On the insertion of n-powers

In algebraic terms, the insertion of $n$-powers in words may be modelled at the language level by considering the pseudovariety of ordered monoids defined by the inequality $1\le x^n$. We compare this pseudovariety with several other natural pseudovarieties of ordered monoids and of monoids associated with the Burnside pseudovariety of groups defined by the identity $x^n=1$. In particular, we are interested in determining the pseudovariety of monoids that it generates, which can be viewed as the problem of determining the Boolean closure of the class of regular languages closed under $n$-power insertions. We exhibit a simple upper bound and show that it satisfies all pseudoidentities which are provable from $1\le x^n$ in which both sides are regular elements with respect to the upper bound

The omega-inequality problem for concatenation hierarchies of star-free languages

The problem considered in this paper is whether an inequality of omega-terms is valid in a given level of a concatenation hierarchy of star-free languages. The main result shows that this problem is decidable for all (integer and half) levels of the Straubing-Th\'erien hierarchy

Locally countable pseudovarieties

The purpose of this paper is to contribute to the theory of profinite semigroups by considering the special class consisting of those all of whose finitely generated closed subsemigroups are countable, which are said to be locally countable. We also call locally countable a pseudovariety V (of finite semigroups) for which all pro-V semigroups are locally countable. We investigate operations preserving local countability of pseudovarieties and show that, in contrast with local finiteness, several natural operations do not preserve it. We also investigate the relationship of a finitely generated profinite semigroup being countable with every element being expressible in terms of the generators using multiplication and the idempotent (omega) power. The two properties turn out to be equivalent if there are only countably many group elements, gathered in finitely many regular J -classes. We also show that the pseudovariety generated by all finite ordered monoids satisfying the inequality 1 6 x n is locally countable if and only if n = 1

On Varieties of Ordered Automata

The Eilenberg correspondence relates varieties of regular languages to pseudovarieties of finite monoids. Various modifications of this correspondence have been found with more general classes of regular languages on one hand and classes of more complex algebraic structures on the other hand. It is also possible to consider classes of automata instead of algebraic structures as a natural counterpart of classes of languages. Here we deal with the correspondence relating positive $\mathcal C$-varieties of languages to positive $\mathcal C$-varieties of ordered automata and we present various specific instances of this correspondence. These bring certain well-known results from a new perspective and also some new observations. Moreover, complexity aspects of the membership problem are discussed both in the particular examples and in a general setting

The Resistance of Oilseed Rape Microspore-Derived Embryos to Osmotic Stress Is Associated With the Accumulation of Energy Metabolism Proteins, Redox Homeostasis, Higher Abscisic Acid, and Cytokinin Contents

The present study aims to investigate the response of rapeseed microspore-derived embryos (MDE) to osmotic stress at the proteome level. The PEG-induced osmotic stress was studied in the cotyledonary stage of MDE of two genotypes: Cadeli (D) and Viking (V), previously reported to exhibit contrasting leaf proteome responses under drought. Two-dimensional difference gel electrophoresis (2D-DIGE) revealed 156 representative protein spots that have been selected for MALDI-TOF/TOF analysis. Sixty-three proteins have been successfully identified and divided into eight functional groups. Data are available via ProteomeXchange with identifier PXD024552. Eight selected protein accumulation trends were compared with real-time quantitative PCR (RT-qPCR). Biomass accumulation in treated D was significantly higher (3-fold) than in V, which indicates D is resistant to osmotic stress. Cultivar D displayed resistance strategy by the accumulation of proteins in energy metabolism, redox homeostasis, protein destination, and signaling functional groups, high ABA, and active cytokinins (CKs) contents. In contrast, the V protein profile displayed high requirements of energy and nutrients with a significant number of stress-related proteins and cell structure changes accompanied by quick downregulation of active CKs, as well as salicylic and jasmonic acids. Genes that were suitable for gene-targeting showed significantly higher expression in treated samples and were identified as phospholipase D alpha, peroxiredoxin antioxidant, and lactoylglutathione lyase. The MDE proteome profile has been compared with the leaf proteome evaluated in our previous study. Different mechanisms to cope with osmotic stress were revealed between the genotypes studied. This proteomic study is the first step to validate MDE as a suitable model for follow-up research on the characterization of new crossings and can be used for preselection of resistant genotypes

Identities of the kauffman monoid K4 and of the Jones Monoid J4

Kauffman monoids Kn and Jones monoids Jn, n=2,3,…, are two families of monoids relevant in knot theory. We prove a somewhat counterintuitive result that the Kauffman monoids K3 and K4 satisfy exactly the same identities. This leads to a polynomial time algorithm to check whether a given identity holds in K4. As a byproduct, we also find a polynomial time algorithm for checking identities in the Jones monoid J4. © Springer Nature Switzerland AG 2020.M. V. Volkov—Supported by Ural Mathematical Center under agreement No. 075-02-2020-1537/1 with the Ministry of Science and Higher Education of the Russian Federation

Interaction of Temperature and Light in the Development of Freezing Tolerance in Plants

Abstract Freezing tolerance is the result of a wide range of physical and biochemical processes, such as the induction of antifreeze proteins, changes in membrane composition, the accumulation of osmoprotectants, and changes in the redox status, which allow plants to function at low temperatures. Even in frost-tolerant species, a certain period of growth at low but nonfreezing temperatures, known as frost or cold hardening, is required for the development of a high level of frost hardiness. It has long been known that frost hardening at low temperature under low light intensity is much less effective than under normal light conditions; it has also been shown that elevated light intensity at normal temperatures may partly replace the cold-hardening period. Earlier results indicated that cold acclimation reflects a response to a chloroplastic redox signal while the effects of excitation pressure extend beyond photosynthetic acclimation, influencing plant morphology and the expression of certain nuclear genes involved in cold acclimation. Recent results have shown that not only are parameters closely linked to the photosynthetic electron transport processes affected by light during hardening at low temperature, but light may also have an influence on the expression level of several other cold-related genes; several cold-acclimation processes can function efficiently only in the presence of light. The present review provides an overview of mechanisms that may explain how light improves the freezing tolerance of plants during the cold-hardening period