Search results for "Exponential function"
showing 10 items of 173 documents
Hessian PDF reweighting meets the Bayesian methods
2014
We discuss the Hessian PDF reweighting - a technique intended to estimate the effects that new measurements have on a set of PDFs. The method stems straightforwardly from considering new data in a usual $\chi^2$-fit and it naturally incorporates also non-zero values for the tolerance, $\Delta\chi^2>1$. In comparison to the contemporary Bayesian reweighting techniques, there is no need to generate large ensembles of PDF Monte-Carlo replicas, and the observables need to be evaluated only with the central and the error sets of the original PDFs. In spite of the apparently rather different methodologies, we find that the Hessian and the Bayesian techniques are actually equivalent if the $\Delta…
PDF reweighting in the Hessian matrix approach
2014
We introduce the Hessian reweighting of parton distribution functions (PDFs). Similarly to the better-known Bayesian methods, its purpose is to address the compatibility of new data and the quantitative modifications they induce within an existing set of PDFs. By construction, the method discussed here applies to the PDF fits that carried out a Hessian error analysis using a non-zero tolerance $\Delta\chi^2$. The principle is validated by considering a simple, transparent example. We are also able to establish an agreement with the Bayesian technique provided that the tolerance criterion is appropriately accounted for and that a purely exponential Bayesian likelihood is assumed. As a practi…
Biophysical parameter retrieval with warped Gaussian processes
2015
This paper focuses on biophysical parameter retrieval based on Gaussian Processes (GPs). Very often an arbitrary transformation is applied to the observed variable (e.g. chlorophyll content) to better pose the problem. This standard practice essentially tries to linearize/uniformize the distribution by applying non-linear link functions like the logarithmic, the exponential or the logistic functions. In this paper, we propose to use a GP model that automatically learns the optimal transformation directly from the data. The so-called warped GP regression (WGPR) presented in [1] models output observations as a parametric nonlinear transformation of a GP. The parameters of such prior model are…
Connections and geodesics in the space of metrics
2015
We argue that the exponential relation $g_{\mu\nu} = \bar{g}_{\mu\rho}\big(\mathrm{e}^h\big)^\rho{}_\nu$ is the most natural metric parametrization since it describes geodesics that follow from the basic structure of the space of metrics. The corresponding connection is derived, and its relation to the Levi-Civita connection and the Vilkovisky-DeWitt connection is discussed. We address the impact of this geometric formalism on quantum gravity applications. In particular, the exponential parametrization is appropriate for constructing covariant quantities like a reparametrization invariant effective action in a straightforward way. Furthermore, we reveal an important difference between Eucli…
A simplified falling-head tecnique for rapid determination of field-saturated hydraulic conductivity
2004
Simplified measurements of the field-saturated hydraulic conductivity, K fs , require short duration experiments, small water volumes, and easily transportable equipment. A simplified falling-head (SFH) technique for the rapid determination of K fs has been developed and tested. The technique consists in applying a small volume of water on a soil surface, confined by a ring inserted a short distance into the soil, and then measuring the time from the application of water to the instant at which the surface area is no longer covered by water. A measurement of the initial and field-saturated soil water contents, and an estimate of the α* parameter of the Gardner's exponential model are then u…
Almost sure rates of mixing for i.i.d. unimodal maps
2002
International audience; It has been known since the pioneering work of Jakobson and subsequent work by Benedicks and Carleson and others that a positive measure set of quadratic maps admit an absolutely continuous invariant measure. Young and Keller-Nowicki proved exponential decay of its correlation functions. Benedicks and Young, and Baladi and Viana studied stability of the density and exponential rate of decay of the Markov chain associated to i.i.d. small perturbations. The almost sure statistical properties of the sample stationary measures of i.i.d. itineraries are more difficult to estimate than the "averaged statistics". Adapting to random systems, on the one hand partitions associ…
The Two-Minutes-Flow-Index (TMFI)
1969
While performing clinical rCBF functional tests it is difficult to maintain the patient in a stationary condition over the entire clearance period. For this reason it has become a common practice to restrict the recording of the clearance curves to the first 2 min [1, 2, 3]. This gives rise to one question: 1. Is it possible to evaluate the information contained in these 2 min of the clearance curve so as to obtain a quantifiable measure for rCBF?
Cooperative Inventory control
2005
In multi-retailer inventory control the possibility of sharing setup costs motivates communication and coordination among the retailers. We solve the problem of finding suboptimal distributed reordering policies that minimize setup, ordering, storage, and shortage costs incurred by the retailers over a finite horizon. Neuro-dynamic programming (NDP) reduces the computational complexity of the solution algorithm from exponential to polynomial on the number of retailers.
Localizing quantum phase slips in one-dimensional Josephson junction chains
2013
Published version of an article in the journal: New Journal of Physics. Also available from the publisher at: http://dx.doi.org/10.1088/1367-2630/15/9/095014 Open Access We studied quantum phase-slip (QPS) phenomena in long one-dimensional Josephson junction series arrays with tunable Josephson coupling. These chains were fabricated with as many as 2888 junctions, where one sample had a separately tunable link in the middle of the chain. Measurements were made of the zero-bias resistance, R0, as well as current-voltage characteristics (IVC). The finite R0 is explained by QPS and shows an exponential dependence on with a distinct change in the exponent at R 0 = RQ = h/4e2. When R0 > R Q, the…
Experimental Evidence of Leaks in Elastic Pipes
2016
Several studies have been carried out in recent decades to establish a relationship between total head and leaks. In literature, the leakage governing equations have been analysed in light of pipe materials, water head, leak dimension or shape. Most of these contributions questioned the classical Torricelli equation, demonstrating through experimental evidence that the classical orifice law can give unsatisfactory results. Nevertheless, starting from the Torricelli equation, other exponential or linear governing equations have been proposed as mathematical models able to reproduce the leakages in water distribution systems (WDSs). To investigate the validity of the proposed governing equati…