11 research outputs found
Accelerating BGV Bootstrapping for Large Using Null Polynomials Over
No full textThe BGV scheme is one of the most popular FHE schemes for computing homomorphic integer arithmetic. The bootstrapping technique of BGV is necessary to evaluate arbitrarily deep circuits homomorphically. However, the BGV bootstrapping performs poorly for large plaintext prime due to its digit removal procedure exhibiting a computational complexity of at least . In this paper, we propose optimizations for the digit removal procedure with large by leveraging the properties of null polynomials over the ring . Specifically, we demonstrate that it is possible to construct low-degree null polynomials based on two observations of the input to the digit removal procedure: 1) the support size of the input can be upper-bounded by ; 2) the size of the lower digits to be removed can be upper-bounded by . Here can be controlled within a narrow interval in our parameter selection, making the degree of these null polynomials much smaller than for large values of . These low-degree null polynomials can significantly reduce the polynomial degrees during homomorphic digit removal, thereby decreasing both running time and capacity consumption. Theoretically, our optimizations reduce the computational cost of extracting a single digit from (by Chen and Han) or (by Geelen et al.) to for some . We implement and benchmark our method on HElib with and . With our optimized digit removal, we achieve a bootstrapping throughput times that in HElib, with the speedup increasing with the value of . For , we accelerate the digit removal step by 80 times and reduce the bootstrapping time from more than 12 hours to less than 14 minutes
Searching for the parallel growth of cities
No full textThree urban growth theories predict parallel growth of cities. The endogenous growth theory predicts deterministic parallel growth; the random growth theory implies that city growth follows Gibrat’s law with a steady-state distribution; and the hybrid growth theory suggests the co-movement of random city growth. This paper uses the Chinese city size data from 1984-2006 and time series econometric techniques to test for parallel growth. The results from various types of stationarity tests on pooled heterogeneous cities show that city growth is random. However, once growth trend and structural change are taken into account, certain groups of cities with common group characteristics, such as similar natural resource endowment or policy regime, grow parallel.Urban growth; Parallel growth; Zipf’s law; Unit root; Structural change
Facile synthesis of monodisperse Mn3O4 tetragonal nanoparticles and their large-scale assembly into highly regular walls by a simple solution route
No full textThe synthesis of high-quality tetragonal Mn3O4 nanoparticles and the large-scale assembly of the nanoparticles into highly regularly walls using a simple solution method at low temperature and surfactant-free conditions was carried on. This synthesis route is easily controllable, well-repeatable, mild, and feasible for application to the fabrication of nanopatterns of other materials. Transmission electron microscopy (TEM) and the corresponding selected-area electron diffraction (SAED) pattern show uniform Mn3O4 tetragonal nanoparticles. The sharp SAED pattern, which can be obtained from any of the nanoparticles within the nanopatterns and parallel lattice fringes in high-resolution TEM (HRTEM) images, indicates that all of the quantum dots are Mn3O4 single crystals aligned along their c axis. The HRTEM images also show a finely dispersed configuration of the nanopatterns.http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000245560200011&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701Chemistry, MultidisciplinaryChemistry, PhysicalNanoscience & NanotechnologyMaterials Science, MultidisciplinaryPhysics, AppliedPhysics, Condensed MatterSCI(E)EI75ARTICLE4606-610
One-pot synthesis of highly crystallined lambda-MnO2 nanodisks assembled from nanoparticles: Morphology evolutions and phase transitions
No full textManganese oxides are important materials in many applications. We describe, for the first time, the facile one-pot synthesis of highly crystallined lambda-MnO2 nanodisks assembled from nanoparticles through a novel wet chemical route. Morphology evolutions, magnetic properties, and phase transitions are also studied by transmission electron microscopy, scanning electron rnicroscopy and thermal gravimetric analysis. A mechanism for the formation of the lambda-MnO2 nanodisks as well as their inner structure is proposed based on controlled experiments. The key to the successful preparation of this novel MnO2 nanostructure has been a synergic control of a surfactant, polyvinylpyrrolidone, and a solvent, dimethyl sulfoxide, capable of stabilizing the microreactors and promoting the assembly of manganese nanoparticles.http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000252287300009&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701Chemistry, PhysicalNanoscience & NanotechnologyMaterials Science, MultidisciplinarySCI(E)EI28ARTICLE2365-36911
One-step solution fabrication of magnetic chains consisting of jingle-bell-shaped cobalt mesospheres
No full textUsing a one-step solution phase approach, the authors have synthesized uniform jingle bell-shaped cobalt mesopheres (550-750 nm) and assembled the mesospheres into long magnetic chains (20-30 mu m). All of the cobalt spheres are hollow with similar to 40 nm thick shells but each contains an similar to 200 nm diameter solid ball. The nano- to mesoscale structures were realized via reaction of CoCl2 center dot 6H(2)O and N2H4 center dot H2O in the presence of polyvinylpyrrolidone (PVP) in an ethylene glycol solution. Magnetic measurements show a coercivity of about 75 Oe with a remnance of 9.6 emu/g at 300 K. We propose a possible mechanism for the formation of the nanoto mesoscale structures. (c) 2006 American Institute of Physics.Physics, AppliedSCI(E)EI0ARTICLE10null8
Integration of inverse nanocone array based bismuth vanadate photoanodes and bandgap-tunable perovskite solar cells for efficient self-powered solar water splitting
No full textBismuth vanadate (BiVO4) has been regarded as a promising photoanode material for photoelectrochemical (PEC) water splitting owing to its rich elemental abundance and relatively narrow bandgap. However, the incompatibility of the penetration depth and short diffusion length limits its performance. To overcome this shortcoming, we develop a cost-effective stamping method to fabricate inverse nanocone array (ICA) substrates for supporting nanoporous Mo-doped BiVO4 films. The ICAs show a remarkable light trapping effect in such a way that the intensive light absorption region is advantageously shifted from the top of the active layer on a planar substrate to the bottom surrounded by the ICA, where charge separation is strikingly more efficient. By integrating the ICA-photoanode with a tailor-made, bandgap-adjustable perovskite solar cell, we devised a PEC-photovoltaic (PEC-PV) tandem device, which has achieved a self-powered STH efficiency of around 6.3%. Our study opens a new avenue for designing solar fuel devices with PEC-PV architectures.NSFC/Hong Kong RGC Research Scheme [N_HKUST610/14]; HK-RGC General Research Funds (GRF) [16312216, 16300915]; HK Innovation and Technology Fund [ITS/219/16]; Shenzhen Peacock PlanSCI(E)ARTICLE3619091-19097
Magnetic nanochains of metal formed by assembly of small nanoparticles
No full textNi nanochains are synthesized with diameters of 150 - 250 nm and lengths of 0.5 - 2 mum by assembly of small nanoparticles, which exhibit a magnetic coercivity over two orders of magnitude larger than that of bulk Ni.Chemistry, MultidisciplinarySCI(E)73ARTICLE232726-272
Uniform magnetic chains of hollow cobalt mesospheres from one-pot synthesis and their assembly in solution
No full textMagnetic chains up to 10 mu m in length formed of hollow cobalt mesospheres (480-850 nm) with a 60 nm thick shell are synthesized by a new soft-assembly protocol. The obtained chains show a saturation magnetization of 37.5 emu g(-1), a remnant magnetization of 1.55 emu g(-1), and a coercivity of ca. 66 Oe at 300 K. A possible mechanism for the formation of the chainlike hollow structures is proposed.Chemistry, MultidisciplinaryChemistry, PhysicalNanoscience & NanotechnologyMaterials Science, MultidisciplinaryPhysics, AppliedPhysics, Condensed MatterSCI(E)EI132ARTICLE3425-4301
