Structure of the set of paraxial optical systems.

The set of paraxial optical systems is the manifold of the group of symplectic matrices. The structure of this group is nontrivial: It is not simply connected and is not of an exponential type. Our analysis clarifies the origin of the metaplectic phase and the inherent limitations for optical map fractionalization. We describe, for the first time to our knowledge, an image girator and a cross girator whose geometric and wave implementations are of interest.

Covariant discretization of axis-symmetric linear optical systems.

We propose a discretization strategy for systems with axial symmetry. This strategy replaces the continuous position coordinates by a discrete set of sensor points, on which the discrete wave fields transform covariantly with the group of 2 x 2 symplectic matrices. We examine polar arrays of sensors (i.e., numbered by radius and angle) and find the complete, orthonormal sets of discrete-waveguide Meixner functions; when the sensors come closer together, these tend to the Laguerre eigenmodes of the continuous waveguide. In particular, the fractional Hankel transforms are discretized in order to define the fractional Hankel-Meixner transforms and similarly for all axis-symmetric linear optical maps. Coherent states appear in the discrete cylindrical waveguide. Covariant discretization leads to the same Wigner phase-space function for both the discrete and the continuum cases. This reinforces a Lie-theoretical model for the phase space of discrete systems.

Fractional Fourier transforms in two dimensions.

We analyze the fractionalization of the Fourier transform (FT), starting from the minimal premise that repeated application of the fractional Fourier transform (FrFT) a sufficient number of times should give back the FT. There is a qualitative increase in the richness of the solution manifold, from U(1) (the circle S1) in the one-dimensional case to U(2) (the four-parameter group of 2 x 2 unitary matrices) in the two-dimensional case [rather than simply U(1) x U(1)]. Our treatment clarifies the situation in the N-dimensional case. The parameterization of this manifold (a fiber bundle) is accomplished through two powers running over the torus T2 = S1 x S1 and two parameters running over the Fourier sphere S2. We detail the spectral representation of the FrFT: The eigenvalues are shown to depend only on the T2 coordinates; the eigenfunctions, only on the S2 coordinates. FrFT's corresponding to special points on the Fourier sphere have for eigenfunctions the Hermite-Gaussian beams and the Laguerre-Gaussian beams, while those corresponding to generic points are SU(2)-coherent states of these beams. Thus the integral transform produced by every Sp(4, R) first-order system is essentially a FrFT.

Generalized Wigner function for the analysis of superresolution systems.

The generalized Wigner function is able to represent light distributions that contain spatial and temporal information. The use of such a generalized Wigner distribution function for analysis and understanding of temporally restricted superresolving systems is demonstrated. These systems gain spatial resolution by conversion of the temporal degrees of freedom to spatial degrees of freedom.

Bidirectional interaction of valproate and lamotrigine in healthy subjects.

OBJECTIVE: To evaluate the steady-state pharmacokinetics of lamotrigine and valproate at three dosing levels of lamotrigine in normal volunteers receiving steady-state therapeutic doses of valproate. METHODS: This was an open-label, randomized, three-way crossover study of 18 normal male volunteers. Subjects received oral valproate (500 mg Depakote twice a day) throughout the study. Each subject subsequently received three oral dosage regimens of lamotrigine (50, 100, or 150 mg/day) for 1 week each, with a 2-week washout period between lamotrigine treatment periods. Valproate and lamotrigine trough plasma samples were determined by a capillary gas chromatography method and immunofluorometric assay, respectively. Urine samples were assayed for 11 valproate metabolites by gas chromatography/mass spectrometry. RESULTS: When compared to other studies in which lamotrigine was administered with no concurrent antiepileptic drug, concomitant valproate markedly increased the half-life of lamotrigine and decreased lamotrigine clearance, without substantial alteration in the linear kinetics of the drug. The addition of lamotrigine was associated with a small but significant 25% decrease in steady-state valproate plasma concentration. Oral clearance of valproate was increased (from 7.2 +/- 1.1 ml/hr/kg before lamotrigine treatment to 9.0 +/- 2.0 ml/hr/kg on day 28; p < 0.05). The formation clearance of the hepatotoxic valproate metabolites, 2-n-propyl-4-pentenoic acid (4-ene-valproate) and 2-propyl-2,4-pentadienoic acid [2(E),4-diene-valproate], was unaffected by lamotrigine administration. CONCLUSIONS: As a consequence of the interaction between lamotrigine and sodium valproate, a dosage reduction of lamotrigine should be considered in patients taking a combination of valproate and lamotrigine.

Pharmacodynamics and pharmacokinetics of cisatracurium in geriatric surgical patients.

BACKGROUND: Cisatracurium, one of ten stereoisomers that comprise atracurium, is more potent than atracurium and has less propensity to release histamine. This study compares the pharmacokinetics and pharmacodynamics of cisatracurium in elderly and young patients. METHODS: Twelve elderly (aged 65-82 yr) and 12 younger patients (aged 30-49 yr) were anesthetized with nitrous oxide, fentanyl, and isoflurane (0.7%, end-tidal). The mechanomyographic response to train-of-four stimulation was assessed every 15 s after the administration of cisatracurium (0.1 mg/kg). Arterial samples were obtained over 6 h. Plasma cisatracurium concentration versus time data were fit to compartmental models. Pharmacokinetic parameters were determined assuming that elimination occurred from the central compartment only. This provides accurate clearance and half-life estimates but underestimates V(ss) (reported herein as V(ss). The pharmacodynamic response was described by the neuromuscular blocking profile. RESULTS: Onset to 90% paralysis (mean +/- SD) was delayed in the elderly (3.4 +/- 1.0 vs. 2.5 +/- 0.6 min). Recovery profiles were the same for both groups. Elimination half-life was minimally prolonged in the elderly (25.5 +/- 3.7 vs. 21.5 +/- 2.4 min). The Vss was larger in the elderly (126 +/- 16 vs. 108 +/- 13 ml/kg), although the clearances were the same for the two groups (5.0 +/- 0.9 vs. 4.6 +/- 0.8 ml.kg(-1).min(-1). CONCLUSIONS: There are minor differences in the pharmacokinetics of cisatracurium between elderly and young patients. These differences are not associated with changes in recovery profile after a single bolus dose, although the mean time to onset was approximately 1 min longer in elderly patients.