Andrew T. Sornborger

Cosmological theory without singularities.

A theory of gravitation is constructed in which all homogeneous and isotropic solutions are nonsingular, and in which all curvature invariants are bounded. All solutions for which curvature invariants approach their limiting values approach de Sitter space. The action for this theory is obtained by a higher-derivative modification of Einsteins theory. We expect that our model can easily be generalized to solve the singularity problem also for anisotropic cosmologies.

A population study of integrate-and-fire-or-burst neurons

Any realistic model of the neuronal pathway from the retina to the visual cortex (V1) must account for the burstingbehavior of neurons in the lateral geniculate nucleus (LGN). A robust but minimal model, the integrate- and-fire-or-burst (IFB) model, has recently been proposed for individual LGN neurons. Based on this, we derive a dynamic population model and study a population of such LGN cells. This population model, the first simulation of its kind evolving in a two-dimensional phase space, is used to study the behavior of bursting populations in response to diverse stimulus conditions.

Drosophila TRPA channel modulates sugar-stimulated neural excitation, avoidance and social response

Drosophila melanogaster postfeeding larvae show food-averse migration toward food-free habitats before metamorphosis. This developmental switching from food attraction to aversion is regulated by a neuropeptide Y (NPY)-related brain signaling peptide. We used the fly larva model to delineate the neurobiological basis of age-restricted response to environmental stimuli. Here we provide evidence for a fructose-responsive chemosensory pathway that modulates food-averse migratory and social behaviors. We found that fructose potently elicited larval food-averse behaviors, and painless (pain), a transient receptor potential channel that is responsive to noxious stimuli, was required for the fructose response. A subset of pain-expressing sensory neurons have been identified that show pain-dependent excitation by fructose. Although evolutionarily conserved avoidance mechanisms are widely appreciated for their roles in stress coping and survival, their biological importance in animal physiology and development remains unknown. Our findings demonstrate how an avoidance mechanism is recruited to facilitate animal development.

Higher order methods for simulations on quantum computers

To implement many-qubit gates for use in quantum simulations on quantum computers efficiently, we develop and present methods reexpressing exp[[minus]i(H[sub 1]+H[sub 2]+[center dot][center dot][center dot])[Delta]t] as a product of factors exp[[minus]iH[sub 1][Delta]t], exp[[minus]iH[sub 2][Delta]t],[hor ellipsis], which is accurate to third or fourth order in [Delta]t. The methods we derive are an extended form of the symplectic method, and can also be used for an integration of classical Hamiltonians on classical computers. We derive both integral and irrational methods, and find the most efficient methods in both cases. [copyright] [ital 1999] [ital The American Physical Society]

Spatiotemporal analysis of optical imaging data

Previous methods for analyzing optical imaging data have relied heavily on temporal averaging. However, response dynamics are rich sources of information. Here, we develop and present a method that combines principal component analysis and multitaper harmonic analysis to extract the statistically significant spatial and temporal response from optical imaging data. We apply the method to both simulated data and experimental optical imaging data from the cat primary visual cortex.

Comparison of Canine Stifle Kinematic Data Collected with Three Different Targeting Models

OBJECTIVE To model the kinematics of the canine stifle in 3 dimensions using the Joint Coordinate System (JCS) and compare the JCS method with linear and segmental models. STUDY DESIGN In vivo biomechanical study. ANIMALS Normal adult mixed breed dogs (n=6). METHODS Dogs had 10 retroreflective markers affixed to the skin on the right pelvic limb. Dogs were walked and trotted 5 times through the calibrated space and the procedure was repeated 5 days later. Sagittal flexion and extension angle waveforms acquired during each trial with all 3 models (JCS, Linear, and Segmental) were produced simultaneously during each gait. The JCS method provided additional internal/external and abduction/adduction angles. Comparison of sagittal flexion and extension angle waveforms was performed with generalized indicator function analysis (GIFA) and Fourier analysis. A normalization procedure was performed. RESULTS Each model provided consistent equivalent sagittal flexion-extension data. The JCS provided consistent additional internal/external and abduction/adduction. Sagittal waveform differences were found between methods and testing days for each dog at a walk and a trot with both GIFA and Fourier analysis. After normalization, differences were less with Fourier analysis and were unaltered with GIFA. CONCLUSIONS Whereas all methods produced similar flexion-extension waveforms, JCS provided additional valuable data. CLINICAL RELEVANCE The JCS model provided sagittal plane flexion/extension data as well as internal/external rotation and abduction/adduction data.

Superconducting phase qubit coupled to a nanomechanical resonator: Beyond the rotating-wave approximation

We consider a simple model of a Josephson junction phase qubit coupled to a solid-state nanoelectromechanical resonator. This and many related qubit-resonator models are analogous to an atom in an electromagnetic cavity. When the systems are weakly coupled and nearly resonant, the dynamics is accurately described by the rotating-wave approximation (RWA) or the Jaynes-Cummings model of quantum optics. However, the desire to develop faster quantum-information-processing protocols necessitates approximate, yet analytic descriptions that are valid for more strongly coupled qubit-resonator systems. Here we present a simple theoretical technique, using a basis of dressed states, to perturbatively account for the leading-order corrections to the RWA. By comparison with exact numerical results, we demonstrate that the method is accurate for moderately strong coupling and provides a useful theoretical tool for describing fast quantum information processing. The method applies to any quantum two-level system linearly coupled to a harmonic oscillator or single-mode boson field.

Extraction of periodic multivariate signals: mapping of voltage-dependent dye fluorescence in the mouse heart

In many experimental circumstances, heart dynamics are, to a good approximation, periodic. For this reason, it makes sense to use high-resolution methods in the frequency domain to visualize the spectrum of imaging data of the heart and to estimate the deterministic signal content and extract the periodic signal from background noise in experimental data. In this paper, we describe the first application of a new method that we call cardiac rhythm analysis which uses a combination of principal component analysis and multitaper harmonic analysis to extract periodic, deterministic signals from high-resolution imaging data of cardiac electrical activity. We show that this method significantly increases the signal-to-noise ratio of our recordings, allowing for better visualization of signal dynamics and more accurate quantification of the properties of electrical conduction. We visualize the spectra of three cardiac data sets of mouse hearts exhibiting sinus rhythm, paced rhythm and monomorphic tachycardia. Then, for pedagogical purposes, we investigate the tachycardia more closely, demonstrating the presence of two distinct periodicities in the re-entrant tachycardia. Analysis of the tachycardia shows that cardiac rhythm analysis not only allows for better visualization of electrical activity, but also provides new opportunities to study multiple periodicities in signal dynamics.

Estimating weak ratiometric signals in imaging data. I. Dual-channel data

Ratiometric fluorescent indicators are becoming increasingly prevalent in many areas of biology. They are used for making quantitative measurements of intracellular free calcium both in vitro and in vivo, as well as measuring membrane potentials, pH, and other important physiological variables of interest to researchers in many subfields. Often, functional changes in the fluorescent yield of ratiometric indicators are small, and the signal-to-noise ratio (SNR) is of order unity or less. In particular, variability in the denominator of the ratio can lead to very poor ratio estimates. We present a statistical optimization method for objectively detecting and estimating ratiometric signals in dual-wavelength measurements of fluorescent, ratiometric indicators that improves on standard methods. With the use of an appropriate statistical model for ratiometric signals and by taking the pixel-pixel covariance of an imaging dataset into account, we are able to extract user-independent spatiotemporal information that retains high resolution in both space and time.

Quantum Simulation of Tunneling in Small Systems

A number of quantum algorithms have been performed on small quantum computers; these include Shors prime factorization algorithm, error correction, Grovers search algorithm and a number of analog and digital quantum simulations. Because of the number of gates and qubits necessary, however, digital quantum particle simulations remain untested. A contributing factor to the system size required is the number of ancillary qubits needed to implement matrix exponentials of the potential operator. Here, we show that a set of tunneling problems may be investigated with no ancillary qubits and a cost of one single-qubit operator per time step for the potential evolution, eliminating at least half of the quantum gates required for the algorithm and more than that in the general case. Such simulations are within reach of current quantum computer architectures.