Simple formulas for lattice paths avoiding certain periodic staircase boundaries

There is a strikingly simple classical formula for the number of lattice paths avoiding the line x = ky when k is a positive integer. We show that the natural generalization of this simple formula continues to hold when the line x = ky is replaced by certain periodic staircase boundaries--but only under special conditions. The simple formula fails in general, and it remains an open question to what extent our results can be further generalized.Comment: Accepted version (JCTA); proof of Corollary 7 expanded, and 2 new refs adde

Investigating intra-host and intra-herd sequence diversity of foot-and-mouth disease virus

Due to the poor-fidelity of the enzymes involved in RNA genome replication, foot-and-mouth disease (FMD) virus samples comprise of unique polymorphic populations. In this study, deep sequencing was utilised to characterise the diversity of FMD virus (FMDV) populations in 6 infected cattle present on a single farm during the series of outbreaks in the UK in 2007. A novel RT–PCR method was developed to amplify a 7.6 kb nucleotide fragment encompassing the polyprotein coding region of the FMDV genome. Illumina sequencing of each sample identified the fine polymorphic structures at each nucleotide position, from consensus level changes to variants present at a 0.24% frequency. These data were used to investigate population dynamics of FMDV at both herd and host levels, evaluate the impact of host on the viral swarm structure and to identify transmission links with viruses recovered from other farms in the same series of outbreaks. In 7 samples, from 6 different animals, a total of 5 consensus level variants were identified, in addition to 104 sub-consensus variants of which 22 were shared between 2 or more animals. Further analysis revealed differences in swarm structures from samples derived from the same animal suggesting the presence of distinct viral populations evolving independently at different lesion sites within the same infected animal

Host reticulocytes provide metabolic reservoirs that can be exploited by malaria parasites

Human malaria parasites proliferate in different erythroid cell types during infection. Whilst Plasmodium vivax exhibits a strong preference for immature reticulocytes, the more pathogenic P. falciparum primarily infects mature erythrocytes. In order to assess if these two cell types offer different growth conditions and relate them to parasite preference, we compared the metabolomes of human and rodent reticulocytes with those of their mature erythrocyte counterparts. Reticulocytes were found to have a more complex, enriched metabolic profile than mature erythrocytes and a higher level of metabolic overlap between reticulocyte resident parasite stages and their host cell. This redundancy was assessed by generating a panel of mutants of the rodent malaria parasite P. berghei with defects in intermediary carbon metabolism (ICM) and pyrimidine biosynthesis known to be important for P. falciparum growth and survival in vitro in mature erythrocytes. P. berghei ICM mutants (pbpepc-, phosphoenolpyruvate carboxylase and pbmdh-, malate dehydrogenase) multiplied in reticulocytes and committed to sexual development like wild type parasites. However, P. berghei pyrimidine biosynthesis mutants (pboprt-, orotate phosphoribosyltransferase and pbompdc-, orotidine 5′-monophosphate decarboxylase) were restricted to growth in the youngest forms of reticulocytes and had a severe slow growth phenotype in part resulting from reduced merozoite production. The pbpepc-, pboprt- and pbompdc- mutants retained virulence in mice implying that malaria parasites can partially salvage pyrimidines but failed to complete differentiation to various stages in mosquitoes. These findings suggest that species-specific differences in Plasmodium host cell tropism result in marked differences in the necessity for parasite intrinsic metabolism. These data have implications for drug design when targeting mature erythrocyte or reticulocyte resident parasites

Characterization of FRO\u3csub\u3e1\u3c/sub\u3e, a Pea Ferric-Chelate Reductase Involved in Root Iron Acquisition

To acquire iron, many plant species reduce soil Fe(III) to Fe(II) by Fe(III)-chelate reductases embedded in the plasma membrane of root epidermal cells. The reduced product is then taken up by Fe(II) transporter proteins. These activities are induced under Fe deficiency. We describe here the FRO1 gene from pea (Pisum sativum), which encodes an Fe(III)-chelate reductase. Consistent with this proposed role, FRO1 shows similarity to other oxidoreductase proteins, and expression of FRO1 in yeast conferred increased Fe(III)-chelate reductase activity. Furthermore, FRO1 mRNA levels in plants correlated with Fe(III)-chelate reductase activity. Sites of FRO1 expression in roots, leaves, and nodules were determined. FRO1 mRNA was detected throughout the root, but was most abundant in the outer epidermal cells. Expression was detected in mesophyll cells in leaves. In root nodules, mRNA was detected in the infection zone and nitrogen-fixing region. These results indicate that FRO1 acts in root Fe uptake and they suggest a role in Fe distribution throughout the plant. Characterization of FRO1 has also provided new insights into the regulation of Fe uptake. FRO1 expression and reductase activity was detected only in Fe-deficient roots of Sparkle, whereas both were constitutive in brz and dgl, two mutants with incorrectly regulated Fe accumulation. In contrast, FRO1 expression was responsive to Fe status in shoots of all three plant lines. These results indicate differential regulation of FRO1 in roots and shoots, and improper FRO1 regulation in response to a shoot-derived signal of iron status in the roots of the brz and dgl mutants

Infrared High-Resolution Spectroscopy of Post-AGB Circumstellar Disks. I. HR 4049 - The Winnowing Flow Observed?

High-resolution infrared spectroscopy in the 2.3-4.6 micron region is reported for the peculiar A supergiant, single-lined spectroscopic binary HR 4049. Lines from the CO fundamental and first overtone, OH fundamental, and several H2O vibration-rotation transitions have been observed in the near-infrared spectrum. The spectrum of HR 4049 appears principally in emission through the 3 and 4.6 micron region and in absorption in the 2 micron region. The 4.6 micron spectrum shows a rich 'forest' of emission lines. All the spectral lines observed in the 2.3-4.6 micron spectrum are shown to be circumbinary in origin. The presence of OH and H2O lines confirm the oxygen-rich nature of the circumbinary gas which is in contrast to the previously detected carbon-rich material. The emission and absorption line profiles show that the circumbinary gas is located in a thin, rotating layer near the dust disk. The properties of the dust and gas circumbinary disk and the spectroscopic orbit yield masses for the individual stars, M_AI~0.58 Msolar and M_MV~0.34 Msolar. Gas in the disk also has an outward flow with a velocity of $\gtrsim$ 1 km/s. The severe depletion of refractory elements but near-solar abundances of volatile elements observed in HR 4049 results from abundance winnowing. The separation of the volatiles from the grains in the disk and the subsequent accretion by the star are discussed. Contrary to prior reports, the HR 4049 carbon and oxygen isotopic abundances are typical AGB values: 12C/13C=6^{+9}_{-4} and 16O/17O>200.Comment: 42 pages, 14 figures, Accepted by Ap

Quantifying geological uncertainty in metamorphic phase equilibria modelling; a Monte Carlo assessment and implications for tectonic interpretations

Pseudosection modelling is rapidly becoming an essential part of a petrologist’s toolkit and often forms the basis of interpreting the tectonothermal evolution of a rock sample, outcrop, or geological region. Of the several factors that can affect the accuracy and precision of such calculated phase diagrams, “geological” uncertainty related to natural petrographic variation at the hand sample- and/or thin section-scale is rarely considered. Such uncertainty influences the sample’s bulk composition, which is the primary control on its equilibrium phase relationships and thus the interpreted pressure–temperature (P–T) conditions of formation. Two case study examples—a garnet–cordierite granofels and a garnet–staurolite–kyanite schist—are used to compare the relative importance that geological uncertainty has on bulk compositions determined via (1) X-ray fluorescence (XRF) or (2) point counting techniques. We show that only minor mineralogical variation at the thin-section scale propagates through the phase equilibria modelling procedure and affects the absolute P–T conditions at which key assemblages are stable. Absolute displacements of equilibria can approach ±1 kbar for only a moderate degree of modal proportion uncertainty, thus being essentially similar to the magnitudes reported for analytical uncertainties in conventional thermobarometry. Bulk compositions determined from multiple thin sections of a heterogeneous garnet–staurolite–kyanite schist show a wide range in major-element oxides, owing to notable variation in mineral proportions. Pseudosections constructed for individual point count-derived bulks accurately reproduce this variability on a case-by-case basis, though averaged proportions do not correlate with those calculated at equivalent peak P–T conditions for a whole-rock XRF-derived bulk composition. The main discrepancies relate to varying proportions of matrix phases (primarily mica) relative to porphyroblasts (primarily staurolite and kyanite), indicating that point counting preserves small-scale petrographic features that are otherwise averaged out in XRF analysis of a larger sample. Careful consideration of the size of the equilibration volume, the constituents that comprise the effective bulk composition, and the best technique to employ for its determination based on rock type and petrographic character, offer the best chance to produce trustworthy data from pseudosection analysis.RMP acknowledges a NERC postgraduate grant (reference number NE/H524781/1) for funding analytical work performed at the University of Oxford, UK

Adaptively-Sound Succinct Arguments for NP from Indistinguishability Obfuscation

A succinct non-interactive argument (SNARG) for $\mathsf{NP}$ allows a prover to convince a verifier that an $\mathsf{NP}$ statement $x$ is true with a proof of size $o(|x| + |w|)$, where $w$ is the associated $\mathsf{NP}$ witness. A SNARG satisfies adaptive soundness if the malicious prover can choose the statement to prove after seeing the scheme parameters. In this work, we provide the first adaptively-sound SNARG for $\mathsf{NP}$ in the plain model assuming sub-exponentially-hard indistinguishability obfuscation, sub-exponentially-hard one-way functions, and either the (polynomial) hardness of the discrete log assumption or the (polynomial) hardness of factoring. This gives the first adaptively-sound SNARG for $\mathsf{NP}$ from falsifiable assumptions. All previous SNARGs for $\mathsf{NP}$ in the plain model either relied on non-falsifiable cryptographic assumptions or satisfied a weak notion of non-adaptive soundness (where the adversary has to choose the statement it proves before seeing the scheme parameters)

Batch Arguments for NP and More from Standard Bilinear Group Assumptions

Non-interactive batch arguments for NP provide a way to amortize the cost of NP verification across multiple instances. They enable a prover to convince a verifier of multiple NP statements with communication much smaller than the total witness length and verification time much smaller than individually checking each instance. In this work, we give the first construction of a non-interactive batch argument for NP from standard assumptions on groups with bilinear maps (specifically, from either the subgroup decision assumption in composite-order groups or from the $k$-Lin assumption in prime-order groups for any $k \ge 1$). Previously, batch arguments for NP were only known from LWE, or a combination of multiple assumptions, or from non-standard/non-falsifiable assumptions. Moreover, our work introduces a new direct approach for batch verification and avoids heavy tools like correlation-intractable hash functions or probabilistically-checkable proofs common to previous approaches. As corollaries to our main construction, we obtain the first publicly-verifiable non-interactive delegation scheme for RAM programs (i.e., a succinct non-interactive argument (SNARG) for P) with a CRS of sublinear size (in the running time of the RAM program), as well as the first aggregate signature scheme (supporting bounded aggregation) from standard assumptions on bilinear maps

A Pure Indistinguishability Obfuscation Approach to Adaptively-Sound SNARGs for NP

We construct an adaptively-sound succinct non-interactive argument (SNARG) for NP in the CRS model from sub-exponentially-secure indistinguishability obfuscation ($i\mathcal{O}$) and sub-exponentially-secure one-way functions. Previously, Waters and Wu (STOC 2024), and subsequently, Waters and Zhandry (CRYPTO 2024) showed how to construct adaptively-sound SNARGs for NP by relying on sub-exponentially-secure indistinguishability obfuscation, one-way functions, and an additional algebraic assumption (i.e., discrete log, factoring, or learning with errors). In this work, we show that no additional algebraic assumption is needed and vanilla (sub-exponentially-secure) one-way functions already suffice in combination with $i\mathcal{O}$

Rumen methanogenic genotypes differ in abundance according to host residual feed intake phenotype and diet type

Methane is an undesirable end product of rumen fermentative activity because of associated environmental impacts and reduced host feed efficiency. Our study characterized the rumen microbial methanogenic community in beef cattle divergently selected for phenotypic residual feed intake (RFI) while offered a high-forage (HF) diet followed by a low-forage (LF) diet. Rumen fluid was collected from 14 high-RFI (HRFI) and 14 low-RFI (LRFI) animals at the end of both dietary periods. 16S rRNA gene clone libraries were used, and methanogen-specific tag-encoded pyrosequencing was carried out on the samples. We found that Methanobrevibacter spp. are the dominant methanogens in the rumen, with Methanobrevibacter smithii being the most abundant species. Differences in the abundance of Methanobrevibacter smithii and Methanosphaera stadtmanae genotypes were detected in the rumen of animals offered the LF compared to the HF diet while the abundance of Methanobrevibacter smithii genotypes was different between HRFI and LRFI animals irrespective of diet. Our results demonstrate that while a core group of methanogen operational taxonomic units (OTUs) exist across diet and phenotype, significant differences were observed in the distribution of genotypes within those OTUs. These changes in genotype abundance may contribute to the observed differences in methane emissions between efficient and inefficient animals