Local first integrals for stochastic differential equations

Poincar\'{e}'s classical results [H. Poincar\'{e}, Sur l'int\'{e}gration des \'{e}quations diff\'{e}rentielles du premier order et du premier degr\'{e} I and II, Rend. Circ. Mat. Palermo 5 (1891) 161-191; 11 (1897) 193-239] first provide a link between the existence of analytic first integrals and the resonant relations for analytic dynamical systems. In this paper, we show that by appropriately selecting the definition of the stochastic local first integrals, we are able to obtain the stochastic version of Poincar\'e non-integrability theorem. More specifically, we introduce two definitions of local first integrals for stochastic differential equations (SDEs) in the sense of probability one and expectation, respectively. We present the necessary conditions for the existence of functionally independent analytic or rational first integrals of SDEs via the resonances. We also show that for given integrable ordinary differential equations with some nondegeneracy conditions, there exists a linear stochastic perturbation such that the corresponding disturbed SDEs have no any analytic first integrals. Some examples are given to illustrate our results

Structure and properties of fluorinated and non‐fluorinated Ba‐coordination polymers – the position of fluorine makes the difference

As the most electronegative element, fluorine has a strong influence on material properties such as absorption behaviour or chemical and thermal stability. Fluorine can be easily integrated into coordination polymers (CPs) via a fluorinated acetate, here trifluoroacetate in Ba(CF3COO)2, or directly via a metal fluorine bond (BaF(CH3COO)). In the present study both possibilities of fluorine integration were tested and their effect on structure and properties of barium coordination polymers was investigated in comparison with the non-fluorinated barium acetate (Ba(CH3COO)2). In addition to the study of their thermal behaviour and their decomposition temperature, the CPs structures were tested for their application as possible anode materials in lithium ion batteries and for their sorption of water and ammonia. The properties of the CPs can be traced back to the individual structural motifs and could thus trigger new design ideas for CPs in LIBs and/or catalysis.HU BerlinBAMPeer Reviewe

High-Entropy Spinel Oxides Produced via Sol-Gel and Electrospinning and Their Evaluation as Anodes in Li-Ion Batteries

In the last few years, high-entropy oxides (HEOs), a new class of single-phase solid solution materials, have attracted growing interest in both academic research and industry for their great potential in a broad range of applications. This work investigates the possibility of producing pure single-phase HEOs with spinel structure (HESOs) under milder conditions (shorter heat treatments at lower temperatures) than standard solid-state techniques, thus reducing the environmental impact. For this purpose, a large set of HESOs was prepared via sol-gel and electrospinning (by using two different polymers). Ten different equimolar combinations of five metals were considered, and the influence of the synthesis method and conditions on the microstructure, morphology and crystalline phase purity of the produced HESOs was investigated by a combination of characterization techniques. On the other hand, the presence of specific metals, such as copper, lead to the formation of minority secondary phase(s). Finally, two representative pure single-phase HESOs were preliminarily evaluated as active anode materials in lithium-ion batteries and possible strategies to enhance their rate capability and cyclability were proposed and successfully implemented. The approaches introduced here can be extensively applied for the optimization of HEO properties targeting different applications.Italian Ministry of University and Research (MUR)Peer Reviewe

Characterization of Duck (Anas platyrhynchos) Short Tandem Repeat Variation by Population-Scale Genome Resequencing

Short tandem repeats (STRs) are usually associated with genetic diseases and gene regulatory functions, and are also important genetic markers for analysis of evolutionary, genetic diversity and forensic. However, for the majority of STRs in the duck genome, their population genetic properties and functional impacts remain poorly defined. Recent advent of next generation sequencing (NGS) has offered an opportunity for profiling large numbers of polymorphic STRs. Here, we reported a population-scale analysis of STR variation using genome resequencing in mallard and Pekin duck. Our analysis provided the first genome-wide duck STR reference including 198,022 STR loci with motif size of 2–6 base pairs. We observed a relatively uneven distribution of STRs in different genomic regions, which indicates that the occurrence of STRs in duck genome is not random, but undergoes a directional selection pressure. Using genome resequencing data of 23 mallard and 26 Pekin ducks, we successfully identified 89,891 polymorphic STR loci. Intensive analysis of this dataset suggested that shorter repeat motif, longer reference tract length, higher purity, and residing outside of a coding region are all associated with an increase in STR variability. STR genotypes were utilized for population genetic analysis, and the results showed that population structure and divergence patterns among population groups can be efficiently captured. In addition, comparison between Pekin duck and mallard identified 3,122 STRs with extremely divergent allele frequency, which overlapped with a set of genes related to nervous system, energy metabolism and behavior. The evolutionary analysis revealed that the genes containing divergent STRs may play important roles in phenotypic changes during duck domestication. The variation analysis of STRs in population scale provides valuable resource for future study of genetic diversity and genome evolution in duck

Identification of orange color-related gene, PhcpcC, in Pyropia haitanensis

Pigmentation-related mutations can be utilized to distinguish between differentially colored sectors of chimeric thalli, thereby facilitating the efficient breeding of economically valuable Pyropia/Porphyra seaweed species. However, the specific trait loci and alleles responsible for Pyropia/Porphyra coloration have yet to be identified, which limits the applicability of coloration mutants for breeding and genetic analyses. In this study, to preserve the genetic integrity of the population, only four-colored thalli were considered when constructing the doubled haploid (DH) Pyropia haitanensis population, which consisted of 480 homozygous offspring lines (representing the largest DH Pyropia/Porphyra population). The offspring lines in the DH population exhibited both wild-type colored and orange sectors, with a segregation ratio of approximately 1:1, indicating that the orange coloration was controlled by a single nuclear gene. Through BSA-seq analysis (99% confidence interval), a candidate region of 0.5 Mb was identified in the P. haitanensis genome. Additionally, a non-synonymous SNP [A/G] was detected at base-pair position 481 in the coding region of PhcpcC, which encodes a phycocyanin-associated rod linker protein. This SNP locus was verified in both DH and natural populations, with the wild-type colored lines having an A base and the orange lines having a G base at this locus. Therefore, PhcpcC may be the gene associated with the orange coloration of P. haitanensis. The molecular marker developed in this study can be employed to exploit pigmentation mutants for breeding and genetic analyses of Pyropia/Porphyra species

KU70 Inhibition Impairs Both Non-Homologous End Joining and Homologous Recombination DNA Damage Repair Through SHP-1 Induced Dephosphorylation of SIRT1 in Adult T-Cell Leukemia-Lymphoma Cells

Background/Aims: Adult T-cell leukemia-lymphoma (ATL) is an aggressive disease which is highly resistant to chemotherapy. Studies show that enhanced ability of DNA damage repair (DDR) in cancer cells plays a key role in chemotherapy resistance. Here, we suggest that defect in DDR related genes might be a promising target to destroy the genome stability of tumor cells. Methods: Since KU70 is highly expressed in Jurkat cells, one of the most representative cell lines of ATL, we knocked down KU70 by shRNA and analyzed the impact of KU70 deficiency in Jurkat cells as well as in NOD-SCID animal models by western blot, immunofluorescence, flow cytometry and measuring DNA repair efficiency. Results: It is observed that silencing of KU70 resulted in accumulated DNA damage and impaired DDR in Jurkat cells, resulting in more apoptosis, decreased cell proliferation and cell cycle arrest. DNA damage leads to DNA double-strand breaks (DSBs), which are processed by either non-homologous end joining(NHEJ) or homologous recombination(HR). In our study, both NHEJ and HR are impaired because of KU70 defect, accompanied with increased protein level of SHP-1, a dephosphorylation enzyme. In turn, SHP-1 led to dephosphorylation of SIRT1, which further impaired HR repair efficiency. Moreover, KU70 deficiency prolonged survival of Jurkat-xenografted mice. Conclusion: These findings suggest that targeting KU70 is a promising target for ATL and might overcome the existing difficulties in chemotherapy

Molecular Characterization and Expression Analysis of Ribosomal Protein S6 Gene in the Cashmere Goat ()

Ribosomal protein (rp) S6 is the substrate of ribosomal protein S6K (S6 kinase) and is involved in protein synthesis by mTOR/S6K/S6 signaling pathway. Some S6 cDNA have been cloned in mammals in recent years but has not been identified in the goat. To facilitate such studies, we cloned the cDNA encoding Cashmere goat (Capra hircus) S6 (GenBank accession GU131122) and then detected mRNA expression in seven tissues by real time PCR and protein expression in testis tissue by immunohistochemisty. Sequence analysis indicated that the obtained goat S6 was a 808 bp product, including a 3′ untranslated region of 58 bp and an open reading frame of 750 bp which predicted a protein of 249 amino acids. The predicted amino acid sequence was highly homologous to cattle, human, mouse and rat S6. Expression analysis indicated S6 mRNA was expressed extensively in detected tissues and S6 protein was expressed in testis tissue

The role of carbonate-fluoride melt immiscibility in shallow REE deposit evolution

The Lugiin Gol nepheline syenite intrusion, Mongolia, hosts a range of carbonatite dikes mineralized in rare-earth elements (REE). Both carbonatites and nepheline syenite-fluoritecalcite veinlets are host to a previously unreported macroscale texture involving pseudographic intergrowths of fluorite and calcite. The inclusions within calcite occur as either pure fluorite, with associated REE minerals within the surrounding calcite, or as mixed calcitefluorite inclusions, with associated zirconosilicate minerals. Consideration of the nature of the texture, and the proportions of fluorite and calcite present (~29 and 71 mol%, respectively), indicates that these textures most likely formed either through the immiscible separation of carbonate and fluoride melts, or from cotectic crystallization of a carbonatefluoride melt. Laser ablation ICP-MS analyses show the pure fluorite inclusions to be depleted in REE relative to the calcite. A model is proposed, in which a carbonate-fluoride melt phase enriched in Zr and the REE, separated from a phonolitic melt, and then either unmixed or underwent cotectic crystallization to generate an REE-rich carbonate melt and an REE-poor fluoride phase. The separation of the fluoride phase (either solid or melt) may have contributed to the enrichment of the carbonate melt in REE, and ultimately its saturation with REE minerals. Previous data have suggested that carbonate melts separated from silicate melts are relatively depleted in the REE, and thus melt immiscibility cannot result in the formation of REE-enriched carbonatites. The observations presented here provide a mechanism by which this could occur, as under either model the textures imply initial separation of a mixed carbonate-fluoride melt from a silicate magma. The separation of an REE-enriched carbonate-fluoride melt from phonolitic magma is a hitherto unrecognized mechanism for REE-enrichment in carbonatites, and may play an important role in the formation of shallow magmatic REE deposits