A Revisit to Quadratic Programming with One Inequality Quadratic Constraint via Matrix Pencil

The quadratic programming over one inequality quadratic constraint (QP1QC) is a very special case of quadratically constrained quadratic programming (QCQP) and attracted much attention since early 1990's. It is now understood that, under the primal Slater condition, (QP1QC) has a tight SDP relaxation (PSDP). The optimal solution to (QP1QC), if exists, can be obtained by a matrix rank one decomposition of the optimal matrix X? to (PSDP). In this paper, we pay a revisit to (QP1QC) by analyzing the associated matrix pencil of two symmetric real matrices A and B, the former matrix of which defines the quadratic term of the objective function whereas the latter for the constraint. We focus on the \undesired" (QP1QC) problems which are often ignored in typical literature: either there exists no Slater point, or (QP1QC) is unbounded below, or (QP1QC) is bounded below but unattainable. Our analysis is conducted with the help of the matrix pencil, not only for checking whether the undesired cases do happen, but also for an alternative way to compute the optimal solution in comparison with the usual SDP/rank-one-decomposition procedure.Comment: 22 pages, 0 figure

The Necessary And Sufficient Condition for Generalized Demixing

Demixing is the problem of identifying multiple structured signals from a superimposed observation. This work analyzes a general framework, based on convex optimization, for solving demixing problems. We present a new solution to determine whether or not a specific convex optimization problem built for generalized demixing is successful. This solution will also bring about the possibility to estimate the probability of success by the approximate kinematic formula

DNA origami protection and molecular interfacing through engineered sequence-defined peptoids

DNA nanotechnology has established approaches for designing programmable and precisely controlled nanoscale architectures through specific Watson−Crick base-pairing, molecular plasticity, and intermolecular connectivity. In particular, superior control over DNA origami structures could be beneficial for biomedical applications, including biosensing, in vivo imaging, and drug and gene delivery. However, protecting DNA origami structures in complex biological fluids while preserving their structural characteristics remains a major challenge for enabling these applications. Here, we developed a class of structurally well-defined peptoids to protect DNA origamis in ionic and bioactive conditions and systematically explored the effects of peptoid architecture and sequence dependency on DNA origami stability. The applicability of this approach for drug delivery, bioimaging, and cell targeting was also demonstrated. A series of peptoids (PE1–9) with two types of architectures, termed as “brush” and “block,” were built from positively charged monomers and neutral oligo-ethyleneoxy monomers, where certain designs were found to greatly enhance the stability of DNA origami. Through experimental and molecular dynamics studies, we demonstrated the role of sequence-dependent electrostatic interactions of peptoids with the DNA backbone. We showed that octahedral DNA origamis coated with peptoid (PE2) can be used as carriers for anticancer drug and protein, where the peptoid modulated the rate of drug release and prolonged protein stability against proteolytic hydrolysis. Finally, we synthesized two alkyne-modified peptoids (PE8 and PE9), conjugated with fluorophore and antibody, to make stable DNA origamis with imaging and cell-targeting capabilities. Our results demonstrate an approach toward functional and physiologically stable DNA origami for biomedical applications

Plasmoid ejection and secondary current sheet generation from magnetic reconnection in laser-plasma interaction

Reconnection of the self-generated magnetic fields in laser-plasma interaction was first investigated experimentally by Nilson {\it et al.} [Phys. Rev. Lett. 97, 255001 (2006)] by shining two laser pulses a distance apart on a solid target layer. An elongated current sheet (CS) was observed in the plasma between the two laser spots. In order to more closely model magnetotail reconnection, here two side-by-side thin target layers, instead of a single one, are used. It is found that at one end of the elongated CS a fan-like electron outflow region including three well-collimated electron jets appears. The ($>1$ MeV) tail of the jet energy distribution exhibits a power-law scaling. The enhanced electron acceleration is attributed to the intense inductive electric field in the narrow electron dominated reconnection region, as well as additional acceleration as they are trapped inside the rapidly moving plasmoid formed in and ejected from the CS. The ejection also induces a secondary CS

Photometric calibration of the Stellar Abundance and Galactic Evolution Survey (SAGES): Nanshan One-meter Wide-field Telescope g, r, and i band imaging data

In this paper, a total of approximately 2.6 million dwarfs were constructed as standard stars, with an accuracy of about 0.01-0.02 mag for each band, by combining spectroscopic data from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope Data Release 7, photometric data from the corrected Gaia Early Data Release 3, and photometric metallicities. Using the spectroscopy based stellar color regression method (SCR method) and the photometric-based SCR method (SCR' method), we performed the relative calibration of the Nanshan One-meter Wide-field Telescope imaging data. Based on the corrected Pan-STARRS DR1 photometry, the absolute calibration was also performed. In the photometric calibration process, we analyzed the dependence of the calibration zero points on different images (observation time), different gates of the CCD detector, and different CCD positions. We found that the stellar flat and the relative gain between different gates depend on time. The amplitude of gain variation in three channels is approximately 0.5%-0.7% relative to the other channel, with a maximum value of 4%. In addition, significant spatial variations of the stellar flat fitting residual are found and corrected. Using repeated sources in the adjacent images, we checked and discovered internal consistency of about 1-2 mmag in all the filters. Using the PS1 magnitudes synthesized by Gaia DR3 BP/RP spectra by the synthetic photometry method, we found that the photometric calibration uniformity is about 1-2 mmag for all the bands, at a spatial resolution of 1.3 degree. A detailed comparison between the spectroscopy-based SCR and photometric-based SCR method magnitude offsets was performed, and we achieved an internal consistency precision of about 2 mmag or better with resolutions of 1.3 degree for all the filters. Which is mainly from the position-dependent errors of the E(B-V) used in SCR' method.Comment: 15 pages in Chinese language, 8 figures, Chinese Science Bulletin accepted and published online (https://www.sciengine.com/CSB/doi/10.1360/TB-2023-0052), see main results in Figures 6, 7 and