On the Intriguing Problem of Counting (n+1,n+2)-Core Partitions into Odd Parts

Tewodros Amdeberhan and Armin Straub initiated the study of enumerating subfamilies of the set of (s,t)-core partitions. While the enumeration of (n+1,n+2)-core partitions into distinct parts is relatively easy (in fact it equals the Fibonacci number F_{n+2}), the enumeration of (n+1,n+2)-core partitions into odd parts remains elusive. Straub computed the first eleven terms of that sequence, and asked for a "formula," or at least a fast way, to compute many terms. While we are unable to find a "fast" algorithm, we did manage to find a "faster" algorithm, which enabled us to compute 23 terms of this intriguing sequence. We strongly believe that this sequence has an algebraic generating function, since a "sister sequence" (see the article), is OEIS sequence A047749 that does have an algebraic generating function. One of us (DZ) is pledging a donation of 100 dollars to the OEIS, in honor of the first person to generate sufficiently many terms to conjecture (and prove non-rigorously) an algebraic equation for the generating function of this sequence, and another 100 dollars for a rigorous proof of that conjecture. Finally, we also develop algorithms that find explicit generating functions for other, more tractable, families of (n+1,n+2)-core partitions.Comment: 12 pages, accompanied by Maple package. This version announces that our questions were all answered by Paul Johnson, and a donation to the OEIS, in his honor, has been mad

Salinity in Autumn-Winter Season and Fruit Quality of Tomato Landraces

Tomato landraces, originated by adaptive responses to local habitats, are considered a valuable resource for many traits of agronomic interest, including fruit nutritional quality. Primary and secondary metabolites are essential determinants of fruit organoleptic quality, and some of them, such as carotenoids and phenolics, have been associated with beneficial proprieties for human health. Landraces' fruit taste and flavour are often preferred by consumers compared to the commercial varieties' ones. In an autumn-winter greenhouse hydroponic experiment, the response of three Southern-Italy tomato landraces (Ciettaicale, Linosa and Corleone) and one commercial cultivar (UC-82B) to different concentrations of sodium chloride (0 mM, 60 mM or 120 mM NaCl) were evaluated. At harvest, no losses in marketable yield were noticed in any of the tested genotypes. However, under salt stress, fresh fruit yield as well as fruit calcium concentration were higher affected in the commercial cultivar than in the landraces. Furthermore, UC-82B showed a trend of decreasing lycopene and total antioxidant capacity with increasing salt concentration, whereas no changes in these parameters were observed in the landraces under 60 mM NaCl. Landraces under 120 mM NaCl accumulated more fructose and glucose in the fruits, while salt did not affect hexoses levels in UC-82B. Ultra-performance liquid chromatography-tandem mass spectrometry analysis revealed differential accumulation of glycoalkaloids, phenolic acids, flavonoids and their derivatives in the fruits of all genotypes under stress. Overall, the investigated Italian landraces showed a different behaviour compared to the commercial variety UC-82B under moderate salinity stress, showing a tolerable compromise between yield and quality attributes. Our results point to the feasible use of tomato landraces as a target to select interesting genetic traits to improve fruit quality under stress conditions

MicroRNAs involvement in fludarabine refractory chronic lymphocytic leukemia

<p>Abstract</p> <p>Background</p> <p>Fludarabine, is one of the most active single agents in the treatment of chronic lymphocytic leukemia (CLL). Over time, however, virtually all CLL patients become fludarabine-refractory. To elucidate whether microRNAs are involved in the development of fludarabine resistance, we analyzed the expression of 723 human miRNAs before and 5-days after fludarabine mono-therapy in 17 CLL patients which were classified as responder or refractory to fludarabine treatment based on NCI criteria.</p> <p>Results</p> <p>By comparing the expression profiles of these two groups of patients, we identified a microRNA signature able to distinguish refractory from sensitive CLLs. The expression of some microRNAs was also able to predict fludarabine resistance of 12 independent CLL patients. Among the identified microRNAs, miR-148a, miR-222 and miR-21 exhibited a significantly higher expression in non-responder patients either before and after fludarabine treatment. After performing messenger RNA expression profile of the same patients, the activation of p53-responsive genes was detected in fludarabine responsive cases only, therefore suggesting a possible mechanism linked to microRNA deregulation in non-responder patients. Importantly, inhibition of miR-21 and miR-222 by anti-miRNA oligonucleotides induced a significant increase in caspase activity in fludarabine-treated p53-mutant MEG-01 cells, suggesting that miR-21 and miR-222 up-regulation may be involved in the establishment of fludarabine resistance.</p> <p>Conclusions</p> <p>This is the first report that reveals the existence of a microRNA profile that differentiate refractory and sensitive CLLs, either before and after fludarabine mono-therapy. A p53 dysfunctional pathway emerged in refractory CLLs and could contribute in explaining the observed miRNA profile. Moreover, this work indicates that specific microRNAs can be used to predict fludarabine resistance and may potentially be used as therapeutic targets, therefore establishing an important starting point for future studies.</p

High-throughput 18K SNP array to assess genetic variability of the main grapevine cultivars from Sicily

The viticulture of Sicily, for its vocation, is one of the most important and ancient forms in Italy. Autochthonous grapevine cultivars, many of which known throughout the world, have always been cultivated in the island from many centuries. With the aim to preserve this large grapevine diversity, previous studies have already started to assess the genetic variability among the Sicilian cultivars by using morphological and microsatellite markers. In this study, simple sequence repeat (SSR) were utilized to verify the true-to-typeness of a large clone collection (101) belonging to 21 biotypes of the most 10 cultivated Sicilian cultivars. Afterwards, 42 Organization Internationale de la Vigne et du Vin (OIV) descriptors and a high-throughput single nucleotide polymorphism (SNP) genotyping array (Vitis18kSNP) were applied to assess genetic variability among cultivars and biotypes of the same cultivar. Ampelographic traits and high-throughput SNP genotyping platforms provided an accuracy estimation of genetic diversity in the Sicilian germplasm, showing the relationships among cultivars by cluster and multivariate analyses. The large SNP panel defined sub-clusters unable to discern among biotypes, previously classified by ampelographic analysis, belonging to each cultivar. These results suggested that a very large number of SNP did not cover the genome regions harboring few morphological traits. Genetic structure of the collection revealed a clear optimum number of groups for K = 3, clustering in the same group a significant portion of family-related genotypes. Parentage analysis highlighted significant relationships among Sicilian grape cultivars and Sangiovese, as already reported, but also the first evidences of the relationships between Nero d’Avola and both Inzolia and Catarratto. Finally, a small panel of highly informative markers (12 SNPs) allowed us to isolate a private profile for each Sicilian cultivar, providing a new tool for cultivar identification

First stage of growth of internal waves instably stratified fluids

A theoretical analysis of the first stage of growth of internal waves in stably stratified fluids is given. It is shown how, during the first stage, the profiles obtained by means of the linearized theory are maintained by the growing waves. The linearized theory seems also to model properly the mixing layers in a stably stratified fluid subject to forcing at the boundaries. The results of this work are confirmed by the analysis of the experimental data for a particular geophysical situation studied in a preceding article

Morphological and Genetic Analysis of Wild Hop (<i>Humulus lupulus</i> L.) Germplasm from Calabria Region in South Italy

Hops (Humulus lupulus L.) constitute a species that grows spontaneously in the region of Calabria (South Italy), but the species’ morphological and genetic characterization have not yet been explored. Thus, we explored some morphological traits related to cones of wild hops from three Calabrian sites: Cosenza (CS), Catanzaro (CZ), and Vibo Valentia (VV). In addition, eight Simple Sequence Repeats (SSR) were adopted to investigate the genetic diversity and population structure of the local germplasm, which were also compared to commercial varieties. Cone length exhibited large variation among the different populations, whereas cone shape was the most discriminant trait according to principal coordinate analysis. Eighty-one alleles were detected with a high mean of alleles per locus (10.12). The SSRs used in the present study were highly informative with a genetic diversity of 0.829 and a PIC value > 0.62, thereby confirming the high genetic variability in Calabria. Finally, genetic structure analysis revealed the existence of two distinct groups regardless of the specimens’ sampling sites. Further studies including other wild hops populations from Calabria will be performed in order to detect specific alleles for new breeding programs

Allelopatic Potential of Dittrichia viscosa (L.) W. Greuter Mediated by VOCs: A Physiological and Metabolomic Approach.

Dittrichia viscosa (L.) W. Greuter is a pioneer species belonging to the Compositae family. It is widespread in the Mediterranean basin, where it is considered invasive. It is a source of secondary metabolites, playing an important ecological role. D. viscosa plant extracts showed a phytotoxic activity on several physiological processes of different species. In the current study, the allelopathic potential of D. viscosa VOCs, released by its foliage, was evaluated on seed germination and root growth of lettuce. The VOCs effect was also studied on lettuce adult plants in microcosm systems, which better mimicked the open field conditions. D. viscosa VOCs inhibited both seed germination and root growth of lettuce. The VOCs composition revealed a large presence of terpenoids, responsible of the effects observed. Moreover, D. viscosa VOCs caused an alteration on plant water status accompanied by oxidative damages and photoinhibition on lettuce adult plants

Emerging Trends in Allelopathy: A Genetic Perspective for Sustainable Agriculture

Over the past decades, a growing interest in allelopathy has been recorded due to the effective use of allelochemicals as growth regulators, bioherbicides, insecticides, and antimicrobial crop protection in the sustainable agriculture field. So far, the genetic aspects of the allelopathic effects have been poorly studied, and the identification of allelopathic genes and/or genomic regions (QTLs) has become a challenge to implement specific breeding programs. Here, we review the recent genetic and genome-based research findings in allelopathy, with a particular emphasis on weed control, which is one of the major crop yield-limiting factors. We discuss the key plant–microorganism interactions, including the cross-kingdom RNAi phenomenon and the involvement of microRNAs in allelopathy. Through this review, we wanted to lay the foundation for advancing knowledge in allelopathy and uncover the areas where research is needed

High-sensitivity assay for monitoring ESR1 mutations in circulating cell-free DNA of breast cancer patients receiving endocrine therapy

Approximately 70% of breast cancers (BCs) express estrogen receptor alpha (ERα) and are treated with endocrine therapy. However, the effectiveness of this therapy is limited by innate or acquired resistance in approximately one-third of patients. Activating mutations in the ESR1 gene that encodes ERα promote critical resistance mechanisms. Here, we developed a high sensitivity approach based on enhanced-ice-COLD-PCR for detecting ESR1 mutations. The method produced an enrichment up to 100-fold and allowed the unambiguous detection of ESR1 mutations even when they consisted of only 0.01% of the total ESR1 allelic fraction. After COLD-PCR enrichment, methods based on next-generation sequencing or droplet-digital PCR were employed to detect and quantify ESR1 mutations. We applied the method to detect ESR1 mutations in circulating free DNA from the plasma of 56 patients with metastatic ER-positive BC. Fifteen of these patients were found to have ESR1 mutations at codons 536–538. This study demonstrates the utility of the enhanced-ice-COLD-PCR approach for simplifying and improving the detection of ESR1 tumor mutations in liquid biopsies. Because of its high sensitivity, the approach may potentially be applicable to patients with non-metastatic disease

Morpho-physiological responses of sugar beet (Beta vulgaris L.) genotypes to drought stress

The identification of morpho-physiological traits related to drought tolerance and high yield potential is a challenge when selecting sugar beet genotypes with greater tolerance to water stress. In this paper, root mor- phological parameters, antioxidant systems, leaf relative water content (RWC) and H?-ATPase activity as key morpho-physiological traits involved in drought tolerance/ susceptibility of sugar beet were studied. Genotypes showing a different drought tolerance index (DTI) but a similar yield potential, under moderate (-0.6 Mpa) and severe (-1.2 MPa) water stress, were selected and their morpho-physiological traits were investigated. The results showed a wide genetic variation in morpho-physiological parameters which demonstrated the different adaptive strategies under moderate and severe drought conditions in sugar beet. In particular, an efficient antioxidant system and redox signalling made some sugar beet genotypes more tolerant to drought stress. The alternative strategy of other genotypes was the reduction of root tissue density, which produced a less dense root system improving the axial hydraulic conductivity. These results could be considered as interesting challenge for a better understanding of the drought tolerance mechanisms in sugar beet