Search results for "Probability."
showing 10 items of 3396 documents
A new hybrid method to improve the ultra-short-term prediction of LOD
2019
Accurate, short-term predictions of Earth orientation parameters (EOP) are needed for many real-time applications including precise tracking and navigation of interplanetary spacecraft, climate forecasting, and disaster prevention. Out of the EOP, the LOD (length of day), which represents the changes in the Earth’s rotation rate, is the most challenging to predict since it is largely affected by the torques associated with changes in atmospheric circulation. In this study, the combination of Copula-based analysis and singular spectrum analysis (SSA) method is introduced to improve the accuracy of the forecasted LOD. The procedure operates as follows: First, we derive the dependence structur…
Predicting maximum annual values of event soil loss by USLE-type models
2017
Abstract Previous experimental investigations showed that a large proportion of total plot soil erosion over a long time period is generally due to relatively few, large storms. Consequently, erosion models able to accurately predict the highest plot soil loss values have practical importance since they could allow to improve the design of soil conservation practices in an area of interest. At present USLE-based models are attractive from a practical point of view, since the input data are generally easy to obtain. The USLE was developed with specific reference to the mean annual temporal scale but it was also applied at the event scale. Other models, such as the USLE-M and the USLE-MM, app…
Exploiting historical rainfall and landslide data in a spatial database for the derivation of critical rainfall thresholds
2017
Critical rainfall thresholds for landslides are powerful tools for preventing landslide hazard. The thresholds are commonly estimated empirically starting from rainfall events that triggered landslides in the past. The creation of the appropriate rainfall–landslide database is one of the main efforts in this approach. In fact, an accurate agreement between the landslide and rainfall information, in terms of location and timing, is essential in order to correctly estimate the rainfall–landslide relationships. A further issue is taking into account the average moisture conditions prior the triggering event, which reasonably may be crucial in determining the sufficient amount of precipitation.…
Conformal measures for multidimensional piecewise invertible maps
2001
Given a piecewise invertible map T:X\to X and a weight g:X\rightarrow\ ]0,\infty[ , a conformal measure \nu is a probability measure on X such that, for all measurable A\subset X with T:A\to TA invertible, \nu(TA)= \lambda \int_{A}\frac{1}{g}\ d\nu with a constant \lambda>0 . Such a measure is an essential tool for the study of equilibrium states. Assuming that the topological pressure of the boundary is small, that \log g has bounded distortion and an irreducibility condition, we build such a conformal measure.
The Liouville theorem and linear operators satisfying the maximum principle
2020
A result by Courr\`ege says that linear translation invariant operators satisfy the maximum principle if and only if they are of the form $\mathcal{L}=\mathcal{L}^{\sigma,b}+\mathcal{L}^\mu$ where $$ \mathcal{L}^{\sigma,b}[u](x)=\text{tr}(\sigma \sigma^{\texttt{T}} D^2u(x))+b\cdot Du(x) $$ and $$ \mathcal{L}^\mu[u](x)=\int \big(u(x+z)-u-z\cdot Du(x) \mathbf{1}_{|z| \leq 1}\big) \,\mathrm{d} \mu(z). $$ This class of operators coincides with the infinitesimal generators of L\'evy processes in probability theory. In this paper we give a complete characterization of the translation invariant operators of this form that satisfy the Liouville theorem: Bounded solutions $u$ of $\mathcal{L}[u]=0$ i…
Monotonicity-based inversion of the fractional Schr\"odinger equation II. General potentials and stability
2019
In this work, we use monotonicity-based methods for the fractional Schr\"odinger equation with general potentials $q\in L^\infty(\Omega)$ in a Lipschitz bounded open set $\Omega\subset \mathbb R^n$ in any dimension $n\in \mathbb N$. We demonstrate that if-and-only-if monotonicity relations between potentials and the Dirichlet-to-Neumann map hold up to a finite dimensional subspace. Based on these if-and-only-if monotonicity relations, we derive a constructive global uniqueness results for the fractional Calder\'on problem and its linearized version. We also derive a reconstruction method for unknown obstacles in a given domain that only requires the background solution of the fractional Sch…
On the stability of the Serrin problem
2008
We investigate stability issues concerning the radial symmetry of solutions to Serrin's overdetermined problems. In particular, we show that, if $u$ is a solution to $\Delta u=n$ in a smooth domain $\Omega \subset \rn$, $u=0$ on $\partial\Omega$ and $|Du|$ is close to 1 on $\partial\Omega$, then $\Omega$ is close to the union of a certain number of disjoint unitary balls.
Contrasting probabilistic and anti-optimization approaches in an applied mechanics problem
2003
Probabilistic and non-probabilistic, anti-optimization analyses of uncertainty are contrasted in this study. Specifically, the comparison of these two competing approaches is conducted for an uniform column, with initial geometric imperfection, subjected to an impact axial load. The reliability of the column is derived for the cases when the initial imperfections posses either (a) uniform probability density, (b) truncated exponential density or (c) generic truncated probability density. The problem is also analyzed in the context of an interval analysis. It is shown that in, the most important near-unity reliability range these two approaches tend to each other. Since the interval analysis…
Itô calculus extended to systems driven by -stable Lévy white noises (a novel clip on the tails of Lévy motion)
2007
Abstract The paper deals with probabilistic characterization of the response of non-linear systems under α -stable Levy white noise input. It is shown that, by properly selecting a clip in the probability density function of the input, the moments of the increments of Levy motion process remain all of the same order ( d t ) , like the increments of the Compound Poisson process. It follows that the Ito calculus extended to Poissonian input, may also be used for α -stable Levy white noise input processes. It is also shown that, when the clip on the tails of the probability of the increments of the Levy motion approaches to infinity, the Einstein–Smoluchowsky equation is restored. Once these c…
An innovative approach to manage uncertainties and stock diversity in the EPBD cost-optimal methodology
2018
The EU Energy Performance of Buildings Directive (EPBD) 2010/31/EU is a step in the right direction to promote near zero energy buildings (NZEB) in a step-wise manner, starting with minimum energy performance and cost optimal thresholds for “reference buildings” (RBs) for each category. Nevertheless, a standard method for defining RBs does not exist, which led to a great divergence between MS in the level of detail used to define RBs for the EPBD cost-optimal analysis. Such lack of harmonisation between MS is further evident given the resulting large discrepancies in energy performance indicators even between countries having similar climate. Furthermore, discrepancies of 30% or higher betw…