Topological Data Analysis of Task-Based fMRI Data from Experiments on Schizophrenia

We use methods from computational algebraic topology to study functional brain networks, in which nodes represent brain regions and weighted edges encode the similarity of fMRI time series from each region. With these tools, which allow one to characterize topological invariants such as loops in high-dimensional data, we are able to gain understanding into low-dimensional structures in networks in a way that complements traditional approaches that are based on pairwise interactions. In the present paper, we use persistent homology to analyze networks that we construct from task-based fMRI data from schizophrenia patients, healthy controls, and healthy siblings of schizophrenia patients. We thereby explore the persistence of topological structures such as loops at different scales in these networks. We use persistence landscapes and persistence images to create output summaries from our persistent-homology calculations, and we study the persistence landscapes and images using $k$-means clustering and community detection. Based on our analysis of persistence landscapes, we find that the members of the sibling cohort have topological features (specifically, their 1-dimensional loops) that are distinct from the other two cohorts. From the persistence images, we are able to distinguish all three subject groups and to determine the brain regions in the loops (with four or more edges) that allow us to make these distinctions

A quantitative central limit theorem for linear statistics of random matrix eigenvalues

It is known that the fluctuations of suitable linear statistics of Haar distributed elements of the compact classical groups satisfy a central limit theorem. We show that if the corresponding test functions are sufficiently smooth, a rate of convergence of order almost $1/n$ can be obtained using a quantitative multivariate CLT for traces of powers that was recently proven using Stein's method of exchangeable pairs.Comment: Title modified; main result stated under slightly weaker conditions; accepted for publication in the Journal of Theoretical Probabilit

Single Proton Knock-Out Reactions from 24,25,26F

The cross sections of the single proton knock-out reactions from 24F, 25F, and 26F on a 12C target were measured at energies of about 50 MeV/nucleon. Ground state populations of 6.6+-.9 mb, 3.8+-0.6 mb for the reactions 12C(24F,23O) and 12C(25F,24O) were extracted, respectively. The data were compared to calculations based on the many-body shell model and the eikonal theory. In the reaction 12C(26F,25O) the particle instability of 25O was confirmed

Geometric anomaly detection in data

This paper describes the systematic application of local topological methods for detecting interfaces and related anomalies in complicated high-dimensional data. By examining the topology of small regions around each point, one can optimally stratify a given dataset into clusters, each of which is in turn well-approximable by a suitable submanifold of the ambient space. Since these approximating submanifolds might have different dimensions, we are able to detect non-manifold like singular regions in data even when none of the data points have been sampled from those singularities. We showcase this method by identifying the intersection of two surfaces in the 24-dimensional space of cyclo-octane conformations, and by locating all the self-intersections of a Henneberg minimal surface immersed in 3-dimensional space. Due to the local nature of the required topological computations, the algorithmic burden of performing such data stratification is readily distributable across several processors

Photometry of VS0329+1250: A New, Short-Period SU Ursae Majoris Star

Time-resolved CCD photometry is presented of the recently-discovered (V~15 at maximum light) eruptive variable star in Taurus, which we dub VS0329+1250. A total of ~20 hr of data obtained over six nights reveals superhumps in the light curves, confirming the star as a member of the SU UMa class of dwarf novae. The superhumps recur with a mean period of 0.053394(7) days (76.89 min), which represents the shortest superhump period known in a classical SU UMa star. A quadratic fit to the timings of superhump maxima reveals that the superhump period was increasing at a rate given by dP/dt ~ (2.1 +/- 0.8) x 10^{-5} over the course of our observations. An empirical relation between orbital period and the absolute visual magnitude of dwarf novae at maximum light, suggests that VS0329+1250 lies at a distance of ~1.2 +/- 0.2 kpc.Comment: V2 - The paper has been modified to incorporate the referee's comments, and has now been accepted for publication in the PASP. The most significant change is that we are now able to confirm that the superhump period was increasing during the course of our observation

Beta-delayed proton emission in the 100Sn region

Beta-delayed proton emission from nuclides in the neighborhood of 100Sn was studied at the National Superconducting Cyclotron Laboratory. The nuclei were produced by fragmentation of a 120 MeV/nucleon 112Sn primary beam on a Be target. Beam purification was provided by the A1900 Fragment Separator and the Radio Frequency Fragment Separator. The fragments of interest were identified and their decay was studied with the NSCL Beta Counting System (BCS) in conjunction with the Segmented Germanium Array (SeGA). The nuclei 96Cd, 98Ing, 98Inm and 99In were identified as beta-delayed proton emitters, with branching ratios bp = 5.5(40)%, 5.5+3 -2%, 19(2)% and 0.9(4)%, respectively. The bp for 89Ru, 91,92Rh, 93Pd and 95Ag were deduced for the first time with bp = 3+1.9 -1.7%, 1.3(5)%, 1.9(1)%, 7.5(5)% and 2.5(3)%, respectively. The bp = 22(1)% for 101Sn was deduced with higher precision than previously reported. The impact of the newly measured bp values on the composition of the type-I X-ray burst ashes was studied.Comment: 15 pages, 14 Figures, 4 Table

Numerical simulation of exciton dynamics in Cu2O at ultra low temperatures within a potential trap

We have studied theoretically the relaxation behaviour of excitons in cuprous oxide (Cu2O) at ultra low temperatures when excitons are confined within a potential trap by solving numerically the Boltzmann equation. As relaxation processes, we have included in this paper deformation potential phonon scattering, radiative and non-radiative decay and Auger decay. The relaxation kinetics has been analysed for temperatures in the range between 0.3K and 5K. Under the action of deformation potential phonon scattering only, we find for temperatures above 0.5K that the excitons reach local equilibrium with the lattice i.e. that the effective local temperature is coming down to bath temperature, while below 0.5K a non-thermal energy distribution remains. Interestingly, for all temperatures the global spatial distribution of excitons does not reach the equilibrium distribution, but stays at a much higher effective temperature. If we include further a finite lifetime of the excitons and the two-particle Auger decay, we find that both the local and the global effective temperature are not coming down to bath temperature. In the first case we find a Bose-Einstein condensation (BEC) to occur for all temperatures in the investigated range. Comparing our results with the thermal equilibrium case, we find that BEC occurs for a significantly higher number of excitons in the trap. This effect could be related to the higher global temperature, which requires an increased number of excitons within the trap to observe the BEC. In case of Auger decay, we do not find at any temperature a BEC due to the heating of the exciton gas