Topological Data Analysis Captures Task-Driven fMRI Profiles in Individual Participants: A Classification Pipeline Based on Persistence.

BOLD-based fMRI is the most widely used method for studying brain function. The BOLD signal while valuable, is beset with unique vulnerabilities. The most notable of these is the modest signal to noise ratio, and the relatively low temporal and spatial resolution. However, the high dimensional complexity of the BOLD signal also presents unique opportunities for functional discovery. Topological Data Analyses (TDA), a branch of mathematics optimized to search for specific classes of structure within high dimensional data may provide particularly valuable applications. In this investigation, we acquired fMRI data in the anterior cingulate cortex (ACC) using a basic motor control paradigm. Then, for each participant and each of three task conditions, fMRI signals in the ACC were summarized using two methods: a) TDA based methods of persistent homology and persistence landscapes and b) non-TDA based methods using a standard vectorization scheme. Finally, using machine learning (with support vector classifiers), classification accuracy of TDA and non-TDA vectorized data was tested across participants. In each participant, TDA-based classification out-performed the non-TDA based counterpart, suggesting that our TDA analytic pipeline better characterized task- and condition-induced structure in fMRI data in the ACC. Our results emphasize the value of TDA in characterizing task- and condition-induced structure in regional fMRI signals. In addition to providing our analytical tools for other users to emulate, we also discuss the unique role that TDA-based methods can play in the study of individual differences in the structure of functional brain signals in the healthy and the clinical brain.

From mathematics to medicine: A practical primer on topological data analysis (TDA) and the development of related analytic tools for the functional discovery of latent structure in fMRI data.

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.

Counting the number of excited states in organic semiconductor systems using topology.

Exciton scattering theory attributes excited electronic states to standing waves in quasi-one-dimensional molecular materials by assuming a quasi-particle picture of optical excitations. The quasi-particle properties at branching centers are described by the corresponding scattering matrices. Here, we identify the topological invariant of a scattering center, referred to as its winding number, and apply topological intersection theory to count the number of quantum states in a quasi-one-dimensional system.

Excited-State Structure Modifications Due to Molecular Substituents and Exciton Scattering in Conjugated Molecules.

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 are 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 quasi-momenta. We exemplify the formulated concepts by analyzing excited states in conjugated phenylacetylenes substituted by perylene.

Chronic alcohol consumption yields sex differences in whole-body glucose production in rats.

AIMS: The effects of chronic alcohol consumption (8 weeks) on glucose kinetics, in the absence (water, 4 g/kg) and presence of an acute ethanol dose (4 g/kg), were examined in 48 h fasted male and female Wistar rats. METHODS: Primed continuous infusions of [6-3H]- and [U-14C]glucose were employed to assess rates of glucose appearance (Ra), glucose disappearance (Rd), and apparent glucose carbon recycling. RESULTS: After injecting the male and female controls with water, there were no significant alterations in glucose kinetics. Compared to controls, chronic alcohol-fed female animals (injected with water) demonstrated significantly lower: glucose Ra, blood glucose concentration, and apparent glucose carbon recycling for a majority of the experimental period. In separate groups injected with ethanol, the glucose Ra fell by 31% for male rats fed the control diet (MC), 43% for male rats fed the ethanol diet (ME), 29% for female rats fed the control diet (FC), and 42% for female rats fed the ethanol diet (FE). Further, compared to controls (MC and FC), the blood glucose concentration was significantly lower prior to and following the ethanol injection for FE. In addition, FE animals had significantly lower rates of glucose Ra and glucose carbon recycling compared to controls prior to and after the ethanol injection. ME animals demonstrated similar declines in glucose Ra (compared to FE), but only after the ethanol injection. Conversely, ME were able to match the decrease in glucose Ra with comparable declines in glucose Rd resulting in blood glucose concentrations that did not differ from controls. CONCLUSIONS: Chronic alcohol consumption results in sex differences in whole-body glucose production and glucose regulation.

Effect of age and endurance training on the capacity for epinephrine-stimulated gluconeogenesis in rat hepatocytes.

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-14C]lactate; 25000 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 +/- 6.2 nmol/mg protein) compared with young controls (C) (78.2 +/- 6.0 nmol/mg protein). The basal HGP was also significantly greater for old T (97.3 +/- 5.9 nmol/mg protein) compared with old C (72.2 +/- 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 +/- 6.5 nmol/mg protein) compared with young C (110.9 +/- 4.8 nmol/mg protein). Similarly, the Vmax was significantly greater for old T (138.2 +/- 5.0 nmol/mg protein) compared with old C (103.9 +/- 2.5 nmol/mg protein). Finally, there was an increase in the EC50 from the hepatocytes of old T (56.2 +/- 6.2 nM) compared with young T (32.6 +/- 4.9 nM). In like manner, there was an increase in the EC50 from the hepatocytes of old C (59.7 +/- 5.8 nM) compared with young C (33.1 +/- 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 EC50 that is independent of training status.