On the Sets of Real Numbers Recognized by Finite Automata in Multiple Bases

This article studies the expressive power of finite automata recognizing sets of real numbers encoded in positional notation. We consider Muller automata as well as the restricted class of weak deterministic automata, used as symbolic set representations in actual applications. In previous work, it has been established that the sets of numbers that are recognizable by weak deterministic automata in two bases that do not share the same set of prime factors are exactly those that are definable in the first order additive theory of real and integer numbers. This result extends Cobham's theorem, which characterizes the sets of integer numbers that are recognizable by finite automata in multiple bases. In this article, we first generalize this result to multiplicatively independent bases, which brings it closer to the original statement of Cobham's theorem. Then, we study the sets of reals recognizable by Muller automata in two bases. We show with a counterexample that, in this setting, Cobham's theorem does not generalize to multiplicatively independent bases. Finally, we prove that the sets of reals that are recognizable by Muller automata in two bases that do not share the same set of prime factors are exactly those definable in the first order additive theory of real and integer numbers. These sets are thus also recognizable by weak deterministic automata. This result leads to a precise characterization of the sets of real numbers that are recognizable in multiple bases, and provides a theoretical justification to the use of weak automata as symbolic representations of sets.Comment: 17 page

Investigating the environmental interpretation of oxygen and carbon isotope data from whole and fragmented bivalve shells

Sclerochronological data from whole bivalve shells have been used extensively to derive palaeoenvironmental information. However, little is known about the relevance of shell fragments more commonly preserved in the sediment record. Here, we investigate the oxygen and carbon isotope composition of Dreissena carinata fragments from a core recovered from Lake Dojran (FYRO Macedonia/Greece) to identify their relevance and efficacy as a proxy in palaeoenvironmental studies. We use a modern Dreissena shell to calibrate the relationship between the bivalve and its contemporary environment, which suggests their isotope composition is primarily a function of temperature and water balance. The range of fragment isotope data from the core overlaps with that of unbroken fossil shells, suggesting the fragments broadly record lakewater conditions across the time of deposition. A comparison of the isotope composition of shell fragments and endogenic carbonate shows an offset between the two sets of data, which is likely due to temperature differences between surface and bottom waters, the timing of carbonate precipitation, and productivity-controlled stratification of the dissolved inorganic carbon pool. Shell fragment isotope data seem to reflect the signal of environmental change recorded in other proxy data from the same core and may potentially be used (like endogenic carbonate) to provide information on past changes in lake level

Parametrization of nonlinear and chaotic oscillations in driven beam-plasma diodes

Nonlinear phenomena in a driven plasma diode are studied using a fluid code and the particle-in-cell simulation code XPDPI. When a uniform electron beam is injected to a bounded diode filled with uniform ion background, the beam is destabilized by the Pierce instability and a perturbation grows to exhibit nonlinear oscillations including chaos. Two standard routes to chaos, period doubling and quasiperiodicity, are observed. Mode lockings of various winding numbers are observed in an ac driven system. A new diagnostic quantity is used to parametrize various nonlinear oscillations.open10

Fitness Landscape of the Fission Yeast Genome.

The relationship between DNA sequence, biochemical function, and molecular evolution is relatively well-described for protein-coding regions of genomes, but far less clear in noncoding regions, particularly, in eukaryote genomes. In part, this is because we lack a complete description of the essential noncoding elements in a eukaryote genome. To contribute to this challenge, we used saturating transposon mutagenesis to interrogate the Schizosaccharomyces pombe genome. We generated 31 million transposon insertions, a theoretical coverage of 2.4 insertions per genomic site. We applied a five-state hidden Markov model (HMM) to distinguish insertion-depleted regions from insertion biases. Both raw insertion-density and HMM-defined fitness estimates showed significant quantitative relationships to gene knockout fitness, genetic diversity, divergence, and expected functional regions based on transcription and gene annotations. Through several analyses, we conclude that transposon insertions produced fitness effects in 66-90% of the genome, including substantial portions of the noncoding regions. Based on the HMM, we estimate that 10% of the insertion depleted sites in the genome showed no signal of conservation between species and were weakly transcribed, demonstrating limitations of comparative genomics and transcriptomics to detect functional units. In this species, 3'- and 5'-untranslated regions were the most prominent insertion-depleted regions that were not represented in measures of constraint from comparative genomics. We conclude that the combination of transposon mutagenesis, evolutionary, and biochemical data can provide new insights into the relationship between genome function and molecular evolution

2D characterization of near-surface V P/V S: surface-wave dispersion inversion versus refraction tomography

International audienceThe joint study of pressure (P-) and shear (S-) wave velocities (Vp and Vs ), as well as their ratio (Vp /Vs), has been used for many years at large scales but remains marginal in near-surface applications. For these applications, and are generally retrieved with seismic refraction tomography combining P and SH (shear-horizontal) waves, thus requiring two separate acquisitions. Surface-wave prospecting methods are proposed here as an alternative to SH-wave tomography in order to retrieve pseudo-2D Vs sections from typical P-wave shot gathers and assess the applicability of combined P-wave refraction tomography and surface-wave dispersion analysis to estimate Vp/Vs ratio. We carried out a simultaneous P- and surface-wave survey on a well-characterized granite-micaschists contact at Ploemeur hydrological observatory (France), supplemented with an SH-wave acquisition along the same line in order to compare Vs results obtained from SH-wave refraction tomography and surface-wave profiling. Travel-time tomography was performed with P- and SH- wave first arrivals observed along the line to retrieve Vtomo p and Vtomo s models. Windowing and stacking techniques were then used to extract evenly spaced dispersion data from P-wave shot gathers along the line. Successive 1D Monte Carlo inversions of these dispersion data were performed using fixed Vp values extracted from Vtomo p the model and no lateral constraints between two adjacent 1D inversions. The resulting 1D Vsw s models were then assembled to create a pseudo-2D Vsw s section, which appears to be correctly matching the general features observed on the section. If the pseudo-section is characterized by strong velocity incertainties in the deepest layers, it provides a more detailed description of the lateral variations in the shallow layers. Theoretical dispersion curves were also computed along the line with both and models. While the dispersion curves computed from models provide results consistent with the coherent maxima observed on dispersion images, dispersion curves computed from models are generally not fitting the observed propagation modes at low frequency. Surface-wave analysis could therefore improve models both in terms of reliability and ability to describe lateral variations. Finally, we were able to compute / sections from both and models. The two sections present similar features, but the section obtained from shows a higher lateral resolution and is consistent with the features observed on electrical resistivity tomography, thus validating our approach for retrieving Vp/Vs ratio from combined P-wave tomography and surface-wave profiling

Age at symptom onset and death and disease duration in genetic frontotemporal dementia : an international retrospective cohort study

Background: Frontotemporal dementia is a heterogenous neurodegenerative disorder, with about a third of cases being genetic. Most of this genetic component is accounted for by mutations in GRN, MAPT, and C9orf72. In this study, we aimed to complement previous phenotypic studies by doing an international study of age at symptom onset, age at death, and disease duration in individuals with mutations in GRN, MAPT, and C9orf72. Methods: In this international, retrospective cohort study, we collected data on age at symptom onset, age at death, and disease duration for patients with pathogenic mutations in the GRN and MAPT genes and pathological expansions in the C9orf72 gene through the Frontotemporal Dementia Prevention Initiative and from published papers. We used mixed effects models to explore differences in age at onset, age at death, and disease duration between genetic groups and individual mutations. We also assessed correlations between the age at onset and at death of each individual and the age at onset and at death of their parents and the mean age at onset and at death of their family members. Lastly, we used mixed effects models to investigate the extent to which variability in age at onset and at death could be accounted for by family membership and the specific mutation carried. Findings: Data were available from 3403 individuals from 1492 families: 1433 with C9orf72 expansions (755 families), 1179 with GRN mutations (483 families, 130 different mutations), and 791 with MAPT mutations (254 families, 67 different mutations). Mean age at symptom onset and at death was 49\ub75 years (SD 10\ub70; onset) and 58\ub75 years (11\ub73; death) in the MAPT group, 58\ub72 years (9\ub78; onset) and 65\ub73 years (10\ub79; death) in the C9orf72 group, and 61\ub73 years (8\ub78; onset) and 68\ub78 years (9\ub77; death) in the GRN group. Mean disease duration was 6\ub74 years (SD 4\ub79) in the C9orf72 group, 7\ub71 years (3\ub79) in the GRN group, and 9\ub73 years (6\ub74) in the MAPT group. Individual age at onset and at death was significantly correlated with both parental age at onset and at death and with mean family age at onset and at death in all three groups, with a stronger correlation observed in the MAPT group (r=0\ub745 between individual and parental age at onset, r=0\ub763 between individual and mean family age at onset, r=0\ub758 between individual and parental age at death, and r=0\ub769 between individual and mean family age at death) than in either the C9orf72 group (r=0\ub732 individual and parental age at onset, r=0\ub736 individual and mean family age at onset, r=0\ub738 individual and parental age at death, and r=0\ub740 individual and mean family age at death) or the GRN group (r=0\ub722 individual and parental age at onset, r=0\ub718 individual and mean family age at onset, r=0\ub722 individual and parental age at death, and r=0\ub732 individual and mean family age at death). Modelling showed that the variability in age at onset and at death in the MAPT group was explained partly by the specific mutation (48%, 95% CI 35\u201362, for age at onset; 61%, 47\u201373, for age at death), and even more by family membership (66%, 56\u201375, for age at onset; 74%, 65\u201382, for age at death). In the GRN group, only 2% (0\u201310) of the variability of age at onset and 9% (3\u201321) of that of age of death was explained by the specific mutation, whereas 14% (9\u201322) of the variability of age at onset and 20% (12\u201330) of that of age at death was explained by family membership. In the C9orf72 group, family membership explained 17% (11\u201326) of the variability of age at onset and 19% (12\u201329) of that of age at death. Interpretation: Our study showed that age at symptom onset and at death of people with genetic frontotemporal dementia is influenced by genetic group and, particularly for MAPT mutations, by the specific mutation carried and by family membership. Although estimation of age at onset will be an important factor in future pre-symptomatic therapeutic trials for all three genetic groups, our study suggests that data from other members of the family will be particularly helpful only for individuals with MAPT mutations. Further work in identifying both genetic and environmental factors that modify phenotype in all groups will be important to improve such estimates. Funding: UK Medical Research Council, National Institute for Health Research, and Alzheimer's Society

Meta-analysis of type 2 Diabetes in African Americans Consortium

Type 2 diabetes (T2D) is more prevalent in African Americans than in Europeans. However, little is known about the genetic risk in African Americans despite the recent identification of more than 70 T2D loci primarily by genome-wide association studies (GWAS) in individuals of European ancestry. In order to investigate the genetic architecture of T2D in African Americans, the MEta-analysis of type 2 DIabetes in African Americans (MEDIA) Consortium examined 17 GWAS on T2D comprising 8,284 cases and 15,543 controls in African Americans in stage 1 analysis. Single nucleotide polymorphisms (SNPs) association analysis was conducted in each study under the additive model after adjustment for age, sex, study site, and principal components. Meta-analysis of approximately 2.6 million genotyped and imputed SNPs in all studies was conducted using an inverse variance-weighted fixed effect model. Replications were performed to follow up 21 loci in up to 6,061 cases and 5,483 controls in African Americans, and 8,130 cases and 38,987 controls of European ancestry. We identified three known loci (TCF7L2, HMGA2 and KCNQ1) and two novel loci (HLA-B and INS-IGF2) at genome-wide significance (4.15 × 10(-94)<P<5 × 10(-8), odds ratio (OR)  = 1.09 to 1.36). Fine-mapping revealed that 88 of 158 previously identified T2D or glucose homeostasis loci demonstrated nominal to highly significant association (2.2 × 10(-23) < locus-wide P<0.05). These novel and previously identified loci yielded a sibling relative risk of 1.19, explaining 17.5% of the phenotypic variance of T2D on the liability scale in African Americans. Overall, this study identified two novel susceptibility loci for T2D in African Americans. A substantial number of previously reported loci are transferable to African Americans after accounting for linkage disequilibrium, enabling fine mapping of causal variants in trans-ethnic meta-analysis studies.Peer reviewe

Calibration of the CMS Drift Tube Chambers and Measurement of the Drift Velocity with Cosmic Rays

Peer reviewe