Quadratic invariants for discrete clusters of weakly interacting waves

We consider discrete clusters of quasi-resonant triads arising from a Hamiltonian three-wave equation. A cluster consists of N modes forming a total of M connected triads. We investigate the problem of constructing a functionally independent set of quadratic constants of motion. We show that this problem is equivalent to an underlying basic linear problem, consisting of finding the null space of a rectangular M × N matrix with entries 1, −1 and 0. In particular, we prove that the number of independent quadratic invariants is equal to J ≡ N − M* ≥ N − M, where M* is the number of linearly independent rows in Thus, the problem of finding all independent quadratic invariants is reduced to a linear algebra problem in the Hamiltonian case. We establish that the properties of the quadratic invariants (e.g., locality) are related to the topological properties of the clusters (e.g., types of linkage). To do so, we formulate an algorithm for decomposing large clusters into smaller ones and show how various invariants are related to certain parts of a cluster, including the basic structures leading to M* < M. We illustrate our findings by presenting examples from the Charney–Hasegawa–Mima wave model, and by showing a classification of small (up to three-triad) clusters

A family of Nikishin systems with periodic recurrence coefficients

Suppose we have a Nikishin system of $p$ measures with the $k$th generating measure of the Nikishin system supported on an interval \Delta_k\subset\er with $\Delta_k\cap\Delta_{k+1}=\emptyset$ for all $k$. It is well known that the corresponding staircase sequence of multiple orthogonal polynomials satisfies a $(p+2)$-term recurrence relation whose recurrence coefficients, under appropriate assumptions on the generating measures, have periodic limits of period $p$. (The limit values depend only on the positions of the intervals $\Delta_k$.) Taking these periodic limit values as the coefficients of a new $(p+2)$-term recurrence relation, we construct a canonical sequence of monic polynomials $\{P_{n}\}_{n=0}^{\infty}$, the so-called \emph{Chebyshev-Nikishin polynomials}. We show that the polynomials $P_{n}$ themselves form a sequence of multiple orthogonal polynomials with respect to some Nikishin system of measures, with the $k$th generating measure being absolutely continuous on $\Delta_{k}$. In this way we generalize a result of the third author and Rocha \cite{LopRoc} for the case $p=2$. The proof uses the connection with block Toeplitz matrices, and with a certain Riemann surface of genus zero. We also obtain strong asymptotics and an exact Widom-type formula for the second kind functions of the Nikishin system for $\{P_{n}\}_{n=0}^{\infty}$.Comment: 30 pages, minor change

Cilia and Mucociliary Clearance

Mucociliary clearance (MCC) is the primary innate defense mechanism of the lung. The functional components are the protective mucous layer, the airway surface liquid layer, and the cilia on the surface of ciliated cells. The cilia are specialized organelles that beat in metachronal waves to propel pathogens and inhaled particles trapped in the mucous layer out of the airways. In health this clearance mechanism is effective, but in patients with primary cilia dyskinesia (PCD) the cilia are abnormal, resulting in deficient MCC and chronic lung disease. This demonstrates the critical importance of the cilia for human health. In this review, we summarize the current knowledge of the components of the MCC apparatus, focusing on the role of cilia in MCC

Force dependent fragility in RNA hairpins

We apply Kramers theory to investigate the dissociation of multiple bonds under mechanical force and interpret experimental results for the unfolding/refolding force distributions of an RNA hairpin pulled at different loading rates using laser tweezers. We identify two different kinetic regimes depending on the range of forces explored during the unfolding and refolding process. The present approach extends the range of validity of the two-states approximation by providing a theoretical framework to reconstruct free-energy landscapes and identify force-induced structural changes in molecular transition states using single molecule pulling experiments. The method should be applicable to RNA hairpins with multiple kinetic barriers.Comment: Latex file, 4 pages+3 figure

Dynamic force spectroscopy of DNA hairpins. II. Irreversibility and dissipation

We investigate irreversibility and dissipation in single molecules that cooperatively fold/unfold in a two state manner under the action of mechanical force. We apply path thermodynamics to derive analytical expressions for the average dissipated work and the average hopping number in two state systems. It is shown how these quantities only depend on two parameters that characterize the folding/unfolding kinetics of the molecule: the fragility and the coexistence hopping rate. The latter has to be rescaled to take into account the appropriate experimental setup. Finally we carry out pulling experiments with optical tweezers in a specifically designed DNA hairpin that shows two-state cooperative folding. We then use these experimental results to validate our theoretical predictions.Comment: 28 pages, 12 figure

Effect of the dynamical phases on the nonlinear amplitudes' evolution

In this Letter we show how the nonlinear evolution of a resonant triad depends on the special combination of the modes' phases chosen according to the resonance conditions. This phase combination is called dynamical phase. Its evolution is studied for two integrable cases: a triad and a cluster formed by two connected triads, using a numerical method which is fully validated by monitoring the conserved quantities known analytically. We show that dynamical phases, usually regarded as equal to zero or constants, play a substantial role in the dynamics of the clusters. Indeed, some effects are (i) to diminish the period of energy exchange $\tau$ within a cluster by 20$$ and more; (ii) to diminish, at time scale $\tau$, the variability of wave energies by 25$$ and more; (iii) to generate a new time scale, $T >> \tau$, in which we observe considerable energy exchange within a cluster, as well as a periodic behaviour (with period $T$) in the variability of modes' energies. These findings can be applied, for example, to the control of energy input, exchange and output in Tokamaks; for explanation of some experimental results; to guide and improve the performance of experiments; to interpret the results of numerical simulations, etc.Comment: 5 pages, 15 figures, submitted to EP

A non-symmetric Yang-Baxter Algebra for the Quantum Nonlinear Schr\"odinger Model

We study certain non-symmetric wavefunctions associated to the quantum nonlinear Schr\"odinger model, introduced by Komori and Hikami using Gutkin's propagation operator, which involves representations of the degenerate affine Hecke algebra. We highlight how these functions can be generated using a vertex-type operator formalism similar to the recursion defining the symmetric (Bethe) wavefunction in the quantum inverse scattering method. Furthermore, some of the commutation relations encoded in the Yang-Baxter equation for the relevant monodromy matrix are generalized to the non-symmetric case.Comment: 31 pages; added some references; minor corrections throughou

A charged particle in a magnetic field - Jarzynski Equality

We describe some solvable models which illustrate the Jarzynski theorem and related fluctuation theorems. We consider a charged particle in the presence of magnetic field in a two dimensional harmonic well. In the first case the centre of the harmonic potential is translated with a uniform velocity, while in the other case the particle is subjected to an ac force. We show that Jarzynski identity complements Bohr-van Leeuwen theorem on the absence of diamagnetism in equilibrium classical system.Comment: 5 pages, minor corrections made and journal reference adde

A novel sequencing-based vaginal health assay combining self-sampling, HPV detection and genotyping, STI detection, and vaginal microbiome analysis

The composition of the vaginal microbiome, including both the presence of pathogens involved in sexually transmitted infections (STI) as well as commensal microbiota, has been shown to have important associations for a woman´s reproductive and general health. Currently, healthcare providers cannot offer comprehensive vaginal microbiome screening, but are limited to the detection of individual pathogens, such as high-risk human papillomavirus (hrHPV), the predominant cause of cervical cancer. There is no single test on the market that combines HPV, STI, and microbiome screening. Here, we describe a novel inclusive vaginal health assay that combines self-sampling with sequencing-based HPV detection and genotyping, vaginal microbiome analysis, and STI-associated pathogen detection. The assay includes genotyping and detection of 14 hrHPV types, 5 low-risk HPV types (lrHPV), as well as the relative abundance of 31 bacterial taxa of clinical importance, including Lactobacillus, Sneathia, Gardnerella, and 3 pathogens involved in STI, with high sensitivity, specificity, and reproducibility. For each of these taxa, reference ranges were determined in a group of 50 self-reported healthy women. The HPV sequencing portion of the test was evaluated against the digene High-Risk HPV HC2 DNA test. For hrHPV genotyping, agreement was 95.3% with a kappa of 0.804 (601 samples); after removal of samples in which the digene hrHPV probe showed cross-reactivity with lrHPV types, the sensitivity and specificity of the hrHPV genotyping assay were 94.5% and 96.6%, respectively, with a kappa of 0.841. For lrHPV genotyping, agreement was 93.9% with a kappa of 0.788 (148 samples), while sensitivity and specificity were 100% and 92.9%, respectively. This novel assay could be used to complement conventional cervical cancer screening, because its self-sampling format can expand access among women who would otherwise not participate, and because of its additional information about the composition of the vaginal microbiome and the presence of pathogens.Fil: Bik, Elisabeth M.. Ubiome;Fil: Bird, Sara W.. Ubiome;Fil: Bustamante, Juan Pablo. Universidad Nacional de Entre Ríos. Instituto de Investigación y Desarrollo en Bioingeniería y Bioinformática - Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Investigación y Desarrollo en Bioingeniería y Bioinformática; ArgentinaFil: Leon, Luis E.. Ubiome