Abstract. Using ideas from algebraic topology and statistical mechanics, we generalize Kirchhoff's network and matrix-tree theorems to finite CW complexes of arbitrary dimension. As an application, we give a formula expressing Reidemeister torsion as an enumeration of higher dimensional spanning trees.

We characterize the classical Boltzmann distribution as the unique solution to a combinatorial Hodge theory problem in homological degree zero on a finite graph. By substituting for the graph a CW complex X and a choice of degree d dim X, we define by direct analogy a higher dimensional Boltzmann distribution q B as a certain real-valued cellular ðd À 1Þ-cycle. We then give an explicit formula for q B . We explain how these ideas relate to the Higher Kirchhoff Network Theorem of Catanzaro et al. (Homol Homotopy Appl 17:165-189, 2015). We also deduce an improved version of the Higher Matrix-Tree Theorems of Catanzaro et al. (Homol Homotopy Appl 17:165-189, 2015).

Chronic alcohol consumption results in sex differences in whole-body glucose production and glucose regulation.

Abstract. We study a generalization of the classical Riemannian Tonnetz to N -tone equally tempered scales (for all N ) and arbitrary triads. We classify all the spaces which result. The torus turns out to be the most common possibility, especially as N grows. Other spaces include 2-simplices, tetrahedra boundaries, and the harmonic strip (in both its cylinder and Möbius band variants). The final and most exotic space we find is something we call a 'circle of tetrahedra boundaries'. These are the Tonnetze for spaces of triads which contain a tritone. They are closely related to Peck's Klein bottle Tonnetz.

Attachment of chemical substituents (such as polar moieties) constitutes an efficient and convenient way to modify physical and chemical properties of conjugated polymers and oligomers.Associated modifications in the molecular electronic states can be comprehensively described by examining scattering of excitons in the polymer's backbone at the scattering center representing the chemical substituent. Here, we implement effective tight-binding models as a tool to examine the analytical properties of the exciton scattering matrices in semi-infinite polymer chains with substitutions. We demonstrate that chemical interactions between the substitution and attached polymer is adequately described by the analytical properties of the scattering matrices. In particular, resonant and bound electronic excitations are expressed via the positions of zeros and poles of the scattering amplitude, analytically continued to complex values of exciton quasimomenta.We exemplify the formulated concepts by analyzing excited states in conjugated phenylacetylenes substituted by perylene.