In this article we give a Galois-theoretic characterization of the canonical theta structure. The Galois property of the canonical theta structure translates into certain p-adic theta relations which are satisfied by the canonical theta null point of the canonical lift. As an application we give a purely algebraic proof of some 2-adic theta identities which describe the set of theta null points...

In this paper, Kolmogorov-Sinai entropy is studied using mathematical modeling of an observer $ Theta $. The relative entropy of a sub-$ sigma_Theta $-algebra having finite atoms is defined and then   the ergodic properties of relative  semi-dynamical systems are investigated.  Also,  a relative version of Kolmogorov-Sinai theorem  is given. Finally, it is proved  that the relative entropy of a...

Hippocampal theta oscillations support encoding of an animal's position during spatial navigation, yet longstanding questions about their impact on locomotion remain unanswered. Combining optogenetic control of hippocampal theta oscillations with electrophysiological recordings in mice, we show that hippocampal theta oscillations regulate locomotion. In particular, we demonstrate that their reg...

The snail Helix nemoralis in negatively geotropic creeping orients upward upon an inclined surface until the angle of the path of progression (theta) is related to the tilt of the surface (alpha) as (Delta sin theta) (Delta sin alpha) = - const.; theta is very nearly a rectilinear function of log sin alpha. The precision of orientation (P.E.(theta)) declines in proportion to increasing sin alph...

Medial septum (MS) plays a critical role in controlling the electrical activity of the hippocampus (HIPP). In particular, theta-rhythmic burst firing of MS neurons is thought to drive lasting HIPP theta oscillations in rats during waking motor activity and REM sleep. Less is known about MS-HIPP interactions in nontheta states such as non-REM sleep, in which HIPP theta oscillations are absent bu...

We use Jacobi theta functions to construct examples of Jacobi forms over number fields. We determine the behavior under modular transformations by regarding certain coefficients of the Jacobi theta functions as specializations of symplectic theta functions. In addition, we show how sums of those Jacobi theta functions appear as a single coefficient of a symplectic theta function. 2000 Mathemati...

The long-term limit motions of individual heavy-tailed (power-law) particle jumps that characterize anomalous diffusion may have different scaling rates in different directions. Operator stable motions [Y(t):t> or =0] are limits of d-dimensional random jumps that are scale-invariant according to c(H)Y(t)=Y(ct), where H is a dxd matrix. The eigenvalues of the matrix have real parts 1/alpha(j), w...

We examined the activity of single cells of the supramammillary nucleus (SUM), the mammillary body (MB), and adjacent regions of the diencephalon with respect to the hippocampal electroencephalogram (EEG) in urethane-anesthetized rats. Twenty-nine of 170 cells were found to discharge synchronously with the theta rhythm of the hippocampus (theta-related neurons). All of the 29 theta-related cell...

‎In this short note‎, ‎we present some inequalities for relative operator entropy which are generalizations of some results obtained by Zou [Operator inequalities associated with Tsallis relative operator entropy‎, ‎{em Math‎. ‎Inequal‎. ‎Appl.}‎ ‎{18} (2015)‎, ‎no‎. ‎2‎, ‎401--406]‎. ‎Meanwhile‎, ‎we also show some new lower and upper bounds for relative operator entropy and Tsallis relative o...