Neural Network Approaches and Their Reproducibility in the Study of Verbal Working Memory and Alzheimer's Disease

As clinical and cognitive neurosciences mature, the need for sophisticated neuroimaging analysis becomes more apparent. Multivariate analysis techniques have recently received increasing attention because they have attractive features that cannot be easily realized by the more commonly used univariate, voxel-wise, techniques. Multivariate approaches evaluate correlation/covariance of activation across brain regions, rather than proceeding on a voxel-by-voxel basis. Thus, their results can be more easily interpreted as a signature of neural networks. Univariate approaches, in contrast, cannot directly address functional connectivity in the brain. Apart from this conceptual difference, the covariance approach can also result in greater statistical power when compared with univariate techniques, which are forced to employ very stringent, and often overly conservative, corrections for voxel-wise multiple comparisons. Multivariate techniques also lend themselves much better to prospective application of results from the analysis of one dataset to entirely new datasets. We provide two examples that illustrate different uses of multivariate techniques in cognitive and clinical neuroscience. We hope this contribution helps facilitate wider dissemination of these techniques in the research communit

Entanglement Generation of Nearly-Random Operators

We study the entanglement generation of operators whose statistical properties approach those of random matrices but are restricted in some way. These include interpolating ensemble matrices, where the interval of the independent random parameters are restricted, pseudo-random operators, where there are far fewer random parameters than required for random matrices, and quantum chaotic evolution. Restricting randomness in different ways allows us to probe connections between entanglement and randomness. We comment on which properties affect entanglement generation and discuss ways of efficiently producing random states on a quantum computer.Comment: 5 pages, 3 figures, partially supersedes quant-ph/040505

A new view on relativity: Part 2. Relativistic dynamics

The Lorentz transformations are represented on the ball of relativistically admissible velocities by Einstein velocity addition and rotations. This representation is by projective maps. The relativistic dynamic equation can be derived by introducing a new principle which is analogous to the Einstein's Equivalence Principle, but can be applied for any force. By this principle, the relativistic dynamic equation is defined by an element of the Lie algebra of the above representation. If we introduce a new dynamic variable, called symmetric velocity, the above representation becomes a representation by conformal, instead of projective maps. In this variable, the relativistic dynamic equation for systems with an invariant plane, becomes a non-linear analytic equation in one complex variable. We obtain explicit solutions for the motion of a charge in uniform, mutually perpendicular electric and magnetic fields. By the above principle, we show that the relativistic dynamic equation for the four-velocity leads to an analog of the electromagnetic tensor. This indicates that force in special relativity is described by a differential two-form

Quantum Pseudorandomness from Cluster-State Quantum Computation

We show how to efficiently generate pseudorandom states suitable for quantum information processing via cluster-state quantum computation. By reformulating pseudorandom algorithms in the cluster-state picture, we identify a strategy for optimizing pseudorandom circuits by properly choosing single-qubit rotations. A Markov chain analysis provides the tool for analyzing convergence rates to the Haar measure and finding the optimal single-qubit gate distribution. Our results may be viewed as an alternative construction of approximate unitary 2-designs

Parameters of Pseudorandom Quantum Circuits

Pseudorandom circuits generate quantum states and unitary operators which are approximately distributed according to the unitarily invariant Haar measure. We explore how several design parameters affect the efficiency of pseudorandom circuits, with the goal of identifying relevant tradeoffs and optimizing convergence. The parameters we explore include the choice of single- and two-qubit gates, the topology of the underlying physical qubit architecture, the probabilistic application of two-qubit gates, as well as circuit size, initialization, and the effect of control constraints. Building on the equivalence between pseudorandom circuits and approximate t-designs, a Markov matrix approach is employed to analyze asymptotic convergence properties of pseudorandom second-order moments to a 2-design. Quantitative results on the convergence rate as a function of the circuit size are presented for qubit topologies with a sufficient degree of symmetry. Our results may be useful towards optimizing the efficiency of random state and operator generation

Simultaneous target state and passive sensors bias estimation

Most of the literature pertaining to target tracking assumes that the sensor data are corrupted by measurement noises that are zero mean (i.e., unbiased) and with known variances (accuracies). However in real tracking systems, measurements from sensors exhibit, typically, biases. For angle-only sensors, imperfect registration leads to Line Of Sight (LOS) measurement biases in azimuth and elevation. In this project we propose a new methodology that uses an exoatmospheric target of opportunity seen in a satellites borne sensor\u27s field of view to estimate the sensor\u27s biases simultaneously with the state of the target. The first step is to formulate a general bias model for synchronized optical sensors; then we use a Maximum Likelihood (ML) approach that leads to a nonlinear least-squares estimation problem for simultaneous estimation of the 3D Cartesian position and velocity components of the target of opportunity and the angle measurement biases of the sensors (two in the present study). Each satellite is equipped with an IR sensor that provides LOS measurements (azimuth and elevation) to the target. The measurements provided by these sensors are assumed to be noisy and biased but perfectly associated, i.e., it is known perfectly that they belong to the same target. The sensor bias and the target state estimates, obtained via Iterative Least Squares (ILS), are shown, by the simulation, to be unbiased

Matrix Element Distribution as a Signature of Entanglement Generation

We explore connections between an operator's matrix element distribution and its entanglement generation. Operators with matrix element distributions similar to those of random matrices generate states of high multi-partite entanglement. This occurs even when other statistical properties of the operators do not conincide with random matrices. Similarly, operators with some statistical properties of random matrices may not exhibit random matrix element distributions and will not produce states with high levels of multi-partite entanglement. Finally, we show that operators with similar matrix element distributions generate similar amounts of entanglement.Comment: 7 pages, 6 figures, to be published PRA, partially supersedes quant-ph/0405053, expands quant-ph/050211

A self-assembling amphiphilic peptide nanoparticle for the efficient entrapment of DNA cargoes up to 100 nucleotides in length

To overcome the low efficiency and cytotoxicity associated with most non-viral DNA delivery systems we developed a purely peptidic self-assembling system that is able to entrap single- and doublestranded DNA of up to 100 nucleotides in length. (HR)3gT peptide design consists of a hydrophilic domain prone to undergo electrostatic interactions with DNA cargo, and a hydrophobic domain at a ratio that promotes the self-assembly into multi-compartment micellar nanoparticles (MCM-NPs). Selfassembled (HR)3gT MCM-NPs range between 100 to 180 nm which is conducive to a rapid and efficient uptake by cells. (HR)3gT MCM-NPs had no adverse effects on HeLa cell viability. In addition, they exhibit long-term structural stability at 4 1C but at 371C, the multi-micellar organization disassembles overtime which demonstrates their thermo-responsiveness. The comparison of (HR)3gT to a shorter, less charged H3gT peptide indicates that the additional arginine residues result in the incorporation of longer DNA segments, an improved DNA entrapment efficiency and an increase cellular uptake. Our unique nonviral system for DNA delivery sets the stage for developing amphiphilic peptide nanoparticles as candidates for future systemic gene delivery

Multivariate Data Analysis for Neuroimaging Data: Overview and Application to Alzheimer's Disease

As clinical and cognitive neuroscience mature, the need for sophisticated neuroimaging analysis becomes more apparent. Multivariate analysis techniques have recently received increasing attention as they have many attractive features that cannot be easily realized by the more commonly used univariate, voxel-wise, techniques. Multivariate approaches evaluate correlation/covariance of activation across brain regions, rather than proceeding on a voxel-by-voxel basis. Thus, their results can be more easily interpreted as a signature of neural networks. Univariate approaches, on the other hand, cannot directly address functional connectivity in the brain. The covariance approach can also result in greater statistical power when compared with univariate techniques, which are forced to employ very stringent, and often overly conservative, corrections for voxel-wise multiple comparisons. Multivariate techniques also lend themselves much better to prospective application of results from the analysis of one dataset to entirely new datasets. Multivariate techniques are thus well placed to provide information about mean differences and correlations with behavior, similarly to univariate approaches, with potentially greater statistical power and better reproducibility checks. In contrast to these advantages is the high barrier of entry to the use of multivariate approaches, preventing more widespread application in the community. To the neuroscientist becoming familiar with multivariate analysis techniques, an initial survey of the field might present a bewildering variety of approaches that, although algorithmically similar, are presented with different emphases, typically by people with mathematics backgrounds. We believe that multivariate analysis techniques have sufficient potential to warrant better dissemination. Researchers should be able to employ them in an informed and accessible manner. The following article attempts to provide a basic introduction with sample applications to simulated and real-world data sets

The Indirect Effect of Age Group on Switch Costs Via Gray Matter Volume and Task-Related Brain Activity

Healthy aging simultaneously affects brain structure, brain function, and cognition. These effects are often investigated in isolation ignoring any relationships between them. It is plausible that age related declines in cognitive performance are the result of age-related structural and functional changes. This straightforward idea is tested in within a conceptual research model of cognitive aging. The current study tested whether age-related declines in task-performance were explained by age-related differences in brain structure and brain function using a task-switching paradigm in 175 participants. Sixty-three young and 112 old participants underwent MRI scanning of brain structure and brain activation. The experimental task was an executive context dual task with switch costs in response time as the behavioral measure. A serial mediation model was applied voxel-wise throughout the brain testing all pathways between age group, gray matter volume, brain activation and increased switch costs, worsening performance. There were widespread age group differences in gray matter volume and brain activation. Switch costs also significantly differed by age group. There were brain regions demonstrating significant indirect effects of age group on switch costs via the pathway through gray matter volume and brain activation. These were in the bilateral precuneus, bilateral parietal cortex, the left precentral gyrus, cerebellum, fusiform, and occipital cortices. There were also significant indirect effects via the brain activation pathway after controlling for gray matter volume. These effects were in the cerebellum, occipital cortex, left precentral gyrus, bilateral supramarginal, bilateral parietal, precuneus, middle cingulate extending to medial superior frontal gyri and the left middle frontal gyri. There were no significant effects through the gray matter volume alone pathway. These results demonstrate that a large proportion of the age group effect on switch costs can be attributed to individual differences in gray matter volume and brain activation. Therefore, age-related neural effects underlying cognitive control are a complex interaction between brain structure and function. Furthermore, the analyses demonstrate the feasibility of utilizing multiple neuroimaging modalities within a conceptual research model of cognitive aging