Form discrete- to continuous-time ergodic theorems

We introduce methods that allow to derive continuous-time versions of various discrete-time ergodic theorems. We then illustrate these methods by giving simple proofs and refinements of some known results as well as establishing new results of interest

A nilpotent IP polynomial multiple recurrence theorem

We generalize the IP-polynomial Szemer\'edi theorem due to Bergelson and McCutcheon and the nilpotent Szemer\'edi theorem due to Leibman. Important tools in our proof include a generalization of Leibman's result that polynomial mappings into a nilpotent group form a group and a multiparameter version of the nilpotent Hales-Jewett theorem due to Bergelson and Leibman.Comment: v4: switch to TeXlive 2016 and biblate

Redistribution of ions within the active layer and upper permafrost, Yamal, Russia

A landslide-affected slope was chosen to study the ionic migration in the active layer and upper portion of permafrost. The research was conducted in two stages, in 1994 and 2001. Several boreholes, in dry and wet environments of the shearing surface of a 1989-landslide, were drilled. A background borehole on an undisturbed site was sampled as well. Each sample, collected from the core, underwent a conventional chemical cation-anion analysis. The results showed desalinization of the active layer and upper permafrost, which occurred in 7 years. Different migration rates noted for various salts determine change of ionic composition from marine pattern to continental, because mobile ions are washed away by surface and subsurface runoff, while the less mobile ones are accumulating in the upper portion of the active layer due to capillary rise and at the active layer base on a geochemical barrier

Linear forms and quadratic uniformity for functions on ZN\mathbb{Z}_N

A very useful fact in additive combinatorics is that analytic expressions that can be used to count the number of structures of various kinds in subsets of Abelian groups are robust under quasirandom perturbations, and moreover that quasirandomness can often be measured by means of certain easily described norms, known as uniformity norms. However, determining which uniformity norms work for which structures turns out to be a surprisingly hard question. In [GW09a] and [GW09b, GW09c] we gave a complete answer to this question for groups of the form $G=\mathbb{F}_p^n$, provided $p$ is not too small. In $\mathbb{Z}_N$, substantial extra difficulties arise, of which the most important is that an "inverse theorem" even for the uniformity norm $\|.\|_{U^3}$ requires a more sophisticated (local) formulation. When $N$ is prime, $\mathbb{Z}_N$ is not rich in subgroups, so one must use regular Bohr neighbourhoods instead. In this paper, we prove the first non-trivial case of the main conjecture from [GW09a].Comment: 66 page

Мониторинг изменений рельефа полигональных торфяников, примыкающих к автодороге Заполярное — Тазовский

The thawing of polygonal ice wedges determines the dynamics of polygonal peatland relief. The polygonal peat plateaus in the Pur-Taz interfluve account for an average of 6,5 % of the total area. The purpose of the proposed study is to establish the short-term rates and direction of change in the plateaus’ relief under the combined action of technogenic and natural factors, using monitoring data for the period 2005–2022. Based on satellite images and orthophotoplans, elements of the peat plateaus have been outlined and their areas have been determined for different time slices. The studies were carried out on a peat plateau immediately adjacent to the highway (T1) and on a background peat plateau at a distance of about 1.5 km from the highway (T2). To identify the natural causes of changes in the relief of the peat plateaus, the influence of climatic parameters is considered. The rates of relief change in natural conditions and under the impact of the highway are also compared. It has been established that in the area to the north-west of the highway the relief of the T1 polygonal peat plateau has stabilized. In the south-east section of T1, degradation has sharply increased after the construction of the highway. Due to the degradation of the polygons, the polygonal troughs expanded. In the background peat plateau T2, the rate of relief degradation is somewhat higher than in the northwestern portion of T1. Comparison of the main climatic parameters and degradation rates of the polygonal relief did not show any clear correlations. Probably, of greater importance are the regime of atmospheric precipitation, the redistribution of surface runoff and recurrence of flooding and drainage of the polygonal troughs, determined by the rhythmic course of the relief degradation.Вытаивание полигонально-жильных льдов (ПЖЛ) определяет динамику рельефа полигональных торфяников. Массивы полигональных торфяников Пур-Тазовского междуречья составляют в среднем 6,5 % от общей площади. Целью исследования является установление краткосрочных темпов и направленности изменения рельефа торфяников под совместным действием техногенных и естественных факторов, основанное на мониторинге за период 2005–2022 гг. По спутниковым снимкам и ортофотопланам оконтурены морфологические элементы торфяника и определены их площади за разные годы. Исследования проведены на торфянике, непосредственно прилегающем к автодороге, покрытой бетонными плитами (Т1), и на фоновом торфянике на удалении примерно в 1,5 км от дороги (Т2). Для выявления естественных причин изменения рельефа торфяников рассмотрено влияние базовых климатических характеристик. Установлено, что на участке к северо-западу от дороги наблюдается стабилизация полигонального торфяника Т1. На юго-восточном участке Т1 деградация после строительства дороги резко усилилась. Полигональные канавы расширялись за счет деградации полигонов. На фоновом торфянике Т2 скорость разрушения поверхности несколько выше, чем на северо-западном участке Т1. Сопоставление основных показателей климата и скоростей деградации полигонального рельефа не дало явных зависимостей. Вероятно, большее значение имеет режим атмосферных осадков, перераспределение поверхностного стока и смена режимов затопления полигональных канав и их дренирования, определяемого ритмичным ходом деградации рельефа

The rice NLR pair Pikp-1/Pikp-2 initiates cell death through receptor cooperation rather than negative regulation

Plant NLR immune receptors are multidomain proteins that can function as specialized sensor/helper pairs. Paired NLR immune receptors are generally thought to function via negative regulation, where one NLR represses the activity of the second and detection of pathogen effectors relieves this repression to initiate immunity. However, whether this mechanism is common to all NLR pairs is not known. Here, we show that the rice NLR pair Pikp-1/Pikp-2, which confers resistance to strains of the blast pathogen Magnaporthe oryzae (syn. Pyricularia oryzae) expressing the AVR-PikD effector, functions via receptor cooperation, with effector-triggered activation requiring both NLRs to trigger the immune response. To investigate the mechanism of Pikp-1/Pikp-2 activation, we expressed truncated variants of these proteins, and made mutations in previously identified NLR sequence motifs. We found that any domain truncation, in either Pikp-1 or Pikp-2, prevented cell death in the presence of AVR-PikD, revealing that all domains are required for activity. Further, expression of individual Pikp-1 or Pikp-2 domains did not result in cell death. Mutations in the conserved P-loop and MHD sequence motifs in both Pikp-1 and Pikp-2 prevented cell death activation, demonstrating that these motifs are required for the function of the two partner NLRs. Finally, we showed that Pikp-1 and Pikp-2 associate to form homo- and hetero-complexes in planta in the absence of AVR-PikD; on co-expression the effector binds to Pikp-1 generating a tri-partite complex. Taken together, we provide evidence that Pikp-1 and Pikp-2 form a fine-tuned system that is activated by AVR-PikD via receptor cooperation rather than negative regulation

Evaluation of metabolomics profiles of grain from maize hybrids derived from near-isogenic GM positive and negative segregant inbreds demonstrates that observed differences cannot be attributed unequivocally to the GM trait

Introduction: Past studies on plant metabolomes have highlighted the influence of growing environments and varietal differences in variation of levels of metabolites yet there remains continued interest in evaluating the effect of genetic modification (GM). Objectives: Here we test the hypothesis that metabolomics differences in grain from maize hybrids derived from a series of GM (NK603, herbicide tolerance) inbreds and corresponding negative segregants can arise from residual genetic variation associated with backcrossing and that the effect of insertion of the GM trait is negligible. Methods: Four NK603-positive and negative segregant inbred males were crossed with two different females (testers). The resultant hybrids, as well as conventional comparator hybrids, were then grown at three replicated field sites in Illinois, Minnesota, and Nebraska during the 2013 season. Metabolomics data acquisition using gas chromatography–time of flight-mass spectrometry (GC–TOF-MS) allowed the measurement of 367 unique metabolite features in harvested grain, of which 153 were identified with small molecule standards. Multivariate analyses of these data included multi-block principal component analysis and ANOVA-simultaneous component analysis. Univariate analyses of all 153 identified metabolites was conducted based on significance testing (α = 0.05), effect size evaluation (assessing magnitudes of differences), and variance component analysis. Results: Results demonstrated that the largest effects on metabolomic variation were associated with different growing locations and the female tester. They further demonstrated that differences observed between GM and non-GM comparators, even in stringent tests utilizing near-isogenic positive and negative segregants, can simply reflect minor genomic differences associated with conventional back-crossing practices. Conclusion: The effect of GM on metabolomics variation was determined to be negligible and supports that there is no scientific rationale for prioritizing GM as a source of variation.</p