We used simultaneously recorded EEG and fMRI to investigate in which areas the BOLD signal correlates with frontal theta power changes, while subjects were quietly lying resting in the scanner with their eyes open. To obtain a reliable estimate of frontal theta power we applied ICA on band-pass filtered (2-9 Hz) EEG data. For each subject we selected the component that best matched the mid-fron...

§0. Introduction §1. The Scheme-Theoretic Fourier Transform §2. Discrete Gaussians and Gauss Sums §3. Review of Degree Computations in [HAT] §4. The Fourier Transform of an Algebraic Theta Function: The Case of an Étale Lagrangian Subgroup §5. The Fourier Transform of an Algebraic Theta Function: The Case of a Lagrangian Subgroup with Nontrivial Multiplicative Part §6. Generic Properties of the...

The singularity structure of a second-order ordinary differential equation with polynomial coefficients often yields the type solution. It is shown that $\theta$-operator method can be used as symbolic computational approach to obtain indicial and recurrence relation. Consequently, leads transformations yield solution in terms special function, if suitable. Hypergeometric Heun-type equations ar...

We study the five-dimensional SU(3)c × U(1)C gauge theory on the orbifold S/Z2 with a mixed Chern-Simons term. We particularly pay attention to the realization of the dynamical rearrangement of the theta parameter for SU(3)c. It is shown that the physics remains invariant under a large gauge transformation which even changes the action, completely removing the theta parameter, because of the Ho...

We apply theta body relaxations to the Ki-cover problem and show polynomial time solvability for certain classes of graphs. In particular, we give an effective relaxation where all Kip-hole facets are valid, and study its relation to an open question of Conforti et al. For the triangle free problem, we show for Kn that the theta body relaxations do not converge by (n−2)/4 steps; we also prove f...

This paper provides a survey of particular values Ramanujan's theta function $\varphi(q)=\sum_{n=-\infty}^{\infty}q^{n^2}$, when $q=e^{-\pi\sqrt{n}}$, where $n$ is positive rational number. First, descriptions the tools used to evaluate functions are given. Second, classical briefly discussed. Third, certain due Ramanujan and later authors Fourth, methods that determine these described. Lastly,...