Search results for "Linear approximation"
showing 10 items of 21 documents
Bayesian Unification of Gradient and Bandit-based Learning for Accelerated Global Optimisation
2017
Bandit based optimisation has a remarkable advantage over gradient based approaches due to their global perspective, which eliminates the danger of getting stuck at local optima. However, for continuous optimisation problems or problems with a large number of actions, bandit based approaches can be hindered by slow learning. Gradient based approaches, on the other hand, navigate quickly in high-dimensional continuous spaces through local optimisation, following the gradient in fine grained steps. Yet, apart from being susceptible to local optima, these schemes are less suited for online learning due to their reliance on extensive trial-and-error before the optimum can be identified. In this…
The next-to-ladder approximation for linear Dyson–Schwinger equations
2007
We solve the linear Dyson Schwinger equation for a massless vertex in Yukawa theory, iterating the first two primitive graphs.
PAINT–SiCon: constructing consistent parametric representations of Pareto sets in nonconvex multiobjective optimization
2014
We introduce a novel approximation method for multiobjective optimization problems called PAINT–SiCon. The method can construct consistent parametric representations of Pareto sets, especially for nonconvex problems, by interpolating between nondominated solutions of a given sampling both in the decision and objective space. The proposed method is especially advantageous in computationally expensive cases, since the parametric representation of the Pareto set can be used as an inexpensive surrogate for the original problem during the decision making process. peerReviewed
Approximation by mappings with singular Hessian minors
2018
Let $\Omega\subset\mathbb R^n$ be a Lipschitz domain. Given $1\leq p<k\leq n$ and any $u\in W^{2,p}(\Omega)$ belonging to the little H\"older class $c^{1,\alpha}$, we construct a sequence $u_j$ in the same space with $\operatorname{rank}D^2u_j<k$ almost everywhere such that $u_j\to u$ in $C^{1,\alpha}$ and weakly in $W^{2,p}$. This result is in strong contrast with known regularity behavior of functions in $W^{2,p}$, $p\geq k$, satisfying the same rank inequality.
A normalized iterative Smoothed Particle Hydrodynamics method
2020
Abstract In this paper we investigate on a normalized iterative approach to improve the Smoothed Particle Hydrodynamics (SPH) estimate of a function. The method iterates on the residuals of an initial SPH approximation to obtain a more accurate solution. The iterative strategy preserves the matrix-free nature of the method, does not require changes on the kernel function and it is not affected by disordered data distribution. The iterative refinement is further improved by ensuring linear approximation order to the starting iterative values. We analyze the accuracy and the convergence of the method with the standard and normalized formulation giving evidence of the enhancements obtained wit…
NEW DEVELOPMENTS ON INVERSE POLYGON MAPPING TO CALCULATE GRAVITATIONAL LENSING MAGNIFICATION MAPS: OPTIMIZED COMPUTATIONS
2011
We derive an exact solution (in the form of a series expansion) to compute gravitational lensing magnification maps. It is based on the backward gravitational lens mapping of a partition of the image plane in polygonal cells (inverse polygon mapping, IPM), not including critical points (except perhaps at the cell boundaries). The zeroth-order term of the series expansion leads to the method described by Mediavilla et al. The first-order term is used to study the error induced by the truncation of the series at zeroth order, explaining the high accuracy of the IPM even at this low order of approximation. Interpreting the Inverse Ray Shooting (IRS) method in terms of IPM, we explain the previ…
One dimensional arrays and solitary tunnel junctions in the weak coulomb blockade regime: CBT thermometry
1997
In this article we review the use of the tunnel junction arrays for primary thermometry. In addition to our basic experimental and theoretical results we stress the insensitivity of this method to the fluctuating background charges, to nonidealities in the array and to magnetic field. Important new results of this article are the low temperature corrections to the half width and depth of the measured conductance dip beyond the linear approximation. We also point ou that short arrays, single tunnel junctions in particular, show interesting deviations from the universal behaviour of the long arrays.
Perturbations of spacetime: gauge transformations and gauge invariance at second order and beyond
1996
We consider in detail the problem of gauge dependence that exists in relativistic perturbation theory, going beyond the linear approximation and treating second and higher order perturbations. We first derive some mathematical results concerning the Taylor expansion of tensor fields under the action of one-parameter families (not necessarily groups) of diffeomorphisms. Second, we define gauge invariance to an arbitrary order $n$. Finally, we give a generating formula for the gauge transformation to an arbitrary order and explicit rules to second and third order. This formalism can be used in any field of applied general relativity, such as cosmological and black hole perturbations, as well …
A Simple Method for the Consecutive Determination of Protonation Constants through Evaluation of Formation Curves
2013
A simple method is presented for the consecutive determination of protonation constants of polyprotic acids based on their formation curves. The procedure is based on generally known equations that describe dissociation equilibria. It has been demonstrated through simulation that the values obtained through the proposed method are sufficiently consistent with the actual values. In contrast with the universally known and applied Bjerrum’s method, no differences in the accuracy of determination of subsequent protonation constant values are observed. The proposed method requires the value of one of the protonation constants (e.g., of the first one, K1) of the polyprotic acid. An iterative meth…