Achieving Super-Resolution in Multi-Rate Sampling Systems via Efficient Semidefinite Programming

Super-resolution theory aims to estimate the discrete components lying in a continuous space that constitute a sparse signal with optimal precision. This work investigates the potential of recent super-resolution techniques for spectral estimation in multi-rate sampling systems. It shows that, under the existence of a common supporting grid, and under a minimal separation constraint, the frequencies of a spectrally sparse signal can be exactly jointly recovered from the output of a semidefinite program (SDP). The algorithmic complexity of this approach is discussed, and an equivalent SDP of minimal dimension is derived by extending the Gram parametrization properties of sparse trigonometric polynomials

Universal two-step crystallization of DNA-functionalized nanoparticles

We examine the crystallization dynamics of nanoparticles reversibly tethered by DNA hybridization. We show that the crystallization happens readily only in a narrow temperature "slot," and always proceeds via a two-step process, mediated by a highly-connected amorphous intermediate. For lower temperature quenches, the dynamics of unzipping strands in the amorphous state is sufficiently slow that crystallization is kinetically hindered. This accounts for the well-documented difficulty of forming crystals in these systems. The strong parallel to the crystallization behavior of proteins and colloids suggests that these disparate systems crystallize in an apparently universal manner.Comment: Accepted for publication in Soft Matte

Compressive Sensing DNA Microarrays

Compressive sensing microarrays (CSMs) are DNA-based sensors that operate using group testing and compressive sensing (CS) principles. In contrast to conventional DNA microarrays, in which each genetic sensor is designed to respond to a single target, in a CSM, each sensor responds to a set of targets. We study the problem of designing CSMs that simultaneously account for both the constraints from CS theory and the biochemistry of probe-target DNA hybridization. An appropriate cross-hybridization model is proposed for CSMs, and several methods are developed for probe design and CS signal recovery based on the new model. Lab experiments suggest that in order to achieve accurate hybridization profiling, consensus probe sequences are required to have sequence homology of at least 80% with all targets to be detected. Furthermore, out-of-equilibrium datasets are usually as accurate as those obtained from equilibrium conditions. Consequently, one can use CSMs in applications in which only short hybridization times are allowed

The Short Range Mechanism of N-N interaction in the Extended Chiral SU(3) Quark Model

We give the comparisons between the chiral SU(3) quark model and the extended chiral SU(3) quark model. The results show that the phase shifts of NN scattering are very similar. However, the short range mechanisms of nucleon-nucleon interaction are totally different. In the chiral SU(3) quark model, the short range interaction is dominantly from OGE, and in the extended chiral SU(3) quark model, it is dominantly from vector meson exchanges.Comment: 4 pages, 1 figure. Contribution talk at MENU2004, to be published in Int. J. Mod. Phys. A (World Sciences

Determination of the Sign of g factors for Conduction Electrons Using Time-resolved Kerr Rotation

The knowledge of electron g factor is essential for spin manipulation in the field of spintronics and quantum computing. While there exist technical difficulties in determining the sign of g factor in semiconductors by the established magneto-optical spectroscopic methods. We develop a time resolved Kerr rotation technique to precisely measure the sign and the amplitude of electron g factor in semiconductors

Block Spin Ground State and 3-Dimensionality of (K,Tl)Fe1.6_{1.6}Se2_2

The magnetic properties and electronic structure of (K,Tl)y Fe1.6 Se2 is studied using first-principles calculations. The ground state is checkerboard antiferromagnetically coupled blocks of the minimal Fe4 squares, with a large block spin moment ~11.2{\mu}B . The magnetic interactions could be modelled with a simple spin model involving both the inter- and intra-block, as well as the n.n. and n.n.n. couplings. The calculations also suggest a metallic ground state except for y = 0.8 where a band gap ~400 - 550 meV opens, showing an antiferromagnetic insulator ground state for (K,Tl)0.8 Fe1.6 Se2 . The electronic structure of the metallic (K,Tl)y Fe1.6 Se2 is highly 3-dimensional with unique Fermi surface structure and topology. These features indicate that the Fe-vacancy ordering is crucial to the physical properties of (K,Tl)y Fe2-x Se2 .Comment: Magnetic coupling constants double checked, journal ref. adde

Convergence of Gradient Descent for Low-Rank Matrix Approximation

This paper provides a proof of global convergence of gradient search for low-rank matrix approximation. Such approximations have recently been of interest for large-scale problems, as well as for dictionary learning for sparse signal representations and matrix completion. The proof is based on the interpretation of the problem as an optimization on the Grassmann manifold and Fubiny-Study distance on this space

Neutrino emission from a GRB afterglow shock during an inner supernova shock breakout

The observations of a nearby low-luminosity gamma-ray burst (GRB) 060218 associated with supernova SN 2006aj may imply an interesting astronomical picture where a supernova shock breakout locates behind a relativistic GRB jet. Based on this picture, we study neutrino emission for early afterglows of GRB 060218-like GRBs, where neutrinos are expected to be produced from photopion interactions in a GRB blast wave that propagates into a dense wind. Relativistic protons for the interactions are accelerated by an external shock, while target photons are basically provided by the incoming thermal emission from the shock breakout and its inverse-Compton scattered component. Because of a high estimated event rate of low-luminosity GRBs, we would have more opportunities to detect afterglow neutrinos from a single nearby GRB event of this type by IceCube. Such a possible detection could provide evidence for the picture described above.Comment: 6 pages, 2 figures, accepted for publication in MNRA