Morita equivalence of multidimensional noncommutative tori

One can describe an $n$-dimensional noncommutative torus by means of an antisymmetric $n\times n$-matrix $\theta$. We construct an action of the group $SO(n,n|\bf Z)$ on the space of antisymmetric matrices and show that, generically, matrices belonging to the same orbit of this group give Morita equivalent tori. Some applications to physics are sketched.Comment: 13 pages. Minor comment corrected. (To appear in the International Journal of Mathematics.

Parameterised Approximation of the Fixation Probability of the Dominant Mutation in the Multi-Type Moran Process

The multi-type Moran process is an evolutionary process on a connected graph $G$ in which each vertex has one of $k$ types and, in each step, a vertex $v$ is chosen to reproduce its type to one of its neighbours. The probability of a vertex $v$ being chosen for reproduction is proportional to the fitness of the type of $v$. So far, the literature was almost solely concerned with the $2$-type Moran process in which each vertex is either healthy (type $0$) or a mutant (type $1$), and the main problem of interest has been the (approximate) computation of the so-called fixation probability, i.e., the probability that eventually all vertices are mutants. In this work we initiate the study of approximating fixation probabilities in the multi-type Moran process on general graphs. Our main result is an FPTRAS (fixed-parameter tractable randomised approximation scheme) for computing the fixation probability of the dominant mutation; the parameter is the number of types and their fitnesses. In the course of our studies we also provide novel upper bounds on the expected absorption time, i.e., the time that it takes the multi-type Moran process to reach a state in which each vertex has the same type.Comment: 14 page

Evaluation of the efficiency and resulting electrical and economic losses of photovoltaic home storage systems

The increase in electricity prices along with a decrease in the price of storage systems has led to a rapid expansion of the photovoltaic (PV) home storage system market, particularly in Germany. In order to be economically viable, PV home storage systems must fulfil certain performance criteria. The overall performance and achievable self-sufficiency ratio of a PV battery home storage system depends on (i) the efficiencies of the system components, (ii) the standby consumption, (iii) the reaction time of the home storage system as well as (iv) the intelligence of the overall system control software. So far, PV home storage system still show very big differences in their performance. However, poor system performance can result in the system being no longer economic viable. Up to now, there have been only a few studies that deal with the evaluation and systematic comparison of the performance of PV home storage systems. For this paper the performance of 12 commercially available PV-battery systems has been analysed with a focus on the overall system efficiency. The efficiency of the systems is mainly influenced by the battery efficiency, power conversion efficiency and standby consumption of the different system components. Therefore, a testing and evaluation method has been developed. In this work the method as well as the results of the systems are presented. A detailed study of the influence of the effects of the individual losses on both total energy and monetary losses was carried out. It is shown that power conversion has the greatest influence on energy and monetary losses. For the systems under evaluation the monetary losses per year due to battery efficiency losses range between 2 €/a and 40 €/a. Monetary losses due to conversion losses range between 33 €/a and 137 €/a and due to standby consumption between 1 €/a and 46 €/a. The individual losses can be summed up to give a total loss, which lies between 44 €/a and 174 €/a

Comparison of Small EV Charging Station\u27s Load Forecasts and its Impact on the Operational Costs

For an energy management system (EMS) of a charging station (CS), information on future load is crucial. Existing models primarily focus on load forecasting for large charging stations. In this study, three different load forecasting models based on real data from a public CS with two charging points are developed. The models include two persistent models and one model that utilizes a machine learning algorithm. To assess the impact of forecasting accuracy on operational costs, a case study with dynamic electricity prices and a stationary battery storage is conducted. Using the load predictions, a mixed-integer linear programming problem is formulated to optimize the scheduling of the stationary battery charging