Behavior of different numerical schemes for population genetic drift problems

In this paper, we focus on numerical methods for the genetic drift problems, which is governed by a degenerated convection-dominated parabolic equation. Due to the degeneration and convection, Dirac singularities will always be developed at boundary points as time evolves. In order to find a \emph{complete solution} which should keep the conservation of total probability and expectation, three different schemes based on finite volume methods are used to solve the equation numerically: one is a upwind scheme, the other two are different central schemes. We observed that all the methods are stable and can keep the total probability, but have totally different long-time behaviors concerning with the conservation of expectation. We prove that any extra infinitesimal diffusion leads to a same artificial steady state. So upwind scheme does not work due to its intrinsic numerical viscosity. We find one of the central schemes introduces a numerical viscosity term too, which is beyond the common understanding in the convection-diffusion community. Careful analysis is presented to prove that the other central scheme does work. Our study shows that the numerical methods should be carefully chosen and any method with intrinsic numerical viscosity must be avoided.Comment: 17 pages, 8 figure

Strain-Induced Spin-Nematic State and Nematic Susceptibility Arising from 2×2 Fe Clusters in KFe_{0.8}Ag_{1.2}Te_{2}.

Spin nematics break spin-rotational symmetry while maintaining time-reversal symmetry, analogous to liquid crystal nematics that break spatial rotational symmetry while maintaining translational symmetry. Although several candidate spin nematics have been proposed, the identification and characterization of such a state remain challenging because the spin-nematic order parameter does not couple directly to experimental probes. KFe_{0.8}Ag_{1.2}Te_{2} (K_{5}Fe_{4}Ag_{6}Te_{10}, KFAT) is a local-moment magnet consisting of well-separated 2×2 Fe clusters, and in its ground state the clusters order magnetically, breaking both spin-rotational and time-reversal symmetries. Using uniform magnetic susceptibility and neutron scattering measurements, we find a small strain induces sizable spin anisotropy in the paramagnetic state of KFAT, manifestly breaking spin-rotational symmetry while retaining time-reversal symmetry, resulting in a strain-induced spin-nematic state in which the 2×2 clusters act as the spin analog of molecules in a liquid crystal nematic. The strain-induced spin anisotropy in KFAT allows us to probe its nematic susceptibility, revealing a divergentlike increase upon cooling, indicating the ordered ground state is driven by a spin-orbital entangled nematic order parameter

Study About the Minimum Value at Risk of Stock Index Futures Hedging Applying Exponentially Weighted Moving Average - Generalized Autoregressive Conditional Heteroskedasticity Model

What investors often wish to insure is that the maximum possible loss of their portfolios falling below a certain value. Namely, the maximum possible loss that a portfolio will lose under normal market fluctuations, with a given confidence level, over a certain time horizon, it is known shortly as “value at risk (VaR).” However, when it comes to the hedging strategy taking in the derivative markets for the minimum VaR, many investors simply thinking it is a hedging ratio in one at beginning, then a lot of effective model came out from both academia and industry over the years.We pioneer deriving a combined and dynamic hedging model- exponentially weighted moving average-generalized autoregressive conditional heteroskedasticity (GARCH) (1,1)-M applicable to the real financial markets based on previous studies. The results in this paper turn out that the model we build is not only excellent for the pursuit for the minimum VaR but also practical for the actual situation where the variances of financial price data are time-varying.In this paper we calculate the optimal decay factor 0.93325 which is the best match to the Hu-Shen 300 stock index market, withdraw uniform 0.9400, and use the Cornish-Fisher function to correct the quantile of the normal distribution, get the final hedging ratios and the minimum VaR. Keywords: Minimum Value At Risk, Hedging Model, Decay Factor, Cornish-Fisher, Exponentially Weighted Moving Average -Generalized Autoregressive Conditional Heteroskedasticity (1,1)-M Model JEL Classification: G1

Epi-illumination SPIM for volumetric imaging with high spatial-temporal resolution.

We designed an epi-illumination SPIM system that uses a single objective and has a sample interface identical to that of an inverted fluorescence microscope with no additional reflection elements. It achieves subcellular resolution and single-molecule sensitivity, and is compatible with common biological sample holders, including multi-well plates. We demonstrated multicolor fast volumetric imaging, single-molecule localization microscopy, parallel imaging of 16 cell lines and parallel recording of cellular responses to perturbations

Zigzag magnetic order in a novel tellurate compound Na4−δ_{4-\delta}NiTeO6_{6} with S\mathit{S} = 1 chains

Na$_{4-\delta}$NiTeO$_{6}$ is a rare example in the transition-metal tellurate family of realizing an $S$ = 1 spin-chain structure. By performing neutron powder diffraction measurements, the ground-state magnetic structure of Na$_{4-\delta}$NiTeO$_{6}$ is determined. These measurements reveal that below $T\rm_{N}$ ${\sim}$ 6.8(2) K, the Ni$^{2+}$ moments form a screwed ferromagnetic (FM) spin-chain structure running along the crystallographic $a$ axis but these FM spin chains are coupled antiferromagnetically along the $b$ and $c$ directions, giving rise to a magnetic propagation vector of $k$ = (0, 1/2, 1/2). This zigzag magnetic order is well supported by first-principles calculations. The moment size of Ni$^{2+}$ spins is determined to be 2.1(1) $\mu$$\rm_{B}$ at 3 K, suggesting a significant quenching of the orbital moment due to the crystalline electric field (CEF) effect. The previously reported metamagnetic transition near $H\rm_{C}$ ${\sim}$ 0.1 T can be understood as a field-induced spin-flip transition. The relatively easy tunability of the dimensionality of its magnetism by external parameters makes Na$_{4-\delta}$NiTeO$_{6}$ a promising candidate for further exploring various types of novel spin-chain physics.Comment: 10 pages, 6 figure

Complete genome sequence of Shigella flexneri 5b and comparison with Shigella flexneri 2a

BACKGROUND: Shigella bacteria cause dysentery, which remains a significant threat to public health. Shigella flexneri is the most common species in both developing and developed countries. Five Shigella genomes have been sequenced, revealing dynamic and diverse features. To investigate the intra-species diversity of S. flexneri genomes further, we have sequenced the complete genome of S. flexneri 5b strain 8401 (abbreviated Sf8401) and compared it with S. flexneri 2a (Sf301). RESULTS: The Sf8401 chromosome is 4.5-Mb in size, a little smaller than that of Sf301, mainly because the former lacks the SHI-1 pathogenicity island (PAI). Compared with Sf301, there are 6 inversions and one translocation in Sf8401, which are probably mediated by insertion sequences (IS). There are clear differences in the known PAIs between these two genomes. The bacteriophage SfV segment remaining in SHI-O of Sf8401 is clearly larger than the remnants of bacteriophage SfII in Sf301. SHI-1 is absent from Sf8401 but a specific related protein is found next to the pheV locus. SHI-2 is involved in one intra-replichore inversion near the origin of replication, which may change the expression of iut/iuc genes. Moreover, genes related to the glycine-betaine biosynthesis pathway are present only in Sf8401 among the known Shigella genomes. CONCLUSION: Our data show that the two S. flexneri genomes are very similar, which suggests a high level of structural and functional conservation between the two serotypes. The differences reflect different selection pressures during evolution. The ancestor of S. flexneri probably acquired SHI-1 and SHI-2 before SHI-O was integrated and the serotypes diverged. SHI-1 was subsequently deleted from the S. flexneri 5b genome by recombination, but stabilized in the S. flexneri 2a genome. These events may have contributed to the differences in pathogenicity and epidemicity between the two serotypes of S. flexneri

Genome dynamics and diversity of Shigella species, the etiologic agents of bacillary dysentery

The Shigella bacteria cause bacillary dysentery, which remains a significant threat to public health. The genus status and species classification appear no longer valid, as compelling evidence indicates that Shigella, as well as enteroinvasive Escherichia coli, are derived from multiple origins of E.coli and form a single pathovar. Nevertheless, Shigella dysenteriae serotype 1 causes deadly epidemics but Shigella boydii is restricted to the Indian subcontinent, while Shigella flexneri and Shigella sonnei are prevalent in developing and developed countries respectively. To begin to explain these distinctive epidemiological and pathological features at the genome level, we have carried out comparative genomics on four representative strains. Each of the Shigella genomes includes a virulence plasmid that encodes conserved primary virulence determinants. The Shigella chromosomes share most of their genes with that of E.coli K12 strain MG1655, but each has over 200 pseudogenes, 300∼700 copies of insertion sequence (IS) elements, and numerous deletions, insertions, translocations and inversions. There is extensive diversity of putative virulence genes, mostly acquired via bacteriophage-mediated lateral gene transfer. Hence, via convergent evolution involving gain and loss of functions, through bacteriophage-mediated gene acquisition, IS-mediated DNA rearrangements and formation of pseudogenes, the Shigella spp. became highly specific human pathogens with variable epidemiological and pathological features