We present an exposition of weighted theta functions, which are weighted generating functions for the norms and distribution of lattice vectors. We derive a decomposition theorem for the space of degree-d homogeneous polynomials in terms of spaces of harmonic polynomials and then prove that the weighted theta functions of Type II lattices are examples of modular forms. Our development of these ...

We consider rational integrable supersymmetric $${\mathfrak {\mathfrak {gl}}_{{{\mathsf {m}}}|{{\mathsf {n}}}}}$$ spin chains in the defining representation and prove isomorphism between a commutative algebra of conserved charges (the Bethe algebra) polynomial ring Wronskian defined by functional relations Baxter Q-functions that we call equations. These equations, contrast to standard nested a...

Abstract This paper focuses on the most prominent theta roles used in the Sindhi language. The study attempts to answer to the research question, ‘How are theta roles prominently used in the Sindhi language?’ The data come from the young native Sindhi speakers. Each verb phrase in the data is examined with the help of Carnie’s (2007) ‘Theta Roles and Thematic Relations’ in order to find the pro...

Abstract This paper focuses on the most prominent theta roles used in the Sindhi language. The study attempts to answer to the research question, ‘How are theta roles prominently used in the Sindhi language?’ The data come from the young native Sindhi speakers. Each verb phrase in the data is examined with the help of Carnie’s (2007) ‘Theta Roles and Thematic Relations’ in order to find the pro...

We used intracranial recordings to study brain oscillations during a working memory task. To analyze sites involved in working memory, we focused on sites at which the elevation of the broadband gamma signal depended on which letter was presented. We tested a previously proposed model according to which different items are active at different phases of the theta cycle (in different gamma cycles...

Quantum theta functions were introduced by the author in [Ma1]. They are certain elements in the function rings of quantum tori. By definition, they satisfy a version of the classical functional equations involving shifts by the multiplicative periods. This paper shows that for a certain subclass of period lattices (compatible with the quantization form), quantum thetas satisfy an analog of ano...

Theta series for exceptional groups have been suggested as a possible description of the eleven-dimensional quantum supermembrane. We present explicit formulae for these automorphic forms whenever the underlying Lie group G is split (or complex) and simply laced. Specifically, we review and construct explicitly the minimal representation of G, generalizing the Schrödinger representation of symp...

Although anatomical, lesion, and imaging studies of the hippocampus indicate qualitatively different information processing along its septo-temporal axis, physiological mechanisms supporting such distinction are missing. We found fundamental differences between the dorsal (dCA3) and the ventral-most parts (vCA3) of the hippocampus in both environmental representation and temporal dynamics. Disc...

The theta-gamma neural coding theory suggests that multiple items are represented in working memory (WM) by a superposition of gamma cycles on theta oscillations. To enable a stable, non-interfering representation of multiple items, such a theta-gamma neural code may be reflected by phase-phase coupling, i.e., a precise locking of gamma subcycles to specific theta phases. Recent data have indic...