Coherent feedback that beats all measurement-based feedback protocols

We show that when the speed of control is bounded, there is a widely applicable minimal-time control problem for which a coherent feedback protocol is optimal, and is faster than all measurement-based feedback protocols, where the latter are defined in a strict sense. The superiority of the coherent protocol is due to the fact that it can exploit a geodesic path in Hilbert space, a path that measurement-based protocols cannot follow.Comment: 4 pages, revtex4-1, 1 png figure; v2: new (now optimal) coherent protocol, new autho

Study of ranking irregularities when evaluating alternatives by using some ELECTRE methods and a proposed new MCDM method based on regret and rejoicing

Multi-criteria decision-making (MCDM) is one of the most widely used decision methodologies in the sciences, business, and engineering worlds. MCDM methods aim at improving the quality of decisions by making the process more explicit, rational, and efficient. One intriguing problem is that oftentimes different methods may yield different answers to the same decision problem. Thus, the issue of evaluating the relative performance of different MCDM methods is raised. One evaluating procedure is to examine the stability of an MCDM method’s mathematical process by checking the validity of its proposed rankings. The ELECTRE II and III methods are two well-known MCDM methods and widely accepted in solving MCDM problems in civil and environmental engineering. However these two methods have never been studied in detail for the validity of their proposed rankings. Thus, the first aim of this thesis is to examine if these two methods suffer of any type of ranking irregularities and analyze the reasons of the phenomenon. As the research results in this thesis revealed, the ELECTRE II and III methods do allow some types of ranking irregularities to happen. For instance, these two methods might change the indication of the best alternative for a given MCDM problem when one of the non-optimal alternatives was replaced by a worse one. The two methods were also evaluated in terms of two other ranking tests and they failed them as well. Two real-life cases are described to demonstrate the occurrence of rank reversals. Then reasons behind the phenomenon are analyzed. Next an empirical study and some real-life case studies were executed and discussed. The results of these examinations show that the rates of those ranking irregularities were rather significant in both the simulated decision problems and the real-life cases studied in this research. However, some recent studies showed that rank reversals could also happen because people may reverse their preferences due to some emotional feelings, like regret and rejoicing. Thus this thesis proposes a new MCDM method which is based on regret and rejoicing. This new method is expected to satisfy a set of critical conditions

A study of regret and rejoicing and a new MCDM method based on them

Multi-criteria decision-making (MCDM) is one of the most widely used decision methodologies in the sciences, business, and engineering worlds. MCDM methods aim at improving the quality of decisions by making the process more explicit, rational, and efficient. One controversial problem is that some well-known MCDM methods, like the additive AHP methods and the ELECTRE II and III methods, may cause some types of rank reversal problems. Rank reversal means that the ranking between two alternatives might be reversed after some variation occurs to the decision problem, like adding a new alternative, dropping an old alternative or replacing a non-optimal alternative by a worse one etc. Usually such a rank reversal is undesirable for decision-making problems. If a method does allow it to happen, the validity of the method could be questioned. However, some recent studies indicate that rank reversals could also happen because of people’s rational preference reversal which may be caused by their emotional feelings, like regret and rejoicing. Since regret and rejoicing may play a pivotal role in evaluating alternatives in MCDM problems, sometimes the decision maker (DM) may want to anticipate these emotional feelings and consider them in the decision-making process. Most of the regret models in the literature use continuous functions to measure this emotional factor. This dissertation proposes to use an approach based on a linguistic scale and pairwise comparisons to measure a DM’s anticipated regret and rejoicing feelings. The approach is shown to exhibit some key advantages over existing approaches. Next a multiplicative MCDM model is adopted to aggregate the alternatives’ associated regret and rejoicing values with their performance values to get their final priorities and then rank them. A simulated numerical example is used to illustrate the process of the proposed method. Some sensitivity analyses which aim at examining how changes of regret and rejoicing values might affect the ranking results of the decision problems are also developed. Then a fuzzy version of the new method is introduced and illustrated by a numerical example. Finally, some concluding remarks are made. Ranking intransitivity and some other issues about the proposed method are analyzed too

Stabilizing Quantum States by Constructive Design of Open Quantum Dynamics

Based on recent work on the asymptotic behavior of controlled quantum Markovian dynamics, we show that any generic quantum state can be stabilized by devising constructively a simple Lindblad-GKS generator that can achieve global asymptotic stability at the desired state. The applications of such result is demonstrated by designing a direct feedback strategy that achieves global stabilization of a qubit state encoded in a noise-protected subspace.Comment: Revised version with stronger proofs showing uniqueness can be achieved in all cases by using the freedom to the choose diagonal elements of both the Hamiltonian and Lindblad operator, and exploiting the fact that the non-existence of two orthogonal eigenvectors of the Lindblad operator is sufficient but not necessary for global asymptotic stability of the target stat

Rationalizing Irrational Beliefs

In this paper, we re-examine various previous experimental studies of the Centipede Game in the literature. These experiments found that players rarely follow the subgame-perfect equilibrium strategies of the game, and various modifications to the game were proposed to explain the outcomes of the experiments. We here offer yet another modification. Players have a choice of whether or not to believe that their opponents use subgame-perfect equilibrium strategies. We define a `behavioral equilibrium' for this game. This equilibrium concept can reproduce the outcomes of those experiments.centipede games, game theory, experimental economics, behavioral economics