Research of expediency of application of AVX512 for modern digital signature schemes implementations

The third stage of the NIST PQC competition is currently underway, which aims to create new post-quantum standards in cryptography. The vast majority of finalists are representatives of lattice-based cryptography. Electronic signatures include the CRYSTALS-Dilithium schemes. This paper investigates the feasibility of using AVX512 to optimize software implementations of NIST PQC finalists among electronic signatures on algebraic lattices. Since the most expensive operation in such schemes is the multiplication of polynomials, the main attention is paid to the optimization of this operation. In particular, the method of realization of theoretical and numerical transformation using AVX512 for electronic signature schemes CRYSTALS-Dilithium is presented in the work. The increase in speed is shown in comparison with the reference optimized author 's implementations.

Transformation cycle between the spherically symmetric correlation function, projected correlation function and differential cross section as implemented inSASfit

Spin-echo-based small-angle neutron scattering techniques like spin-echo SANS (SESANS) or spin-echo modulated SANS (SEMSANS) as well as dark-field (DF) imaging are directly sensitive to \tilde{G}(\delta), which is the projection of the scattering length density autocorrelation function \tilde{\gamma}(r). Here, a simplified transformation cycle relating the spherically symmetric correlation function \tilde{\gamma}(r), the projected correlation function \tilde{G}(\delta) and the macroscopic small-angle scattering cross section dΣ/dΩ is introduced. The suggested changes to the cycle make it easier to include size distribution on an absolute scale if the data from the different techniques are fitted simultaneously. As up to now only very few analytical expressions for the projected correlation function are known, a numerical transformation of known scattering functions into the projected correlation function in theSASfitsoftware package is supplied. Furthermore, a new analytical expression for the projected correlation function for polymers that can be described by the generalized Gaussian coil model is provided. For this polymer model, the Hankel transform used to calculate \tilde{G}(0) from the SANS signal is divergent for a certain parameter range describing a polymer in a good solvent and finite in the case of a poor solvent. It is therefore a suitable example of how the experimentally availableqrange can strongly influence the obtained results.

RESEARCH OF TEMPERATURE PROFILES IN THE WELL IN THE COURSE OF PUMPING LIQUID ON THE BASIS OF NUMERICAL INVERSION OF ISEGER

The analysis of a temperature profile in the trunk of a vertical well when pumping liquid was carried out. The paper describes the application of an algorithm of the inverse numerical transformation with use of Gaussian quadratures (Iseger's method) to a task about a temperature profile under conditions of a short-term liquid pumping into the well. Analytical dependences are constructed on the basis of a method of the Laplace-Carson integral transformation of decomposition. The inverse transition is carried out on the basis of numerical inversion with use of Gaussian quadratures (Iseger's method).

Taxonomic and numerical sufficiency in depth- and salinity-controlled marine paleocommunities

Numerical and taxonomic resolution of compositional data sets affects investigators’ abilities to detect and measure relationships between communities and environmental factors. We test whether varying numerical (untransformed, square-root- and fourth-root-transformed relative abundance and presence–absence data) and taxonomic (species, genera, families) resolutions reveals different insights into early to middle Miocene molluscan communities along bathymetric and salinity gradients. The marine subtidal has a more even species-abundance distribution, a higher number of rare species, and higher species:family and species:genus ratios than the three habitats—marine and estuarine intertidal, estuarine subtidal—with higher fluctuations in salinity and other physical parameters. Taxonomic aggregation and numerical transformation of data result in very different ordinations, although all habitats differ significantly from one another at all taxonomic and numerical levels. Rank correlations between species-level and higher-taxon, among-sample dissimilarities are very high for proportional abundance and decrease strongly with increasing numerical transformation, most notably in the two intertidal habitats. The proportion of variation explained by depth is highest for family-level data, decreases gradually with numerical transformation, and is higher in marine than in estuarine habitats. The proportion of variation explained by salinity is highest for species-level data, increases gradually with numerical transformation, and is higher in subtidal than in intertidal habitats. Therefore, there is no single best numerical and taxonomic resolution for the discrimination of communities along environmental gradients: the “best” resolution depends on the environmental factor considered and the nature of community response to it. Different numerical and taxonomic transformations capture unique aspects of metacommunity assembly along environmental gradients that are not detectable at a single level of resolution. We suggest that simultaneous analyses of community gradients at multiple taxonomic and numerical resolutions provide novel insights into processes responsible for spatial and temporal community stability.

Concept of Phase Cycling in Pulsed Magnetic Resonance Using Sinusoidal Magnetic Field Modulation

In conventional pulsed magnetic resonance suppression of unwanted signals is achieved by changing pulse phases with respect to the reference signal and spin magnetization phase. This method is called phase cycling. An alternative approach is suggested to separate the unwanted signals from the spin echo by using magnetic field modulation. Precession frequency of the spins, and therefore phases of free indication decays and echo signals, can be controlled by the selection of modulation parameters. This enables phase cycling. Since the signal is detected in the presence of the changing magnetic field, which drives spin precession, the echo signal is frequency-modulated. Numerical transformation into an accelerating reference frame associated with the Larmor frequency restores the signal to a form that would have been observed in the absence of modulation. The suggested phase cycling method is analyzed in detail for the two pulse spin echo case.

CNC Transformation Method for the Study

This paper describes the need for transformation of CNC machine tools, CNC machine tools and a brief introduction to the content and transformation of the advantages and disadvantages, but focuses on how the transformation of CNCmachine tools including CNC system selection, transformation NC modificationof the main mechanical components and CNC transformation of the main steps,and cited several examples of digital transformation, and finallyshows the numerical transformation of the problem and made recommendations.