A geometric view of cryptographic equation solving

This paper considers the geometric properties of the Relinearisation algorithm and of the XL algorithm used in cryptology for equation solving. We give a formal description of each algorithm in terms of projective geometry, making particular use of the Veronese variety. We establish the fundamental geometrical connection between the two algorithms and show how both algorithms can be viewed as being equivalent to the problem of finding a matrix of low rank in the linear span of a collection of matrices, a problem sometimes known as the MinRank problem. Furthermore, we generalise the XL algorithm to a geometrically invariant algorithm, which we term the GeometricXL algorithm. The GeometricXL algorithm is a technique which can solve certain equation systems that are not easily soluble by the XL algorithm or by Groebner basis methods

Universal energy and magnetisation distributions in the Blume-Capel and Baxter-Wu models

We analyse the probability distribution functions of the energy and magnetisation of the two-dimensional Blume-Capel and Baxter-Wu models with spin values S ∈ {1/2, 1, 3/2} in the presence of a crystal field ∆. By employing extensive single-spin flip Monte Carlo simulations and a recently developed method of studying the zeros of the energy probability distribution we are able to probe, with a good numerical accuracy, several critical characteristics of the transitions. Additionally, the universal aspects of these transitions are scrutinised by computing the corresponding probability distribution functions. The energy distribution has been underutilised in the literature when compared to that of the magnetisation. Somewhat surprisingly, however, the former appears to be more robust in characterising the universality class for both models upon varying the crystal field ∆ than the latter. Finally, our analysis suggests that in contrast to the Blume-Capel ferromagnet, the Baxter-Wu model appears to suffer from strong finite-size effects, especially upon increasing ∆ and S, that obscure the application of traditional finite-size scaling approaches

A New Algorithm For The Generation Of Unitarity-Compatible Integration By Parts Relations

Many multi-loop calculations make use of integration by parts relations to reduce the large number of complicated Feynman integrals that arise in such calculations to a simpler basis of master integrals. Recently, Gluza, Kajda, and Kosower argued that the reduction to master integrals is complicated by the presence of integrals with doubled propagator denominators in the integration by parts relations and they introduced a novel reduction procedure which eliminates all such integrals from the start. Their approach has the advantage that it automatically produces integral bases which mesh well with generalized unitarity. The heart of their procedure is an algorithm which utilizes the weighty machinery of computational commutative algebra to produce complete sets of unitarity-compatible integration by parts relations. In this paper, we propose a conceptually simpler algorithm for the generation of complete sets of unitarity-compatible integration by parts relations based on recent results in the mathematical literature. A striking feature of our algorithm is that it can be described entirely in terms of straightforward linear algebra.Comment: 20 pages; My apologies to Krzysztof Kajda for misspelling his name in v1; in v3: the labeling of the variables in (4.5) and eqs. (4.20) and (4.21) was adjusted to match the notation used in the rest of Section 4. I thank York Schroeder for pointing out the notational inconsistenc

CH4 emission estimates from an active landfill site inferred from a combined approach of CFD modelling and in situ FTIR measurements

Globally, the waste sector contributes to nearly a fifth of anthropogenic methane emitted to the atmosphere and is the second largest source of methane in the UK. In recent years great improvements to reduce those emissions have been achieved by installation of methane recovery systems at landfill sites and subsequently methane emissions reported in national emission inventories have been reduced. Nevertheless, methane emissions of landfills remain uncertain and quantification of emission fluxes is essential to verify reported emission inventories and to monitor changes in emissions. Here we present a new approach for methane emission quantification from a complex source like a landfill site by applying a Computational Fluid Dynamics (CFD) model to calibrated in situ measurements of methane as part of a field campaign at a landfill site near Ipswich, UK, in August 2014. The methane distribution for different meteorological scenarios is calculated with the CFD model and compared to methane mole fractions measured by an in situ Fourier Transform Infrared (FTIR) spectrometer downwind of the prevailing wind direction. Assuming emissions only from the active site, a mean daytime flux of 0.83 mg m−2 s−1, corresponding to 53.26 kg h−1, was estimated. The addition of a secondary source area adjacent to the active site, where some methane hotspots were observed, improved the agreement between the simulated and measured methane distribution. As a result, the flux from the active site was reduced slightly to 0.71 mg m−2 s−1 (45.56 kg h−1), at the same time an additional flux of 0.32 mg m−2 s−1 (30.41 kg h−1) was found from the secondary source area. This highlights the capability of our method to distinguish between different emission areas of the landfill site, which can provide more detailed information about emission source apportionment compared to other methods deriving bulk emissions

MOLECULAR BIOLOGY AND PHYSIOLOGY Fiber Initiation in 18 Cultivars and Experimental Lines of Three Gossypium Species

ABSTRACT A new technique was developed to study the cotton fiber initiation process and fiber initial densities. The goal was to provide an additional tool to cotton breeders and geneticists interested in fiber improvement. The objectives were to assess whether fiber initiation patterns reported for some Gossypium hirsutum L. and G. barbadense L. cultivars extend to a more diverse range of cultivars/lines; and to test if there is a relationship between fiber initials density, lint percentage, and fiber characteristics. This study was performed with 17 cultivars and experimental lines of G. hirsutum (upland cotton) and G. barbadense (Pima cotton) and one G. arboreum L. accession. The ovules were extracted from flowers at the day of anthesis and 1 and 2 d thereafter, stained with a fluorescent dye, DiOC 6 (3) (3,3′-dihexyloxacarbocyanine iodide), and observed under a light microscope. Staining cotton fiber initials with DiOC 6 (3) enabled the evaluation of a greater number of samples than the more time-consuming scanning electron microscopy protocols to assess the fiber initiation process. There were significant differences in fiber initial densities among cultivars and lines but these did not cluster into "upland" and "Pima" types as had been expected. Upland and Pima fiber initiation occurred at anthesis, whereas Sea Island Pima initiation was delayed a day. A delay in fiber initiation was also confirmed in fuzzless mutant lines. Fiber initial densities were not found to be useful predictors of lint percentage

BrainFrame: A node-level heterogeneous accelerator platform for neuron simulations

Objective. The advent of high-performance computing (HPC) in recent years has led to its increasing use in brain studies through computational models. The scale and complexity of such models are constantly increasing, leading to challenging computational requirements. Even though modern HPC platforms can often deal with such challenges, the vast diversity of the modeling field does not permit for a homogeneous acceleration platform to effectively address the complete array of modeling requirements. Approach. In this paper we propose and build BrainFrame, a heterogeneous acceleration platform that incorporates three distinct acceleration technologies, an Intel Xeon-Phi CPU

Expert consensus guidelines for the genetic diagnosis of Alport syndrome

Recent expert guidelines recommend genetic testing for the diagnosis of Alport syndrome. Here, we describe current best practice and likely future developments. In individuals with suspected Alport syndrome, all three COL4A5, COL4A3 and COL4A4 genes should be examined for pathogenic variants, probably by high throughput-targeted next generation sequencing (NGS) technologies, with a customised panel for simultaneous testing of the three Alport genes. These techniques identify up to 95% of pathogenic COL4A variants. Where causative pathogenic variants cannot be demonstrated, the DNA should be examined for deletions or insertions by re-examining the NGS sequencing data or with multiplex ligation-dependent probe amplification (MLPA). These techniques identify a further 5% of variants, and the remaining few changes include deep intronic splicing variants or cases of somatic mosaicism. Where no pathogenic variants are found, the basis for the clinical diagnosis should be reviewed. Genes in which mutations produce similar clinical features to Alport syndrome (resulting in focal and segmental glomerulosclerosis, complement pathway disorders, MYH9-related disorders, etc.) should be examined. NGS approaches have identified novel combinations of pathogenic variants in Alport syndrome. Two variants, with one in COL4A3 and another in COL4A4, produce a more severe phenotype than an uncomplicated heterozygous change. NGS may also identify further coincidental pathogenic variants in genes for podocyte-expressed proteins that also modify the phenotype. Our understanding of the genetics of Alport syndrome is evolving rapidly, and both genetic and non-genetic factors are likely to contribute to the observed phenotypic variability

On the external forcing of global eruptive activity in the past 300 years

The decryption of the temporal sequence of volcanic eruptions is a key step in better anticipating future events. Volcanic activity is the result of a complex interaction between internal and external processes, with time scales spanning multiple orders of magnitude. We review periodicities that have been detected or correlated with volcanic eruptions/phenomena and interpreted as resulting from external forces. Taking a global perspective and longer time scales than a few years, we approach this interaction by analyzing three time series using singular spectral analysis: the global number of volcanic eruptions (NVE) between 1700 and 2022, the number of sunspots (ISSN), a proxy for solar activity, the polar motion (PM) and length of day (lod), two proxies for gravitational force. Several pseudo-periodicities are common to NVE and ISSN, in addition to the 11-year Schwabe cycle that has been reported in previous work, but NVE shares even more periodicities with PM. These quasi-periodic components range from ~5 to ~130 years. We interpret our analytical results in light of the Laplace's paradigm and propose that, similarly to the movement of Earth's rotation axis, global eruptive activity is modulated by commensurable orbital moments of the Jovian planets, whose influence is also detected in solar activity