Planar digraphs for automatic complexity

We show that the digraph of a nondeterministic finite automaton witnessing the automatic complexity of a word can always be taken to be planar. In the case of total transition functions studied by Shallit and Wang, planarity can fail. Let $s_q(n)$ be the number of binary words $x$ of length $n$ having nondeterministic automatic complexity $A_N(x)=q$. We show that $s_q$ is eventually constant for each $q$ and that the eventual constant value of $s_q$ is computable.Comment: Theory and Applications of Models of Computation (TAMC 2019), Lecture Notes in Computer Science 11436 (2019

Random Planar Lattices and Integrated SuperBrownian Excursion

In this paper, a surprising connection is described between a specific brand of random lattices, namely planar quadrangulations, and Aldous' Integrated SuperBrownian Excursion (ISE). As a consequence, the radius r_n of a random quadrangulation with n faces is shown to converge, up to scaling, to the width r=R-L of the support of the one-dimensional ISE. More generally the distribution of distances to a random vertex in a random quadrangulation is described in its scaled limit by the random measure ISE shifted to set the minimum of its support in zero. The first combinatorial ingredient is an encoding of quadrangulations by trees embedded in the positive half-line, reminiscent of Cori and Vauquelin's well labelled trees. The second step relates these trees to embedded (discrete) trees in the sense of Aldous, via the conjugation of tree principle, an analogue for trees of Vervaat's construction of the Brownian excursion from the bridge. From probability theory, we need a new result of independent interest: the weak convergence of the encoding of a random embedded plane tree by two contour walks to the Brownian snake description of ISE. Our results suggest the existence of a Continuum Random Map describing in term of ISE the scaled limit of the dynamical triangulations considered in two-dimensional pure quantum gravity.Comment: 44 pages, 22 figures. Slides and extended abstract version are available at http://www.loria.fr/~schaeffe/Pub/Diameter/ and http://www.iecn.u-nancy.fr/~chassain

On k-partitions of multisets with equal sums

We study the number of ordered k-partitions of a multiset with equal sums, having elements α1,…,αn and multiplicities m1,…,mn. Denoting this number by Sk(α1,…,αn;m1,…,mn), we find the generating function, derive an integral formula, and illustrate the results by numerical examples. The special case involving the set {1,…,n} presents particular interest and leads to the new integer sequences Sk(n), Qk(n), and Rk(n), for which we provide explicit formulae and combinatorial interpretations. Conjectures in connection to some superelliptic Diophantine equations and an asymptotic formula are also discussed. The results extend previous work concerning 2- and 3-partitions of multisets.Unitatea Executiva pentru Finantarea Invatamantului Superior, a Cercetarii, Dezvoltarii si Inovari

Biopsy confirmation of metastatic sites in breast cancer patients:clinical impact and future perspectives

Determination of hormone receptor (estrogen receptor and progesterone receptor) and human epidermal growth factor receptor 2 status in the primary tumor is clinically relevant to define breast cancer subtypes, clinical outcome,and the choice of therapy. Retrospective and prospective studies suggest that there is substantial discordance in receptor status between primary and recurrent breast cancer. Despite this evidence and current recommendations,the acquisition of tissue from metastatic deposits is not routine practice. As a consequence, therapeutic decisions for treatment in the metastatic setting are based on the features of the primary tumor. Reasons for this attitude include the invasiveness of the procedure and the unreliable outcome of biopsy, in particular for biopsies of lesions at complex visceral sites. Improvements in interventional radiology techniques mean that most metastatic sites are now accessible by minimally invasive methods, including surgery. In our opinion, since biopsies are diagnostic and changes in biological features between the primary and secondary tumors can occur, the routine biopsy of metastatic disease needs to be performed. In this review, we discuss the rationale for biopsy of suspected breast cancer metastases, review issues and caveats surrounding discordance of biomarker status between primary and metastatic tumors, and provide insights for deciding when to perform biopsy of suspected metastases and which one (s) to biopsy. We also speculate on the future translational implications for biopsy of suspected metastatic lesions in the context of clinical trials and the establishment of bio-banks of biopsy material taken from metastatic sites. We believe that such bio-banks will be important for exploring mechanisms of metastasis. In the future,advances in targeted therapy will depend on the availability of metastatic tissue

Digital PCR methods improve detection sensitivity and measurement precision of low abundance mtDNA deletions

Mitochondrial DNA (mtDNA) mutations are a common cause of primary mitochondrial disorders, and have also been implicated in a broad collection of conditions, including aging, neurodegeneration, and cancer. Prevalent among these pathogenic variants are mtDNA deletions, which show a strong bias for the loss of sequence in the major arc between, but not including, the heavy and light strand origins of replication. Because individual mtDNA deletions can accumulate focally, occur with multiple mixed breakpoints, and in the presence of normal mtDNA sequences, methods that detect broad-spectrum mutations with enhanced sensitivity and limited costs have both research and clinical applications. In this study, we evaluated semi-quantitative and digital PCR-based methods of mtDNA deletion detection using double-stranded reference templates or biological samples. Our aim was to describe key experimental assay parameters that will enable the analysis of low levels or small differences in mtDNA deletion load during disease progression, with limited false-positive detection. We determined that the digital PCR method significantly improved mtDNA deletion detection sensitivity through absolute quantitation, improved precision and reduced assay standard error

Construction and Random Generation of Hypergraphs with Prescribed Degree and Dimension Sequences

We propose algorithms for construction and random generation of hypergraphs without loops and with prescribed degree and dimension sequences. The objective is to provide a starting point for as well as an alternative to Markov chain Monte Carlo approaches. Our algorithms leverage the transposition of properties and algorithms devised for matrices constituted of zeros and ones with prescribed row- and column-sums to hypergraphs. The construction algorithm extends the applicability of Markov chain Monte Carlo approaches when the initial hypergraph is not provided. The random generation algorithm allows the development of a self-normalised importance sampling estimator for hypergraph properties such as the average clustering coefficient.We prove the correctness of the proposed algorithms. We also prove that the random generation algorithm generates any hypergraph following the prescribed degree and dimension sequences with a non-zero probability. We empirically and comparatively evaluate the effectiveness and efficiency of the random generation algorithm. Experiments show that the random generation algorithm provides stable and accurate estimates of average clustering coefficient, and also demonstrates a better effective sample size in comparison with the Markov chain Monte Carlo approaches.Comment: 21 pages, 3 figure

Progression of the first stage of spontaneous labour: A prospective cohort study in two sub-Saharan African countries.

BACKGROUND: Escalation in the global rates of labour interventions, particularly cesarean section and oxytocin augmentation, has renewed interest in a better understanding of natural labour progression. Methodological advancements in statistical and computational techniques addressing the limitations of pioneer studies have led to novel findings and triggered a re-evaluation of current labour practices. As part of the World Health Organization's Better Outcomes in Labour Difficulty (BOLD) project, which aimed to develop a new labour monitoring-to-action tool, we examined the patterns of labour progression as depicted by cervical dilatation over time in a cohort of women in Nigeria and Uganda who gave birth vaginally following a spontaneous labour onset. METHODS AND FINDINGS: This was a prospective, multicentre, cohort study of 5,606 women with singleton, vertex, term gestation who presented at ≤ 6 cm of cervical dilatation following a spontaneous labour onset that resulted in a vaginal birth with no adverse birth outcomes in 13 hospitals across Nigeria and Uganda. We independently applied survival analysis and multistate Markov models to estimate the duration of labour centimetre by centimetre until 10 cm and the cumulative duration of labour from the cervical dilatation at admission through 10 cm. Multistate Markov and nonlinear mixed models were separately used to construct average labour curves. All analyses were conducted according to three parity groups: parity = 0 (n = 2,166), parity = 1 (n = 1,488), and parity = 2+ (n = 1,952). We performed sensitivity analyses to assess the impact of oxytocin augmentation on labour progression by re-examining the progression patterns after excluding women with augmented labours. Labour was augmented with oxytocin in 40% of nulliparous and 28% of multiparous women. The median time to advance by 1 cm exceeded 1 hour until 5 cm was reached in both nulliparous and multiparous women. Based on a 95th percentile threshold, nulliparous women may take up to 7 hours to progress from 4 to 5 cm and over 3 hours to progress from 5 to 6 cm. Median cumulative duration of labour indicates that nulliparous women admitted at 4 cm, 5 cm, and 6 cm reached 10 cm within an expected time frame if the dilatation rate was ≥ 1 cm/hour, but their corresponding 95th percentiles show that labour could last up to 14, 11, and 9 hours, respectively. Substantial differences exist between actual plots of labour progression of individual women and the 'average labour curves' derived from study population-level data. Exclusion of women with augmented labours from the study population resulted in slightly faster labour progression patterns. CONCLUSIONS: Cervical dilatation during labour in the slowest-yet-normal women can progress more slowly than the widely accepted benchmark of 1 cm/hour, irrespective of parity. Interventions to expedite labour to conform to a cervical dilatation threshold of 1 cm/hour may be inappropriate, especially when applied before 5 cm in nulliparous and multiparous women. Averaged labour curves may not truly reflect the variability associated with labour progression, and their use for decision-making in labour management should be de-emphasized

Recombination deficient mutant of Caulobacter crescentus

A recombination-deficient (Rec - ) strain of Caulobacter crescentus has been isolated from a collection of mutants sensitive to ultraviolet irradiation. The Rec - mutant fails to give recombinants following ϕCr30-mediated generalized transduction or following RP4-mediated conjugation. The recombination frequency in the Rec - strain is at least 5000-fold lower than in the wild type strains. The Rec - mutant is indistinguishable from wild type in terms of morphology, growth rate, viability, and phage sensitivities, differing only in properties known to be associated with recA -type mutations in other organisms: recombination frequency, ultraviolet sensitivity, and Weigle reactivation. The map location of the rec-526 allele has not been identified, but rec-526 can be cotransferred with the fla-169 mutation by RP4-mediated conjugation at low frequency. This apparent linkage has been used to move the rec mutation to other strains. The Rec - mutant resembles recA strains of other organisms and provides a healthy strain severely deficient in recombination for use in complementation and cloning studies involving C. crescentus .Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47559/1/438_2004_Article_BF00383006.pd