SDPNAL++: A Majorized Semismooth Newton-CG Augmented Lagrangian Method for Semidefinite Programming with Nonnegative Constraints

In this paper, we present a majorized semismooth Newton-CG augmented Lagrangian method, called SDPNAL$+$, for semidefinite programming (SDP) with partial or full nonnegative constraints on the matrix variable. SDPNAL$+$ is a much enhanced version of SDPNAL introduced by Zhao, Sun and Toh [SIAM Journal on Optimization, 20 (2010), pp.~1737--1765] for solving generic SDPs. SDPNAL works very efficiently for nondegenerate SDPs but may encounter numerical difficulty for degenerate ones. Here we tackle this numerical difficulty by employing a majorized semismooth Newton-CG augmented Lagrangian method coupled with a convergent 3-block alternating direction method of multipliers introduced recently by Sun, Toh and Yang [arXiv preprint arXiv:1404.5378, (2014)]. Numerical results for various large scale SDPs with or without nonnegative constraints show that the proposed method is not only fast but also robust in obtaining accurate solutions. It outperforms, by a significant margin, two other competitive publicly available first order methods based codes: (1) an alternating direction method of multipliers based solver called SDPAD by Wen, Goldfarb and Yin [Mathematical Programming Computation, 2 (2010), pp.~203--230] and (2) a two-easy-block-decomposition hybrid proximal extragradient method called 2EBD-HPE by Monteiro, Ortiz and Svaiter [Mathematical Programming Computation, (2013), pp.~1--48]. In contrast to these two codes, we are able to solve all the 95 difficult SDP problems arising from the relaxations of quadratic assignment problems tested in SDPNAL to an accuracy of $10^{-6}$ efficiently, while SDPAD and 2EBD-HPE successfully solve 30 and 16 problems, respectively.Comment: 43 pages, 1 figure, 5 table

Proto-Model of an Infrared Wide-Field Off-Axis Telescope

We develop a proto-model of an off-axis reflective telescope for infrared wide-field observations based on the design of Schwarzschild-Chang type telescope. With only two mirrors, this design achieves an entrance pupil diameter of 50 mm and an effective focal length of 100 mm. We can apply this design to a mid-infrared telescope with a field of view of 8 deg X 8 deg. In spite of the substantial advantages of off-axis telescopes in the infrared compared to refractive or on-axis reflective telescopes, it is known to be difficult to align the mirrors in off-axis systems because of their asymmetric structures. Off-axis mirrors of our telescope are manufactured at the Korea Basic Science Institute (KBSI). We analyze the fabricated mirror surfaces by fitting polynomial functions to the measured data. We accomplish alignment of this two-mirror off-axis system using a ray tracing method. A simple imaging test is performed to compare a pinhole image with a simulated prediction.Comment: 14 pages, 16 figure

Melittin restores proteasome function in an animal model of ALS

Amyotrophic lateral sclerosis (ALS) is a paralyzing disorder characterized by the progressive degeneration and death of motor neurons and occurs both as a sporadic and familial disease. Mutant SOD1 (mtSOD1) in motor neurons induces vulnerability to the disease through protein misfolding, mitochondrial dysfunction, oxidative damage, cytoskeletal abnormalities, defective axonal transport- and growth factor signaling, excitotoxicity, and neuro-inflammation

CIB1 protects against MPTP-induced neurotoxicity through inhibiting ASK1.

Calcium and integrin binding protein 1 (CIB1) is a calcium-binding protein that was initially identified as a binding partner of platelet integrin αIIb. Although CIB1 has been shown to interact with multiple proteins, its biological function in the brain remains unclear. Here, we show that CIB1 negatively regulates degeneration of dopaminergic neurons in a mouse model of Parkinson\u27s disease using 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP). Genetic deficiency of the CIB1 gene enhances MPTP-induced neurotoxicity in dopaminergic neurons in CIB1(-/-) mice. Furthermore, RNAi-mediated depletion of CIB1 in primary dopaminergic neurons potentiated 1-methyl-4-phenyl pyrinidium (MPP(+))-induced neuronal death. CIB1 physically associated with apoptosis signal-regulating kinase 1 (ASK1) and thereby inhibited the MPP(+)-induced stimulation of the ASK1-mediated signaling cascade. These findings suggest that CIB1 plays a protective role in MPTP/MPP(+)-induced neurotoxicity by blocking ASK1-mediated signaling

Diethyl 2-{4-diethyl­amino-2-[(dimethyl­carbamothio­yl)­oxy]benzyl­idene}malonate

In the title compound, C21H30N2O5S, the plane of the dimeth­yl–thio­carbamic group makes a dihedral angle of 78.41 (7)° with the central benzene ring. One of the carbonyl groups in the α,β-unsaturated malonate side chain makes a dihedral angle of 8.73 (10)° with the central benzene ring, while the other carbonyl group makes a dihedral angle of 81.52 (8)°