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.

fMRI is the preeminent method for collecting signals from the human brain in vivo, for using these signals in the service of functional discovery, and relating these discoveries to anatomical structure. Numerous computational and mathematical techniques have been deployed to extract information from the fMRI signal. Yet, the application of Topological Data Analyses (TDA) remain limited to certain sub-areas such as connectomics (that is, with summarized versions of fMRI data). While connectomics is a natural and important area of application of TDA, applications of TDA in the service of extracting structure from the (non-summarized) fMRI data itself are heretofore nonexistent. “Structure” within fMRI data is determined by dynamic fluctuations in spatially distributed signals over time, and TDA is well positioned to help researchers better characterize mass dynamics of the signal by rigorously capturing shape within it. To accurately motivate this idea, we a) survey an established method in TDA (“persistent homology”) to reveal and describe how complex structures can be extracted from data sets generally, and b) describe how persistent homology can be applied specifically to fMRI data. We provide explanations for some of the mathematical underpinnings of TDA (with expository figures), building ideas in the following sequence: a) fMRI researchers can and should use TDA to extract structure from their data; b) this extraction serves an important role in the endeavor of functional discovery, and c) TDA approaches can complement other established approaches toward fMRI analyses (for which we provide examples). We also provide detailed applications of TDA to fMRI data collected using established paradigms, and offer our software pipeline for readers interested in emulating our methods. This working overview is both an inter-disciplinary synthesis of ideas (to draw researchers in TDA and fMRI toward each other) and a detailed description of methods that can motivate collaborative research.

We prove 'twisted' versions of Kirchhoff's network theorem and Kirchhoff's matrix-tree theorem on connected finite graphs. Twisting here refers to chains with coefficients in a flat unitary line bundle.

Sumida, Ken D., Steven M. Arimoto, Michael J. Catanzaro, and Frank Frisch. Effect of age and endurance training on the capacity for epinephrine-stimulated gluconeogenesis in rat hepatocytes. J Appl Physiol 95: 712-719, 2003; 10.1152/japplphysiol.01125.2002.-The effects of endurance training on hepatic glucose production (HGP) from lactate were examined in 24-h-fasted young (4 mo) and old (24 mo) male Fischer 344 rats by using the isolated-hepatocyte technique. The liver cells were incubated for 30 min with 5 mM lactate ([U-14 C]lactate; 25,000 dpm/ml) and nine different concentrations of epinephrine (Epi). Basal HGP (with lactate only and no Epi) was significantly greater for young trained (T) (99.6 Ϯ 6.2 nmol/mg protein) compared with young controls (C) (78.2 Ϯ 6.0 nmol/mg protein). The basal HGP was also significantly greater for old T (97.3 Ϯ 5.9 nmol/mg protein) compared with old C (72.2 Ϯ 3.9 nmol/mg protein). After the incubation with the various concentrations of Epi, Hanes-Woolf plots were generated to determine kinetic constants (Vmax and EC50). Maximal Epi-stimulated hepatic glucose production (Vmax) was significantly greater for young T (142.5 Ϯ 6.5 nmol/mg protein) compared with young C (110.9 Ϯ 4.8 nmol/mg protein). Similarly, the V max was significantly greater for old T (138.2 Ϯ 5.0 nmol/mg protein) compared with old C (103.9 Ϯ 2.5 nmol/mg protein). Finally, there was an increase in the EC 50 from the hepatocytes of old T (56.2 Ϯ 6.2 nM) compared with young T (32.6 Ϯ 4.9 nM). In like manner, there was an increase in the EC 50 from the hepatocytes of old C (59.7 Ϯ 5.8 nM) compared with young C (33.1 Ϯ 2.7 nM). The results suggest that training elevates HGP in the basal and maximally Epi-stimulated condition, but with age there is a decline in EC 50 that is independent of training status. liver; lactate; glucose production; exercise THE BRAIN AND NERVE TISSUES depend on the maintenance of blood glucose to sustain a concentration gradient for extraction (16). When liver glycogen stores become depleted, hepatic gluconeogenesis becomes an essential component in an organism's ability to maintain blood glucose levels. Endurance training has been shown to resist the decrements in blood glucose concentrations during prolonged exercise despite depletion of hepatic glycogen stores (7). Our laboratory has previously demonstrated an enhanced hepatic gluconeogenic capacity attributable to endurance training in rats (7,32,33). The augmentation in glucose production ability in the liver could help to account for the maintenance of blood glucose levels in trained animals during prolonged exercise when hepatic glycogen stores become depleted (8). Conversely, recent reports have demonstrated age-related declines in hepatic gluconeogenic capacity (25)(26)(27). This loss in liver function could compromise the ability of an elderly individual to respond to a given stress. However, reports from demonstrate that endurance training can help to offset the age-related decline in the liver's glucose production capacity.Hor...