbation and τ is a dimensionless variable. The second-order adiabatic perturbation scheme is found to be an excellent approach for calculating the ac-field Floquet solutions in our test case studies of a simple one-dimensional time-periodic model Hamiltonian. It is straightforward to implement the perturbation approach presented here for calculating atomic and molecular energy shifts (positions) due to the interaction with low-frequency ac-fields using high-level electronic structure methods. This is enabled since standard quantum chemistry packages allow the calculations of atomic and molecular energy shifts due to the interaction with dc-fields. In addition to the shift of the energy positions, the energy widths (inverse lifetimes) can be obtained at the same level of theory. These energy shifts are functions of the laser parameters (low frequency, intensity, and polarization).

The results obtained in our previous paper are now extended to the case of stationary axially symmetric dyonic black boles within the theory of two electromagnetic potentials. We slightly enlarge the classical Ernst formalism by introducing, with the aid of the $t$- and $\varphi$-components of the dual potential $B_\mu$, the magnetic potential $\Phi_m$ which, similar to the known electric potential $\Phi_e$, also takes constant value on the black hole horizon. We analyze in detail the case of the dyonic Kerr-Newman black hole and show how the Komar mass must be evaluated correctly in this stationary dyonic model. In particular, we rigorously prove the validity of the standard Tomimatsu mass formula and point out that attempts to "improve" it made in recent years are explained by misunderstanding of the auxiliary role that singular potentials play in the description of magnetic charges. Our approach is symmetrical with respect to electric and magnetic charges and, like in the static case considered earlier, Dirac strings of all kind are excluded from the physical picture of the stationary black hole dyonic spacetimes.

To improve the performance of typical first-order bandgap references, a high precision bandgap voltage reference with second-order curvature correction is proposed in this paper. Utilizing a temperature independent current (has nothing to do with the temperature of first order) and a proportional to absolute temperature (PTAT) current, a proportional to the square of temperature (PTAT2) current can be generated, which can be further used to compensate the second-order term in the Taylor-series expansion of the diode voltage, and the precision of the voltage reference is improved. The design was verified in a Bi-CMOS process, and simulation results showed that the temperature of the designed voltage reference was 10 ppm/°C at the temperature range from −45°C to 125°C and the consumed current was 7 µA at 5V supply voltage.

In this work, we develop a general perturbative procedure to determine the off-equatorial plane deflections in the weak deflection limit in general stationary and axisymmetric spacetimes, enabling the existence of the generalized Carter constant. Deflections of both null and timelike rays, with the finite distance effect of the source and detector considered, are obtained as dual series of and . These deflections enable a set of exact gravitational lensing equations from which the apparent angular positions of the images are solved. The method and general results are then applied to the Kerr-Newmann, Kerr-Sen, and rotating Simpson-Visser spacetimes to study the effect of the spin and characteristic (effective) charge of the spacetimes and the source altitude on the deflection angles and image apparent angles. We find that, generally, both the spacetime spin and charge affect only the deflections from the second non-trivial order, whereas the source altitude influences the deflection from the leading order. Because of this, measuring the effects of the spacetime spin and charge from the apparent locations of the images in gravitational lensing in realistic scenarios is difficult. We also present the off-equatorial deflections in the rotating Bardeen, Hayward, Ghosh, and Tinchev black hole spacetimes.

A systematic theory of the conductance measurements of noninvasive (weak probe) scanning gate microscopy is presented that provides an interpretation of what precisely is being measured. A scattering approach is used to derive explicit expressions for the first- and second-order conductance changes due to the perturbation by the tip potential in terms of the scattering states of the unperturbed structure. In the case of a quantum point contact, the first-order correction dominates at the conductance steps and vanishes on the plateaux where the second-order term dominates. Both corrections are nonlocal for a generic structure. Only in special cases, such as that of a centrally symmetric quantum point contact in the conductance quantization regime, can the second-order correction be unambiguously related with the local current density. In the case of an abrupt quantum point contact, we are able to obtain analytic expressions for the scattering eigenfunctions and thus evaluate the resulting conductance corrections.

The Pancharatnam phase for the entangled state of a single three-level atom interacting with a single electromagnetic field mode has been studied. The exact results are employed to perform a careful investigation of the influence of the second-order correction to Rayleigh scattering on the atomic level occupation probabilities as well as the Pancharatnam phase. It is shown that the Pancharatnam phase explicity contains information about the statistics of the field and atomic coherence. The addition of a second-order correction term has an important effect on the properties of the Pancharatnam phase. The results show that the effect of the second-order correction term changes the quasi-period of the Pancharatnam phase evolution.

Muon capture by a nucleus with an arbitrary spin is considered. Second-order terms in 1/M in the effective weak-interaction Hamiltonian are taken into account. New terms in the Hamiltonian associated with the nucleon-nucleus potential are found. A general expression for the angular distribution of neutrinos (recoil nuclei) is derived for polarized muons and oriented target nuclei. Second-order contributions to the amplitudes M u (k) are obtained. This allows one to calculate second-order corrections to any integral and correlation characteristics in muon capture that are expressed in terms of M u (k).

Prognostic Value of Late Heart Rate Recovery After Treadmill Exercise

A new approach for predicting the extreme response of structures