Interpretations of Presburger Arithmetic in Itself

Presburger arithmetic PrA is the true theory of natural numbers with addition. We study interpretations of PrA in itself. We prove that all one-dimensional self-interpretations are definably isomorphic to the identity self-interpretation. In order to prove the results we show that all linear orders that are interpretable in (N,+) are scattered orders with the finite Hausdorff rank and that the ranks are bounded in terms of the dimension of the respective interpretations. From our result about self-interpretations of PrA it follows that PrA isn't one-dimensionally interpretable in any of its finite subtheories. We note that the latter was conjectured by A. Visser.Comment: Published in proceedings of LFCS 201

Final Hazard Categorization for the Remediation of the 116-C-3 Chemical Waste Tanks

This final hazard categorization (FHC) document examines the hazards, identifies appropriate controls to manage the hazards, and documents the commitments for the 116-C-3 Chemical Waste Tanks Remediation Project. The remediation activities analyzed in this FHC are based on recommended treatment and disposal alternatives described in the Engineering Evaluation for the Remediation to the 116-C-3 Chemical Waste Tanks (BHI 2005e)

Symmetric multiparty-controlled teleportation of an arbitrary two-particle entanglement

We present a way for symmetric multiparty-controlled teleportation of an arbitrary two-particle entangled state based on Bell-basis measurements by using two Greenberger-Horne-Zeilinger states, i.e., a sender transmits an arbitrary two-particle entangled state to a distant receiver, an arbitrary one of the $n+1$ agents via the control of the others in a network. It will be shown that the outcomes in the cases that $n$ is odd or it is even are different in principle as the receiver has to perform a controlled-not operation on his particles for reconstructing the original arbitrary entangled state in addition to some local unitary operations in the former. Also we discuss the applications of this controlled teleporation for quantum secret sharing of classical and quantum information. As all the instances can be used to carry useful information, its efficiency for qubits approaches the maximal value.Comment: 9 pages, 3 figures; the revised version published in Physical Review A 72, 022338 (2005). The detail for setting up a GHZ-state quantum channel is adde

Rapid bursts of androgen-binding protein (Abp) gene duplication occurred independently in diverse mammals

<p>Abstract</p> <p>Background</p> <p>The draft mouse (<it>Mus musculus</it>) genome sequence revealed an unexpected proliferation of gene duplicates encoding a family of secretoglobin proteins including the androgen-binding protein (ABP) α, β and γ subunits. Further investigation of 14 α-like (<it>Abpa</it>) and 13 β- or γ-like (<it>Abpbg</it>) undisrupted gene sequences revealed a rich diversity of developmental stage-, sex- and tissue-specific expression. Despite these studies, our understanding of the evolution of this gene family remains incomplete. Questions arise from imperfections in the initial mouse genome assembly and a dearth of information about the gene family structure in other rodents and mammals.</p> <p>Results</p> <p>Here, we interrogate the latest 'finished' mouse (<it>Mus musculus</it>) genome sequence assembly to show that the <it>Abp </it>gene repertoire is, in fact, twice as large as reported previously, with 30 <it>Abpa </it>and 34 <it>Abpbg </it>genes and pseudogenes. All of these have arisen since the last common ancestor with rat (<it>Rattus norvegicus</it>). We then demonstrate, by sequencing homologs from species within the <it>Mus </it>genus, that this burst of gene duplication occurred very recently, within the past seven million years. Finally, we survey <it>Abp </it>orthologs in genomes from across the mammalian clade and show that bursts of <it>Abp </it>gene duplications are not specific to the murid rodents; they also occurred recently in the lagomorph (rabbit, <it>Oryctolagus cuniculus</it>) and ruminant (cattle, <it>Bos taurus</it>) lineages, although not in other mammalian taxa.</p> <p>Conclusion</p> <p>We conclude that <it>Abp </it>genes have undergone repeated bursts of gene duplication and adaptive sequence diversification driven by these genes' participation in chemosensation and/or sexual identification.</p

Efficient symmetric multiparty quantum state sharing of an arbitrary m-qubit state

We present a scheme for symmetric multiparty quantum state sharing of an arbitrary $m$-qubit state with $m$ Greenberger-Horne-Zeilinger states following some ideas from the controlled teleportation [Phys. Rev. A \textbf{72}, 02338 (2005)]. The sender Alice performs $m$ Bell-state measurements on her $2m$ particles and the controllers need only to take some single-photon product measurements on their photons independently, not Bell-state measurements, which makes this scheme more convenient than the latter. Also it does not require the parties to perform a controlled-NOT gate on the photons for reconstructing the unknown $m$-qubit state and it is an optimal one as its efficiency for qubits approaches the maximal value.Comment: 6 pages, no figures; It simplifies the process for sharing an arbitrary m-qubit state in Phys. Rev. A 72, 022338 (2005) (quant-ph/0501129

ALBATROSS: Publicly AttestabLe BATched Randomness Based On Secret Sharing

In this paper we present ALBATROSS, a family of multiparty randomness generation protocols with guaranteed output delivery and public verification that allows to trade off corruption tolerance for a much improved amortized computational complexity. Our basic stand alone protocol is based on publicly verifiable secret sharing (PVSS) and is secure under in the random oracle model under the decisional Diffie-Hellman (DDH) hardness assumption. We also address the important issue of constructing Universally Composable randomness beacons, showing two UC versions of Albatross: one based on simple UC NIZKs and another one based on novel efficient ``designated verifier\u27\u27 homomorphic commitments. Interestingly this latter version can be instantiated from a global random oracle under the weaker Computational Diffie-Hellman (CDH) assumption. An execution of ALBATROSS with $n$ parties, out of which up to $t=(1/2-\epsilon)\cdot n$ are corrupt for a constant $\epsilon>0$, generates $\Theta(n^2)$ uniformly random values, requiring in the worst case an amortized cost per party of $\Theta(\log n)$ exponentiations per random value. We significantly improve on the SCRAPE protocol (Cascudo and David, ACNS 17), which required $\Theta(n^2)$ exponentiations per party to generate one uniformly random value. This is mainly achieved via two techniques: first, the use of packed Shamir secret sharing for the PVSS; second, the use of linear $t$-resilient functions (computed via a Fast Fourier Transform-based algorithm) to improve the randomness extraction

Integrated genome and transcriptome sequencing identifies a noncoding mutation in the genome replication factor DONSON as the cause of microcephaly-micromelia syndrome

While next-generation sequencing has accelerated the discovery of human disease genes, progress has been largely limited to the "low hanging fruit" of mutations with obvious exonic coding or canonical splice site impact. In contrast, the lack of high-throughput, unbiased approaches for functional assessment of most noncoding variants has bottlenecked gene discovery. We report the integration of transcriptome sequencing (RNA-seq), which surveys all mRNAs to reveal functional impacts of variants at the transcription level, into the gene discovery framework for a unique human disease, microcephaly-micromelia syndrome (MMS). MMS is an autosomal recessive condition described thus far in only a single First Nations population and causes intrauterine growth restriction, severe microcephaly, craniofacial anomalies, skeletal dysplasia, and neonatal lethality. Linkage analysis of affected families, including a very large pedigree, identified a single locus on Chromosome 21 linked to the disease (LOD > 9). Comprehensive genome sequencing did not reveal any pathogenic coding or canonical splicing mutations within the linkage region but identified several nonconserved noncoding variants. RNA-seq analysis detected aberrant splicing in DONSON due to one of these noncoding variants, showing a causative role for DONSON disruption in MMS. We show that DONSON is expressed in progenitor cells of embryonic human brain and other proliferating tissues, is co-expressed with components of the DNA replication machinery, and that Donson is essential for early embryonic development in mice as well, suggesting an essential conserved role for DONSON in the cell cycle. Our results demonstrate the utility of integrating transcriptomics into the study of human genetic disease when DNA sequencing alone is not sufficient to reveal the underlying pathogenic mutation

Laboratory Measurement of Volatile Ice Vapor Pressures with a Quartz Crystal Microbalance

Nitrogen, carbon monoxide, and methane are key materials in the far outer Solar System where their high volatility enables them to sublimate, potentially driving activity at very low temperatures. Knowledge of their vapor pressures and latent heats of sublimation at relevant temperatures is needed to model the processes involved. We describe a method for using a quartz crystal microbalance to measure the sublimation flux of these volatile ices in the free molecular flow regime, accounting for the simultaneous sublimation from and condensation onto the quartz crystal to derive vapor pressures and latent heats of sublimation. We find vapor pressures to be somewhat lower than previous estimates in literature, with carbon monoxide being the most discrepant of the three species, almost an order of magnitude lower than had been thought. These results have important implications across a variety of astrophysical and planetary environments

Emergent global patterns of ecosystem structure and function from a mechanistic general ecosystem model

Anthropogenic activities are causing widespread degradation of ecosystems worldwide, threatening the ecosystem services upon which all human life depends. Improved understanding of this degradation is urgently needed to improve avoidance and mitigation measures. One tool to assist these efforts is predictive models of ecosystem structure and function that are mechanistic: based on fundamental ecological principles. Here we present the first mechanistic General Ecosystem Model (GEM) of ecosystem structure and function that is both global and applies in all terrestrial and marine environments. Functional forms and parameter values were derived from the theoretical and empirical literature where possible. Simulations of the fate of all organisms with body masses between 10 µg and 150,000 kg (a range of 14 orders of magnitude) across the globe led to emergent properties at individual (e.g., growth rate), community (e.g., biomass turnover rates), ecosystem (e.g., trophic pyramids), and macroecological scales (e.g., global patterns of trophic structure) that are in general agreement with current data and theory. These properties emerged from our encoding of the biology of, and interactions among, individual organisms without any direct constraints on the properties themselves. Our results indicate that ecologists have gathered sufficient information to begin to build realistic, global, and mechanistic models of ecosystems, capable of predicting a diverse range of ecosystem properties and their response to human pressures