Simultaneous Matrix Diagonalization for Structural Brain Networks Classification

This paper considers the problem of brain disease classification based on connectome data. A connectome is a network representation of a human brain. The typical connectome classification problem is very challenging because of the small sample size and high dimensionality of the data. We propose to use simultaneous approximate diagonalization of adjacency matrices in order to compute their eigenstructures in more stable way. The obtained approximate eigenvalues are further used as features for classification. The proposed approach is demonstrated to be efficient for detection of Alzheimer's disease, outperforming simple baselines and competing with state-of-the-art approaches to brain disease classification

U-dual fluxes and Generalized Geometry

We perform a systematic analysis of generic string flux compactifications, making use of Exceptional Generalized Geometry (EGG) as an organizing principle. In particular, we establish the precise map between fluxes, gaugings of maximal 4d supergravity and EGG, identifying the complete set of gaugings that admit an uplift to 10d heterotic or type IIB supegravity backgrounds. Our results reveal a rich structure, involving new deformations of 10d supergravity backgrounds, such as the RR counterparts of the $\beta$-deformation. These new deformations are expected to provide the natural extension of the $\beta$-deformation to full-fledged F-theory backgrounds. Our analysis also provides some clues on the 10d origin of some of the particularly less understood gaugings of 4d supergravity. Finally, we derive the explicit expression for the effective superpotential in arbitrary N = 1 heterotic or type IIB orientifold compactifications, for all the allowed fluxes.Comment: 58 pages, 6 table

Distributions of charged massive scalars and fermions from evaporating higher-dimensional black holes

A detailed numerical analysis is performed to obtain the Hawking spectrum for charged, massive brane scalars and fermions on the approximate background of a brane charged rotating higher-dimensional black hole constructed in arXiv:0907.5107. We formulate the problem in terms of a "spinor-like" first order system of differential wave equations not only for fermions, but for scalars as well and integrate it numerically. Flux spectra are presented for non-zero mass, charge and rotation, confirming and extending previous results based on analytic approximations. In particular we describe an inverted charge splitting at low energies, which is not present in four or five dimensions and increases with the number of extra dimensions. This provides another signature of the evaporation of higher-dimensional black holes in TeV scale gravity scenarios.Comment: 19 pages, 6 figures, minor typos corrected, 1 page added with a discussion on higher spins, added reference

Black holes in supergravity and integrability

Stationary black holes of massless supergravity theories are described by certain geodesic curves on the target space that is obtained after dimensional reduction over time. When the target space is a symmetric coset space we make use of the group-theoretical structure to prove that the second order geodesic equations are integrable in the sense of Liouville, by explicitly constructing the correct amount of Hamiltonians in involution. This implies that the Hamilton-Jacobi formalism can be applied, which proves that all such black hole solutions, including non-extremal solutions, possess a description in terms of a (fake) superpotential. Furthermore, we improve the existing integration method by the construction of a Lax integration algorithm that integrates the second order equations in one step instead of the usual two step procedure. We illustrate this technology with a specific example.Comment: 44 pages, small typos correcte

Stability analysis and quasinormal modes of Reissner Nordstr{\o}m Space-time via Lyapunov exponent

We explicitly derive the proper time $(\tau)$ principal Lyapunov exponent ($\lambda_{p}$) and coordinate time ($t$) principal Lyapunov exponent ($\lambda_{c}$) for Reissner Nordstr{\o}m (RN) black hole (BH) . We also compute their ratio. For RN space-time, it is shown that the ratio is $\frac{\lambda_{p}}{\lambda_{c}}=\frac{r_{0}}{\sqrt{r_{0}^2-3Mr_{0}+2Q^2}}$ for time-like circular geodesics and for Schwarzschild BH it is $\frac{\lambda_{p}}{\lambda_{c}}=\frac{\sqrt{r_{0}}}{\sqrt{r_{0}-3M}}$. We further show that their ratio $\frac{\lambda_{p}}{\lambda_{c}}$ may vary from orbit to orbit. For instance, Schwarzschild BH at innermost stable circular orbit(ISCO), the ratio is $\frac{\lambda_{p}}{\lambda_{c}}\mid_{r_{ISCO}=6M}=\sqrt{2}$ and at marginally bound circular orbit (MBCO) the ratio is calculated to be $\frac{\lambda_{p}}{\lambda_{c}}\mid_{r_{mb}=4M}=2$. Similarly, for extremal RN BH the ratio at ISCO is $\frac{\lambda_{p}}{\lambda_{c}}\mid_{r_{ISCO}=4M}=\frac{2\sqrt{2}}{\sqrt{3}}$. We also further analyse the geodesic stability via this exponent. By evaluating the Lyapunov exponent, it is shown that in the eikonal limit , the real and imaginary parts of the quasi-normal modes of RN BH is given by the frequency and instability time scale of the unstable null circular geodesics.Comment: Accepted in Pramana, 07/09/201

Patterns of progressive atrophy vary with age in Alzheimer's disease patients

Age is not only the greatest risk factor for Alzheimer's disease (AD) but also a key modifier of disease presentation and progression. Here, we investigate how longitudinal atrophy patterns vary with age in mild cognitive impairment (MCI) and AD. Data comprised serial longitudinal 1.5-T magnetic resonance imaging scans from 153 AD, 339 MCI, and 191 control subjects. Voxel-wise maps of longitudinal volume change were obtained and aligned across subjects. Local volume change was then modeled in terms of diagnostic group and an interaction between group and age, adjusted for total intracranial volume, white-matter hyperintensity volume, and apolipoprotein E genotype. Results were significant at p < 0.05 with family-wise error correction for multiple comparisons. An age-by-group interaction revealed that younger AD patients had significantly faster atrophy rates in the bilateral precuneus, parietal, and superior temporal lobes. These results suggest younger AD patients have predominantly posterior progressive atrophy, unexplained by white-matter hyperintensity, apolipoprotein E, or total intracranial volume. Clinical trials may benefit from adapting outcome measures for patient groups with lower average ages, to capture progressive atrophy in posterior cortices

Fake supersymmetry versus Hamilton-Jacobi

We explain when the first-order Hamilton-Jacobi equations for black holes (and domain walls) in (gauged) supergravity, reduce to the usual first-order equations derived from a fake superpotential. This turns out to be equivalent to the vanishing of a newly found constant of motion and we illustrate this with various examples. We show that fake supersymmetry is a necessary condition for having physically sensible extremal black hole solutions. We furthermore observe that small black holes become scaling solutions near the horizon. When combined with fake supersymmetry, this leads to a precise extension of the attractor mechanism to small black holes: The attractor solution is such that the scalars move on specific curves, determined by the black hole charges, that are purely geodesic, although there is a non-zero potential.Comment: 20 pages, v2: Typos corrected, references adde

Kerr-AdS and its Near-horizon Geometry: Perturbations and the Kerr/CFT Correspondence

We investigate linear perturbations of spin-s fields in the Kerr-AdS black hole and in its near-horizon geometry (NHEK-AdS), using the Teukolsky master equation and the Hertz potential. In the NHEK-AdS geometry we solve the associated angular equation numerically and the radial equation exactly. Having these explicit solutions at hand, we search for linear mode instabilities. We do not find any (non-)axisymmetric instabilities with outgoing boundary conditions. This is in agreement with a recent conjecture relating the linearized stability properties of the full geometry with those of its near-horizon geometry. Moreover, we find that the asymptotic behaviour of the metric perturbations in NHEK-AdS violates the fall-off conditions imposed in the formulation of the Kerr/CFT correspondence (the only exception being the axisymmetric sector of perturbations).Comment: 26 pages. 4 figures. v2: references added. matches published versio