B\"acklund transformations for the second Painlev\'e hierarchy: a modified truncation approach

The second Painlev\'e hierarchy is defined as the hierarchy of ordinary differential equations obtained by similarity reduction from the modified Korteweg-de Vries hierarchy. Its first member is the well-known second Painlev\'e equation, P2. In this paper we use this hierarchy in order to illustrate our application of the truncation procedure in Painlev\'e analysis to ordinary differential equations. We extend these techniques in order to derive auto-B\"acklund transformations for the second Painlev\'e hierarchy. We also derive a number of other B\"acklund transformations, including a B\"acklund transformation onto a hierarchy of P34 equations, and a little known B\"acklund transformation for P2 itself. We then use our results on B\"acklund transformations to obtain, for each member of the P2 hierarchy, a sequence of special integrals.Comment: 12 pages in LaTeX 2.09 (uses ioplppt.sty), to appear in Inverse Problem

Climate Process Team on internal wave–driven ocean mixing

Author Posting. © American Meteorological Society, 2017. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Bulletin of the American Meteorological Society 98 (2017): 2429-2454, doi:10.1175/BAMS-D-16-0030.1.Diapycnal mixing plays a primary role in the thermodynamic balance of the ocean and, consequently, in oceanic heat and carbon uptake and storage. Though observed mixing rates are on average consistent with values required by inverse models, recent attention has focused on the dramatic spatial variability, spanning several orders of magnitude, of mixing rates in both the upper and deep ocean. Away from ocean boundaries, the spatiotemporal patterns of mixing are largely driven by the geography of generation, propagation, and dissipation of internal waves, which supply much of the power for turbulent mixing. Over the last 5 years and under the auspices of U.S. Climate Variability and Predictability Program (CLIVAR), a National Science Foundation (NSF)- and National Oceanic and Atmospheric Administration (NOAA)-supported Climate Process Team has been engaged in developing, implementing, and testing dynamics-based parameterizations for internal wave–driven turbulent mixing in global ocean models. The work has primarily focused on turbulence 1) near sites of internal tide generation, 2) in the upper ocean related to wind-generated near inertial motions, 3) due to internal lee waves generated by low-frequency mesoscale flows over topography, and 4) at ocean margins. Here, we review recent progress, describe the tools developed, and discuss future directions.We are grateful to U.S. CLIVAR for their leadership in instigating and facilitating the Climate Process Team program. We are indebted to NSF and NOAA for sponsoring the CPT series.2018-06-0

Bacterial RuBisCO Is Required for Efficient Bradyrhizobium/Aeschynomene Symbiosis

Rhizobia and legume plants establish symbiotic associations resulting in the formation of organs specialized in nitrogen fixation. In such organs, termed nodules, bacteria differentiate into bacteroids which convert atmospheric nitrogen and supply the plant with organic nitrogen. As a counterpart, bacteroids receive carbon substrates from the plant. This rather simple model of metabolite exchange underlies symbiosis but does not describe the complexity of bacteroids' central metabolism. A previous study using the tropical symbiotic model Aeschynomene indica/photosynthetic Bradyrhizobium sp. ORS278 suggested a role of the bacterial Calvin cycle during the symbiotic process. Herein we investigated the role of two RuBisCO gene clusters of Bradyrhizobium sp. ORS278 during symbiosis. Using gene reporter fusion strains, we showed that cbbL1 but not the paralogous cbbL2 is expressed during symbiosis. Congruently, CbbL1 was detected in bacteroids by proteome analysis. The importance of CbbL1 for symbiotic nitrogen fixation was proven by a reverse genetic approach. Interestingly, despite its symbiotic nitrogen fixation defect, the cbbL1 mutant was not affected in nitrogen fixation activity under free living state. This study demonstrates a critical role for bacterial RuBisCO during a rhizobia/legume symbiotic interaction

Timing the Landmark Events in the Evolution of Clear Cell Renal Cell Cancer: TRACERx Renal.

Clear cell renal cell carcinoma (ccRCC) is characterized by near-universal loss of the short arm of chromosome 3, deleting several tumor suppressor genes. We analyzed whole genomes from 95 biopsies across 33 patients with clear cell renal cell carcinoma. We find hotspots of point mutations in the 5' UTR of TERT, targeting a MYC-MAX-MAD1 repressor associated with telomere lengthening. The most common structural abnormality generates simultaneous 3p loss and 5q gain (36% patients), typically through chromothripsis. This event occurs in childhood or adolescence, generally as the initiating event that precedes emergence of the tumor's most recent common ancestor by years to decades. Similar genomic changes drive inherited ccRCC. Modeling differences in age incidence between inherited and sporadic cancers suggests that the number of cells with 3p loss capable of initiating sporadic tumors is no more than a few hundred. Early development of ccRCC follows well-defined evolutionary trajectories, offering opportunity for early intervention

Genomic, Pathway Network, and Immunologic Features Distinguishing Squamous Carcinomas

This integrated, multiplatform PanCancer Atlas study co-mapped and identified distinguishing molecular features of squamous cell carcinomas (SCCs) from five sites associated with smokin

Determinants of anti-PD-1 response and resistance in clear cell renal cell carcinoma.

ADAPTeR is a prospective, phase II study of nivolumab (anti-PD-1) in 15 treatment-naive patients (115 multiregion tumor samples) with metastatic clear cell renal cell carcinoma (ccRCC) aiming to understand the mechanism underpinning therapeutic response. Genomic analyses show no correlation between tumor molecular features and response, whereas ccRCC-specific human endogenous retrovirus expression indirectly correlates with clinical response. T cell receptor (TCR) analysis reveals a significantly higher number of expanded TCR clones pre-treatment in responders suggesting pre-existing immunity. Maintenance of highly similar clusters of TCRs post-treatment predict response, suggesting ongoing antigen engagement and survival of families of T cells likely recognizing the same antigens. In responders, nivolumab-bound CD8+ T cells are expanded and express GZMK/B. Our data suggest nivolumab drives both maintenance and replacement of previously expanded T cell clones, but only maintenance correlates with response. We hypothesize that maintenance and boosting of a pre-existing response is a key element of anti-PD-1 mode of action

Genomic architecture and evolution of clear cell renal cell carcinomas defined by multiregion sequencing

Clear cell renal carcinomas (ccRCCs) can display intratumor heterogeneity (ITH). We applied multiregion exome sequencing (M-seq) to resolve the genetic architecture and evolutionary histories of ten ccRCCs. Ultra-deep sequencing identified ITH in all cases. We found that 73–75% of identified ccRCC driver aberrations were subclonal, confounding estimates of driver mutation prevalence. ITH increased with the number of biopsies analyzed, without evidence of saturation in most tumors. Chromosome 3p loss and VHL aberrations were the only ubiquitous events. The proportion of C>T transitions at CpG sites increased during tumor progression. M-seq permits the temporal resolution of ccRCC evolution and refines mutational signatures occurring during tumor development