Composite Cyclotomic Fourier Transforms with Reduced Complexities

Discrete Fourier transforms~(DFTs) over finite fields have widespread applications in digital communication and storage systems. Hence, reducing the computational complexities of DFTs is of great significance. Recently proposed cyclotomic fast Fourier transforms (CFFTs) are promising due to their low multiplicative complexities. Unfortunately, there are two issues with CFFTs: (1) they rely on efficient short cyclic convolution algorithms, which has not been investigated thoroughly yet, and (2) they have very high additive complexities when directly implemented. In this paper, we address both issues. One of the main contributions of this paper is efficient bilinear 11-point cyclic convolution algorithms, which allow us to construct CFFTs over GF$(2^{11})$. The other main contribution of this paper is that we propose composite cyclotomic Fourier transforms (CCFTs). In comparison to previously proposed fast Fourier transforms, our CCFTs achieve lower overall complexities for moderate to long lengths, and the improvement significantly increases as the length grows. Our 2047-point and 4095-point CCFTs are also first efficient DFTs of such lengths to the best of our knowledge. Finally, our CCFTs are also advantageous for hardware implementations due to their regular and modular structure.Comment: submitted to IEEE trans on Signal Processin

Elaboration and characterization of nanoplate structured alpha-Fe2O3 films by Ag3PO4

A new strategy for surface treatment of hematite nanoplates for efficient photoelectrochemical (PEC) performances is proposed. Silver orthophosphate (Ag₃PO₄) has been adopted to mediate the formation of α-Fe₂O₃ films. Phosphate ions in Ag₃PO₄ is found to cause a significant morphology change during annealing process, from β-FeOOH nanorod arrays to hematite nanoplates. Meanwhile, Ag ions is doped into α-Fe₂O₃ film. The obtained nanoplate structured Fe₂O₃ –Ag–P films demonstrate much higher photoelectrochemical performance as photoanodes than the bare Fe₂O₃ nanorod thin films. The effects of phosphate and silver ions on the morphology, surface characteristics and the PEC properties of the photoanodes are investigated

Reduced-Complexity Decoder of Long Reed-Solomon Codes Based on Composite Cyclotomic Fourier Transforms

Long Reed-Solomon (RS) codes are desirable for digital communication and storage systems due to their improved error performance, but the high computational complexity of their decoders is a key obstacle to their adoption in practice. As discrete Fourier transforms (DFTs) can evaluate a polynomial at multiple points, efficient DFT algorithms are promising in reducing the computational complexities of syndrome based decoders for long RS codes. In this paper, we first propose partial composite cyclotomic Fourier transforms (CCFTs) and then devise syndrome based decoders for long RS codes over large finite fields based on partial CCFTs. The new decoders based on partial CCFTs achieve a significant saving of computational complexities for long RS codes. Since partial CCFTs have modular and regular structures, the new decoders are suitable for hardware implementations. To further verify and demonstrate the advantages of partial CCFTs, we implement in hardware the syndrome computation block for a $(2720, 2550)$ shortened RS code over GF$(2^{12})$. In comparison to previous results based on Horner's rule, our hardware implementation not only has a smaller gate count, but also achieves much higher throughputs.Comment: 7 pages, 1 figur

CaSiO3 microstructure modulating the in vitro and in vivo bioactivity of poly(lactide-co-glycolide) microspheres

Poly (lactide-co-glycolide) (PLGA) microspheres have been used for regenerative medicine due to their ability for drug delivery and generally good biocompatibility, but they lack adequate bioactivity for bone repair application. CaSiO3 (CS) has been proposed as a new class of material suitable for bone tissue repair due to its excellent bioactivity. In this study, we set out to incorporate CS into PLGA microspheres to investigate how the phase structure (amorphous and crystal) of CS influences the in vitro and in vivo bioactivity of the composite microspheres, with a view to the application for bone regeneration. X-ray diffraction (XRD), N2 adsorption-desorption analysis and scanning electron microscopy (SEM) were used to analyze the phase structure, surface area/pore volume, and microstructure of amorphous CS (aCS) and crystal CS (cCS), as well as their composite microspheres. The in vitro bioactivity of aCS and cCS – PLGA microspheres was evaluated by investigating their apatite-mineralization ability in simulated body fluids (SBF) and the viability of human bone mesenchymal stem cells (BMSCs). The in vivo bioactivity was investigated by measuring their de novo bone-formation ability. The results showed that the incorporation of both aCS and cCS enhanced the in vitro and in vivo bioactivity of PLGA microspheres. cCS/PLGA microspheres improved better in vitro BMSC viability and de novo bone-formation ability in vivo, compared to aCS/PLGA microspheres. Our study indicates that controlling the phase structure of CS is a promising method to modulate the bioactivity of polymer microsphere system for potential bone tissue regeneration

Weak antilocalization in epitaxial graphene: evidence for chiral electrons

Transport in ultrathin graphite grown on silicon carbide is dominated by the electron-doped epitaxial layer at the interface. Weak anti-localization in 2D samples manifests itself as a broad cusp-like depression in the longitudinal resistance for magnetic fields 10 mT$< B <$ 5 T. An extremely sharp weak-localization resistance peak at B=0 is also observed. These features quantitatively agree with graphene weak-(anti)localization theory implying the chiral electronic character of the samples. Scattering contributions from the trapped charges in the substrate and from trigonal warping due to the graphite layer on top are tentatively identified. The Shubnikov-de Haas oscillations are remarkably small and show an anomalous Berry's phase.Comment: 5 pages, 4 figures. Minor change

In situ growth of ultrathin Co-MOF nanosheets on Α-Fe2O3 hematite nanorods for efficient photoelectrochemical water oxidation

Efficient charge transport is an important factor in photoelectrochemical (PEC) water splitting. The charge transfer at the semiconductor/electrolyte interface is of great importance, especially for the complex water oxidation reaction. In this study, we explored the feasibility of improving charge transfer efficiency at the interface of semiconductor/electrolyte by in situ growth of Co based Metal-Organic Frame work (Co-MOF) through a facile ion-exchanging method. Under optimized conditions, the Co-MOF nanosheet-modified hematite gave a photocurrent density of 2.0 mA cm−2 (200% improvement) at 1.23 VRHE with a cathodic shift of 180 mV in the photocurrent onset potential, in comparison to bare α-Fe2O3 (0.71 mA cm−[email protected] VRHE). To elucidate the role of Co-MOF, X-ray photoelectron spectroscopy, electrochemical impedance spectroscopy and Mott-Schottky measurements were carried out. It was found that the atomically distributed Co2+ in Co-MOF possessed excellent hole storage capability and charge transfer efficiency, as evidenced by the high surface capacitance and extremely low surface charge transfer resistance