On Solving L-SR1 Trust-Region Subproblems

In this article, we consider solvers for large-scale trust-region subproblems when the quadratic model is defined by a limited-memory symmetric rank-one (L-SR1) quasi-Newton matrix. We propose a solver that exploits the compact representation of L-SR1 matrices. Our approach makes use of both an orthonormal basis for the eigenspace of the L-SR1 matrix and the Sherman-Morrison-Woodbury formula to compute global solutions to trust-region subproblems. To compute the optimal Lagrange multiplier for the trust-region constraint, we use Newton's method with a judicious initial guess that does not require safeguarding. A crucial property of this solver is that it is able to compute high-accuracy solutions even in the so-called hard case. Additionally, the optimal solution is determined directly by formula, not iteratively. Numerical experiments demonstrate the effectiveness of this solver.Comment: 2015-0

Convergence Analysis of Fixed Point Chance Constrained Optimal Power Flow Problems

For optimal power flow problems with chance constraints, a particularly effective method is based on a fixed point iteration applied to a sequence of deterministic power flow problems. However, a priori, the convergence of such an approach is not necessarily guaranteed. This article analyses the convergence conditions for this fixed point approach, and reports numerical experiments including for large IEEE networks

An LDLTLDL^T Trust-Region Quasi-Newton Method

For quasi-Newton methods in unconstrained minimization, it is valuable to develop methods that are robust, i.e., methods that converge on a large number of problems. Trust-region algorithms are often regarded to be more robust than line-search methods, however, because trust-region methods are computationally more expensive, the most popular quasi-Newton implementations use line-search methods. To fill this gap, we develop a trust-region method that updates an $LDL^T$ factorization, scales quadratically with the size of the problem, and is competitive with a conventional line-search method

PLSS: A Projected Linear Systems Solver

We propose iterative projection methods for solving square or rectangular consistent linear systems $Ax = b$. Projection methods use sketching matrices (possibly randomized) to generate a sequence of small projected subproblems, but even the smaller systems can be costly. We develop a process that appends one column each iteration to the sketching matrix and that converges in a finite number of iterations independent of whether the sketch is random or deterministic. In general, our process generates orthogonal updates to the approximate solution $x_k$. By choosing the sketch to be the set of all previous residuals, we obtain a simple recursive update and convergence in at most rank($A$) iterations (in exact arithmetic). By choosing a sequence of identity columns for the sketch, we develop a generalization of the Kaczmarz method. In experiments on large sparse systems, our method (PLSS) with residual sketches is competitive with LSQR, and our method with residual and identity sketches compares favorably to state-of-the-art randomized methods

Shape-Changing Trust-Region Methods Using Multipoint Symmetric Secant Matrices

In this work, we consider methods for large-scale and nonconvex unconstrained optimization. We propose a new trust-region method whose subproblem is defined using a so-called "shape-changing" norm together with densely-initialized multipoint symmetric secant (MSS) matrices to approximate the Hessian. Shape-changing norms and dense initializations have been successfully used in the context of traditional quasi-Newton methods, but have yet to be explored in the case of MSS methods. Numerical results suggest that trust-region methods that use densely-initialized MSS matrices together with shape-changing norms outperform MSS with other trust-region methods

Dynamic L-type CaV1.2 channel trafficking facilitates CaV1.2 clustering and cooperative gating.

L-type CaV1.2 channels are key regulators of gene expression, cell excitability and muscle contraction. CaV1.2 channels organize in clusters throughout the plasma membrane. This channel organization has been suggested to contribute to the concerted activation of adjacent CaV1.2 channels (e.g. cooperative gating). Here, we tested the hypothesis that dynamic intracellular and perimembrane trafficking of CaV1.2 channels is critical for formation and dissolution of functional channel clusters mediating cooperative gating. We found that CaV1.2 moves in vesicular structures of circular and tubular shape with diverse intracellular and submembrane trafficking patterns. Both microtubules and actin filaments are required for dynamic movement of CaV1.2 vesicles. These vesicles undergo constitutive homotypic fusion and fission events that sustain CaV1.2 clustering, channel activity and cooperative gating. Our study suggests that CaV1.2 clusters and activity can be modulated by diverse and unique intracellular and perimembrane vesicular dynamics to fine-tune Ca2+ signals

Treatment intensification in HIV-infected Patients is associated With reduced Frequencies of regulatory T cells

In untreated HIV infection, the efficacy of T cell responses decreases over the disease course, resulting in disease progression. The reasons for this development are not completely understood. However, immunosuppressive cells are supposedly crucially involved. Treatment strategies to avoid the induction of these cells preserve immune functions and are therefore the object of intense research efforts. In this study, we assessed the effect of treatment intensification [= 5-drug antiretroviral therapy (ART)] on the development of suppressive cell subsets. The New Era (NE) study recruited patients with primary HIV infection (PHI) or chronically HIV-infected patients with conventional ART (CHI) and applied an intensified 5-drug regimen containing maraviroc and raltegravir for several years. We compared the frequencies of the immune suppressive cells, namely, the myeloid-derived suppressor cells (MDSCs), regulatory B cells (Bregs), and regulatory T cells (Tregs), of the treatment intensification patients to the control groups, especially to the patients with conventional 3-drug ART, and analyzed the Gag/Nef-specific CD8 T cell responses. There were no differences between PHI and CHI in the NE population (p > 0.11) for any of the studied cell types. Polymorphonuclear myeloid-derived suppressor cell (PMN-MDSC), monocytic myeloid-derived suppressor cell (M-MDSC), and the Breg frequencies were comparable to those of patients with a 3-drug ART. However, the Treg levels were significantly lower in the NE patients than those in 3ART-treated individuals and other control groups (p = 0.0033). The Gag/Nef-specific CD8 T cell response was broader (p = 0.0134) with a higher magnitude (p = 0.026) in the NE population than that in the patients with conventional ART. However, we did not find a correlation between the frequency of the immune suppressive cells and the interferon-gamma+ CD8 T cell response. In the treatment intensification subjects, the frequencies of the immune suppressive cells were comparable or lower than those of the conventional ART-treated subjects, with surprisingly broad HIV-specific CD8 T cell responses, suggesting a preservation of immune function with the applied treatment regimen. Interestingly, these effects were seen in both treatment intensification subpopulations and were not attributed to the start of treatment in primary infection

Music and the brain: disorders of musical listening

The study of the brain bases for normal musical listening has advanced greatly in the last 30 years. The evidence from basic and clinical neuroscience suggests that listening to music involves many cognitive components with distinct brain substrates. Using patient cases reported in the literature, we develop an approach for understanding disordered musical listening that is based on the systematic assessment of the perceptual and cognitive analysis of music and its emotional effect. This approach can be applied both to acquired and congenital deficits of musical listening, and to aberrant listening in patients with musical hallucinations. Both the bases for normal musical listening and the clinical assessment of disorders now have a solid grounding in systems neuroscience

Useful Compact Representations for Data-Fitting

For minimization problems without 2nd derivative information, methods that estimate Hessian matrices can be very effective. However, conventional techniques generate dense matrices that are prohibitive for large problems. Limited-memory compact representations express the dense arrays in terms of a low rank representation and have become the state-of-the-art for software implementations on large deterministic problems. We develop new compact representations that are parameterized by a choice of vectors and that reduce to existing well known formulas for special choices. We demonstrate effectiveness of the compact representations for large eigenvalue computations, tensor factorizations and nonlinear regressions