Abstract. We propose, analyze, and test an alternating minimization algorithm for recovering images from blurry and noisy observations with total variation (TV) regularization. This algorithm arises from a new half-quadratic model applicable to not only the anisotropic but also the isotropic forms of TV discretizations. The per-iteration computational complexity of the algorithm is three fast Fourier transforms. We establish strong convergence properties for the algorithm including finite convergence for some variables and relatively fast exponential (or q-linear in optimization terminology) convergence for the others. Furthermore, we propose a continuation scheme to accelerate the practical convergence of the algorithm. Extensive numerical results show that our algorithm performs favorably in comparison to several state-of-the-art algorithms. In particular, it runs orders of magnitude faster than the lagged diffusivity algorithm for TV-based deblurring. Some extensions of our algorithm are also discussed.

Titanium dioxide (TiO2 ) nanocrystals are prepared by a hydrolysis process of tetrabutyl titanate. Nanocrystal samples with various sizes of 6.8-27.9 nm are obtained after annealing from 100 to 650 °C. The crystal structures and the average particle sizes are examined using x-ray diffraction. Raman scattering was employed to investigate the evolution of the anatase phase in the nanocrystals during annealing. Phonon confinement and non-stoichiometry effects are responsible for the blueshift and broadening of the lowest-frequency E g Raman mode. The influence of interfacial vibrations on the Raman linewidth is also discussed.

Monoclonal antibodies have therapeutic potential for treating diseases of the central nervous system, but their accumulation in the brain is limited by the blood-brain barrier (BBB). Here, we show that reducing the affinity of an antibody for the transferrin receptor (TfR) enhances receptor-mediated transcytosis of the anti-TfR antibody across the BBB into the mouse brain where it reaches therapeutically relevant concentrations. Anti-TfR antibodies that bind with high affinity to TfR remain associated with the BBB, whereas lower-affinity anti-TfR antibody variants are released from the BBB into the brain and show a broad distribution 24 hours after dosing. We designed a bispecific antibody that binds with low affinity to TfR and with high affinity to the enzyme β-secretase (BACE1), which processes amyloid precursor protein into amyloid-β (Aβ) peptides including those associated with Alzheimer's disease. Compared to monospecific anti-BACE1 antibody, the bispecific antibody accumulated in the mouse brain and led to a greater reduction in brain Aβ after a single systemic dose. TfR-facilitated transcytosis of this bispecific antibody across the BBB may enhance its potency as an anti-BACE1 therapy for treating Alzheimer's disease.

Abstract. The matrix completion problem is to recover a low-rank matrix from a subset of its entries. The main solution strategy for this problem has been based on nuclear-norm minimization which requires computing singular value decompositions -a task that is increasingly costly as matrix sizes and ranks increase. To improve the capacity of solving large-scale problems, we propose a low-rank factorization model and construct a nonlinear successive over-relaxation (SOR) algorithm that only requires solving a linear least squares problem per iteration. Convergence of this nonlinear SOR algorithm is analyzed. Numerical results show that the algorithm can reliably solve a wide range of problems at a speed at least several times faster than many nuclear-norm minimization algorithms.

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A biodegradable drug delivery system (DDS) is one the most promising therapeutic strategies for cancer therapy. Here, we propose a unique concept of light activation of black phosphorus (BP) at hydrogel nanostructures for cancer therapy. A photosensitizer converts light into heat that softens and melts drug-loaded hydrogel-based nanostructures. Drug release rates can be accurately controlled by light intensity, exposure duration, BP concentration, and hydrogel composition. Owing to sufficiently deep penetration of near-infrared (NIR) light through tissues, our BP-based system shows high therapeutic efficacy for treatment of s.c. cancers. Importantly, our drug delivery system is completely harmless and degradable in vivo. Together, our work proposes a unique concept for precision cancer therapy by external light excitation to release cancer drugs. If these findings are successfully translated into the clinic, millions of patients with cancer will benefit from our work.

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Graphene, with its excellent physical, chemical, and mechanical properties, holds tremendous potential for a wide variety of biomedical applications. As research on graphene-based nanomaterials is still at a nascent stage, due to the very short time span since its initial report in 2004, a focused review on this topic is timely and necessary. In this feature review, we first summarize the results from toxicity studies of graphene and its derivatives. Although literature reports have mixed findings, we emphasize that the key question is not how toxic graphene itself is, but how to modify and functionalize it and its derivatives so that they do not exhibit acute/chronic toxicity, can be cleared from the body over time, and thereby can be best used for biomedical applications. Next, we discuss in detail the exploration of graphene-based nanomaterials for tissue engineering, molecular imaging, and drug/gene delivery applications. The future of graphene-based nanomaterials in biomedicine looks brighter than ever, and it is expected that they will find a wide range of biomedical applications with future research effort and interdisciplinary collaboration.