On some third parts of nearly complete digraphs

AbstractFor the complete digraph DKn with n⩾3, its half as well as its third (or near-third) part, both non-self-converse, are exhibited. A backtracking method for generating a tth part of a digraph is sketched. It is proved that some self-converse digraphs are not among the near-third parts of the complete digraph DK5 in four of the six possible cases. For n=9+6k,k=0,1,…, a third part D of DKn is found such that D is a self-converse oriented graph and all D-decompositions of DKn have trivial automorphism group

Kite systems of order 8;Embedding of kite systems into bowtie systems

This article consist of two parts. In the first part, we enumerate the kite systems of order 8; in the second part, we consider embedding kite systems into bowtie systems

The seating couple problem in even case

In this paper we consider the seating couple problem with an even number of seats, which, using graph theory terminology, can be stated as follows. Given a positive even integer $v=2n$ and a list $L$ containing $n$ positive integers not exceeding $n$, is it always possible to find a perfect matching of $K_v$ whose list of edge-lengths is $L$? Up to now a (non-constructive) solution is known only when all the edge-lengths are coprime with $v$. In this paper we firstly present some necessary conditions for the existence of a solution. Then, we give a complete constructive solution when the list consists of one or two distinct elements, and when the list consists of consecutive integers $1,2,\ldots,x$, each one appearing with the same multiplicity. Finally, we propose a conjecture and some open problems.Comment: 16 page

Targeting the NEDP1 enzyme to ameliorate ALS phenotypes through stress granule disassembly

The elimination of aberrant inclusions is regarded as a therapeutic approach in neurodegeneration. In amyotro-phic lateral sclerosis (ALS), mutations in proteins found within cytoplasmic condensates called stress granules (SGs) are linked to the formation of pathological SGs, aberrant protein inclusions, and neuronal toxicity. We found that inhibition of NEDP1, the enzyme that processes/deconjugates the ubiquitin-like molecule NEDD8, promotes the disassembly of physiological and pathological SGs. Reduction in poly(ADP-ribose) polymerase1 activity through hyper-NEDDylation is a key mechanism for the observed phenotype. These effects are related to improved cell survival in human cells, and in C. elegans, nedp1 deletion ameliorates ALS phenotypes related to animal motility. Our studies reveal NEDP1 as potential therapeutic target for ALS, correlated to the disassembly of pathological SGs

Factorizations of complete graphs into brooms

Let r and n be positive integers with r<2n. A broom of order 2n is the union of the path on P2n−r−1 and the star K1,r, plus one edge joining the center of the star to an endpoint of the path. It was shown by Kubesa (2005) [10] that the broom factorizes the complete graph K2n for odd n and View the MathML source. In this note we give a complete classification of brooms that factorize K2n by giving a constructive proof for all View the MathML source (with one exceptional case) and by showing that the brooms for View the MathML source do not factorize the complete graph K2n.Web of Science31261093108

Study of Venturia inaequalis pseudothecia development and apple scab severity under Polish conditions

Studies conducted during 2009-2013 at the Experimental Orchard located in the central region of Poland showed that the highest number of V. inaequalis pseudothecia occurred on ‘McIntosh’ and ‘Cortland’ leaves. A smaller number of pseudothecia was found on the leaves of the Alwa and Jonagold cultivars, but there were no statistical differences. The first discharges of ascospores were noted at a similar time on the leaves of all of the apple cultivars, usually at the end of March or in early April. For the forecasting of ascospore discharges and dates of critical periods, a simulation model by RIMpro was used. The number of critical periods and apple scab severity differed in each season. The most critical periods (above 20) were recorded in 2010 and 2013, which also corresponded with a high severity of apple scab. The number of infected leaves and fruits on the untreated trees of the very susceptible cultivar McIntosh reached nearly 100% during these seasons. In other years, the severity of the disease on the same apple trees was lower and amounted to 30-54% of infected leaves and 23-80% of infected fruits

Prawna regulacja sektora kryptowalut na poziomie unijnym w aspekcie rozporządzenia MiCA

The intensive development of a new sector of the financial market — the crypto-assets market — is accompanied by a lack of coherent regulation in this area. The European Union has decided to take action to ensure legal protection of cryptoassets. The goal of this article is to discuss the essence of the proposal for a regulation on crypto-assets markets, hereinafter referred to as the MiCA (Markets in Crypto-Assets Regulation), which is part of the public finance regulation package adopted by the European Commission. The purpose of introducing the legal framework is to prepare for the upcoming digital revolution and to build an economy adapted to developing technologies. The article will discuss the most important issues regarding the MiCA regulation.Intensywnemu rozwojowi nowego sektora rynku finansowego: rynku kryptoaktywów towarzyszy brak spójnej regulacji w jego zakresie. Unia Europejska zdecydowała się na podjęcie działań służących zapewnieniu ochrony prawnej w obszarze kryptoaktywów. Przedmiotem niniejszego artykułu jest omówienie istoty, składającego się na pakiet regulacji dotyczących finansów publicznych podjęty przez Komisję Europejską, wniosku rozporządzenia w sprawie rynków kryptoaktywów (dalej: rozporządzenie MiCA — ang. Markets in Crypto-Assets Regulation). Celami wprowadzenia ram prawnych są przygotowanie na nadchodzącą rewolucję cyfrową oraz zbudowanie gospodarki przystosowanej do rozwijających się technologii. W artykule poruszone zostaną najważniejsze zagadnienia dotyczące rozporządzenia MiCA

Approches de biologie chimique dans la voie NEDD8

Une famille de petites protéines, appelée famille des molécules d'ubiquitine (Ubls), joue un rôle essentiel dans de nombreux aspects de la réponse au stress. Des défauts dans les composants de la famille de l'ubiquitine sont souvent retrouvés dans les pathologies, notamment dans certain type de cancer et les maladies neurodégénératives.L'une des Ubls qui présente le plus d'identité et de similarité avec l'Ubiquitine est NEDD8. NEDD8 fonctionne de manière similaire à Ub mais utilise un mécanisme de conjugaison distinct. La modification de NEDD8 est essentielle au maintien de l'homéostasie de la cellule car elle joue un rôle majeur dans la régulation de la viabilité, de la croissance et du développement. Pour cette raison, de nombreux composants de NEDD8 ont été dérégulés dans de nombreux cancers. NEDD8 peut modifier un large éventail de substrat protéique, et peut également s’auto-modifier entrainant la création de chaînes polyNEDD8. Récemment, la présence de chaînes polyNEDD8 a été liée à la régulation de la mort cellulaire - apoptose et parthanatos. De plus, il a été récemment rapporté que NEDD8 pendant un stress protéotoxique peut être employé par la machinerie de conjugaison Ub. Cela aboutit à la création de chaînes NEDD8 hybrides tels que NEDD8-Ub et NEDD8-SUMO. En effet, des articles récents ont montré que NEDD8 a non seulement la capacité de modifier Ub mais également SUMO-2. La présence des chaînes hybrides NEDD8 a été liée à la création d'agrégats nucléaires formés pendant le stress protéotoxique, ce qui peut jouer un rôle protecteur pendant l'exposition au stress.Connaissant l'importance de la régulation des protéines par la NEDDylation, nous étions également conscients du manque de connaissances sur le mécanisme qui joue un rôle dans la création et la déconjugaison des différentes entités NEDD8. Jusqu'à présent, deux enzymes déNEDDylantes ont été signalées, mais aucune enzyme n'a été testée pour sa capacité à reconnaître et à traiter les chaînes hybrides NEDD8. De plus, nos connaissances sur les ligases E3 responsables de la NEDDylation du substrat, bien qu'en expansion, sont encore très limitées. De plus, étant donné que NEDD8 peut s’auto-modifier via l’utilisation de l’une de ses dix lysines, elle peut générer une très large gamme de signaux par la formation de chaînes polyNEDD8 et hybrides NEDD8. Ces chaines peuvent être reconnues de la même manière que les chaînes polyUb, mais aucune étude ne s'est concentrée sur la détermination de leurs interacteurs jusqu'à présent.Dans ce travail, nous nous sommes concentrés sur l'exploration de ces mécanismes inconnus de conjugaison et de déconjugaison de NEDD8 mentionnées précédemment. En utilisant des approches de biologie chimique, nous avons testé une variété d'enzymes et déterminé que les chaînes polyNEDD8 sont exclusivement traitées par l'enzyme NEDP1. Cependant, la déconjugaison des chaînes hybrides NEDD8 nécessite l'action coordonnée de différentes enzymes de déconjugaison avec une spécificité distincte pour Ub ou SUMO. Nous avons également utilisé des dimères NEDD8-NEDD8 et NEDD8-Ub synthétisés chimiquement afin de rechercher leurs interacteurs et utiliser les données recueillies pour approfondir nos connaissances sur la biologie des chaînes hybrides NEDD8 dans les agrégats nucléaires. En utilisant les sondes NEDD8-Dha, nous avons identifié un groupe de protéines qui sont potentiellement impliquées dans la machinerie de NEDDylation. Par la confirmation biologique des résultats obtenus, nous avons montré que les ARNt ligases - GARS et SARS fonctionnent comme des ligases E3 de NEDD8. De plus, RNF20 fonctionne également comme une NEDD8 E3 ligase responsable de la NEDDylation de l'histone H2B mais aussi de PARP1 - une des protéines acteurs clés dans la formation des SG.Understanding how organisms respond to environmental stress has critical implications both on quality of life and treatment of diseases. Organisms have developed a series of sophisticated processes to detect and repair such damages. A family of small proteins called the family of Ubiquitin molecules (Ubls), play a critical role in many aspects of the stress response. Defects in components of the Ubiquitin family are often found in pathologic conditions including cancer and neurodegenerative diseases. Understanding how the ubiquitin family is involved in the cellular stress response is an important step in the understanding of this process and can lead to the development of novel therapeutic approaches to treat diseases caused by malfunction of this system.One of the Ubls that has the highest identity and similarity to Ubiquitin is NEDD8. NEDD8 works in a similar manner to Ub, using a distinct conjugation machinery. NEDD8 modification is essential for maintaining the homeostasis of the cell as it plays a major role in the regulation of viability, growth, and development. Because of that, many components of NEDD8 have been found deregulated in many cancers. NEDD8 can modify a wide range of substrate proteins, including itself, which results in the creation of polyNEDD8 chains. Recently the presence of polyNEDD8 chains has been linked to the regulation of cell death – apoptosis and parthanatos. Moreover, it has been recently reported that NEDD8 during proteotoxic stress can be employed by the Ub conjugation machinery. This results in the creation of hybrid NEDD8 chains where except for NEDD8, we can also find Ub and SUMO, as recent papers have shown that NEDD8 has the ability to modify Ub and SUMO-2. The presence of the hybrid NEDD8 chains was linked with the creation of nuclear aggregates formed during proteotoxic stress, which can play a potential protective role during stress exposure.Knowing how important the regulation of proteins through NEDDylation is, we were also aware of the lack of knowledge about the machinery that plays a role in the creation and deconjugation of different NEDD8 entities. So far two deNEDDylating enzymes were reported but no enzyme was tested for its ability to recognise and process the hybrid NEDD8 chains. Moreover, our knowledge about E3 ligases that are responsible for substrate NEDDylation, even though expanding, is still very limited. Additionally, NEDD8 having ten lysines through which it can modify itself, can generate a very broad range of signals through polyNEDD8 and hybrid NEDD8 chain formation, which can be recognised similarly to polyUb chains, yet no studies have focused on determining their interactors so far.In this work, we focused on exploring the beforementioned unknown elements of the NEDD8 conjugation and deconjugation machineries. Using chemical biology approaches we tested a variety of enzymes and determined that polyNEDD8 chains are exclusively processed by the NEDP1 enzyme, however, deconjugation of hybrid NEDD8 chains requires the coordinated action of different deconjugating enzymes with distinct specificity for Ub or SUMO. We also employed chemically synthesized NEDD8-NEDD8 and NEDD8-Ub dimers in order to look for their interactors and used the gathered data to deepen our knowledge about the biology of hybrid NEDD8 chains in nuclear aggregates. Using NEDD8-Dha probes we identified a group of proteins that are potentially involved in the NEDDylation machinery. Through biological confirmation of obtained results we have shown that tRNA ligases – GARS and SARS are working as NEDD8 E3 ligases. Moreover, RNF20 is also working as a NEDD8 E3 ligase responsible for NEDDylation of histone H2B but also PARP1 – one of the proteins that are key players in the formation of SG