Unknown I.I.D. Prophets: Better Bounds, Streaming Algorithms, and a New Impossibility

A prophet inequality states, for some α ∈ [0, 1], that the expected value achievable by a gambler who sequentially observes random variables X1, . . . , Xn and selects one of them is at least an α fraction of the maximum value in the sequence. We obtain three distinct improvements for a setting that was first studied by Correa et al. (EC, 2019) and is particularly relevant to modern applications in algorithmic pricing. In this setting, the random variables are i.i.d. from an unknown distribution and the gambler has access to an additional βn samples for some β ≥ 0. We first give improved lower bounds on α for a wide range of values of β; specifically, α ≥ (1 + β)/e when β ≤ 1/(e − 1), which is tight, and α ≥ 0.648 when β = 1, which improves on a bound of around 0.635 due to Correa et al. (SODA, 2020). Adding to their practical appeal, specifically in the context of algorithmic pricing, we then show that the new bounds can be obtained even in a streaming model of computation and thus in situations where the use of relevant data is complicated by the sheer amount of data available. We finally establish that the upper bound of 1/e for the case without samples is robust to additional information about the distribution, and applies also to sequences of i.i.d. random variables whose distribution is itself drawn, according to a known distribution, from a finite set of known candidate distributions. This implies a tight prophet inequality for exchangeable sequences of random variables, answering a question of Hill and Kertz (Contemporary Mathematics, 1992), but leaves open the possibility of better guarantees when the number of candidate distributions is small, a setting we believe is of strong interest to applications

Phosphorylation of zinc channel ZIP7 drives MAPK, PI3K and mTOR growth and proliferation signalling

Zinc is an essential trace element participating in diverse biological processes. Cellular zinc levels are strictly controlled by two families of transport proteins: ZIP channels (SLC39A) and ZnT transporters (SLC30A). ZIP channels increase cytosolic zinc levels by importing zinc into cells or releasing zinc from intracellular stores such as the ER. Among all the 14 human members of the ZIP family, ZIP7 is a gatekeeper of zinc release from intracellular stores, requiring post-translational activation by phosphorylation on residues S275 and S276, resulting in activation of multiple downstream pathways. Employing site-directed mutagenesis, we investigated the importance of these individual serine residues as well as other predicted phosphorylation sites on ZIP7, showing that all four sites are required for maximal ZIP7 activation. Using phosphor-protein arrays, we also discovered the major signalling pathways that were activated as a direct result of ZIP7-mediated zinc release from intracellular stores. These data reveal the role of ZIP7-mediated zinc release from intracellular stores in driving major pathways, such as MAPK, mTOR and PI3K-AKT, involved in providing cell survival and proliferation and often over activated in cancer

The ZIP6/ZIP10 heteromer is essential for the zinc-mediated trigger of mitosis

Zinc has been known to be essential for cell division for over 40 years but the molecular pathways involved remain elusive. Cellular zinc import across biological membranes necessitates the help of zinc transporters such as the SLC39A family of ZIP transporters. We have discovered a molecular process that explains why zinc is required for cell division, involving two highly regulated zinc transporters, as a heteromer of ZIP6 and ZIP10, providing the means of cellular zinc entry at a specific time of the cell cycle that initiates a pathway resulting in the onset of mitosis. Crucially, when the zinc influx across this heteromer is blocked by ZIP6 or ZIP10 specific antibodies, there is no evidence of mitosis, confirming the requirement for zinc influx as a trigger of mitosis. The zinc that influxes into cells to trigger mitosis additionally changes the phosphorylation state of STAT3 converting it from a transcription factor to a protein that complexes with this heteromer and pS38Stathmin, the form allowing microtubule rearrangement as required in mitosis. This discovery now explains the specific cellular role of ZIP6 and ZIP10 and how they have special importance in the mitosis process compared to other ZIP transporter family members. This finding offers new therapeutic opportunities for inhibition of cell division in the many proliferative diseases that exist, such as cancer

Expression of auxin-binding protein1 during plum fruit ontogeny supports the potential role of auxin in initiating and enhancing climacteric ripening

Auxin-binding protein1 (ABP1) is an active element involved in auxin signaling and plays critical roles in auxin-mediated plant development. Here, we report the isolation and characterization of a putative sequence from Prunus salicina L., designated PslABP1. The expected protein exhibits a similar molecular structure to that of well-characterized maize-ABP1; however, PslABP1 displays more sequence polarity in the active-binding site due to substitution of some crucial amino-acid residues predicted to be involved in auxin-binding. Further, PslABP1 expression was assessed throughout fruit ontogeny to determine its role in fruit development. Comparing the expression data with the physiological aspects that characterize fruit-development stages indicates that PslABP1 up-regulation is usually associated with the signature events that are triggered in an auxin-dependent manner such as floral induction, fruit initiation, embryogenesis, and cell division and elongation. However, the diversity in PslABP1 expression profile during the ripening process of early and late plum cultivars seems to be due to the variability of endogenous auxin levels among the two cultivars, which consequently can change the levels of autocatalytic ethylene available for the fruit to co-ordinate ripening. The effect of auxin on stimulating ethylene production and in regulating PslABP1 was investigated. Our data suggest that auxin is involved in the transition of the mature green fruit into the ripening phase and in enhancing the ripening process in both auxin- and ethylene-dependent manners thereafter

Is increased time to diagnosis and treatment in symptomatic cancer associated with poorer outcomes?:Systematic review

background: It is unclear whether more timely cancer diagnosis brings favourable outcomes, with much of the previous evidence, in some cancers, being equivocal. We set out to determine whether there is an association between time to diagnosis, treatment and clinical outcomes, across all cancers for symptomatic presentations. methods: Systematic review of the literature and narrative synthesis. results: We included 177 articles reporting 209 studies. These studies varied in study design, the time intervals assessed and the outcomes reported. Study quality was variable, with a small number of higher-quality studies. Heterogeneity precluded definitive findings. The cancers with more reports of an association between shorter times to diagnosis and more favourable outcomes were breast, colorectal, head and neck, testicular and melanoma. conclusions: This is the first review encompassing many cancer types, and we have demonstrated those cancers in which more evidence of an association between shorter times to diagnosis and more favourable outcomes exists, and where it is lacking. We believe that it is reasonable to assume that efforts to expedite the diagnosis of symptomatic cancer are likely to have benefits for patients in terms of improved survival, earlier-stage diagnosis and improved quality of life, although these benefits vary between cancers

On the role of ethylene, auxin and a GOLVEN-like peptide hormone in the regulation of peach ripening

BACKGROUND: In melting flesh peaches, auxin is necessary for system-2 ethylene synthesis and a cross-talk between ethylene and auxin occurs during the ripening process. To elucidate this interaction at the transition from maturation to ripening and the accompanying switch from system-1 to system-2 ethylene biosynthesis, fruits of melting flesh and stony hard genotypes, the latter unable to produce system-2 ethylene because of insufficient amount of auxin at ripening, were treated with auxin, ethylene and with 1-methylcyclopropene (1-MCP), known to block ethylene receptors. The effects of the treatments on the different genotypes were monitored by hormone quantifications and transcription profiling. RESULTS: In melting flesh fruit, 1-MCP responses differed according to the ripening stage. Unexpectedly, 1-MCP induced genes also up-regulated by ripening, ethylene and auxin, as CTG134, similar to GOLVEN (GLV) peptides, and repressed genes also down-regulated by ripening, ethylene and auxin, as CTG85, a calcineurin B-like protein. The nature and transcriptional response of CTG134 led to discover a rise in free auxin in 1-MCP treated fruit. This increase was supported by the induced transcription of CTG475, an IAA-amino acid hydrolase. A melting flesh and a stony hard genotype, differing for their ability to synthetize auxin and ethylene amounts at ripening, were used to study the fine temporal regulation and auxin responsiveness of genes involved in the process. Transcriptional waves showed a tight interdependence between auxin and ethylene actions with the former possibly enhanced by the GLV CTG134. The expression of genes involved in the regulation of ripening, among which are several transcription factors, was similar in the two genotypes or could be rescued by auxin application in the stony hard. Only GLV CTG134 expression could not be rescued by exogenous auxin. CONCLUSIONS: 1-MCP treatment of peach fruit is ineffective in delaying ripening because it stimulates an increase in free auxin. As a consequence, a burst in ethylene production speeding up ripening occurs. Based on a network of gene transcriptional regulations, a model in which appropriate level of CTG134 peptide hormone might be necessary to allow the correct balance between auxin and ethylene for peach ripening to occur is proposed. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s12870-016-0730-7) contains supplementary material, which is available to authorized users