Variable Weighted Ordered Subset Image Reconstruction Algorithm

We propose two variable weighted iterative reconstruction algorithms (VW-ART and VW-OS-SART) to improve the algebraic reconstruction technique (ART) and simultaneous algebraic reconstruction technique (SART) and establish their convergence. In the two algorithms, the weighting varies with the geometrical direction of the ray. Experimental results with both numerical simulation and real CT data demonstrate that the VW-ART has a significant improvement in the quality of reconstructed images over ART and OS-SART. Moreover, both VW-ART and VW-OS-SART are more promising in convergence speed than the ART and SART, respectively

Weak degeneracy of planar graphs and locally planar graphs

Weak degeneracy is a variation of degeneracy which shares many nice properties of degeneracy. In particular, if a graph $G$ is weakly $d$-degenerate, then for any $(d + 1)$-list assignment $L$ of $G$, one can construct an $L$-coloring of $G$ by a modified greedy coloring algorithm. It is known that planar graphs of girth 5 are 3-choosable and locally planar graphs are 5-choosable. This paper strengthens these results and proves that planar graphs of girth 5 are weakly 2-degenerate and locally planar graphs are weakly 4-degenerate.Comment: 13page

Verification of Bell Nonlocality by Violating Quantum Monogamy Relations

Quantum nonlocality as a witness of entanglement plays a crucial role in various fields. Existing quantum monogamy relations rule out the possibility of simultaneous violations of any Bell inequalities with partial statistics generated from one Bell experiment on any multipartite entanglement or post-quantum sources. In this paper, we report an efficient method to construct multipartite Bell test based on any Bell inequalities. We demonstrate that violating these monogamy relations can dynamically witness simultaneous Bell nonlocalities of partial systems. We conduct a tripartite experiment to verify quantum nonlocalities by violating a tripartite monogamy relation using a maximally entangled two-photon state.Comment: Maintext is included. SI is included in the published version (open access

Dipole field driven morphology evolution in biomimetic vaterite

Morphology evolution is an important process in naturally occurring biominerals. To investigate the interaction between biomolecules and inorganic components in the construction of biominerals, biomimetic hexagonal prism vaterite crystals were hydrothermally prepared through a reaction of urea with calcium nitrate tetrahydrate, whilst gelatin was added as a structure directing agent. An extraordinary morphology evolution was observed. The time dependent growth was investigated by using X-ray diffraction, scanning electron microscopy, transmission electron microscopy and thermogravimetric analysis. In the early stages, vaterite nanocrystallites, ~5 nm in diameter, underwent aggregation with gelatin molecules and precursor molecules into 50 nm sized clusters. Some nanoneedles, consisting of self-orientated nanocrystallites embedded within a soft gelatin matrix, were developed on the surface of disordered cores to form spherulite particles, with a similar morphology to natural spherulite biominerals. Further growth was affected by the high viscosity of gelatin, resulting in ellipsoid particles composed of spherulitically ordered needles. It is proposed that surface adsorbed gelatin induces the formation of dipoles in the nanocrystallites and interaction between the dipoles is the driving force of the alignment of the nanocrystallites. Further growth might create a relatively strong and mirror-symmetric dipolar field, followed by a morphology change from ellipsoidal with a cell-division like splitting, to twin-cauliflower, dumbbell, cylindrical and finally to hexagonal prism particles. In this morphology evolution, the alignment of the crystallites changes from 1D linear manner (single crystal like) to 3D radial pattern, and finally to mirror symmetric 1D linear manner. This newly proposed mechanism sheds light on the microstructural evolution in many biomimetic materials and biominerals.PostprintPeer reviewe

Efficient Private SCO for Heavy-Tailed Data via Clipping

We consider stochastic convex optimization for heavy-tailed data with the guarantee of being differentially private (DP). Prior work on this problem is restricted to the gradient descent (GD) method, which is inefficient for large-scale problems. In this paper, we resolve this issue and derive the first high-probability bounds for the private stochastic method with clipping. For general convex problems, we derive excess population risks \Tilde{O}\left(\frac{d^{1/7}\sqrt{\ln\frac{(n \epsilon)^2}{\beta d}}}{(n\epsilon)^{2/7}}\right) and \Tilde{O}\left(\frac{d^{1/7}\ln\frac{(n\epsilon)^2}{\beta d}}{(n\epsilon)^{2/7}}\right) under bounded or unbounded domain assumption, respectively (here $n$ is the sample size, $d$ is the dimension of the data, $\beta$ is the confidence level and $\epsilon$ is the private level). Then, we extend our analysis to the strongly convex case and non-smooth case (which works for generalized smooth objectives with H$\ddot{\text{o}}$lder-continuous gradients). We establish new excess risk bounds without bounded domain assumption. The results above achieve lower excess risks and gradient complexities than existing methods in their corresponding cases. Numerical experiments are conducted to justify the theoretical improvement