On the structure of Gröbner bases for graph coloring ideals

In this thesis, we look at a well-known connection between the graph coloring problem and the solvability of certain systems of polynomial equations. In particular, we examine the connection between the structure of a graph and the structure of the Gröbner bases of the graph’s coloring ideal. From a theoretical viewpoint, we show some properties of such Gröbner bases, and we develop a polynomial-time algorithm to compute a Gröbner basis for chordal graphs. From the experimental side, we state results about specific Gröbner bases and about the Gröbner fan for a variety of graph families. Moreover, some heuristics and techniques are explored that reduce the computational complexity. The relevance of heuristic methods is justified by a section about expected intrinsic hardness of Gröbner basis computations

Gr\"obner Bases and Nullstellens\"atze for Graph-Coloring Ideals

We revisit a well-known family of polynomial ideals encoding the problem of graph-$k$-colorability. Our paper describes how the inherent combinatorial structure of the ideals implies several interesting algebraic properties. Specifically, we provide lower bounds on the difficulty of computing Gr\"obner bases and Nullstellensatz certificates for the coloring ideals of general graphs. For chordal graphs, however, we explicitly describe a Gr\"obner basis for the coloring ideal, and provide a polynomial-time algorithm.Comment: 16 page

Tunable coupling of transmission-line microwave resonators mediated by an rf SQUID

10 pags., 5 figs.We realize tunable coupling between two superconducting transmission line resonators. The coupling is mediated by a non-hysteretic rf SQUID acting as a flux-tunable mutual inductance between the resonators. We present a spectroscopic characterization of the device. In particular, we observe couplings g/2π ranging between –320 MHz and 37 MHz. In the case of g 0, the microwave power cross transmission between the two resonators is reduced by almost four orders of magnitude as compared to the case where the coupling is switched on.The authors acknowledge support from the German Research Foundation through SFB 631 and FE 1564/1-1; the EU projects CCQED, PROMISCE and SCALEQIT; the doctorate program ExQM of the Elite Network of Bavaria; the Spanish MINECO projects FIS2012-33022, FIS2012-36673-C03-02, and FIS2015-69983-P; the CAM Research Network QUITEMAD+; the Basque Government IT472-10 and UPV/EHU UFI 11/55

Toward a self-learning governance loop for competitive multi-attribute MAS

Competitive Multi-Agent Systems (MAS) are inherently hard to control due to agent autonomy and strategic behavior, which is particularly problematic when there are system-level objectives to be achieved or specific environmental states to be avoided.Existing methods mostly assume specific knowledge about agent preferences, utilities and strategies, neglecting the fact that actions are not always directly linked to genuine agent preferences, but can also reflect anticipated competitor behavior, be a concession to a superior adversary or simply be intended to mislead other agents. This assumption both reduces applicability to real-world systems and opens room for manipulation.We therefore propose a new governance approach for Multi-Attribute MAS which relies exclusively on publicly observable actions and transitions, and uses the acquired knowledge to purposefully restrict action spaces, thereby achieving the system's objectives while preserving a high level of autonomy for the agents

Collaboration as an emergent property of self-organizing software systems

Given an open, dynamically adaptive software system whose components are agents with their respective interests, goals and objectives, this PhD project will develop a methodology to allow the components to establish collaboration without the governance of a central control unit, but rather as an emergent function of the system itself. The interaction of the components relies on different layers of abstraction, providing a generic communication protocol as well as semantic integration and overarching rules (‘laws of nature’). The work focuses on modeling and analyzing the top layer of this framework: An emergent Governance Layer which allows the components to strategically interact with each other, aggregates individual preferences, and has the ability to reconcile interests and to lead to collaborative actions in a meaningful way

Achieving emergent governance in competitive multi-agent systems

Our PhD research is concerned with the task of achieving cooperation in a system of competitive agents which cannot be explicitly controlled. To this end, it examines the problem from the system’s point of view, without restricting the agents’ behavior or requiring specific knowledge about their decision-making. The governance of the MAS will be achieved via a dynamically adaptive governing policy based on a set of rules, which leaves full autonomy to the individual agents, but reacts to their actions via suitable changes of the environment. The mechanism is designed to lead to system-level cooperation while only assuming that the agents follow their own self-interested motives

Achieving emergent governance in competitive multi-agent systems

Our PhD research is concerned with the task of achieving cooperation in a system of competitive agents which cannot be explicitly controlled. To this end, it examines the problem from the system’s point of view, without restricting the agents’ behavior or requiring specific knowledge about their decision-making. The governance of the MAS will be achieved via a dynamically adaptive governing policy based on a set of rules, which leaves full autonomy to the individual agents, but reacts to their actions via suitable changes of the environment. The mechanism is designed to lead to system-level cooperation while only assuming that the agents follow their own self-interested motives