Approximately bisimilar symbolic models for nonlinear control systems

Control systems are usually modeled by differential equations describing how physical phenomena can be influenced by certain control parameters or inputs. Although these models are very powerful when dealing with physical phenomena, they are less suitable to describe software and hardware interfacing the physical world. For this reason there is a growing interest in describing control systems through symbolic models that are abstract descriptions of the continuous dynamics, where each "symbol" corresponds to an "aggregate" of states in the continuous model. Since these symbolic models are of the same nature of the models used in computer science to describe software and hardware, they provide a unified language to study problems of control in which software and hardware interact with the physical world. Furthermore the use of symbolic models enables one to leverage techniques from supervisory control and algorithms from game theory for controller synthesis purposes. In this paper we show that every incrementally globally asymptotically stable nonlinear control system is approximately equivalent (bisimilar) to a symbolic model. The approximation error is a design parameter in the construction of the symbolic model and can be rendered as small as desired. Furthermore if the state space of the control system is bounded the obtained symbolic model is finite. For digital control systems, and under the stronger assumption of incremental input-to-state stability, symbolic models can be constructed through a suitable quantization of the inputs.Comment: Corrected typo

Minimal resistance of curves under the single impact assumption

We consider the hollow on the half-plane $\{ (x,y) : y \le 0 \} \subset \mathbb{R}^2$ defined by a function $u : (-1,\, 1) \to \mathbb{R}$, $u(x) < 0$, and a vertical flow of point particles incident on the hollow. It is assumed that $u$ satisfies the so-called single impact condition (SIC): each incident particle is elastically reflected by graph$(u)$ and goes away without hitting the graph of $u$ anymore. We solve the problem: find the function $u$ minimizing the force of resistance created by the flow. We show that the graph of the minimizer is formed by two arcs of parabolas symmetric to each other with respect to the $y$-axis. Assuming that the resistance of $u \equiv 0$ equals 1, we show that the minimal resistance equals $\pi/2 - 2\arctan(1/2) \approx 0.6435$. This result completes the previously obtained result [SIAM J. Math. Anal., 46 (2014), pp. 2730--2742] stating in particular that the minimal resistance of a hollow in higher dimensions equals 0.5. We additionally consider a similar problem of minimal resistance, where the hollow in the half-space $\{(x_1,\ldots,x_d, y) : y \le 0 \} \subset \mathbb{R}^{d+1}$ is defined by a radial function $U$ satisfying the SIC, $U(x) = u(|x|)$, with $x = (x_1,\ldots,x_d)$, $u(\xi) < 0$ for $0 \le \xi < 1$, and $u(\xi) = 0$ for $\xi \ge 1$, and the flow is parallel to the $y$-axis. The minimal resistance is greater than 0.5 (and coincides with 0.6435 when d = 1) and converges to 0.5 as $d \to \infty$

Prospects for an experiment to measure BR(KL→π0ννˉK_L\to\pi^0\nu\bar{\nu}) at the CERN SPS

Precise measurements of the branching ratios for the $K\to\pi\nu\bar{\nu}$ decays can provide unique constraints on CKM unitarity and, potentially, evidence for new physics. It is important to measure both decay modes, $K^+\to\pi^+\nu\bar{\nu}$ and $K_L\to\pi^0\nu\bar{\nu}$, since different new physics models affect the rates for each channel differently. We are investigating the feasibility of performing a measurement of BR($K_L\to\pi^0\nu\bar{\nu}$) using a high-energy secondary neutral beam at the CERN SPS in a successor experiment to NA62. The planned experiment would reuse some of the NA62 infrastructure, including possibly the NA48 liquid-krypton calorimeter. The mean momentum of $K_L$ mesons decaying in the fiducial volume is 70 GeV; the decay products are boosted forward, so that less demanding performance is required from the large-angle photon veto detectors. On the other hand, the layout poses particular challenges for the design of the small-angle vetoes, which must reject photons from $K_L$ decays escaping through the beam pipe amidst an intense background from soft photons and neutrons in the beam. We present some preliminary conclusions from our feasibility studies, summarizing the design challenges faced and the sensitivity obtainable for the measurement of BR($K_L\to\pi^0\nu\bar{\nu}$).Comment: 6 pages, 5 figures. Prepared for the proceedings of the 2016 International Conference on Kaon Physics (KAON 2016), Birmingham, UK, 14-17 September 201

Electroweak Vacuum Stability in light of BICEP2

We consider the effect of a period of inflation with a high energy density upon the stability of the Higgs potential in the early universe. The recent measurement of a large tensor-to-scalar ratio, $r_T \sim 0.16$, by the BICEP-2 experiment possibly implies that the energy density during inflation was very high, comparable with the GUT scale. Given that the standard model Higgs potential is known to develop an instability at $\Lambda \sim 10^{10}$ GeV this means that the resulting large quantum fluctuations of the Higgs field could destabilize the vacuum during inflation, even if the Higgs field starts at zero expectation value. We estimate the probability of such a catastrophic destabilisation given such an inflationary scenario and calculate that for a Higgs mass of $m_h=125.5$ GeV that the top mass must be less than $m_t\sim 172$ GeV. We present two possible cures: a direct coupling between the Higgs and the inflaton and a non-zero temperature from dissipation during inflation.Comment: 5 pages, 4 figures. Typos corrected, results unchanged, matches version submitted to journa

Precision determination of the top-quark mass

Precision determinations of the top-quark mass require theory predictions with a well-defined mass parameter in a given renormalization scheme. The top-quark's running mass in the MSbar scheme can be extracted with good precision from the total cross section at next-to-next-to-leading order in QCD. The Monte Carlo top-quark mass parameter measured from comparison to events with top-quark decay products is not identical with the pole mass. Its translation to the pole mass scheme introduces an additional uncertainty of the order of 1 GeV.Comment: Presented at Loops and Legs in Quantum Field Theory 2014, Weimar, Germany and Large Hadron Collider Physics 2014, New York, US

Modeling and Analysis of Bus Contention for Hardware Accelerators in FPGA SoCs (Artifact)

This artifact provides the means for reproducing the experiments presented in the paper "Modeling and Analysis of Bus Contention for Hardware Accelerators in FPGA SoC". In particular, it provides the means and describes how to replicate the experimental study that has been carried out to evaluate the proposed analysis with synthetic workloads