We use the functional representation of Heisenberg-Weyl group and obtain equation for the spectrum of the model, which is more complicated than Bethes ones, but can be written explicitly through theta functions.

In this paper, we construct cataclysm deformations for $\theta$-Anosov representations into a semisimple non-compact connected real Lie group $G$ with finite center, where $\theta \subset \Delta$ is subset of the simple roots that invariant under opposition involution. These generalize Thurston's cataclysms on Teichm\"uller space and Dreyer's Borel-Anosov $\mathrm{PSL}(n, \mathbb{R})$. We expre...

We examine the emergence of collective dynamical structures and complexity in a network of interacting populations of neuronal oscillators. Each population consists of a heterogeneous collection of globally-coupled theta neurons, which are a canonical representation of Type-1 neurons. For simplicity, the populations are arranged in a fully autonomous driver-response configuration, and we obtain...

Accomplishing even simple tasks depend on neuronal circuits to configure how incoming sensory stimuli map onto responses. Controlling these stimulus-response (SR) mapping rules relies on a cognitive control network comprising the anterior cingulate cortex (ACC). Single neurons within the ACC convey information about currently relevant SR mapping rules and signal unexpected action outcomes, whic...

We derive a precise relation of poles Eisenstein series associated to the cuspidal datum $\chi\otimes\sigma$ and lowest occurrence theta lifts automorphic representation $\sigma$ unitary group, where $\chi$ is conjugate self-dual character. A key ingredient proof computation period integrals truncated series.

In this paper, we construct a splitting of the metaplectic cover of the reductive dual pairs of orthogonal and symplectic groups or the reductive dual pairs of unitary groups over a nonarchimedean local field with respect to a generalized lattice model of the Weil representation. We also prove a result concerning the splitting that we construct and the theta dichotomy for unitary group. The spl...

We study the differential equations governing mirror symmetry of elliptic curves, and obtain a characterization of the ODEs which give rise to the integral q-expansion of mirror maps. Through theta function representation of the defining equation, we express the mirror correspondence in terms of theta constants. By investigating the elliptic curves in X9-family, the identification of the Landau...

Oscillatory fluctuations of local field potentials (LFPs) in the theta (4-8 Hz) and gamma (25-140 Hz) band are held to play a mechanistic role in various aspects of memory including the representation and off-line maintenance of events and sequences of events, the assessment of novelty, the induction of plasticity during encoding, as well as the consolidation and the retrieval of stored memorie...

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...