Analysis of amplitude and phase characteristics for delta, theta, and alpha bands at localized time instant from EEG signals is important for the characterizing information processing in the brain. In this paper, complex demodulation method was used to analyze EEG (Electroencephalographic) signal, particularly for auditory evoked potential response signal, with sufficient time resolution and de...

Both episodic memory and spatial navigation require temporal encoding of the relationships between events or locations. In a linear maze, ordered spatial distances between sequential locations were represented by the temporal relations of hippocampal place cell pairs within cycles of theta oscillation in a compressed manner. Such correlations could arise due to spike "phase precession" of indep...

Using the Malliavin calculus in time inhomogeneous jump-diffusion models, we obtain an expression for the sensitivity Theta of an option price (with respect to maturity) as the expectation of the option payoff multiplied by a stochastic weight. This expression is used to design efficient numerical algorithms that are compared to traditional finite difference methods for the computation of Theta...

The main goal of this paper is to give a modular type representation for the infinite product (1−x)(1−xq)(1−xq)(1−xq) · · · . It is shown that this representation essentially contains the well-known modular formulae either for Dedekind’s eta function, Jacobi theta function or for certain Lambert series. Thus a new and unified approach is outlined for the study of elliptic and modular functions ...

In this paper, we define the Schrödinger-Weil representation for the Jacobi group and construct covariant maps for the Schrödinger-Weil representation. Using these covariant maps, we construct Jacobi forms with respect to an arithmetic subgroup of the Jacobi group.

In this work, we aim to prove the theta dichotomy conjecture for dual dual pairs of type ( ̃ Sp(W ),O(V )) with dim(V ) odd. The crux of the proof relies on the analysis the reducibility of a certain a degenerate principal series representation of the group ̃ Sp(W ′) having double the rank of ̃ Sp(W ). This analysis is carried out by way of a normalized standard intertwining operator which is al...

Trajectory planning is an essential part of systems controlling autonomous entities such as vehicles or robots. It requires not only finding spatial curves but also that dynamic properties of the vehicles (such as speed limits for certain maneuvers) must be followed. In this paper, we present an approach for augmenting existing path planning methods to support basic dynamic constraints, concret...

Hippocampal theta is a 4-12 Hz rhythm associated with episodic memory, and although it has been studied extensively, the cellular mechanisms underlying its generation are unclear. The complex interactions between different interneuron types, such as those between oriens-lacunosum-moleculare (OLM) interneurons and bistratified cells (BiCs), make their contribution to network rhythms difficult to...