Generic Theory of Geometrodynamics from Noether's theorem for the Diff(M) symmetry group

We work out the most general theory for the interaction of spacetime geometry and matter fields---commonly referred to as geometrodynamics---for spin-$0$ and spin-$1$ particles. The minimum set of postulates to be introduced is that (i) the action principle should apply and that(ii) the total action should by form-invariant under the (local) diffeomorphism group. The second postulate thus implements the Principle of General Relativity. According to Noether's theorem, this physical symmetry gives rise to a conserved Noether current, from which the complete set of theories compatible with both postulates can be deduced. This finally results in a new generic Einstein-type equation, which can be interpreted as an energy-momentum balance equation emerging from the Lagrangian $L_{R}$ for the source-free dynamics of gravitation and the energy-momentum tensor of the source system $L_{0}$. Provided that the system has no other symmetries---such as SU$(N)$---the canonical energy-momentum tensor turns out to be the correct source term of gravitation. For the case of massive spin particles, this entails an increased weighting of the kinetic energy over the mass in their roles as the source of gravity as compared to the metric energy momentum tensor, which constitutes the source of gravity in Einstein's General Relativity. We furthermore confirm that a massive vector field necessarily acts as a source for torsion of spacetime. Thus, from the viewpoint of our generic Einstein-type equation, Einstein's General Relativity constitutes the particular case for spin-$0$ and massless spin particle fields, and the Hilbert Lagrangian $L_{R,H}$ as the model for the source-free dynamics of gravitation.Comment: 33 page

Antidepressant drugs and the response in the placebo group: the real problem lies in our understanding of the issue

In a recent paper, Horder and colleagues (Horder et al., 2010, J Psychopharmacol 25: 1277–1288) have suggested that the mainproblem in the Kirsch analysis is methodological. We argue that the results are similar irrespective of the method used. In our opinion the data suggest that placebo and drug effects are non-additive: antidepressants act independently of depression severity, while the placebo effect is present only in milder cases. While the response in the placebo group is due to unstable ‘noise’ and ‘artefacts’, the medication effect is reliable, valid and stable

Real-time soft shadows using a single light sample

We present a real-time rendering algorithm that generates soft shadows of dynamic scenes using a single light sample. As a depth-map algorithm it can handle arbitrary shadowed surfaces. The shadow-casting surfaces, however, should satisfy a few geometric properties to prevent artifacts. Our algorithm is based on a bivariate attenuation function, whose result modulates the intensity of a light causing shadows. The first argument specifies the distance of the occluding point to the shadowed point; the second argument measures how deep the shadowed point is inside the shadow. The attenuation function can be implemented using dependent texture accesses; the complete implementation of the algorithm can be accelerated by today's graphics hardware. We outline the implementation, and discuss details of artifact prevention and filtering

Organisation der Bauproduktion nach dem Vorbild industrieller Produktionssysteme : Entwicklung eines Gestaltungsmodells eines Ganzheitlichen Produktionssystems für den Bauunternehmer

Im Bauwesen wurde Mitte der 90er Jahre begonnen, singuläre Gestaltungsprinzipien und Methoden der Lean Production zu adaptieren sowie neue bauspezifische Methoden zu entwickeln (Lean Construction). In der vorliegenden Arbeit werden die bisweilen einzeln betrachteten Methodenbausteine zu einem Ganzheitlichen Produktionssystem Modell für Bauproduktions-Unternehmen zusammengeführt und vervollständigt. Dieses Bau-PSM ist ein Ordnungsrahmen für die Transformation in ein "leanes" Bauunternehmen

Organisation der Bauproduktion nach dem Vorbild industrieller Produktionssysteme : Entwicklung eines Gestaltungsmodells eines Ganzheitlichen Produktionssystems für den Bauunternehmer

Im Bauwesen wurde Mitte der 90er Jahre begonnen, singuläre Gestaltungsprinzipien und Methoden der Lean Production zu adaptieren sowie neue bauspezifische Methoden zu entwickeln (Lean Construction). In der vorliegenden Arbeit werden die bisweilen einzeln betrachteten Methodenbausteine zu einem Ganzheitlichen Produktionssystem Modell für Bauproduktions-Unternehmen zusammengeführt und vervollständigt. Dieses Bau-PSM ist ein Ordnungsrahmen für die Transformation in ein ""leanes"" Bauunternehmen

The Benefits of Model-Based Generalization in Reinforcement Learning

Model-Based Reinforcement Learning (RL) is widely believed to have the potential to improve sample efficiency by allowing an agent to synthesize large amounts of imagined experience. Experience Replay (ER) can be considered a simple kind of model, which has proved extremely effective at improving the stability and efficiency of deep RL. In principle, a learned parametric model could improve on ER by generalizing from real experience to augment the dataset with additional plausible experience. However, owing to the many design choices involved in empirically successful algorithms, it can be very hard to establish where the benefits are actually coming from. Here, we provide theoretical and empirical insight into when, and how, we can expect data generated by a learned model to be useful. First, we provide a general theorem motivating how learning a model as an intermediate step can narrow down the set of possible value functions more than learning a value function directly from data using the Bellman equation. Second, we provide an illustrative example showing empirically how a similar effect occurs in a more concrete setting with neural network function approximation. Finally, we provide extensive experiments showing the benefit of model-based learning for online RL in environments with combinatorial complexity, but factored structure that allows a learned model to generalize. In these experiments, we take care to control for other factors in order to isolate, insofar as possible, the benefit of using experience generated by a learned model relative to ER alone

Torsional dark energy in quadratic gauge gravity

The Covariant Canonical Gauge theory of Gravity (CCGG) is a gauge field formulation of gravity which a priori includes non-metricity and torsion. It extends the Lagrangian of Einstein's theory of general relativity by terms at least quadratic in the Riemann-Cartan tensor. This paper investigates the implications of metric compatible CCGG on cosmological scales. For a totally anti-symmetric torsion tensor we derive the resulting equations of motion in a Friedmann-Lema\^itre-Robertson-Walker (FLRW) Universe. In the limit of a vanishing quadratic Riemann-Cartan term, the arising modifications of the Friedmann equations are shown to be equivalent to spatial curvature. Furthermore, the modified Friedmann equations are investigated in detail in the early and late times of the Universe's history. It is demonstrated that in addition to the standard $\Lambda$CDM behaviour of the scale factor, there exist novel time dependencies, emerging due to the presence of torsion and the quadratic Riemann-Cartan term. Finally, at late times, we present how the accelerated expansion of the Universe can be understood as a geometric effect of spacetime through torsion, rendering the introduction of a cosmological constant redundant. In such a scenario it is possible to compute an expected value for the parameters of the postulated gravitational Hamiltonian/Lagrangian and to provide a lower bound on the vacuum energy of matter.Comment: 10 pages, 3 figures; Added reference