Implementation of an Optimal First-Order Method for Strongly Convex Total Variation Regularization

We present a practical implementation of an optimal first-order method, due to Nesterov, for large-scale total variation regularization in tomographic reconstruction, image deblurring, etc. The algorithm applies to $\mu$-strongly convex objective functions with $L$-Lipschitz continuous gradient. In the framework of Nesterov both $\mu$ and $L$ are assumed known -- an assumption that is seldom satisfied in practice. We propose to incorporate mechanisms to estimate locally sufficient $\mu$ and $L$ during the iterations. The mechanisms also allow for the application to non-strongly convex functions. We discuss the iteration complexity of several first-order methods, including the proposed algorithm, and we use a 3D tomography problem to compare the performance of these methods. The results show that for ill-conditioned problems solved to high accuracy, the proposed method significantly outperforms state-of-the-art first-order methods, as also suggested by theoretical results.Comment: 23 pages, 4 figure

Proteomic changes in serum of first onset, antidepressant drug-naïve major depression patients

Major depressive disorder (MDD) is a complex and multi-factorial disorder. Although genetic factors and other molecular aspects of MDD have been widely studied, the underlying pathological mechanisms are still mostly unknown. We sought to investigate the pathophysiology of MDD by identifying and characterising serum molecular differences and their correlation to symptom severity in first onset, antidepressant drug-naïve MDD patients. We performed an exploratory molecular profiling study on serum samples of MDD patients and controls using multiplex immunoassay and label-free liquid chromatography mass spectrometry in data independent mode (LC-MSE). We included two independent cohorts of first onset, antidepressant drug-naïve MDD patients (n = 23 and 15) and matched controls (n = 42 and 21) in our study in order to validate the results. The main outcome included the following list of circulatory molecules changing and/or correlating to symptom severity: angiotensin-converting enzyme, acute phase proteins (e.g. ferritin and serotransferrin), brain-derived neurotrophic factor, complement component C4-B, cortisol, cytokines (e.g. macrophage migration inhibitory factor and interleukin-16), extracellular newly identified receptor for advanced glycosylation end products-binding protein, growth hormone and superoxide dismutase-1. This study provides evidence of an increased pro-inflammatory and oxidative stress response, followed by a hyperactivation of the HPA-axis in the acute stages of first onset MDD, as well as a dysregulation in growth factor pathways. These findings help to elucidate MDD related pathways in more detail and further studies may lead to identification of novel drug targets, inc

Dynamics of Non-adiabatic Charged Cylindrical Gravitational Collapse

This paper is devoted to study the dynamics of gravitational collapse in the Misner and Sharp formalism. We take non-viscous heat conducting charged anisotropic fluid as a collapsing matter with cylindrical symmetry. The dynamical equations are derived and coupled with the transport equation for heat flux obtained from the M$\ddot{u}$ller-Israel-Stewart causal thermodynamic theory. We discuss the role of anisotropy, electric charge and radial heat flux over the dynamics of the collapse with the help of coupled equation.Comment: 15 pages, accepted for publication in Astrophys. Space Sc

Space-time inhomogeneity, anisotropy and gravitational collapse

We investigate the evolution of non-adiabatic collapse of a shear-free spherically symmetric stellar configuration with anisotropic stresses accompanied with radial heat flux. The collapse begins from a curvature singularity with infinite mass and size on an inhomogeneous space-time background. The collapse is found to proceed without formation of an even horizon to singularity when the collapsing configuration radiates all its mass energy. The impact of inhomogeneity on various parameters of the collapsing stellar configuration is examined in some specific space-time backgrounds.Comment: To appear in Gen. Relativ. Gra

Partially Annealed Disorder and Collapse of Like-Charged Macroions

Charged systems with partially annealed charge disorder are investigated using field-theoretic and replica methods. Charge disorder is assumed to be confined to macroion surfaces surrounded by a cloud of mobile neutralizing counterions in an aqueous solvent. A general formalism is developed by assuming that the disorder is partially annealed (with purely annealed and purely quenched disorder included as special cases), i.e., we assume in general that the disorder undergoes a slow dynamics relative to fast-relaxing counterions making it possible thus to study the stationary-state properties of the system using methods similar to those available in equilibrium statistical mechanics. By focusing on the specific case of two planar surfaces of equal mean surface charge and disorder variance, it is shown that partial annealing of the quenched disorder leads to renormalization of the mean surface charge density and thus a reduction of the inter-plate repulsion on the mean-field or weak-coupling level. In the strong-coupling limit, charge disorder induces a long-range attraction resulting in a continuous disorder-driven collapse transition for the two surfaces as the disorder variance exceeds a threshold value. Disorder annealing further enhances the attraction and, in the limit of low screening, leads to a global attractive instability in the system.Comment: 21 pages, 2 figure

Local mean-field study of capillary condensation in silica aerogels

We apply local mean-field (i.e. density functional) theory to a lattice model of a fluid in contact with a dilute, disordered gel network. The gel structure is described by a diffusion-limited cluster aggregation model. We focus on the influence of porosity on both the hysteretic and the equilibrium behavior of the fluid as one varies the chemical potential at low temperature. We show that the shape of the hysteresis loop changes from smooth to rectangular as the porosity increases and that this change is associated to disorder-induced out-of-equilibrium phase transitions that differ on adsorption and on desorption. Our results provide insight in the behavior of $^4$He in silica aerogels.Comment: 19 figure

A weakly stable algorithm for general Toeplitz systems

We show that a fast algorithm for the QR factorization of a Toeplitz or Hankel matrix A is weakly stable in the sense that R^T.R is close to A^T.A. Thus, when the algorithm is used to solve the semi-normal equations R^T.Rx = A^Tb, we obtain a weakly stable method for the solution of a nonsingular Toeplitz or Hankel linear system Ax = b. The algorithm also applies to the solution of the full-rank Toeplitz or Hankel least squares problem.Comment: 17 pages. An old Technical Report with postscript added. For further details, see http://wwwmaths.anu.edu.au/~brent/pub/pub143.htm

Quasinormal modes of Schwarzschild black holes in four and higher dimensions

We make a thorough investigation of the asymptotic quasinormal modes of the four and five-dimensional Schwarzschild black hole for scalar, electromagnetic and gravitational perturbations. Our numerical results give full support to all the analytical predictions by Motl and Neitzke, for the leading term. We also compute the first order corrections analytically, by extending to higher dimensions, previous work of Musiri and Siopsis, and find excellent agreement with the numerical results. For generic spacetime dimension number D the first-order corrections go as $\frac{1}{n^{(D-3)/(D-2)}}$. This means that there is a more rapid convergence to the asymptotic value for the five dimensional case than for the four dimensional case, as we also show numerically.Comment: 12 pages, 5 figures, RevTeX4. v2. Typos corrected, references adde

Development of a blood-based molecular biomarker test for identification of schizophrenia before disease onset

Recent research efforts have progressively shifted towards preventative psychiatry and prognostic identification of individuals before disease onset. We describe the development of a serum biomarker test for the identification of individuals at risk of developing schizophrenia based on multiplex immunoassay profiling analysis of 957 serum samples. First, we conducted a meta-analysis of five independent cohorts of 127 first-onset drug-naive schizophrenia patients and 204 controls. Using least absolute shrinkage and selection operator regression, we identified an optimal panel of 26 biomarkers that best discriminated patients and controls. Next, we successfully validated this biomarker panel using two independent validation cohorts of 93 patients and 88 controls, which yielded an area under the curve (AUC) of 0.97 (0.95-1.00) for schizophrenia detection. Finally, we tested its predictive performance for identifying patients before onset of psychosis using two cohorts of 445 pre-onset or at-risk individuals. The predictive performance achieved by the panel was excellent for identifying USA military personnel (AUC: 0.90 (0.86-0.95)) and help-seeking prodromal individuals (AUC: 0.82 (0.71-0.93)) who developed schizophrenia up to 2 years after baseline sampling. The performance increased further using the latter cohort following the incorporation of CAARMS (Comprehensive Assessment of At-Risk Mental State) positive subscale symptom scores into the model (AUC: 0.90 (0.82-0.98)). The current findings may represent the first successful step towards a test that could address the clinical need for early intervention in psychiatry. Further developments of a combined molecular/symptom-based test will aid clinicians in the identification of vulnerable patients early in the disease process, allowing more effective therapeutic intervention before overt disease onset

Radiative Decay Modes of the D0D^{0} Meson

Using data recorded by the CLEO-II detector at CESR we have searched for four radiative decay modes of the $D^0$ meson: $D^0\to\phi\gamma$, $D^0\to\omega\gamma$, $D^0\to\bar{K}^{*}\gamma$, and $D^0\to\rho^0\gamma$. We obtain 90% CL upper limits on the branching ratios of these modes of $1.9\times 10^{-4}$, $2.4\times 10^{-4}$, $7.6\times 10^{-4}$ and $2.4\times 10^{-4}$ respectively.Comment: 15 page postscript file, postscript file also available through http://w4.lns.cornell.edu/public/CLN