Remarks on the k-error linear complexity of p(n)-periodic sequences

Recently the first author presented exact formulas for the number of 2ⁿn-periodic binary sequences with given 1-error linear complexity, and an exact formula for the expected 1-error linear complexity and upper and lower bounds for the expected k-error linear complexity, k >2, of a random 2ⁿn-periodic binary sequence. A crucial role for the analysis played the Chan-Games algorithm. We use a more sophisticated generalization of the Chan-Games algorithm by Ding et al. to obtain exact formulas for the counting function and the expected value for the 1-error linear complexity for pⁿn-periodic sequences over Fp, p prime. Additionally we discuss the calculation of lower and upper bounds on the k-error linear complexity of pⁿn-periodic sequences over Fp

How to determine linear complexity and kk-error linear complexity in some classes of linear recurring sequences

Several fast algorithms for the determination of the linear complexity of $d$-periodic sequences over a finite field \F_q, i.e. sequences with characteristic polynomial $f(x) = x^d-1$, have been proposed in the literature. In this contribution fast algorithms for determining the linear complexity of binary sequences with characteristic polynomial $f(x) = (x-1)^d$ for an arbitrary positive integer $d$, and $f(x) = (x^2+x+1)^{2^v}$ are presented. The result is then utilized to establish a fast algorithm for determining the $k$-error linear complexity of binary sequences with characteristic polynomial $(x^2+x+1)^{2^v}$

A construction of bent functions from plateaued functions

In this presentation, a technique for constructing bent functions from plateaued functions is introduced and analysed. This generalizes earlier techniques for constructing bent from near-bent functions. Using this construction, we obtain a big variety of inequivalent bent functions, some weakly regular and some non-weakly regular. Classes of bent function with some additional properties that enable the construction of strongly regular graphs are constructed, and explicit expressions for bent functions with maximal degree are presented

Number and dissimilarity of global change factors influences soil properties and functions

Soil biota and functions are impacted by various anthropogenic stressors, including climate change, chemical pollution or microplastics. These stressors do not occur in isolation, and soil properties and functions appear to be directionally driven by the number of global change factors acting simultaneously. Building on this insight, we here hypothesize that co-acting factors with more diverse effect mechanisms, or higher dissimilarity, have greater impacts on soil properties and functions. We created a factor pool of 12 factors and calculated dissimilarity indices of randomly-chosen co-acting factors based on the measured responses of soil properties and functions to the single factors. Results show that not only was the number of factors important, but factor dissimilarity was also key for predicting factor joint effects. By analyzing deviations of soil properties and functions from three null model predictions, we demonstrate that higher factor dissimilarity and a larger number of factors could drive larger deviations from null models and trigger more frequent occurrence of synergistic factor net interactions on soil functions (decomposition rate, cellulase, and β-glucosidase activity), which provides mechanistic insights for understanding high-dimensional effects of factors. Our work highlights the importance of considering factor similarity in future research on interacting factors

Concurrent anthropogenic stressors affect plant–soil systems with different plant diversity levels

Plant diversity strongly influences ecosystem functioning. Due to human activities, ecosystems are increasingly threatened by the co-occurrence of numerous anthropogenic pressures, but how they respond to this multifaceted phenomenon is poorly documented, and what role plant diversity plays in this process has not been investigated so far. Here, plant–soil systems with different plant diversity levels (3 vs 9 species) were subjected to an increasing number of anthropogenic stressors (0, 1, 2, 5, and 8). Results show that soil properties and functions were directionally driven by stressor number, irrespective of plant diversity level, and plant functional group evenness declined continuously along the stressor number gradient. The impact of stressors on plant–soil systems varied depending on plant diversity, and when plant diversity was higher, concurrent stressors may have interacted more to affect plant–soil systems. Notably, increasing the stressor number tended to diminish the effects of plant diversity. This study represents a first attempt to address the effect of plant diversity under multi-stressor combinations and highlights the importance of emphasizing plant–soil systems in the research field of multifactorial global change. We also suggest that efforts should be made to reduce the number of coacting stressors when managing plant–soil ecosystems

Soil Storage Conditions Alter the Effects of Tire Wear Particles on Microbial Activities in Laboratory Tests

In this study, we focused on the fact that soil storage conditions in the laboratory have never been considered as a key factor potentially leading to high variation when measuring effects of microplastics on soil microbial activity. We stored field-collected soils under four different conditions [room-temperature storage, low-temperature storage (LS), air drying (AD), and heat drying] prior to the experiment. Each soil was treated with tire wear particles (TWPs), and soil microbial activities and water aggregate stability were investigated after soil incubation. As a result, microbial activities, including soil respiration and three enzyme activities (β-glucosidase, N-acetyl-β-glucosaminidase, and phosphatase), were shown to depend on soil storage conditions. Soil respiration rates increased with the addition of TWPs, and the differences from the control group (no TWPs added) were more pronounced in the AD TWP treatment than in soils stored under other conditions. In contrast, phosphatase activity followed an opposing trend after the addition of TWPs. The AD soil had higher phosphatase activity after the addition of TWPs, while the LS soil had a lower level than the control group. We suggest that microplastic effects in laboratory experiments can strongly depend on soil storage conditions

Diversity of organic amendments increases soil functions and plant growth

Management practices, for example, in an agricultural context, are often tested in isolation or in pairwise interaction, but rarely using a higher number of jointly applied practices. In a proof-of-concept study, we test the effects of combining up to five management practices. Effects seen on soil and plant performance suggest that it may be worth to systematically and broadly examine the effects of higher order management combinations

Combined Application of Multiple Global Change Factors Negatively Influences Key Soil Processes across an Urban Gradient in Berlin, Germany

Urbanization is a growing phenomenon affecting soils worldwide. Urban centers have been highlighted as hotspots for global change factors due to heightened anthropogenic activity. However, few studies have investigated the multifaceted impacts of global change factors (GCFs) acting in concert with urban soils. Thus, the objective of this study was to add GCFs in different combinations (0, 1, 2, 5, and 8 simultaneously) in three high-urbanity and three low-urbanity soils in Berlin and to evaluate their effects on soil parameters and functions. We hypothesized four potential outcomes of soil process responses to GCF exposure, Site-Specific Resistance, General Susceptibility, Low-Urbanity Resistance, and High-Urbanity Resistance. We provide evidence for the negative impacts of individual and multiple GCF application on litter decomposition, water repellency, and water-stable aggregates. Additionally, we highlight the General Susceptibility of litter decomposition to GCF exposure regardless of urbanity, as well as the Low-Urbanity Resistance of water repellency and High-Urbanity Resistance of water-stable aggregates under increased exposure to GCFs. This study expands on evidence of the growing threat of global change factors in urban settings and highlights some potential consequences regarding soil function

Root colonization by arbuscular mycorrhizal fungi is reduced in tomato plants sprayed with fungicides

Arbuscular mycorrhizal fungi (AMF) form symbioses with many agricultural crops and can improve plant biomass and health. The performance of the AM symbiosis is context dependent, for example, usually the inoculation of the AMF Rhizophagus irregularis benefits plant biomass, but benefits can be suppressed by high soil fertility levels. Nevertheless, the importance of many other agricultural management practices on AMF, such as fungicides application, is poorly understood. Also, pesticide regulations usually neglect a comprehensive safety testing of fungicides on AMF and lawmakers require empirical support to improve such laws. The objective of this study was to evaluate the effects of spraying fungicides on tomato plants and the subsequent root colonization of plants grown in natural soil containing AMF and inoculated with R. irregularis. We detected that the inoculation of R. irregularis increased the total root colonization of the control plants that did not receive fungicides and that spraying the plants with the fungicides Signum® and Topas® reduced total root colonization. The effect on specific AM fungal structures was variable according to the product. Signum® reduced the occurrence of arbuscules, while Topas® reduced the occurrence of AM hyphae in the colonized roots. Cuprozin® did not reduce total root colonization but reduced the occurrence of AM vesicles. Sampling time was also relevant. Effects were detected at 90 days, but not at 35 days. Our results show that fungicides safety should be evaluated for their effects on root colonization of crops in non-sterilized soils and at adequate sampling time

Combined application of up to ten pesticides decreases key soil processes

Natural systems are under increasing pressure by a range of anthropogenic global change factors. Pesticides represent a nearly ubiquitously occurring global change factor and have the potential to affect soil functions. Currently the use of synthetic pesticides is at an all-time high with over 400 active ingredients being utilized in the EU alone, with dozens of these pesticides occurring concurrently in soil. However, we presently do not understand the impacts of the potential interaction of multiple pesticides when applied simultaneously. Using soil collected from a local grassland, we utilize soil microcosms to examine the role of both rate of change and number of a selection of ten currently used pesticides on soil processes, including litter decomposition, water stable aggregates, aggregate size, soil pH, and EC. Additionally, we used null models to enrich our analyses to examine potential patterns caused by interactions between pesticide treatments. We find that both gradual and abrupt pesticide application have negative consequences for soil processes. Notably, pesticide number plays a significant role in affecting soil health. Null models also reveal potential synergistic behavior between pesticides which can further their consequences on soil processes. Our research highlights the complex impacts of pesticides, and the need for environmental policy to address the threats posed by pesticides