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

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

RYE COVER CROP AS A SOURCE OF BIOMASS FEEDSTOCK: AN ECONOMIC PERSPECTIVE

ABSTRACT As more emphasis is placed on biopower and biofuels, the availability of biomass feedstock is taking center stage. The growth of the biomass feedstock market is further strengthened by the implementation of new regulations and federal programs. One option for biomass feedstock is the removal of cover crops, such as cereal rye. An experiment was initiated to compare three rye residue management techniques (residue retained, residue harvested or removed, and no rye cover control) and four nitrogen fertilizer treatments (0, 45, 90, 125 lb ac -1 ). Initial findings from this study show that the removal of rye cover crops for biomass feedstock is a viable option for producers, given the assumptions in the study. Further investigation is needed to determine the complete economic impact of removing rye cover crop for biomass feedstock

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

AMR Sign - An Arthroscopic S-shaped Fold Signifying Adequate Medial Meniscus Repair

Introduction: The preferred management of medial meniscus tears has notably moved from meniscectomies towards repair. With a higher volume of meniscal repairs being done all across the world with every passing day, the lack of an objective and definitive sign suggesting the adequacy of its repair is daunting. The purpose of our study was to introduce a unique and novel arthroscopic sign formed after adequate repair of the medial meniscus, the AMR (Adequacy of Medial meniscus Repair) sign. We hypothesised that it is not only the objective end point for repair, but can also form the indicator for excellent clinical, functional, and radiological outcome even in the long term. Materials and methods: This was a multicentric, prospective study initiated by the corresponding author, and the findings validated subsequently by the other authors. Overall, it included 804 patients of isolated medial meniscus tear operated with arthroscopic all-inside technique between January 2014 and December 2017. Patients were segregated into three groups based on whether an S-shaped curve in the free, inner edge of the medial meniscus sign was formed post-repair, lost after further tightening, or not formed upon subjective completion of repair. All the patients were followed-up and evaluated based of medial joint line tenderness, McMurray’s test for medial meniscus, IKDC score, WOMET score, and radiologically using an MRI at the terminal follow-up. Results: The mean terminal follow-up was 42.34±4.54 months. There was significant (p<0.01) improvement in all patients at the terminal follow-up post-surgery, irrespective of the group. The group in which AMR sign was formed and maintained showed a significantly better functional outcome on terminal follow-up as well as lower failure rates compared to the other two groups. Conclusion: AMR sign is an S-shaped fold at the inner, free edge of medial meniscus, formed after an adequate repair of isolated medial meniscus tear, as viewed on arthroscopy. It is an objective sign denoting regained integrity of the collagen architecture of the medial meniscus following repair. It is also a reliable indicator of excellent long term functional, clinical, and radiological outcome and also lower failure rates in patients after arthroscopic medial meniscus repair

Physical activity and exercise for the prevention and management of mild cognitive impairment and dementia: a collaborative international guideline

Background: Physical activity and exercise have been suggested as effective interventions for the prevention and management of mild cognitive impairment (MCI) and dementia, but there are no international guidelines. Objectives: To create a set of evidence- and expert consensus-based prevention and management recommendations regarding physical activity (any bodily movement produced by skeletal muscles that results in energy expenditure) and exercise (a subset of physical activity that is planned, structured, repetitive), applicable to a range of individuals from healthy older adults to those with MCI/dementia. Methods: Guideline content was developed with input from several scientific and lay representatives’ societies. A systematic search across multidisciplinary databases was carried out until October 2021. Recommendations for prevention and management were developed according to the GRADE and complemented by consensus statements from the expert panels. Recommendations: Physical activity may be considered for the primary prevention of dementia. In people with MCI there is continued uncertainty about the role of physical activity in slowing the conversion to dementia. Mind–body interventions have the greatest supporting evidence. In people with moderate dementia, exercise may be used for maintaining disability and cognition. All these recommendations were based on a very low/low certainty of evidence. Conclusions: Although the scientific evidence on the beneficial role of physical activity and exercise in preserving cognitive functions in subjects with normal cognition, MCI or dementia is inconclusive, this panel, composed of scientific societies and other stakeholders, recommends their implementation based on their beneficial effects on almost all facets of health

Adaptation and validation of the Patient Expectations and Satisfaction with Prenatal Care instrument among Brazilian pregnant women

Objective: to adapt and validate the Patient Expectations and Satisfaction with Prenatal Care instrument for use in Brazil. It contains 41 items divided into two dimensions: expectations and satisfaction. The adapted version was submitted to analysis for stability, convergent construct validity, and internal consistency (Cronbach’s alpha) for distinct groups and dimensions. Method: 119 pregnant women receiving prenatal care were interviewed and 26 of these women answered the instrument twice (retest). Internal consistency was appropriate (Cronbach’s alpha ≥ 0.70); test-retest presented strong correlation (r=0.82; p<0.001) for the domain expectations and moderate correlation (r=0.66; p<0.001) for the satisfaction domain. The analysis confirmed that the instrument’s adapted version is valid in the studied group. Results: there is strong evidence for the validity and reliability of the instrument’s adaptation. Conclusion: the instrument needs to be tested in groups of pregnant women with different social characteristics.CAPESCAPE

Design and management of image processing pipelines within CPS: Acquired experience towards the end of the FitOptiVis ECSEL Project

Cyber-Physical Systems (CPSs) are dynamic and reactive systems interacting with processes, environment and, sometimes, humans. They are often distributed with sensors and actuators, characterized for being smart, adaptive, predictive and react in real-time. Indeed, image- and video-processing pipelines are a prime source for environmental information for systems allowing them to take better decisions according to what they see. Therefore, in FitOptiVis, we are developing novel methods and tools to integrate complex image- and video-processing pipelines. FitOptiVis aims to deliver a reference architecture for describing and optimizing quality and resource management for imaging and video pipelines in CPSs both at design- and run-time. The architecture is concretized in low-power, high-performance, smart components, and in methods and tools for combined design-time and run-time multi-objective optimization and adaptation within system and environment constraints