ASCENS: Engineering Autonomic Service-Component Ensembles

Today’s developers often face the demanding task of developing software for ensembles: systems with massive numbers of nodes, operating in open and non-deterministic environments with complex interactions, and the need to dynamically adapt to new requirements, technologies or environmental conditions without redeployment and without interruption of the system’s functionality. Conventional development approaches and languages do not provide adequate support for the problems posed by this challenge. The goal of the ASCENS project is to develop a coherent, integrated set of methods and tools to build software for ensembles. To this end we research foundational issues that arise during the development of these kinds of systems, and we build mathematical models that address them. Based on these theories we design a family of languages for engineering ensembles, formal methods that can handle the size, complexity and adaptivity required by ensembles, and software-development methods that provide guidance for developers. In this paper we provide an overview of several research areas of ASCENS: the SOTA approach to ensemble engineering and the underlying formal model called GEM, formal notions of adaptation and awareness, the SCEL language, quantitative analysis of ensembles, and finally software-engineering methods for ensembles

Optimal Control and Synchronization of Dynamic Ensemble Systems

Ensemble control involves the manipulation of an uncountably infinite collection of structurally identical or similar dynamical systems, which are indexed by a parameter set, by applying a common control without using feedback. This subject is motivated by compelling problems in quantum control, sensorless robotic manipulation, and neural engineering, which involve ensembles of linear, bilinear, or nonlinear oscillating systems, for which analytical control laws are infeasible or absent. The focus of this dissertation is on novel analytical paradigms and constructive control design methods for practical ensemble control problems. The first result is a computational method %based on the singular value decomposition (SVD) for the synthesis of minimum-norm ensemble controls for time-varying linear systems. This method is extended to iterative techniques to accommodate bounds on the control amplitude, and to synthesize ensemble controls for bilinear systems. Example ensemble systems include harmonic oscillators, quantum transport, and quantum spin transfers on the Bloch system. To move towards the control of complex ensembles of nonlinear oscillators, which occur in neuroscience, circadian biology, electrochemistry, and many other fields, ideas from synchronization engineering are incorporated. The focus is placed on the phenomenon of entrainment, which refers to the dynamic synchronization of an oscillating system to a periodic input. Phase coordinate transformation, formal averaging, and the calculus of variations are used to derive minimum energy and minimum mean time controls that entrain ensembles of non-interacting oscillators to a harmonic or subharmonic target frequency. In addition, a novel technique for taking advantage of nonlinearity and heterogeneity to establish desired dynamical structures in collections of inhomogeneous rhythmic systems is derived

“Wave-Packet Reduction” and the quantum character of the actualization of potentia

Werner Heisenberg introduced the notion of quantum potentia in order to accommodate the indeterminism associated with quantum measurement. Potentia captures the capacity of the system to be found to possess a property upon a corresponding sharp measurement in which it is actualized. The specific potentiae of the individual system are represented formally by the complex amplitudes in the measurement bases of the eigenstate in which it is prepared. All predictions for future values of system properties can be made by an experimenter using the probabilities which are the squared moduli of these amplitudes that are the diagonal elements of the density matrix description of the pure ensemble to which the system, so prepared, belongs. Heisenberg considered the change of the ensemble attribution following quantum measurement to be analogous to the classical change in Gibbs’ thermodynamics when measurement of the canonical ensemble enables a microcanonical ensemble description. This analogy, presented by Heisenberg as operating at the epistemic level, is analyzed here. It has led some to claim not only that the change of the state in measurement is classical mechanical, bringing its quantum character into question, but also that Heisenberg held this to be the case. Here, these claims are shown to be incorrect, because the analogy concerns the change of ensemble attribution by the experimenter upon learning the result of the measurement, not the actualization of the potentia responsible for the change of the individual system state which—in Heisenberg’s interpretation of quantum mechanics—is objective in nature and independent of the experimenter’s knowledge

Irreversible photon transfer in an ensemble of Λ\Lambda-type atoms and photon diode

We show that a pair of quantized cavity modes interacting with a spectrally broadened ensemble of Lambda-type atoms is analogous to an ensemble of two level systems coupled to a bosonic reservoir. This provides the possibility for an irreversible photon transfer between photon modes. The density of states as well as the quantum state of the reservoir can be engineered allowing the observation of effects such as the quantum Zeno- and anti-Zeno effect, the destructive interference of decay channels and the decay in a squeezed vacuum. As a particular application we discuss a photon diode, i.e. a device which directs a single photon from anyone of two input ports to a common output port.Comment: 5 pages, 2 figure