Representation of Finite Abelian Group Elements by Subsequence Sums

Let $G\cong C_{n_1}\oplus ... \oplus C_{n_r}$ be a finite and nontrivial abelian group with $n_1|n_2|...|n_r$. A conjecture of Hamidoune says that if $W=w_1... w_n$ is a sequence of integers, all but at most one relatively prime to $|G|$, and $S$ is a sequence over $G$ with $|S|\geq |W|+|G|-1\geq |G|+1$, the maximum multiplicity of $S$ at most $|W|$, and $\sigma(W)\equiv 0\mod |G|$, then there exists a nontrivial subgroup $H$ such that every element $g\in H$ can be represented as a weighted subsequence sum of the form $g=\sum_{i=1}^{n}w_is_i$, with $s_1... s_n$ a subsequence of $S$. We give two examples showing this does not hold in general, and characterize the counterexamples for large $|W|\geq {1/2}|G|$. A theorem of Gao, generalizing an older result of Olson, says that if $G$ is a finite abelian group, and $S$ is a sequence over $G$ with $|S|\geq |G|+D(G)-1$, then either every element of $G$ can be represented as a $|G|$-term subsequence sum from $S$, or there exists a coset $g+H$ such that all but at most $|G/H|-2$ terms of $S$ are from $g+H$. We establish some very special cases in a weighted analog of this theorem conjectured by Ordaz and Quiroz, and some partial conclusions in the remaining cases, which imply a recent result of Ordaz and Quiroz. This is done, in part, by extending a weighted setpartition theorem of Grynkiewicz, which we then use to also improve the previously mentioned result of Gao by showing that the hypothesis $|S|\geq |G|+D(G)-1$ can be relaxed to $|S|\geq |G|+d^*(G)$, where d^*(G)=\Sum_{i=1}^{r}(n_i-1). We also use this method to derive a variation on Hamidoune's conjecture valid when at least $d^*(G)$ of the $w_i$ are relatively prime to $|G|$

Expression and Function of GABA Receptors in Myelinating Cells

Myelin facilitates the fast transmission of nerve impulses and provides metabolic support to axons. Differentiation of oligodendrocyte progenitor cells (OPCs) and Schwann cell (SC) precursors is critical for myelination during development and myelin repair in demyelinating disorders. Myelination is tightly controlled by neuron-glia communication and requires the participation of a wide repertoire of signals, including neurotransmitters such as glutamate, ATP, adenosine, or gamma-aminobutyric acid (GABA). GABA is the main inhibitory neurotransmitter in the central nervous system (CNS) and it is also present in the peripheral nervous system (PNS). The composition and function of GABA receptors (GABARs) are well studied in neurons, while their nature and role in glial cells are still incipient. Recent studies demonstrate that GABA-mediated signaling mechanisms play relevant roles in OPC and SC precursor development and function, and stand out the implication of GABARs in oligodendrocyte (OL) and SC maturation and myelination. In this review, we highlight the evidence supporting the novel role of GABA with an emphasis on the molecular identity of the receptors expressed in these glial cells and the possible signaling pathways involved in their actions. GABAergic signaling in myelinating cells may have potential implications for developing novel reparative therapies in demyelinating diseases.This work was supported by CIBERNED (CB06/05/0076; CM) and by grants from the Ministry of Economy and Competitiveness, Government of Spain (SAF2016-75292-R and PID2019-109724RB-I00; CM), Basque Government (IT1203-19; CM), CONACYT-Mexico (No. 252121; RA), PAPIIT-UNAM-Mexico (IN203519; RA) and NIH (R21AG053740 and R21MH113177; AL). MS-R was hired thanks to the Gangoiti Foundation (Bilbao). LB-C and RO hold fellowships from Basque Government and CONACYT-Mexico, respectively

Transcriptome analyses throughout chili pepper fruit development reveal novel insights into the domestication process

Chili pepper (Capsicum spp.) is an important crop, as well as a model for fruit development studies and domestication. Here, we performed a time-course experiment to estimate standardized gene expression profiles with respect to fruit development for six domesticated and four wild chili pepper ancestors. We sampled the transcriptomes every 10 days from flowering to fruit maturity, and found that the mean standardized expression profiles for domesticated and wild accessions significantly differed. The mean standardized expression was higher and peaked earlier for domesticated vs. wild genotypes, particularly for genes involved in the cell cycle that ultimately control fruit size. We postulate that these gene expression changes are driven by selection pressures during domestication and show a robust network of cell cycle genes with a time shift in expression, which explains some of the differences between domesticated and wild phenotypes

Increased risk of type I errors in cluster randomised trials with small or medium numbers of clusters: a review, reanalysis,and simulation study

Background: Cluster randomised trials (CRTs) are commonly analysed using mixed-effects models or generalised estimating equations (GEEs). However, these analyses do not always perform well with the small number of clusters typical of most CRTs. They can lead to increased risk of a type I error (finding a statistically significant treatment effect when it does not exist) if appropriate corrections are not used. Methods: We conducted a small simulation study to evaluate the impact of using small-sample corrections for mixed-effects models or GEEs in CRTs with a small number of clusters. We then reanalysed data from TRIGGER, a CRT with six clusters, to determine the effect of using an inappropriate analysis method in practice. Finally, we reviewed 100 CRTs previously identified by a search on PubMed in order to assess whether trials were using appropriate methods of analysis. Trials were classified as at risk of an increased type I error rate if they did not report using an analysis method which accounted for clustering, or if they had fewer than 40 clusters and performed an individual-level analysis without reporting the use of an appropriate small-sample correction. Results: Our simulation study found that using mixed-effects models or GEEs without an appropriate correction led to inflated type I error rates, even for as many as 70 clusters. Conversely, using small-sample corrections provided correct type I error rates across all scenarios. Reanalysis of the TRIGGER trial found that inappropriate methods of analysis gave much smaller P values (P ≤ 0.01) than appropriate methods (P = 0.04–0.15). In our review, of the 99 trials that reported the number of clusters, 64 (65 %) were at risk of an increased type I error rate; 14 trials did not report using an analysis method which accounted for clustering, and 50 trials with fewer than 40 clusters performed an individual-level analysis without reporting the use of an appropriate correction. Conclusions: CRTs with a small or medium number of clusters are at risk of an inflated type I error rate unless appropriate analysis methods are used. Investigators should consider using small-sample corrections with mixed-effects models or GEEs to ensure valid results. Abbreviations: CRT, Cluster randomised trial; CI, Confidence interval; GEE, Generalised estimating equations; TRIGGER, Trial in Gastrointestinal Transfusio

Autogenic Training Relaxation Helping Postpartum Mothers to Achieve Successful Breastfeeding on Early Lactation Period

Introduction: The numbers of breastfeeding failures are mostly caused by mothers` disbelief to themselves. One method that can be done to overcome these problems in accordance with the self-care nursing theory is the autogenic training relaxation. This method teaches mothers to be self-sufficient in building a positive intention and motivation to help the process of breastfeeding. This study aimed to examine the influence of autogenic training relaxation to the effectiveness of breastfeeding and the enhancement of breast milk volume on maternal postpartum. Method: By using an experimental posttest only-non equivalent control group design, 26 samples were taken based on the criteria and divided into two groups by matching technuiqe. autogenic training was given through MP3 Player for 3 weeks. Post-test observation conducted on the third week by home visit. Via Christi Breastfeeding Assessment Tool Jan Riordan modifications used to assess the effectiveness of breastfeeding, and to measure the milk ejection volume, used weighing test using electronic baby scales. Data were analyzed using one-tailed independent t test with α ≤ 0.05. Result: The analysis showed that mothers who did autogenic training relaxation could breastfeed more effectively and had greater average volume of milk ejection than the control group (p = 0.000 and p = 0.001). Discussion: It can be concluded that autogenic relaxation training techniques affect the effectiveness of breastfeeding and breast milk volume. These results can be considered that autogenic training as an intervention in program of support for breastfeeding mothers

A novel a-L-Arabinofuranosidase of Family 43 Glycoside Hydrolase (Ct43Araf ) from Clostridium thermocellum

Articles in International JournalsThe study describes a comparative analysis of biochemical, structural and functional properties of two recombinant derivatives from Clostridium thermocellum ATCC 27405 belonging to family 43 glycoside hydrolase. The family 43 glycoside hydrolase encoding a-L-arabinofuranosidase (Ct43Araf) displayed an N-terminal catalytic module CtGH43 (903 bp) followed by two carbohydrate binding modules CtCBM6A (405 bp) and CtCBM6B (402 bp) towards the C-terminal. Ct43Araf and its truncated derivative CtGH43 were cloned in pET-vectors, expressed in Escherichia coli and functionally characterized. The recombinant proteins displayed molecular sizes of 63 kDa (Ct43Araf) and 34 kDa (CtGH43) on SDS-PAGE analysis. Ct43Araf and CtGH43 showed optimal enzyme activities at pH 5.7 and 5.4 and the optimal temperature for both was 50uC. Ct43Araf and CtGH43 showed maximum activity with rye arabinoxylan 4.7 Umg21 and 5.0 Umg21, respectively, which increased by more than 2-fold in presence of Ca2+ and Mg2+ salts. This indicated that the presence of CBMs (CtCBM6A and CtCBM6B) did not have any effect on the enzyme activity. The thin layer chromatography and high pressure anion exchange chromatography analysis of Ct43Araf hydrolysed arabinoxylans (rye and wheat) and oat spelt xylan confirmed the release of L-arabinose. This is the first report of a-L-arabinofuranosidase from C. thermocellum having the capacity to degrade both pnitrophenol- a-L-arabinofuranoside and p-nitrophenol-a-L-arabinopyranoside. The protein melting curves of Ct43Araf and CtGH43 demonstrated that CtGH43 and CBMs melt independently. The presence of Ca2+ ions imparted thermal stability to both the enzymes. The circular dichroism analysis of CtGH43 showed 48% b-sheets, 49% random coils but only 3% a-helices