Undecidability of Two-dimensional Robot Games

Robot game is a two-player vector addition game played on the integer lattice $\mathbb{Z}^n$. Both players have sets of vectors and in each turn the vector chosen by a player is added to the current configuration vector of the game. One of the players, called Eve, tries to play the game from the initial configuration to the origin while the other player, Adam, tries to avoid the origin. The problem is to decide whether or not Eve has a winning strategy. In this paper we prove undecidability of the robot game in dimension two answering the question formulated by Doyen and Rabinovich in 2011 and closing the gap between undecidable and decidable cases

Optimal control of nonlinear systems: a predictive control approach

A new nonlinear predictive control law for a class of multivariable nonlinear systems is presented in this paper. It is shown that the closed-loop dynamics under this nonlinear predictive controller explicitly depend on design parameters (prediction time and control order). The main features of this result are that an explicitly analytical form of the optimal predictive controller is given, on-line optimisation is not required, stability of the closed-loop system is guaranteed, the whole design procedure is transparent to designers and the resultant controller is easy to implement. By establishing the relationship between the design parameters and time-domain transient, it is shown that the design of an optimal generalised predictive controller to achieve desired time-domain specifications for nonlinear systems can be performed by looking up tables. The design procedure is illustrated by designing an autopilot for a missile

On Boltzmann vs. Gibbs and the Equilibrium in Statistical Mechanics

In a recent article, Werndl and Frigg discuss the relationship between the Boltzmannian and Gibbsian framework of statistical mechanics, addressing in particular the question when equilibrium values calculated in both frameworks agree. In this paper, I address conceptual confusions that could arise from their discussion, concerning in particular the authors' use of "Boltzmann equilibrium". I also clarify the status of the Khinchin condition for the equivalence of Boltzmannian and Gibbsian, and show that it follows under the assumptions proposed by Werndl and Frigg from standard arguments in probability theory

Data-driven Modeling and Coordination of Large Process Structures

In the engineering domain, the development of complex products (e.g., cars) necessitates the coordination of thousands of (sub-)processes. One of the biggest challenges for process management systems is to support the modeling, monitoring and maintenance of the many interdependencies between these sub-processes. The resulting process structures are large and can be characterized by a strong relationship with the assembly of the product; i.e., the sub-processes to be coordinated can be related to the different product components. So far, sub-process coordination has been mainly accomplished manually, resulting in high efforts and inconsistencies. IT support is required to utilize the information about the product and its structure for deriving, coordinating and maintaining such data-driven process structures. In this paper, we introduce the COREPRO framework for the data-driven modeling of large process structures. The approach reduces modeling efforts significantly and provides mechanisms for maintaining data-driven process structures

General model of photon-pair detection with an image sensor

We develop an analytic model that relates intensity correlation measurements performed by an image sensor to the properties of photon pairs illuminating it. Experiments using both an effective single-photon counting (SPC) camera and a linear electron-multiplying charge-coupled device (EMCCD) camera confirm the model

A duality theorem for a four dimensional Willmore energy

We prove an analog of Bryant's duality theorem for a four dimensional Willmore energy $\mathcal{E}_{GR}$ obtained by Graham-Reichert and Zhang. We show that for an immersion $\Phi$ from a four dimensional compact manifold without boundary $\Sigma$ into $\mathbb{R}^5$, the energy $\mathcal{E}_{GR}(\Phi)$ is equal to two energies on its conformal Gauss map $Y$. One defined only in terms of the image of $Y$, which is the analog of the area functional for Willmore surfaces, and an other one defined on maps from $\Sigma$ into the De Sitter space $\mathbb{S}^{5,1}$, which is the analog of the Dirichlet energy for Willmore surfaces. We prove that even when restricted to immersions of a given topological manifold $\Sigma^4$, $\mathcal{E}_{GR}$ is never bounded from below on the set of immersions from $\Sigma$ into $\mathbb{R}^5$. We exhibit a second conformally invariant energy $\mathcal{E}_P$ which is bounded from below and whose construction is closer to the two dimensional Willmore energy.Comment: 49 page