Asymptotically exponential hitting times and metastability: a pathwise approach without reversibility

We study the hitting times of Markov processes to target set $G$, starting from a reference configuration $x_0$ or its basin of attraction. The configuration $x_0$ can correspond to the bottom of a (meta)stable well, while the target $G$ could be either a set of saddle (exit) points of the well, or a set of further (meta)stable configurations. Three types of results are reported: (1) A general theory is developed, based on the path-wise approach to metastability, which has three important attributes. First, it is general in that it does not assume reversibility of the process, does not focus only on hitting times to rare events and does not assume a particular starting measure. Second, it relies only on the natural hypothesis that the mean hitting time to $G$ is asymptotically longer than the mean recurrence time to $x_0$ or $G$. Third, despite its mathematical simplicity, the approach yields precise and explicit bounds on the corrections to exponentiality. (2) We compare and relate different metastability conditions proposed in the literature so to eliminate potential sources of confusion. This is specially relevant for evolutions of infinite-volume systems, whose treatment depends on whether and how relevant parameters (temperature, fields) are adjusted. (3) We introduce the notion of early asymptotic exponential behavior to control time scales asymptotically smaller than the mean-time scale. This control is particularly relevant for systems with unbounded state space where nucleations leading to exit from metastability can happen anywhere in the volume. We provide natural sufficient conditions on recurrence times for this early exponentiality to hold and show that it leads to estimations of probability density functions

Hydrodynamics in the wake of a pitching foil

The effect of flexibility on the hydrodynamic loads and on the flow structures generated on a rectangular foil when oscillating in pitch has been studied. Hydrodynamic loads were measured with a 6-axes balance, and the flow structures were investigated by using a Digital Particle Image Velocimetry (DPIV). It is known from nature's fin based propulsion mechanisms, that appendage stiffness plays an important role in their propulsive efficiency. We have studied four different stiffnesses, ranging from completely rigid to highly flexible. Optimal efficiency has been observed for an intermediate case. In this case, a moderately stronger trailing-edge vortex system takes place. A very high level of flexibility of the foil results in a reduction of efficiency.Comment: 4 pages, 4 figures, there are two videos include

Puzzles in quarkonium hadronic transitions with two pion emission

The anomalously large rates of some hadronic transitions from quarkonium are studied using QCD multipole expansion (QCDME) in the framework of a constituent quark model which has been successful in describing hadronic phenomenology. The hybrid intermediate states needed in the QCDME method are calculated in a natural extension of our constituent quark model based on the Quark Confining String (QCS) scheme. Some of the anomalies are explained due to the presence of an hybrid state with a mass near the mass of the decaying resonance whereas other are justified by the presence of molecular components in the wave function. Some unexpected results are pointed out.Comment: Conference proceedings of the XI Quark Confinement and the Hadron Spectrum (CONFINEMENT XI). Saint Petersburg (Russia) from 8 to 12 September 201

Optimal detection of changepoints with a linear computational cost

We consider the problem of detecting multiple changepoints in large data sets. Our focus is on applications where the number of changepoints will increase as we collect more data: for example in genetics as we analyse larger regions of the genome, or in finance as we observe time-series over longer periods. We consider the common approach of detecting changepoints through minimising a cost function over possible numbers and locations of changepoints. This includes several established procedures for detecting changing points, such as penalised likelihood and minimum description length. We introduce a new method for finding the minimum of such cost functions and hence the optimal number and location of changepoints that has a computational cost which, under mild conditions, is linear in the number of observations. This compares favourably with existing methods for the same problem whose computational cost can be quadratic or even cubic. In simulation studies we show that our new method can be orders of magnitude faster than these alternative exact methods. We also compare with the Binary Segmentation algorithm for identifying changepoints, showing that the exactness of our approach can lead to substantial improvements in the accuracy of the inferred segmentation of the data.Comment: 25 pages, 4 figures, To appear in Journal of the American Statistical Associatio

Nonleptonic B→D(∗)DsJ(∗)B \to D^{(*)}D_{sJ}^{(*)} decays and the nature of the orbitally excited charmed-strange mesons

The Belle Collaboration has recently reported a study of the decays $B \to D_{s1}(2536)^{+}\bar{D}^{(\ast)}$ and has given also estimates of relevant ratios between branching fractions of decays $B \to D^{(\ast)}D_{sJ}^{(\ast)}$ providing important information to check the structure of the $D_{s0}^{\ast}(2317)$, $D_{s1}(2460)$ and $D_{s1}(2536)$ mesons. The disagreement between experimental data and Heavy Quark Symmetry has been used as an indication that $D_{s0}^{\ast}(2317)$ and $D_{s1}(2460)$ mesons could have a more complex structure than the canonical $c\bar{s}$ one. We analyze these ratios within the framework of a constituent quark model, which allows us to incorporate the effects given by finite $c$-quark mass corrections. Our findings are that while the $D_{s1}(2460)$ meson could have a sizable non-$q\bar{q}$ component, the $D_{s0}^{\ast}(2317)$ and $D_{s1}(2536)$ mesons seem to be well described by a pure $q\bar{q}$ structure.Comment: 13 pages, 1 figur