Achievable Outage Rate Regions for the MISO Interference Channel

We consider the slow-fading two-user multiple-input single-output (MISO) interference channel. We want to understand which rate points can be achieved, allowing a non-zero outage probability. We do so by defining four different outage rate regions. The definitions differ on whether the rates are declared in outage jointly or individually and whether the transmitters have instantaneous or statistical channel state information (CSI). The focus is on the instantaneous CSI case with individual outage, where we propose a stochastic mapping from the rate point and the channel realization to the beamforming vectors. A major contribution is that we prove that the stochastic component of this mapping is independent of the actual channel realization.Comment: Accepted for publication in IEEE Wireless Communications Letter

Efficient Computation of Pareto Optimal Beamforming Vectors for the MISO Interference Channel with Successive Interference Cancellation

We study the two-user multiple-input single-output (MISO) Gaussian interference channel where the transmitters have perfect channel state information and employ single-stream beamforming. The receivers are capable of performing successive interference cancellation, so when the interfering signal is strong enough, it can be decoded, treating the desired signal as noise, and subtracted from the received signal, before the desired signal is decoded. We propose efficient methods to compute the Pareto-optimal rate points and corresponding beamforming vector pairs, by maximizing the rate of one link given the rate of the other link. We do so by splitting the original problem into four subproblems corresponding to the combinations of the receivers' decoding strategies - either decode the interference or treat it as additive noise. We utilize recently proposed parameterizations of the optimal beamforming vectors to equivalently reformulate each subproblem as a quasi-concave problem, which we solve very efficiently either analytically or via scalar numerical optimization. The computational complexity of the proposed methods is several orders-of-magnitude less than the complexity of the state-of-the-art methods. We use the proposed methods to illustrate the effect of the strength and spatial correlation of the channels on the shape of the rate region.Comment: Accepted for publication in IEEE Transactions on Signal Processin

Relative arbitrage: sharp time horizons and motion by curvature

We characterize the minimal time horizon over which any equity market with d ≥ 2 stocks and sufficient intrinsic volatility admits relative arbitrage. If d ∈ {2, 3}, the minimal time horizon can be computed explicitly, its value being zero if √ d = 2 and 3/(2π) if d = 3. If d ≥ 4, the minimal time horizon can be characterized via the arrival time function of a geometric flow of the unit simplex in R d that we call the minimum curvature flow

Convergence of local supermartingales

We characterize the event of convergence of a local supermartingale. Conditions are given in terms of its predictable characteristics and quadratic variation. The notion of stationarily local integrability plays a key role

On concentration of the empirical measure for general transport costs

Let $\mu$ be a probability measure on $\mathbb{R}^d$ and $\mu_N$ its empirical measure with sample size $N$. We prove a concentration inequality for the optimal transport cost between $\mu$ and $\mu_N$ for cost functions with polynomial local growth, that can have superpolynomial global growth. This result generalizes and improves upon estimates of Fournier and Guillin. The proof combines ideas from empirical process theory with known concentration rates for compactly supported $\mu$. By partitioning $\mathbb{R}^d$ into annuli, we infer a global estimate from local estimates on the annuli and conclude that the global estimate can be expressed as a sum of the local estimate and a mean-deviation probability for which efficient bounds are known

Möglichkeiten und Probleme bei der Anwendung der Klebtechnik

Nur wenn eine klebgerecht ausgeführte Konstruktion mit dem richtigen Klebstoff nach optimaler Oberflächenbehandlung und mit angepssten Abbindebedingungen gefertigt wird, sind Klebverbindungen von maximaler Festigkeit und Alterungsbeständigkeit zu erzielen. Am Beispiel von Bremsbelägen wird gezeigt, dass bei einer entsprechenden Erprobung auch sogenannte Sicherheitsteile durch Kleben hergestellt werden könne