对一种快速双重指数模算法的复杂度研究

最近提出了一种采用标准符号数二进制码(canonic signed-digit binary representation,CSDBR)来计算AXBY(modN)的快速双重指数模算法.该算法声明当指数的长度为k时,该算法平均仅需要1.306k次模乘.由于已知的此类算法至少需要1.503k次模乘,该算法具有明显的性能优势.然而,无论是该算法的提出者还是其他研究者均没有给出正确的复杂度分析.本文通过利用马尔科夫链模型对该算法进行正式的复杂度研究并进行一定规模的统计实验后证实,实际上该算法平均需要1.556k次模乘.这项研究的意义在于揭示到目前为止,基于标准符号数位码的双重指数模算法的最高性能仍然无法降低到1.5k次模乘以下.     

Horses damp the spring in their step.

The muscular work of galloping in horses is halved by storing and returning elastic strain energy in spring-like muscle-tendon units.These make the legs act like a child's pogo stick that is tuned to stretch and recoil at 2.5 strides per second. This mechanism is optimized by unique musculoskeletal adaptations: the digital flexor muscles have extremely short fibres and significant passive properties, whereas the tendons are very long and span several joints. Length change occurs by a stretching of the spring-like digital flexor tendons rather than through energetically expensive length changes in the muscle. Despite being apparently redundant for such a mechanism, the muscle fibres in the digital flexors are well developed. Here we show that the mechanical arrangement of the elastic leg permits it to vibrate at a higher frequency of 30-40 Hz that could cause fatigue damage to tendon and bone. Furthermore, we show that the digital flexor muscles have minimal ability to contribute to or regulate significantly the 2.5-Hz cycle of movement, but are ideally arranged to damp these high-frequency oscillations in the limb.     

Magma storage beneath Axial volcano on the Juan de Fuca mid-ocean ridge.

Axial volcano, which is located near the intersection of the Juan de Fuca ridge and the Cobb-Eickelberg seamount chain beneath the northeast Pacific Ocean, is a locus of volcanic activity thought to be associated with the Cobb hotspot. The volcano rises 700 metres above the ridge, has substantial rift zones extending about 50 kilometres to the north and south, and has erupted as recently as 1998 (ref. 2). Here we present seismological data that constrain the three-dimensional velocity structure beneath the volcano. We image a large low-velocity zone in the crust, consisting of a shallow magma chamber and a more diffuse reservoir in the lower crust, and estimate the total magma volume in the system to be between 5 and 21 km3. This volume is two orders of magnitude larger than the amount of melt emplaced during the most recent eruption (0.1-0.2 km3). We therefore infer that such volcanic events remove only a small portion of the reservoir that they tap, which must accordingly be long-lived compared to the eruption cycle. On the basis of magma flux estimates, we estimate the crustal residence time of melt in the volcanic system to be a few hundred to a few thousand years.     

Chemistry of ion coordination and hydration revealed by a K+ channel-Fab complex at 2.0 A resolution.

Ion transport proteins must remove an ion's hydration shell to coordinate the ion selectively on the basis of its size and charge. To discover how the K+ channel solves this fundamental aspect of ion conduction, we solved the structure of the KcsA K+ channel in complex with a monoclonal Fab antibody fragment at 2.0 A resolution. Here we show how the K+ channel displaces water molecules around an ion at its extracellular entryway, and how it holds a K+ ion in a square antiprism of water molecules in a cavity near its intracellular entryway. Carbonyl oxygen atoms within the selectivity filter form a very similar square antiprism around each K+ binding site, as if to mimic the waters of hydration. The selectivity filter changes its ion coordination structure in low K+ solutions. This structural change is crucial to the operation of the selectivity filter in the cellular context, where the K+ ion concentration near the selectivity filter varies in response to channel gating.     

An Adaptive Design for Six Sigma（ ADFSS ） ： a Simulated Annealing and Regression Analysis Embedded Approach

Design for six sigma (DFSS) is a powerful approach of designing products,processes,and services with the objective of meeting the needs of customers in a cost-effective manner.DFSS activities are class...     

Mars' volatile and climate history.

There is substantial evidence that the martian volatile inventory and climate have changed markedly throughout the planet's history. Clues come from areas as disparate as the history and properties of the deep interior, the composition of the crust and regolith, the morphology of the surface, composition of the present-day atmosphere, and the nature of the interactions between the upper atmosphere and the solar wind. We piece together the relevant observations into a coherent view of the evolution of the martian climate, focusing in particular on the observations that provide the strongest constraints.     

Cyclin-dependent kinases prevent DNA re-replication through multiple mechanisms.

The stable propagation of genetic information requires that the entire genome of an organism be faithfully replicated once and only once each cell cycle. In eukaryotes, this replication is initiated at hundreds to thousands of replication origins distributed over the genome, each of which must be prohibited from re-initiating DNA replication within every cell cycle. How cells prevent re-initiation has been a long-standing question in cell biology. In several eukaryotes, cyclin-dependent kinases (CDKs) have been implicated in promoting the block to re-initiation, but exactly how they perform this function is unclear. Here we show that B-type CDKs in Saccharomyces cerevisiae prevent re-initiation through multiple overlapping mechanisms, including phosphorylation of the origin recognition complex (ORC), downregulation of Cdc6 activity, and nuclear exclusion of the Mcm2-7 complex. Only when all three inhibitory pathways are disrupted do origins re-initiate DNA replication in G2/M cells. These studies show that each of these three independent mechanisms of regulation is functionally important.     

香港室内氡水平及其与建筑物表面氡析出率的关系

本文报导用活性炭盒吸附方法对香港室内氡浓度的测量结果及其浓度分布规律。对室内氡浓度与建筑物表面氡析出率的关系进行了分析研究。证实室内空气中的氡主要来源于建材中的镭,而氡浓度水平只决定于室内建筑物表面氡的析出率及通风状况。