2,945 research outputs found

    Spanning tree generating functions and Mahler measures

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    We define the notion of a spanning tree generating function (STGF) ∑anzn\sum a_n z^n, which gives the spanning tree constant when evaluated at z=1,z=1, and gives the lattice Green function (LGF) when differentiated. By making use of known results for logarithmic Mahler measures of certain Laurent polynomials, and proving new results, we express the STGFs as hypergeometric functions for all regular two and three dimensional lattices (and one higher-dimensional lattice). This gives closed form expressions for the spanning tree constants for all such lattices, which were previously largely unknown in all but one three-dimensional case. We show for all lattices that these can also be represented as Dirichlet LL-series. Making the connection between spanning tree generating functions and lattice Green functions produces integral identities and hypergeometric connections, some of which appear to be new.Comment: 26 pages. Dedicated to F Y Wu on the occasion of his 80th birthday. This version has additional references, additional calculations, and minor correction

    Characterizing temporary hydrological regimes at a European scale

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    Monthly duration curves have been constructed from climate data across Europe to help address the relative frequency of ecologically critical low flow stages in temporary rivers, when flow persists only in disconnected pools in the river bed. The hydrological model is 5 based on a partitioning of precipitation to estimate water available for evapotranspiration and plant growth and for residual runoff. The duration curve for monthly flows has then been analysed to give an estimate of bankfull flow based on recurrence interval. The corresponding frequency for pools is then based on the ratio of bank full discharge to pool flow, arguing from observed ratios of cross-sectional areas at flood 10 and low flows to estimate pool flow as 0.1% of bankfull flow, and so estimate the frequency of the pool conditions that constrain survival of river-dwelling arthropods and fish. The methodology has been applied across Europe at 15 km resolution, and can equally be applied under future climatic scenarios

    Breaking the self-averaging properties of spatial galaxy fluctuations in the Sloan Digital Sky Survey - Data Release Six

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    Statistical analyses of finite sample distributions usually assume that fluctuations are self-averaging, i.e. that they are statistically similar in different regions of the given sample volume. By using the scale-length method, we test whether this assumption is satisfied in several samples of the Sloan Digital Sky Survey Data Release Six. We find that the probability density function (PDF) of conditional fluctuations, filtered on large enough spatial scales (i.e., r>30 Mpc/h), shows relevant systematic variations in different sub-volumes of the survey. Instead for scales r<30 Mpc/h the PDF is statistically stable, and its first moment presents scaling behavior with a negative exponent around one. Thus while up to 30 Mpc/h galaxy structures have well-defined power-law correlations, on larger scales it is not possible to consider whole sample average quantities as meaningful and useful statistical descriptors. This situation is due to the fact that galaxy structures correspond to density fluctuations which are too large in amplitude and too extended in space to be self-averaging on such large scales inside the sample volumes: galaxy distribution is inhomogeneous up to the largest scales, i.e. r ~ 100 Mpc/h, probed by the SDSS samples. We show that cosmological corrections, as K-corrections and standard evolutionary corrections, do not qualitatively change the relevant behaviors. Finally we show that the large amplitude galaxy fluctuations observed in the SDSS samples are at odds with the predictions of the standard LCDM model of structure formation.(Abridged version).Comment: 32 pages, 28 figures, accepted for publication in Astronomy and Astrophysics. A higher resolution version is available at http://pil.phys.uniroma1.it/~sylos/fsl_highlights.html . Version v2 has been corrected to match the published on

    Conformational landscapes of DNA polymerase I and mutator derivatives establish fidelity checkpoints for nucleotide insertion

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    The fidelity of DNA polymerases depends on conformational changes that promote the rejection of incorrect nucleotides before phosphoryl transfer. Here, we combine single-molecule FRET with the use of DNA polymerase I and various fidelity mutants to highlight mechanisms by which active-site side chains influence the conformational transitions and free-energy landscape that underlie fidelity decisions in DNA synthesis. Ternary complexes of high fidelity derivatives with complementary dNTPs adopt mainly a fully closed conformation, whereas a conformation with a FRET value between those of open and closed is sparsely populated. This intermediate-FRET state, which we attribute to a partially closed conformation, is also predominant in ternary complexes with incorrect nucleotides and, strikingly, in most ternary complexes of low-fidelity derivatives for both correct and incorrect nucleotides. The mutator phenotype of the low-fidelity derivatives correlates well with reduced affinity for complementary dNTPs and highlights the partially closed conformation as a primary checkpoint for nucleotide selection

    Mechanistic and evolutionary insights into a type V-M CRISPR–Cas effector enzyme

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    RNA-guided type V CRISPR–Cas12 effectors provide adaptive immunity against mobile genetic elements (MGEs) in bacteria and archaea. Among diverse Cas12 enzymes, the recently identified Cas12m2 (CRISPR–Cas type V-M) is highly compact and has a unique RuvC active site. Although the non-canonical RuvC triad does not permit dsDNA cleavage, Cas12m2 still protects against invading MGEs through transcriptional silencing by strong DNA binding. However, the molecular mechanism of RNA-guided genome inactivation by Cas12m2 remains unknown. Here we report cryo-electron microscopy structures of two states of Cas12m2–CRISPR RNA (crRNA)–target DNA ternary complexes and the Cas12m2–crRNA binary complex, revealing structural dynamics during crRNA–target DNA heteroduplex formation. The structures indicate that the non-target DNA strand is tightly bound to a unique arginine-rich cluster in the recognition (REC) domains and the non-canonical active site in the RuvC domain, ensuring strong DNA-binding affinity of Cas12m2. Furthermore, a structural comparison of Cas12m2 with TnpB, a putative ancestor of Cas12 enzymes, suggests that the interaction of the characteristic coiled-coil REC2 insertion with the protospacer-adjacent motif-distal region of the heteroduplex is crucial for Cas12m2 to engage in adaptive immunity. Collectively, our findings improve mechanistic understanding of diverse type V CRISPR–Cas effectors and provide insights into the evolution of TnpB to Cas12 enzymes.</p

    Direct and indirect control of the initiation of meiotic recombination by DNA damage checkpoint mechanisms in budding yeast

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    Meiotic recombination plays an essential role in the proper segregation of chromosomes at meiosis I in many sexually reproducing organisms. Meiotic recombination is initiated by the scheduled formation of genome-wide DNA double-strand breaks (DSBs). The timing of DSB formation is strictly controlled because unscheduled DSB formation is detrimental to genome integrity. Here, we investigated the role of DNA damage checkpoint mechanisms in the control of meiotic DSB formation using budding yeast. By using recombination defective mutants in which meiotic DSBs are not repaired, the effect of DNA damage checkpoint mutations on DSB formation was evaluated. The Tel1 (ATM) pathway mainly responds to unresected DSB ends, thus the sae2 mutant background in which DSB ends remain intact was employed. On the other hand, the Mec1 (ATR) pathway is primarily used when DSB ends are resected, thus the rad51 dmc1 double mutant background was employed in which highly resected DSBs accumulate. In order to separate the effect caused by unscheduled cell cycle progression, which is often associated with DNA damage checkpoint defects, we also employed the ndt80 mutation which permanently arrests the meiotic cell cycle at prophase I. In the absence of Tel1, DSB formation was reduced in larger chromosomes (IV, VII, II and XI) whereas no significant reduction was found in smaller chromosomes (III and VI). On the other hand, the absence of Rad17 (a critical component of the ATR pathway) lead to an increase in DSB formation (chromosomes VII and II were tested). We propose that, within prophase I, the Tel1 pathway facilitates DSB formation, especially in bigger chromosomes, while the Mec1 pathway negatively regulates DSB formation. We also identified prophase I exit, which is under the control of the DNA damage checkpoint machinery, to be a critical event associated with down-regulating meiotic DSB formation

    Long-term use of Everolimus in patients with Tuberous Sclerosis Complex: final results from the EXIST-1 study

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    BACKGROUND: Everolimus, a mammalian target of rapamycin (mTOR) inhibitor, has demonstrated efficacy in treating subependymal giant cell astrocytomas (SEGAs) and other manifestations of tuberous sclerosis complex (TSC). However, long-term use of mTOR inhibitors might be necessary. This analysis explored long-term efficacy and safety of everolimus from the conclusion of the EXIST-1 study (NCT00789828). Methods and FINDINGS: EXIST-1 was an international, prospective, double-blind, placebo-controlled phase 3 trial examining everolimus in patients with new or growing TSC-related SEGA. After a double-blind core phase, all remaining patients could receive everolimus in a long-term, open-label extension. Everolimus was initiated at a dose (4.5 mg/m 2 /day) titrated to a target blood trough of 5-15 ng/mL. SEGA response rate (primary end point) was defined as the proportion of patients achieving confirmed ≥50% reduction in the sum volume of target SEGA lesions from baseline in the absence of worsening nontarget SEGA lesions, new target SEGA lesions, and new or worsening hydrocephalus. Of 111 patients (median age, 9.5 years) who received ≥1 dose of everolimus (median duration, 47.1 months), 57.7% (95% confidence interval [CI], 47.9-67.0) achieved SEGA response. Of 41 patients with target renal angiomyolipomas at baseline, 30 (73.2%) achieved renal angiomyolipoma response. In 105 patients with ≥1 skin lesion at baseline, skin lesion response rate was 58.1%. Incidence of adverse events (AEs) was comparable with that of previous reports, and occurrence of emergent AEs generally decreased over time. The most common AEs (≥30% incidence) suspected to be treatment-related were stomatitis (43.2%) and mouth ulceration (32.4%). CONCLUSIONS: Everolimus use led to sustained reduction in tumor volume, and new responses were observed for SEGA and renal angiomyolipoma from the blinded core phase of the study. These findings support the hypothesis that everolimus can safely reverse multisystem manifestations of TSC in a significant proportion of patients. Trial Registration ClinicalTrials.gov NCT0078982
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