Type 1 and 2 sets for series of translates of functions

Suppose Lambda is a discrete infinite set of nonnegative real numbers. We say that Lambda is type 1 if the series s(x)=Sigma lambda is an element of Lambda f(x+lambda) satisfies a zero-one law. This means that for any non-negative measurable f:R ->[0,+infinity) either the convergence set C(f,Lambda)={x:s(x)<+infinity}=R modulo sets of Lebesgue zero, or its complement the divergence set D(f,Lambda)={x:s(x)=+infinity}=R modulo sets of measure zero. If Lambda is not type 1 we say that Lambda is type 2.The exact characterization of type 1 and type 2 sets is not known. In this paper we continue our study of the properties of type 1 and 2 sets. We discuss sub and supersets of type 1 and 2 sets and give a complete and simple characterization of a subclass of dyadic type 1 sets. We discuss the existence of type 1 sets containing infinitely many elements independent over the rationals. Finally, we consider unions and Minkowski sums of type 1 and 2 sets

Random constructions for translates of non-negative functions

Suppose A is a discrete infinite set of nonnegative real numbers. We say that A is type 2 if the series s(x) = Sigma lambda Lambda f (x + lambda) does not satisfy a zero-one law. This means that we can find a non-negative measurable "witness function" f : R -> [0,+ infinity) such that both the convergence set C(f, Lambda) ={x : s(x) < + infinity} and its complement the divergence set D (f, Lambda) = {x : s(x) = +infinity} are of positive Lebesgue measure. If Lambda is not type 2 we say that A is type 1. The main result of our paper answers a question raised by Z. Buczolich, J-P. Kahane, and D. Mauldin. By a random construction we show that one can always choose a witness function which is the characteristic function of a measurable set. We also consider the effect on the type of a set A if we randomly delete its elements. Motivated by results concerning weighted sums Sigma c(n)f(nx)and the Khinchin conjecture, we also discuss some results about weighted sum

Oxidative DNA damage bypass in Arabidopsis thaliana requires DNA polymerase λ and proliferating cell nuclear antigen 2

The oxidized base 7,8-oxoguanine (8-oxo-G) is the most common DNA lesion generated by reactive oxygen species. This lesion is highly mutagenic due to the frequent misincorporation of A opposite 8-oxo-G during DNA replication. In mammalian cells, the DNA polymerase (pol) family X enzyme DNA pol l catalyzes the correct incorporation of C opposite 8-oxo-G, together with the auxiliary factor proliferating cell nuclear antigen (PCNA). Here, we show that Arabidopsis thaliana DNA pol l, the only member of the X family in plants, is as efficient in performing error-free translesion synthesis past 8-oxo-G as its mammalian homolog. Arabidopsis, in contrast with animal cells, possesses two genes for PCNA. Using in vitro and in vivo approaches, we observed that PCNA2, but not PCNA1, physically interacts with DNA pol l, enhancing its fidelity and efficiency in translesion synthesis. The levels of DNA pol l in transgenic plantlets characterized by overexpression or silencing of Arabidopsis POLL correlate with the ability of cell extracts to perform error-free translesion synthesis. The important role of DNA pol l is corroborated by the observation that the promoter of POLL is activated by UV and that both overexpressing and silenced plants show altered growth phenotypes

Optimisation of the Schizosaccharomyces pombe urg1 expression system

The ability to study protein function in vivo often relies on systems that regulate the presence and absence of the protein of interest. Two limitations for previously described transcriptional control systems that are used to regulate protein expression in fission yeast are: the time taken for inducing conditions to initiate transcription and the ability to achieve very low basal transcription in the "OFF-state". In previous work, we described a Cre recombination-mediated system that allows the rapid and efficient regulation of any gene of interest by the urg1 promoter, which has a dynamic range of approximately 75-fold and which is induced within 30-60 minutes of uracil addition. In this report we describe easy-to-use and versatile modules that can be exploited to significantly tune down P urg1 "OFF-levels" while maintaining an equivalent dynamic range. We also provide plasmids and tools for combining P urg1 transcriptional control with the auxin degron tag to help maintain a null-like phenotype. We demonstrate the utility of this system by improved regulation of HO-dependent site-specific DSB formation, by the regulation Rtf1-dependent replication fork arrest and by controlling Rhp18(Rad18)-dependent post replication repair

Factors influencing the fracture of nickel-titanium rotary instruments

Abstract Mart|¤ n B, Zelada G, Varela P, Bahillo JG, Maga¤ n F, Ahn S, Rodr|¤ guez C

Regulation of Translesion Synthesis DNA Polymerase η by Monoubiquitination

DNA polymerase eta is a Y family polymerase involved in translesion synthesis (TLS). Its action is initiated by simultaneous interaction between the PIP box in pol eta and PCNA and between the UBZ in pol eta and monoubiquitin attached to PCNA. Whereas monoubiquitination of PCNA is required for its interaction with pol eta during TLS, we now show that monoubiquitination of pol eta inhibits this interaction, preventing its functions in undamaged cells. Identification of monoubiquitination sites within pol eta nuclear localization signal (NLS) led to the discovery that pol eta NLS directly contacts PCNA, forming an extended pol eta-PCNA interaction surface. We name this the PCNA-interacting region (PIR) and show that its monoubiquitination is downregulated by various DNA-damaging agents. We propose that this mechanism ensures optimal availability of nonubiquitinated, TLS-competent pol eta after DNA damage. Our work shows how monoubiquitination can either positively or negatively regulate the assembly of a protein complex, depending on which substrates are targeted by ubiquitin

Breastfeeding Self-Efficacy: A Systematic Review of Psychometric Properties Using COSMIN

Background: Breastfeeding self-efficacy has been proven to play a predictive role in enhancing breastfeeding initiation and continuation. Breastfeeding self-efficacy measurement tools have facilitated healthcare professionals’ early identification and support of women at higher risk of early discontinuation of breastfeeding. Research Aim: The aim of this study was to assess the psychometric properties of breastfeeding self-efficacy measurement tools. Method: A systematic review was carried out in three phases. Phase One comprised a systematic literature review performed in PubMed, SCOPUS, Web of Science, and Cochrane Database of Systematic Reviews from February 2021 to January 2023, including 36 studies for final analysis. Phase Two provided a quality appraisal of the psychometric properties of each of the seven breastfeeding self-efficacy measurement tools, according to COnsensus-based Standards for the selection of health Measurement Instrument checklist (COSMIN) guidelines. Phase Three summarized and graded the overall quality of evidence using the Grading of Recommendations Assessment, Development, and Evaluation (GRADE) modified approach. Result: The included articles comprised 9,225 participants and seven breastfeeding self-efficacy measurement tools. The Breastfeeding Self-Efficacy Scale, Breastfeeding Self-Efficacy Scale – Short Form (BSES-SF), and Prenatal Breastfeeding Self-Efficacy Scale were supported by Grade A evidence sustaining their validity and reliability to assess breastfeeding self-efficacy in the continuum of maternity care. The BSES-SF is the most feasible tool in clinical practice and the most utilized internationally, available in 15 languages. Conclusion: This systematic review provided a Grade A recommendation on breastfeeding measurement tools that will be helpful both for clinical and research purposes