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Abstract We continue the study of random matrix universality in two-dimensional conformal field theories. This is facilitated by expanding the spectral form factor in a basis of modular invariant eigenfunctions of the Laplacian on the fundamental domain. The focus of this paper is on the discrete part of the spectrum, which consists of the Maass cusp forms. Both their eigenvalues and Fourier coefficients are sporadic discrete numbers with interesting statistical properties and relations to analytic number theory; this is referred to as ‘arithmetic chaos’. We show that the near-extremal spectral form factor at late times is only sensitive to a statistical average over these erratic features. Nevertheless, complete information about their statistical distributions is encoded in the spectral form factor if all its spin sectors exhibit universal random matrix eigenvalue repulsion (a ‘linear ramp’). We ‘bootstrap’ the spectral correlations between the cusp form basis functions that correspond to a universal linear ramp and show that they are unique up to theory-dependent subleading corrections. The statistical treatment of cusp forms provides a natural avenue to fix the subleading corrections in a minimal way, which we observe leads to the same correlations as those described by the [torus]×[interval] wormhole amplitude in AdS3 gravity.

This paper reintroduces the Effortless Assessment Research System (EARS), 4 years and 10,000 participants after its initial launch. EARS is a mobile sensing tool that affords researchers the opportunity to collect naturalistic, behavioral data via participants’ naturalistic smartphone use. The first section of the paper highlights improvements made to EARS via a tour of EARS’s capabilities—the most important of which is the expansion of EARS to the iOS operating system. Other improvements include better keyboard integration for the collection of typed text; full control of survey design and administration for research teams; and the addition of a researcher-facing EARS dashboard, which facilitates survey design, the enrollment of participants, and the tracking of participants. The second section of the paper goes behind the scenes to describe 3 challenges faced by the EARS developers—remote participant enrollment and tracking, keeping EARS running in the background, and continuous attention and effort toward data protection—and how those challenges shaped the design of the app.

Abstract Wildfires are increasingly impacting high‐elevation forests in the western United States that accumulate seasonal snowpacks, presenting a major disturbance to a critical water reservoir for the region. In the first winter following the 2020 Cameron Peak wildfire in Colorado, the peak snow water equivalent in a high burn severity forest was 17%–25% less than nearby unburned sites. The loss of the forest canopy and a lower surface albedo led to an increasingly positive net shortwave radiation balance in the burned area, resulting in melt rates that were 82%–144% greater than unburned sites and snow disappearance occurred 11–13 days earlier. Late‐season snow storms temporarily buried soot, thus increasing the albedo and delaying melt‐out by an estimated 4 days per storm in our study area. While these storms temporarily reduce the higher melt rates imposed by wildfire impacts, SNOTEL measurements show that they occur non‐uniformly across the western U.S.

Abstract When does a holographic CFT with a boundary added to it (a BCFT) also have a ‘good’ holographic dual with a localized gravitating end-of-the-world brane? We argue that the answer to this question is almost never. By studying Lorentzian BCFT correlators, we characterize constraints imposed on a BCFT by the existence of a bulk causal structure. We argue that approximate ‘bulk brane’ singularities place restrictive constraints on the spectrum of a BCFT that are not expected to be true generically. We discuss how similar constraints implied by bulk causality might apply in higher-dimensional holographic descriptions of BCFTs involving a degenerating internal space. We suggest (although do not prove) that even these higher-dimensional holographic duals are not generic.

In this paper, we survey the emerging design space of expandable structures in robotics, with a focus on how such structures may improve human-robot interactions. We detail various implementation considerations for researchers seeking to integrate such structures in their own work and describe how expandable structures may lead to novel forms of interaction for a variety of different robots and applications, including structures that enable robots to alter their form to augment or gain entirely new capabilities, such as enhancing manipulation or navigation, structures that improve robot safety, structures that enable new forms of communication, and structures for robot swarms that enable the swarm to change shape both individually and collectively. To illustrate how these considerations may be operationalized, we also present three case studies from our own research in expandable structure robots, sharing our design process and our findings regarding how such structures enable robots to produce novel behaviors that may capture human attention, convey information, mimic emotion, and provide new types of dynamic affordances.

Abstract We study two novel approaches to efficiently encoding universal constraints imposed by conformal symmetry, and describe applications to quantum chaos in higher dimensional CFTs. The first approach consists of a reformulation of the shadow operator formalism and kinematic space techniques. We observe that the shadow operator associated with the stress tensor (or other conserved currents) can be written as the descendant of a field ε with negative dimension. Computations of stress tensor contributions to conformal blocks can be systematically organized in terms of the “soft mode” ε, turning them into a simple diagrammatic perturbation theory at large central charge. Our second (equivalent) approach concerns a theory of reparametrization modes, generalizing previous studies in the context of the Schwarzian theory and two-dimensional CFTs. Due to the conformal anomaly in even dimensions, gauge modes of the conformal group acquire an action and are shown to exhibit the same dynamics as the soft mode ε that encodes the physics of the stress tensor shadow. We discuss the calculation of the conformal partial waves or the conformal blocks using our effective field theory. The separation of conformal blocks from shadow blocks is related to gauging of certain symmetries in our effective field theory of the soft mode. These connections explain and generalize various relations between conformal blocks, shadow operators, kinematic space, and reparametrization modes. As an application we study thermal physics in higher dimensions and argue that the theory of reparametrization modes captures the physics of quantum chaos in Rindler space. This is also supported by the observation of the pole skipping phenomenon in the conformal energy-energy two-point function on Rindler space.

A method is presented that reconstructs the amplitude and phase of an unknown time-dependent pure-state wave function entirely from experimental position data. No assumptions about the wave function are needed. At a series of times, a large collection of position data is taken, but no measurements of momentum or energy are necessary. The momenta, however, are required for the reconstruction of the wave function and are supplied by analysis of the position data via quantum particle trajectories. Simulations of the method are provided for helium atoms in single and double slit experiments., (© 2011 American Physical Society)

The scattered wave formalism developed for a quantum subsystem interacting with reservoirs through open boundaries is applied to one- or two-dimensional barrier scattering and quantum transistors. The total wave function is divided into incident and scattered components. Markovian outgoing wave boundary conditions are imposed on the scattered or total wave function by either the ratio or polynomial methods. For barrier scattering problems, accurate time-dependent transmission probabilities are obtained through the integration of the modified time-dependent Schrödinger equations for the scattered wave function. For quantum transistors, the time-dependent transport is studied for a quantum wave packet propagating through the conduction channel of a field effect transistor. This study shows that the scattered wave formalism significantly reduces computational effort relative to other open boundary methods and demonstrates wide applications to quantum dynamical processes.

A Cauchy initial-value approach to the complex-valued quantum Hamilton-Jacobi equation (QHJE) is investigated for multidimensional systems. In this approach, ray segments foliate configuration space which is laminated by surfaces of constant action. The QHJE incorporates all quantum effects through a term involving the divergence of the quantum momentum function (QMF). The divergence term may be expressed as a sum of two terms, one involving displacement along the ray and the other incorporating the local curvature of the action surface. It is shown that curvature of the wave front may be computed from coefficients of the first and second fundamental forms from differential geometry that are associated with the surface. Using the expression for the divergence, the QHJE becomes a Riccati-type ordinary differential equation (ODE) for the complex-valued QMF, which is parametrized by the arc length along the ray. In order to integrate over possible singularities in the QMF, a stable and accurate Möbius propagator is introduced. This method is then used to evolve rays and wave fronts for four systems in two and three dimensions. From the QMF along each ray, the wave function can be easily computed. Computational difficulties that may arise are described and some ways to circumvent them are presented., (© 2011 American Institute of Physics)

The scattered wave formalism is developed for a quantum subsystem interacting with the external environment through open boundaries. The total wave function is divided into incident and scattered components and Markovian outgoing wave boundary conditions are applied to the scattered wave function. This formalism significantly reduces the computational effort relative to other methods which rely on Green functions and memory kernels. The method is applied to one-dimensional barrier scattering and to a three-dimensional model for the field effect transistor.

Complex-extended Bohmian mechanics is investigated by analytically continuing the wave function in polar form into the complex plane. We derive the complex-extended version of the quantum Hamilton-Jacobi equation and the continuity equation in Bohmian mechanics. Complex-extended Bohmian mechanics recovers the standard real-valued Bohmian mechanics on the real axis. The trajectories on the real axis are in accord with the standard real-valued Bohmian trajectories. The trajectories launched away from the real axis never intersect the real axis, and they display symmetry with respect to the real axis. Trajectories display hyperbolic deflection around nodes of the wave function in the complex plane.

Wave-packet interference is investigated within the complex quantum Hamilton-Jacobi formalism using a hydrodynamic description. Quantum interference leads to the formation of the topological structure of quantum caves in space-time Argand plots. These caves consist of the vortical and stagnation tubes originating from the isosurfaces of the amplitude of the wave function and its first derivative. Complex quantum trajectories display counterclockwise helical wrapping around the stagnation tubes and hyperbolic deflection near the vortical tubes. The string of alternating stagnation and vortical tubes is sufficient to generate divergent trajectories. Moreover, the average wrapping time for trajectories and the rotational rate of the nodal line in the complex plane can be used to define the lifetime for interference features.

In two previous studies, the time-dependent scattering of a wave packet from a Gaussian barrier was investigated computationally in the complex z-plane. One of these involved the 'direct' propagation of the wave packet in the complex space, and the other used numerical analytic continuation techniques to generate the dynamics in the complex plane from the wave function computed on the real-axis. In the current study, the dynamics of exact quantum trajectories are analyzed for the same barrier scattering problem. Thousands of quantum trajectories were launched from positions near the center of the initial wave packet. These trajectories were computed by integrating equations-of-motion involving the quantum momentum function, which was obtained from the time-dependent wave function and its derivative. In order to analyze the dynamics, many trajectories were plotted on space-time diagrams. Particular emphasis was placed upon trajectories undergoing reflection in the barrier region. Some groups of strongly correlated trajectories form long-lived highly organized patterns, including helical wrappings around a series of stagnation filaments. These curves alternate with quasi-nodes where the amplitude of the wave function reaches low values. In addition, other trajectories for short times follow hyperbolic paths as they propagate near vorticity tubes surrounding these quasi-nodes.

The time-dependent scattering of a wave packet from a Gaussian barrier is investigated computationally in the complex z-plane. The initial wave packet and the potential energy are obtained through analytic continuation from functions specified on the real-axis. The wave packet is then propagated on the two-dimensional grid. For a low initial wave packet energy, the time evolution is followed by plotting the following functions: |ψ(z,t)|, real(ψ(z,t)), and the quantum momentum function (QMF), p(z,t). In the reflected packet, an important role is played by ripples (quasi-nodes) forming above the real axis. As these quasi-nodes move down across the real axis, they are 'detected' as 'interference oscillations' in the density. In contrast, the component of the packet below the real axis makes a significant contribution to the transmitted packet. Vector maps of the QMF show hyperbolic flow around quasi-nodes and counterclockwise circular flow around transient stagnation points, where the QMF vanishes. However, when the Pólya vector field (defined by P(z,t) = p*(z,t)) is plotted, circular counterclockwise flow is obtained near the quasi-nodes. The real and imaginary parts of the quantum action function S(z,t) are plotted and the vorticity, defined by the curl of the Pólya field, is used to pinpoint regions of nonanalyticity in the QMF.

The moving boundary truncation (MBT) method is a time-dependent adaptive method that can significantly reduce the number of grid points needed to perform accurate wave packet propagation while maintaining stability. This work presents a more robust variation of the method. Significant improvements have been made that allow the MBT method to be applied to any potential energy surface and used with any propagation method. The new variation of MBT is applied to the collinear H + H(2) reaction (using a LEPS potential) to demonstrate the stability and accuracy. Reaction probabilities are calculated for the three-dimensional nonrotating O((3)P) + H(2) and O((3)P) + HD reactions to demonstrate that the MBT can be used with a variety of numerical propagation techniques.

Quantum streamlines are investigated in the framework of the quantum Hamilton-Jacobi formalism. The local structures of the quantum momentum function (QMF) and the Polya vector field near a stagnation point or a pole are analyzed. Streamlines near a stagnation point of the QMF may spiral into or away from it, or they may become circles centered on this point or straight lines. Additionally, streamlines near a pole display east-west and north-south opening hyperbolic structure. On the other hand, streamlines near a stagnation point of the Polya vector field for the QMF display general hyperbolic structure, and streamlines near a pole become circles enclosing the pole. Furthermore, the local structures of the QMF and the Polya vector field around a stagnation point are related to the first derivative of the QMF; however, the magnitude of the asymptotic structures for these two fields near a pole depends only on the order of the node in the wave function. Two nonstationary states constructed from the eigenstates of the harmonic oscillator are used to illustrate the local structures of these two fields and the dynamics of the streamlines near a stagnation point or a pole. This study presents the abundant dynamics of the streamlines in the complex space for one-dimensional time-dependent problems.

Quantum vortices are investigated in the framework of the quantum Hamilton-Jacobi formalism. A quantum vortex forms around a node in the wave function in the complex space, and the quantized circulation integral originates from the discontinuity in the real part of the complex action. Although the quantum momentum field displays hyperbolic flow around a node, the corresponding Polya vector field displays circular flow. It is shown that the Polya vector field of the quantum momentum function is parallel to contours of the probability density. A nonstationary state constructed from eigenstates of the harmonic oscillator is used to illustrate the formation of a transient excited state quantum vortex, and the coupled harmonic oscillator is used to illustrate quantization of the circulation integral in the multidimensional complex space. This study not only analyzes the formation of quantum vortices but also demonstrates the local structures for the quantum momentum field and for the Polya vector field near a node of the wave function.

One-dimensional time-independent scattering problems are investigated in the framework of the quantum Hamilton-Jacobi formalism. The equation for the local approximate quantum trajectories near the stagnation point of the quantum momentum function is derived, and the first derivative of the quantum momentum function is related to the local structure of quantum trajectories. Exact complex quantum trajectories are determined for two examples by numerically integrating the equations of motion. For the soft potential step, some particles penetrate into the nonclassical region, and then turn back to the reflection region. For the barrier scattering problem, quantum trajectories may spiral into the attractors or from the repellers in the barrier region. Although the classical potentials extended to complex space show different pole structures for each problem, the quantum potentials present the same second-order pole structure in the reflection region. This paper not only analyzes complex quantum trajectories and the total potentials for these examples but also demonstrates general properties and similar structures of the complex quantum trajectories and the quantum potentials for one-dimensional time-independent scattering problems.

To facilitate the search for isochrones when using complex-valued trajectory methods for quantum barrier scattering calculations, the structure and shape of isochrones in the complex plane were studied. Isochrone segments were categorized based on their distinguishing features, which are shared by each situation studied: High and low energy wave packets, scattering from both thick and thin Gaussian and Eckart barriers of varying height. The characteristic shape of the isochrone is a trifurcated system: Trajectories that transmit the barrier are launched from the lower branch (T), while the middle and upper branches form the segments for reflected trajectories (F and B). In addition, a model is presented for the curved section of the lower branch (from which transmitted trajectories are launched), and important features of the complex extension of the initial wave packet are identified.

One of the major obstacles in employing complex-valued trajectory methods for quantum barrier scattering calculations is the search for isochrones. In this study, complex-valued derivative propagation method trajectories in the arbitrary Lagrangian-Eulerian frame are employed to solve the complex Hamilton-Jacobi equation for quantum barrier scattering problems employing constant velocity trajectories moving along rectilinear paths whose initial points can be in the complex plane or even along the real axis. It is shown that this effectively removes the need for isochrones for barrier transmission problems. Model problems tested include the Eckart, Gaussian, and metastable quadratic+cubic potentials over a variety of wave packet energies. For comparison, the "exact" solution is computed from the time-dependent Schrodinger equation via pseudospectral methods.

In this study, an analysis of the one-dimensional Eckart and Gaussian barrier scattering problems is undertaken using approximate quantum trajectories. Individual quantum trajectories are computed using the derivative propagation method (DPM). Both real-valued and complex-valued DPM quantum trajectories are employed. Of interest are the deep tunneling and the higher energy barrier scattering problems in cases in which the scattering barrier is "thick" by comparison to the width of the initial wave packet. For higher energy scattering problems, it is found that real-valued DPM trajectories very accurately reproduce the transmitted probability densities at low orders when compared to large fixed-grid calculations. However, higher orders must be introduced to obtain good probabilities for deep tunneling problems. Complex-valued DPM is found to accurately reproduce transmitted probability densities at low order for both the deep tunneling and the higher energy scattering problems. Of particular note, complex-classical trajectories are found to very nearly give the exact result for the deep barrier tunneling scattering problem, and the complex DPM converges well at high orders for these thick barrier scattering problems. A variety of analyses are performed to elucidate the dynamics of complex-valued DPM trajectories. The complex-extended barrier potentials are examined in detail, including an analysis of the complex force. Of particular interest are initial conditions for complex-valued DPM trajectories known as isochrones. All trajectories launched from an isochrone arrive on the real axis on the transmitted side of the barrier at the same time. The computation and properties of isochrones as well as the behavior of the initial wave packet in the complex plane are also examined.

The quantum Hamilton-Jacobi equation for the action function is approximately solved by propagating individual Lagrangian quantum trajectories in complex-valued phase space. Equations of motion for these trajectories are derived through use of the derivative propagation method (DPM), which leads to a hierarchy of coupled differential equations for the action function and its spatial derivatives along each trajectory. In this study, complex-valued classical trajectories (second order DPM), along which is transported quantum phase information, are used to study low energy barrier transmission for a model two-dimensional system involving either an Eckart or Gaussian barrier along the reaction coordinate coupled to a harmonic oscillator. The arrival time for trajectories to reach the transmitted (product) region is studied. Trajectories launched from an "equal arrival time surface," defined as an isochrone, all reach the real-valued subspace in the transmitted region at the same time. The Rutherford-type diffraction of trajectories around poles in the complex extended Eckart potential energy surface is described. For thin barriers, these poles are close to the real axis and present problems for computing the transmitted density. In contrast, for the Gaussian barrier or the thick Eckart barrier where the poles are further from the real axis, smooth transmitted densities are obtained. Results obtained using higher-order quantum trajectories (third order DPM) are described for both thick and thin barriers, and some issues that arise for thin barriers are examined.

One-dimensional scattering problems are investigated in the framework of the quantum Hamilton-Jacobi formalism. First, the pole structure of the quantum momentum function for scattering wave functions is analyzed. The significant differences of the pole structure of this function between scattering wave functions and bound state wave functions are pointed out. An accurate computational method for the quantum Hamilton-Jacobi equation for general one-dimensional scattering problems is presented to obtain the scattering wave function and the reflection and transmission coefficients. The computational approach is demonstrated by analysis of scattering from a one-dimensional potential barrier. We not only present an alternative approach to the numerical solution of the wave function and the reflection and transmission coefficients but also provide a computational aspect within the quantum Hamilton-Jacobi formalism. The method proposed here should be useful for general one-dimensional scattering problems.

An accurate computational method for the one-dimensional quantum Hamilton-Jacobi equation is presented. The Mobius propagation scheme, which can accurately pass through singularities, is used to numerically integrate the quantum Hamilton-Jacobi equation for the quantum momentum function. Bound state wave functions are then synthesized from the phase integral using the antithetic cancellation technique. Through this procedure, not only the quantum momentum functions but also the wave functions are accurately obtained. This computational approach is demonstrated through two solvable examples: the harmonic oscillator and the Morse potential. The excellent agreement between the computational and the exact analytical results shows that the method proposed here may be useful for solving similar quantum mechanical problems.

The reactive scattering of a wave packet is studied by the quantum trajectory method for a model system with up to 25 Morse vibrational modes. The equations of motion are formulated in curvilinear reaction path coordinates with the restriction to a planar reaction path. Spatial derivatives are evaluated by the least squares method using contracted basis sets. Dynamical results, including trajectory evolution and time-dependent reaction probabilities, are presented and analyzed. For the case of one Morse vibrational mode, the results are in good agreement with those derived through direct numerical integration of the time-dependent Schrodinger equation.

The dynamics of ensembles containing thousands of quantum trajectories are studied for multidimensional systems undergoing reactive scattering. The Hamiltonian and equations of motion are formulated in curvilinear reaction path coordinates, for the case of a planar (zero-torsion) reaction path. In order to enhance the computational efficiency, an improved least squares fitting procedure is introduced. This scheme involves contracted basis sets and the use of inner and outer stencils around points where fitting is performed. This method is applied to reactive systems with 50-200 harmonic vibrational modes which are coupled to motion along the reaction coordinate. Dynamical results, including trajectory evolution and time-dependent reaction probabilities, are presented and power law scaling of computation time with the number of vibrational modes is described.

Ensembles of quantum trajectories are evolved to study time-dependent reaction dynamics in multidimensional systems with up to 25 vibrational modes. The equations of motion are formulated in curvilinear reaction path coordinates and all coupling terms are retained, including those involving curvature of the reaction path. The model potential is a Gaussian barrier along the translational coordinate coupled to M vibrational modes. Spatial derivatives needed to propagate the trajectories are evaluated by least squares fitting in a contracted basis set. Stable propagation of the trajectory ensembles was carried out until complete bifurcation into reflected and reactive subensembles. The reaction probabilities were evaluated by Monte Carlo integration of the multidimensional smooth transmitted densities. Computational results, including trajectory plots and time-dependent reaction probabilities, are presented for M = 1, 5, and 25 vibrational modes.

In a previous publication [J. Chem. Phys. 118, 9911 (2003)], the derivative propagation method (DPM) was introduced as a novel numerical scheme for solving the quantum hydrodynamic equations of motion (QHEM) and computing the time evolution of quantum mechanical wave packets. These equations are a set of coupled, nonlinear partial differential equations governing the time evolution of the real-valued functions C and S in the complex action, S=C(r,t) + iS(r,t)/Planck's over 2pi, where Psi(r,t)=exp(S). Past numerical solutions to the QHEM were obtained via ensemble trajectory propagation, where the required first- and second-order spatial derivatives were evaluated using fitting techniques such as moving least squares. In the DPM, however, equations of motion are developed for the derivatives themselves, and a truncated set of these are integrated along quantum trajectories concurrently with the original QHEM equations for C and S. Using the DPM quantum effects can be included at various orders of approximation; no spatial fitting is involved; there is no basis set expansion; and single, uncoupled quantum trajectories can be propagated (in parallel) rather than in correlated ensembles. In this study, the DPM is extended from previous one-dimensional (1D) results to calculate transmission probabilities for 2D and 3D wave packet evolution on coupled Eckart barrier/harmonic oscillator surfaces. In the 2D problem, the DPM results are compared to standard numerical integration of the time-dependent Schrodinger equation. Also in this study, the practicality of implementing the DPM for systems with many more degrees of freedom is discussed.

A conceptually simple approach, the covering function method (CFM), is developed to cope with the node problem in the hydrodynamic formulation of quantum mechanics. As nodes begin to form in a scattering wave packet (detected by a monitor function), a nodeless covering wave function is added to it yielding a total function that is also nodeless. Both local and global choices for the covering function are described. The total and covering functions are then propagated separately in the hydrodynamic picture. At a later time, the actual wave function is recovered from the two propagated functions. The results obtained for Eckart barrier scattering in one dimension are in excellent agreement with exact results, even for very long propagation times t=1.2 ps. The capability of the CFM is also demonstrated for multidimensional propagation of a vibrationally excited wave packet.

The Caldeira-Leggett master equation, expressed in Lindblad form, has been used in the numerical study of the effect of a thermal environment on the dynamics of the scattering of a wave packet from a repulsive Eckart barrier. The dynamics are studied in terms of phase space trajectories associated with the distribution function, W(q,p,t). The equations of motion for the trajectories include quantum terms that introduce nonlocality into the motion, which imply that an ensemble of correlated trajectories needs to be propagated. However, use of the derivative propagation method (DPM) allows each trajectory to be propagated individually. This is achieved by deriving equations of motion for the partial derivatives of W(q,p,t) that appear in the master equation. The effects of dissipation on the trajectories are studied and results are shown for the transmission probability. On short time scales, decoherence is demonstrated by a swelling of trajectories into momentum space. For a nondissipative system, a comparison is made of the DPM with the "exact" transmission probability calculated from a fixed grid calculation., (Copyright 2004 American Institute of Physics)

Oligodendrogliomas (OGs) are rare in children and have not been well characterized from a molecular viewpoint. In adults, losses on chromosomes 1p and/or 19q are common in "oligodendroglial" neoplasms and are highly associated with chemosensitivity and greater length of survival, especially in the anaplastic category. We have analyzed the 1p/19q status of pediatric OGs and compared it with similar alterations in adult OGs. Paraffin sections from 26 pediatric OGs (21 WHO Grade II OGs: 2 anaplastic oligodendrogliomas [AOGs]: and 3 mixed oligo-astrocytomas [MOA]) were retrieved. Fluorescence in situ hybridization (FISH) was performed using probes spanning the 1p32 and 19q13 regions. In tumors from children 0 to 9 years of age (n = 15), none had any deletions on 1p or 19q, but 2 had polysomies for 1p and/or 19q. All are alive and 4 have had recurrences. In tumors from children > 9 years, losses were identified on chromosomes 1p (5/11; 45%) and/or 19q (3/11; 27%), but to a much lesser extent than that observed in adult OGs. Tumors from 6 older patients also had polysomies for 1p and/or 19q. Although the majority of the older children are alive, 4 had recurrences. Curiously, 2 of the older children with AOGs had combined losses and polysomies on 1p and 19q, but responded poorly to treatment and died within a year. We conclude that alterations on 1p or 19q are infrequent in pediatric compared to adult OGs and are virtually absent in OGs presenting in the first decade of life. Compared to adults therefore, different genetic pathways are likely involved in the pathogenesis of most pediatric OGs. Genomic screening on a larger series is clearly indicated to delineate the unique molecular characteristics of these rare pediatric tumors.

The dynamics of a swarm of quantum trajectories is investigated for systems involving the interaction of an active mode (the subsystem) with an M-mode harmonic reservoir (the bath). Equations of motion for the position, velocity, and action function for elements of the probability fluid are integrated in the Lagrangian (moving with the fluid) picture of quantum hydrodynamics. These fluid elements are coupled through the Bohm quantum potential and as a result evolve as a correlated ensemble. Wave function synthesis along the trajectories permits an exact description of the quantum dynamics for the evolving probability fluid. The approach is fully quantum mechanical and does not involve classical or semiclassical approximations. Computational results are presented for three systems involving the interaction on an active mode with M=1, 10, and 15 bath modes. These results include configuration space trajectory evolution, flux analysis of the evolving ensemble, wave function synthesis along trajectories, and energy partitioning along specific trajectories. These results demonstrate the feasibility of using a small number of quantum trajectories to obtain accurate quantum results on some types of open quantum systems that are not amenable to standard quantum approaches involving basis set expansions or Eulerian space-fixed grids.

We present the time-domain theory of spectral filters, starting with the basic propositions of the theory of measurement in quantum mechanics, and develop its parameter-free implementation in the traditional correlation function as well as the filter diagonalization (FD) form. The present study unifies all the time-domain spectral filter algorithms in the literature, under a single theme which is based on the notion of selective measurements. For specific numerical purposes, we have selected Chebyshev polynomials for developing the time propagator and this permits us to carry out the relevent time integrals fully analytically and obtain FD equations in a numerically convenient form. We also argue that the FD method is a particular realization of the general spectral filter goal and it is constrained, in general, by the time-energy uncertainty regime at least as much as the correlation-function-based method. To contrast the performance of the correlation function and the FD methods, we have carried out the detailed numerical experiments on a model system, which suggest that the FD method needs almost as much time propagation as the correlation function method, in order to identify the correct spectrum. The difference lies in the procedure for the exact location of eigenvalue positions, for which the FD method employs a diagonalization step while the correlation function method involves the location of zeros.

The H + H(2) exchange reaction constitutes an excellent benchmark with which to test dynamical theories against experiments. The H + D(2) (vibrational quantum number v = 0, rotational quantum number j = 0) reaction has been studied in crossed molecular beams at a collision energy of 1.28 electron volts, with the use of the technique of Rydberg atom time-of-flight spectroscopy. The experimental resolution achieved permits the determination of fully rovibrational state-resolved differential cross sections. The high-resolution data allow a detailed assessment of the applicability and quality of quasi-classical trajectory (QCT) and quantum mechanical (QM) calculations. The experimental results are in excellent agreement with the QM results and in slightly worse agreement with the QCT results. This theoretical reproduction of the experimental data was achieved without explicit consideration of geometric phase effects.

Five constructions containing deletions of the promoter from an auxin-inducible gene of Arabidopsis thaliana, AtAux2-11, were fused to the coding region of the reporter gene LacZ, which encodes beta-galactosidase, and a polyadenylation 3'-untranslated nopaline synthase sequence from Agrobacterium. These chimeric genes were introduced into Arabidopsis by Agrobacterium tumefaciens-mediated transformation, and expression of the gene was examined by spectrophotometric and histochemical analyses. A 600 bp fragment from the AtAux2-11 promoter conferred histochemical patterns of staining similar to the longest 5' promoter tested, a 3.0 kb fragment. Localization of AtAux2-11/LacZ activity in the transgenic plants revealed spatial and temporal expression patterns that correlated with tissues and cells undergoing physiological processes modulated by auxin. LacZ activity was expressed in the elongating region of roots, etiolated hypocotyls, and anther filaments. Expression was detected in the vascular cylinder of the root and the vascular tissue, epidermis, and cortex of the hypocotyl, and filament. The AtAux2-11/LacZ gene was preferentially expressed in cells on the elongating side of hypocotyls undergoing gravitropic curvature. Expression of the chimeric gene in the hypocotyls of light-grown seedlings was less than that in etiolated seedling hypocotyls. The AtAux2-11/LacZ gene was active in the root cap, and expression in the root stele increased at sites of lateral root initiation. Staining was evident in cell types that develop lignified cell walls, e.g. trichomes, anther endothecial cells, and especially developing xylem. The chimeric gene was not expressed in primary meristems. While the magnitude of expression increased after application of exogenous auxin (2,4-D), the histochemical localization of AtAux2-11/LacZ remained unchanged. Transgenic plants with a 600 bp promoter construct (-0.6 kb AtAux2-11/LacZ) had higher levels of basal and auxin-inducible expression than plants with a 3.0 kb promoter construct. Transgenic plants with a -500 bp promoter had levels of expression similar to the -3.0 kb construct. The -0.6 kb AtAux2-11/LacZ gene responded maximally to a concentration of 5 x 10(-6) to 5 x 10(-5) M 2,4-D and was responsive to as little as 5 x 10(-8) M. The evidence presented here suggests that this gene may play a role in several auxin-mediated developmental and physiological processes.

The expression patterns of three members of a gene family that encodes proline-rich proteins in soybean (SbPRPs) were examined using in situ hybridization experiments. In most instances, the expression of SbPRP genes was intense in a limited number of cell types of a particular organ. SbPRP1 RNA was localized in several cell types of soybean hypocotyls, including cells within the phloem and xylem. SbPRP1 expression increased within epidermal cells in the elongating and mature regions of the hypocotyl; expression was detected also in lignified cells surrounding the hilum of mature seeds. SbPRP2 RNA was present in cortical cells and in the vascular tissue of the hypocotyl, especially cells of the phloem. This gene was expressed also in the inner integuments of the mature seed coat. SbPRP3 RNA was localized specifically to the endodermoid layer of cells surrounding the stele in the elongating region of the hypocotyl, as well as in the epidermal cells of leaves and cotyledons. These data show that members of this gene family exhibit cell-specific expression. The members of the SbPRP gene family are expressed in different types of cells and in some cell types that also express the glycine-rich protein or hydroxyproline-rich glycoprotein classes of genes.

A computational model of the flow of activity in a vertically organized slab of cat primary visual cortex (area 17) has been developed. The membrane potential of each cell in the model, as a function of time, is given by the solution of a system of first order, coupled, non-linear differential equations. When firing threshold is exceeded, an action potential waveform is "pasted" in. The behavior of the model following a brief simulated stimulus to afferents from the dorsal lateral geniculate nucleus (dLGN) is explored. Excitatory and inhibitory post-synaptic potential (E and IPSP) latencies, as a function of cortical depth, were generated by the model. These data were compared with the experimental literature. In general, good agreement was found for EPSPs. Many disynaptic inhibitory inputs were found to be "masked" by the firing of action potentials in the model. To our knowledge this phenomenon has not been reported in the experimental literature. The model demonstrates that whether a cell exhibits disynaptic or polysynaptic PSP latencies is not a fixed consequence of anatomical connectivity, but rather, can be influenced by connection strengths, and may be influenced by the ongoing pattern of activity in the cortex.

A method for modeling anatomical connectivity for a vertically organized slab of cortical tissue in mammalian primary visual cortex has been developed. The modeled slab covers 500 x 500 microns of cortical surface and extends vertically throughout the full depth of the cortex. The model slab was divided into 6 laminae and neuronal somata were distributed in three dimensions through the slab in accordance with experimentally derived cell densities. Axonal and dendritic arborizations were modeled as line segments. A total of 17 morphological types of neurons were included. Connectivity was established based on proximity between axonal and dendritic arbors. There is good general agreement between the vertical distribution of connections generated by the model and the vertical distribution of synapses observed for cat area 17. In all layers, fewer connections were generated in the model than synapses in cat area 17. This is due, at least in part, to the exclusion of long range intracortical projections and sources of afferent input other than the dorsal lateral geniculate nucleus from the model. The connection scheme described here will be used in conjunction with a physiology model to model vertical signal flow, and will be expanded further to model receptive fields of cortical neurons.