Covariant Hamiltonian Field Theory

A consistent, local coordinate formulation of covariant Hamiltonian field theory is presented. Whereas the covariant canonical field equations are equivalent to the Euler-Lagrange field equations, the covariant canonical transformation theory offers more general means for defining mappings that preserve the form of the field equations than the usual Lagrangian description. It is proved that Poisson brackets, Lagrange brackets, and canonical 2-forms exist that are invariant under canonical transformations of the fields. The technique to derive transformation rules for the fields from generating functions is demonstrated by means of various examples. In particular, it is shown that the infinitesimal canonical transformation furnishes the most general form of Noether's theorem. We furthermore specify the generating function of an infinitesimal space-time step that conforms to the field equations.Comment: 93 pages, no figure

Truncated unity functional renormalization group for multiband systems with spin-orbit coupling

Although the functional renormalization group (fRG) is by now a well-established method for investigating correlated electron systems, it is still undergoing significant technical and conceptual improvements. In particular, the motivation to optimally exploit the parallelism of modern computing platforms has recently led to the development of the "truncated-unity" functional renormalization group (TU-fRG). Here, we review this fRG variant, and we provide its extension to multiband systems with spin-orbit coupling. Furthermore, we discuss some aspects of the implementation and outline opportunities and challenges ahead for predicting the ground-state ordering and emergent energy scales for a wide class of quantum materials.Comment: consistent with published version in Frontiers in Physics (2018

Crosscutting, what is and what is not? A Formal definition based on a Crosscutting Pattern

Crosscutting is usually described in terms of scattering and tangling. However, the distinction between these concepts is vague, which could lead to ambiguous statements. Sometimes, precise definitions are required, e.g. for the formal identification of crosscutting concerns. We propose a conceptual framework for formalizing these concepts based on a crosscutting pattern that shows the mapping between elements at two levels, e.g. concerns and representations of concerns. The definitions of the concepts are formalized in terms of linear algebra, and visualized with matrices and matrix operations. In this way, crosscutting can be clearly distinguished from scattering and tangling. Using linear algebra, we demonstrate that our definition generalizes other definitions of crosscutting as described by Masuhara & Kiczales [21] and Tonella and Ceccato [28]. The framework can be applied across several refinement levels assuring traceability of crosscutting concerns. Usability of the framework is illustrated by means of applying it to several areas such as change impact analysis, identification of crosscutting at early phases of software development and in the area of model driven software development

Forecasting Player Behavioral Data and Simulating in-Game Events

Understanding player behavior is fundamental in game data science. Video games evolve as players interact with the game, so being able to foresee player experience would help to ensure a successful game development. In particular, game developers need to evaluate beforehand the impact of in-game events. Simulation optimization of these events is crucial to increase player engagement and maximize monetization. We present an experimental analysis of several methods to forecast game-related variables, with two main aims: to obtain accurate predictions of in-app purchases and playtime in an operational production environment, and to perform simulations of in-game events in order to maximize sales and playtime. Our ultimate purpose is to take a step towards the data-driven development of games. The results suggest that, even though the performance of traditional approaches such as ARIMA is still better, the outcomes of state-of-the-art techniques like deep learning are promising. Deep learning comes up as a well-suited general model that could be used to forecast a variety of time series with different dynamic behaviors

COFFEE -- An MPI-parallelized Python package for the numerical evolution of differential equations

COFFEE (ConFormal Field Equation Evolver) is a Python package primarily developed to numerically evolve systems of partial differential equations over time using the method of lines. It includes a variety of time integrators and finite differencing stencils with the summation-by-parts property, as well as pseudo-spectral functionality for angular derivatives of spin-weighted functions. Some additional capabilities include being MPI-parallelisable on a variety of different geometries, HDF data output and post processing scripts to visualize data, and an actions class that allows users to create code for analysis after each timestep.Comment: 12 pages, 1 figure, accepted to be published in Software