Adaptive learning in multiagent systems: a forecasting methodology based on error analysis

Electricity markets are complex environments, involving a large number of different entities, playing in a dynamic scene to obtain the best advantages and profits. MASCEM is a multi-agent electricity market simu-lator to model market players and simulate their operation in the market. Market players are entities with specific characteristics and objectives, making their decisions and interacting with other players. MASCEM pro-vides several dynamic strategies for agents’ behaviour. This paper presents a method that aims to provide market players strategic bidding capabilities, allowing them to obtain the higher possible gains out of the market. This method uses an auxiliary forecasting tool, e.g. an Artificial Neural Net-work, to predict the electricity market prices, and analyses its forecasting error patterns. Through the recognition of such patterns occurrence, the method predicts the expected error for the next forecast, and uses it to adapt the actual forecast. The goal is to approximate the forecast to the real value, reducing the forecasting error.

Stability and error analysis for a numerical scheme to approximate elastic flow

Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik, Univ., Dissertation, 2015

Evaluation of Software Development Practices through Error Analysis

This thesis studies evaluation of software development practices through an error analysis. The work presents software development process, software testing, software errors, error classification and software process improvement methods. The practical part of the work presents results from the error analysis of one software process. It also gives improvement ideas for the project. It was noticed that the classification of the error data was inadequate in the project. Because of this it was impossible to use the error data effectively. With the error analysis we were able to show that there were deficiencies in design and analyzing phases, implementation phase and in testing phase. The work gives ideas for improving error classification and for software development practices.

Error analysis of a Monte Carlo algorithm for computing bilinear forms of matrix powers

In this paper we present error analysis for a Monte Carlo algorithm for evaluating bilinear forms of matrix powers. An almost Optimal Monte Carlo (MAO) algorithm for solving this problem is formulated. Results for the structure of the probability error are presented and the construction of robust and interpolation Monte Carlo algorithms are discussed. Results are presented comparing the performance of the Monte Carlo algorithm with that of a corresponding deterministic algorithm. The two algorithms are tested on a well balanced matrix and then the effects of perturbing this matrix, by small and large amounts, is studied.

Error analysis of Trefftz-discontinuous Galerkin methods for the time-harmonic Maxwell equations

In this paper, we extend to the time-harmonic Maxwell equations the p-version analysis technique developed in [R. Hiptmair, A. Moiola and I. Perugia, Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the p-version, SIAM J. Numer. Anal., 49 (2011), 264-284] for Trefftz-discontinuous Galerkin approximations of the Helmholtz problem. While error estimates in a mesh-skeleton norm are derived parallel to the Helmholtz case, the derivation of estimates in a mesh-independent norm requires new twists in the duality argument. The particular case where the local Trefftz approximation spaces are built of vector-valued plane wave functions is considered, and convergence rates are derived.

On aposteriori error analysis of dG schemes approximating hyperbolic conservation laws

This contribution is concerned with aposteriori error analysis of discontinuous Galerkin (dG) schemes approximating hyperbolic conservation laws. In the scalar case the aposteriori analysis is based on the L1 contraction property and the doubling of variables technique. In the system case the appropriate stability framework is in L2, based on relative entropies. It is only applicable if one of the solutions, which are compared to each other, is Lipschitz. For dG schemes approximating hyperbolic conservation laws neither the entropy solution nor the numerical solution need to be Lipschitz. We explain how this obstacle can be overcome using a reconstruction approach which leads to an aposteriori error estimate.

A priori error analysis of space–time Trefftz discontinuous Galerkin methods for wave problems

We present and analyse a space–time discontinuous Galerkin method for wave propagation problems. The special feature of the scheme is that it is a Trefftz method, namely that trial and test functions are solution of the partial differential equation to be discretised in each element of the (space–time) mesh. The method considered is a modification of the discontinuous Galerkin schemes of Kretzschmar et al. (2014) and of Monk & Richter (2005). For Maxwell’s equations in one space dimension, we prove stability of the method, quasi-optimality, best approximation estimates for polynomial Trefftz spaces and (fully explicit) error bounds with high order in the meshwidth and in the polynomial degree. The analysis framework also applies to scalar wave problems and Maxwell’s equations in higher space dimensions. Some numerical experiments demonstrate the theoretical results proved and the faster convergence compared to the non-Trefftz version of the scheme.

A navigation system for percutaneous needle interventions based on PET/CT images: design, workflow and error analysis of soft tissue and bone punctures

Percutaneous needle intervention based on PET/CT images is effective, but exposes the patient to unnecessary radiation due to the increased number of CT scans required. Computer assisted intervention can reduce the number of scans, but requires handling, matching and visualization of two different datasets. While one dataset is used for target definition according to metabolism, the other is used for instrument guidance according to anatomical structures. No navigation systems capable of handling such data and performing PET/CT image-based procedures while following clinically approved protocols for oncologic percutaneous interventions are available. The need for such systems is emphasized in scenarios where the target can be located in different types of tissue such as bone and soft tissue. These two tissues require different clinical protocols for puncturing and may therefore give rise to different problems during the navigated intervention. Studies comparing the performance of navigated needle interventions targeting lesions located in these two types of tissue are not often found in the literature. Hence, this paper presents an optical navigation system for percutaneous needle interventions based on PET/CT images. The system provides viewers for guiding the physician to the target with real-time visualization of PET/CT datasets, and is able to handle targets located in both bone and soft tissue. The navigation system and the required clinical workflow were designed taking into consideration clinical protocols and requirements, and the system is thus operable by a single person, even during transition to the sterile phase. Both the system and the workflow were evaluated in an initial set of experiments simulating 41 lesions (23 located in bone tissue and 18 in soft tissue) in swine cadavers. We also measured and decomposed the overall system error into distinct error sources, which allowed for the identification of particularities involved in the process as well as highlighting the differences between bone and soft tissue punctures. An overall average error of 4.23 mm and 3.07 mm for bone and soft tissue punctures, respectively, demonstrated the feasibility of using this system for such interventions. The proposed system workflow was shown to be effective in separating the preparation from the sterile phase, as well as in keeping the system manageable by a single operator. Among the distinct sources of error, the user error based on the system accuracy (defined as the distance from the planned target to the actual needle tip) appeared to be the most significant. Bone punctures showed higher user error, whereas soft tissue punctures showed higher tissue deformation error.

Methods for automatic error analysis of numerical algorithms /

Vita.

An error analysis of solutions to sparse linear programming problems,

"Supported in part by the Advanced Research Projects Agency ... contract no. US AF 30(602) 4144."