We present an active approach for discriminating different materials by impulsively contacting (hitting) them, and sensing and interpreting the resulting sounds. In theory, the angle of internal friction is diagnostic of material, but invariant over object shape. In our experiments, we observe that the angle of internal friction is not invariant over the frequency of the sound spectrum for whic...

The paper deals with the asymptotic behavior of the bridge of a Gaussian process conditioned to stay in n fixed points at n fixed past instants. In particular, functional large deviation results are stated for small time. Several examples are considered: integrated or not fractional Brownian motion,m-fold integrated Brownian motion. As an application, the asymptotic behavior of the exit probabi...

For any α-stable Lévy process with jumps on both sides, where α ∈ (1, 2), we find the Mellin transform of the first hitting time of the origin and give an expression for its density. This complements existing work in the symmetric case and the spectrally one-sided case; cf. [38, 19] and [33, 36], respectively. We appeal to the Lamperti– Kiu representation of Chaumont et al. [16] for real-valued...

Let $T_{\rho}$ be an irrational rotation on a unit circle $S^{1}\simeq [0,1)$. Consider the sequence $\{\mathcal{P}_{n}\}$ of increasing partitions $S^{1}$. Define hitting times $N_{n}(\mathcal{P}_n;x,y):= \inf\{j\geq 1\mid T^{j}_{\rho}(y)\in P_{n}(x)\}$, where $P_{n}(x)$ is element $\mathcal{P}_{n}$ containing $x$. D. Kim and B. Seo in [9] proved that rescaled $K_n(\mathcal{Q}_n;x,y):= \frac{\...

In standard planar first-passage percolation [11] each pair x and y of nearest-neighbor of Z has an edge connecting them and each edge is equipped with a non-negative random variable (passage time) which may be interpreted as the time it takes for an infection to be transmitted from x to y. We assume these random variables are i.i.d. with a continuous distribution F. The passage time t(γ) for a...

The concept of the ”transient effect” is examined in respect of a ”mean first passage time”. It is demonstrated that the time the fissioning system stays inside the barrier is much larger than suggested by the transient time, and that no enhancement of emission of neutrons over that given by Kramers’ rate formula ought to be considered.

A description of the sequence of interspike intervals and of the subsequent firing times for single neurons is performed by means of an instantaneous return process in the presence of refractoriness. Every interspike interval consists of an absolute refractory period of fixed duration followed by a period of relative refractoriness whose duration is described by the first-passage time of the mo...