Muller’s ratchet clicks in finite time

We consider the accumulation of deleterious mutations in an asexual population, a phenomenon known as Muller’s ratchet, using the continuous time model proposed by Alison et al. (2009) [4]. We show that for any parameter λ>0$\lambda >0$ (the rate at which mutations occur), for any α>0$\alpha >0$ (the toxicity of the mutations) and for any size N>0$N>0$ of the population, the ratchet clicks a.s. in finite time. That is to say the minimum number of deleterious mutations in the population goes to infinity a.s.     

A Reduced Order Model for Control of a Single Reactor Activated Sludge Process

The IAWQ activated sludge model no 1, slightly modified by adding a nitrogen limiting growth function for heterotrophic microorganisms, has been validated on a sequencing single sludge wastewater reactor doing nitrification and denitrification. However, this model is too complex to be used for control design. The main purpose of this paper is to show how it is possible to simplify the full model from biological and mathematical considerations. Properties of observability, controllability and theoretical identifiability have been analyzed. The parameter identification has been carried out by using the simplex method of Nelder & Mead. Simulation results performed over a range of six hours (two aerobic / anoxic cycles), show that there exists a good fit between the simulated solution and the actual behavior of a lab scale pilot plant.     

Positive cooperativity in the template-directed synthesis of monodisperse macromolecules

Two series of oligorotaxanes R and R' that contain -CH(2)NH(2)(+)CH(2)- recognition sites in their dumbbell components have been synthesized employing template-directed protocols. [24]Crown-8 rings self-assemble by a clipping strategy around each and every recognition site using equimolar amounts of 2,6-pyridinedicarboxaldehyde and tetraethyleneglycol bis(2-aminophenyl) ether to efficiently provide up to a [20]rotaxane. In the R series, the -NH(2)(+)- recognition sites are separated by trismethylene bridges, whereas in the R' series the spacers are p-phenylene linkers. The underpinning idea here is that in the former series, the recognition sites are strategically positioned 3.5 ? apart from one another so as to facilitate efficient [π···π] stacking between the aromatic residues in contiguous rings in the rotaxanes and consequently, a discrete rigid and rod-like conformation is realized; these noncovalent interactions are absent in the latter series rendering them conformationally flexible/nondiscrete. Although in the R' series, the [3]-, [4]-, [8]-, and [12]rotaxanes were isolated after reaction times of <5-30 min in yields of 72-85%, in the R series, the [3]-, [4]-, [5]-, [8]-, [12]-, [16]-, and [20]rotaxanes were isolated in <5 min to 14 h in 88-98% yields. It follows that while in the R' series the higher order oligorotaxanes are formed in lower yields more rapidly, in the R series, the higher order oligorotaxanes are formed in higher yields more slowly. In the R series, the high percentage yields are sustained throughout, despite the fact that up to 39 components are participating in the template-directed self-assembly process. Simple arithmetic reveals that the conversion efficiency for each imine bond formation peaks at 99.9% in the R series and 99.3% in the R' series. This maintenance of reaction efficiency in the R series can be ascribed to positive cooperativity, that is, when one ring is formed it aids and abets the formation of subsequent rings presumably because of stabilizing extended [π···π] stacking interactions between the arene units. Experiments have been performed wherein the dumbbell is starved of the macrocyclic components, and up to five times more of the fully saturated rotaxane is formed than is predicted based on a purely statistical outcome, providing a clear indication that positive cooperativity is operative. Moreover, it would appear that as the R series is traversed from the [3]- to the [4]- to the [5]rotaxane, the cooperativity becomes increasingly positive. This kind of cooperative behavior is not observed for the analogous oligorotaxanes in the R' series. The conventional bevy of analytical techniques (e.g., HR-MS (ESI) and both (1)H and (13)C NMR spectroscopy) help establish the fact that all the oligorotaxanes are pure and monodisperse. Evidence of efficient [π···π] stacking between contiguous arene units in the rings in the R series is revealed by (1)H NMR spectroscopy. Ion-mobility mass spectrometry performed on the R and R' series yielded the collisional cross sections (CCSs), confirming the rigidity of the R oligorotaxanes and the flexibility of the R' ones. The extended [π···π] stacking interactions are found to be present in the solid-state structures of the [3]- and [4]rotaxanes in the R series and also on the basis of molecular mechanics calculations performed on the entire series of oligomers. The collective data presented herein supports our original design in that the extended [π···π] stacking between contiguous arene units in the rings of the R series of oligorotaxanes facilitate an essentially rigid rod-like conformation with evidence that positive cooperativity improves the efficiency of their formation. This situation stands in sharp contrast to the conformationally flexible R' series where the oligorotaxanes form with no cooperativity.     

Large deviations estimates for the multiscale analysis of heart rate variability

In the realm of multiscale signal analysis, multifractal analysis provides a natural and rich framework to measure the roughness of a time series. As such, it has drawn special attention of both mathematicians and practitioners, and led them to characterize relevant physiological factors impacting the heart rate variability. Notwithstanding these considerable progresses, multifractal analysis almost exclusively developed around the concept of Legendre singularity spectrum, for which efficient and elaborate estimators exist, but which are structurally blind to subtle features like non-concavity or, to a certain extent, non scaling of the distributions. Large deviations theory allows bypassing these limitations but it is only very recently that performing estimators were proposed to reliably compute the corresponding large deviations singularity spectrum. In this article, we illustrate the relevance of this approach, on both theoretical objects and on human heart rate signals from the Physionet public database. As conjectured, we verify that large deviations principles reveal significant information that otherwise remains hidden with classical approaches, and which can be reminiscent of some physiological characteristics. In particular we quantify the presence/absence of scale invariance of RR signals.     

Limiting laws of supercritical branching random walks

In this Note, we make explicit the limit law of the renormalized supercritical branching random walk, giving credit to a conjecture formulated in Barral et al. (2012) [5] for a continuous analogue of the branching random walk. Also, in the case of a branching random walk on a homogeneous tree, we express the law of the corresponding limiting renormalized Gibbs measures, confirming, in this discrete model, conjectures formulated by physicists (Derrida and Spohn, 1988 [9]) about the Poisson–Dirichlet nature of the jumps in the limit, and precising the conjecture by giving the spatial distribution of these jumps.     

Skew Killing spinors

We study the existence of a skew Killing spinor on 2- and 3-dimensional Riemannian spin manifolds. We establish the integrability conditions and prove that these spinor fields correspond to twistor spinors in the two dimensional case while, up to a conformal change of the metric, they correspond to parallel spinors in the three dimensional case.     

Nontrivial examples of coupled equations for Kähler metrics and Yang-Mills connections

We provide nontrivial examples of solutions to the system of coupled equations introduced by M. García-Fernández for the uniformization problem of a triple (M; L; E), where E is a holomorphic vector bundle over a polarized complex manifold (M, L), generalizing the notions of both constant scalar curvature Kähler metric and Hermitian-Einstein metric.     

Computational polarization imaging from a single speckle image

We experimentally demonstrate that imaging of the degree of polarization (DOP) can be achieved from a single intensity image acquired under coherent illumination. This computational technique is based on the analysis of the speckle characteristics in a statistically homogeneous neighborhood of the pixel. Over a variety of samples obtained experimentally, we show that a simple calibration step allows this method to quickly and simply provide correct estimated values of the DOP, with precision in agreement with theoretical predictions. It is shown that unlike linear polarimetric contrast imaging, this method remains valid on birefringent samples.