Sampling and reconstruction of operators

We study the recovery of operators with bandlimited Kohn-Nirenberg symbol from the action of such operators on a weighted impulse train, a procedure we refer to as operator sampling. Kailath, and later Kozek and the authors have shown that operator sampling is possible if the symbol of the operator is bandlimited to a set with area less than one. In this paper we develop explicit reconstruction formulas for operator sampling that generalize reconstruction formulas for bandlimited functions. We give necessary and sufficient conditions on the sampling rate that depend on size and geometry of the bandlimiting set. Moreover, we show that under mild geometric conditions, classes of operators bandlimited to an unknown set of area less than one-half permit sampling and reconstruction. A similar result considering unknown sets of area less than one was independently achieved by Heckel and Boelcskei. Operators with bandlimited symbols have been used to model doubly dispersive communication channels with slowly-time-varying impulse response. The results in this paper are rooted in work by Bello and Kailath in the 1960s.Comment: Submitted to IEEE Transactions on Information Theor

Rethinking Bivens: Legitimacy and Constitutional Adjudication

The Supreme Court\u27s decision in Bivens v. Six Unknown Named Agents of the Federal Bureau of Narcotics provides an uncertain framework for the enforcement of constitutional rights against the federal government. Rather than recognizing a federal common law right of action for use in every case, the Court views itself as devising actions on a case-by-case basis in light of a range of factors. Critics on all sides question the Court\u27s approach, doubting either its power to fashion federal common law or the tendency of its case-by-case analysis to create gaps in constitutional enforcement. Particularly when compared with actions under section 1983—the statutory predicate for constitutional tort claims against state actors—the Bivens action has a hit or miss quality that may reflect lingering doubts about the legitimacy of the Court\u27s role. This Essay argues that the Court should abandon its case-by-case approach in favor of routine recognition of Bivens claims. In 1974 and more clearly in the Westfall Act of 1988, Congress adopted amendments to the Federal Tort Claims Act that assume the availability of suits against federal officers for violations of the Constitution. Congress\u27s decision to ratify and preserve the Bivens action provides a legislative foundation for such claims that answers longstanding questions of legitimacy. After tracing the history of the Westfall Act, the Essay explores the doctrinal implications of the proposed switch to a routinely available Bivens action. Rather than advocating a dramatic break with the past, the Essay proposes to harmonize cases in the Bivens line with certain doctrines that shape the availability of remedies under section 1983. The resulting body of law will provide a more coherent Bivens framework and will ensure that constitutional rights apply with equal force to the interactions between individuals and officials at all levels of our federal governmen

Eine künstliche Intelligenz für das Kartenspiel Tichu

Tichu ist ein Kartenspiel, bei dem klassische Suchalgorithmen aufgrund der Unkenntnis der Verteilung der Karten nicht effizient angewendet werden können. In dieser Arbeit wird eine künstliche Intelligenz vorgestellt, die trotz dieser Schwierigkeit stark spielt und alle Entscheidungen in kurzer Zeit trifft. Dies wird mit einem einfachen Suchalgorithmus und einer komplexen Bewertungsfunktion erreicht, wobei der Bewertungsfunktion insbesondere ein Modell der Initiative einer Aktion zugrunde liegt. Die mit diesem Ansatz erzielte Spielstärke der künstlichen Intelligenz ist mit der Spielstärke durchschnittlicher menschlicher Spieler vergleichbar. Es zeigt sich, dass mittels komplexer, hinter der Bewertungsfunktion stehender Modelle auf einen Suchalgorithmus mit hoher Suchtiefe bei Tichu verzichtet werden kann

Zeitreihenanalyse auf dünnen Gittern

Zeitreihen sind Mengen von zeitlich geordneten Beobachtungen und fallen bei nahezu allen messbaren Daten an. In dieser Arbeit wird das Vorhersageproblem für Zeitreihen untersucht, für das viele praktische Anwendungen existieren, darunter die Vorhersage von Börsendaten. Für die Untersuchung von Zeitreihen können Gitter-basierte Ansätze verwendet werden. Bei diesen treten jedoch bei hohen Problemdimensionen unpraktikabel große Rechenzeiten auf. In dieser Arbeit wird eine Methode zur Zeitreihenanalyse mit dünnen Gittern vorgestellt, die es erlaubt, Lösungen für Probleme mit höherer Dimensionalität zu berechnen. Die durchgeführten Experimente zeigen dabei, dass für einige Datensätze Vorhersagen mit sehr hoher Qualität berechnet werden. Gleichzeitig ist die benötigte Rechenzeit für viele zeitkritische Anwendungen bereits ausreichend. Um das Anwendungsspektrum der Methode weiter zu vergrößern, werden Optimierungen vorgestellt, mit denen die benötigte Rechenzeit weiter verringert wird

The Scalability-Efficiency/Maintainability-Portability Trade-off in Simulation Software Engineering: Examples and a Preliminary Systematic Literature Review

Large-scale simulations play a central role in science and the industry. Several challenges occur when building simulation software, because simulations require complex software developed in a dynamic construction process. That is why simulation software engineering (SSE) is emerging lately as a research focus. The dichotomous trade-off between scalability and efficiency (SE) on the one hand and maintainability and portability (MP) on the other hand is one of the core challenges. We report on the SE/MP trade-off in the context of an ongoing systematic literature review (SLR). After characterizing the issue of the SE/MP trade-off using two examples from our own research, we (1) review the 33 identified articles that assess the trade-off, (2) summarize the proposed solutions for the trade-off, and (3) discuss the findings for SSE and future work. Overall, we see evidence for the SE/MP trade-off and first solution approaches. However, a strong empirical foundation has yet to be established; general quantitative metrics and methods supporting software developers in addressing the trade-off have to be developed. We foresee considerable future work in SSE across scientific communities.Comment: 9 pages, 2 figures. Accepted for presentation at the Fourth International Workshop on Software Engineering for High Performance Computing in Computational Science and Engineering (SEHPCCSE 2016