A General Transfer-Function Approach to Noise Filtering in Open-Loop Quantum Control

We present a general transfer-function approach to noise filtering in open-loop Hamiltonian engineering protocols for open quantum systems. We show how to identify a computationally tractable set of fundamental filter functions, out of which arbitrary transfer filter functions may be assembled up to arbitrary high order in principle. Besides avoiding the infinite recursive hierarchy of filter functions that arises in general control scenarios, this fundamental filter-functions set suffices to characterize the error suppression capabilities of the control protocol in both the time and frequency domain. We prove that the resulting notion of filtering order reveals conceptually distinct, albeit complementary, features of the controlled dynamics as compared to the order of error cancellation, traditionally defined in the Magnus sense. Examples and implications are discussed.Comment: Paper plus supplementary material. 10 pages, 1 figure. Unnumbered equation between 2 and 3 corrected. Results are unchange

Lieb-Robinson bounds, Arveson spectrum and Haag-Ruelle scattering theory for gapped quantum spin systems

We consider translation invariant gapped quantum spin systems satisfying the Lieb-Robinson bound and containing single-particle states in a ground state representation. Following the Haag-Ruelle approach from relativistic quantum field theory, we construct states describing collisions of several particles, and define the corresponding $S$-matrix. We also obtain some general restrictions on the shape of the energy-momentum spectrum. For the purpose of our analysis we adapt the concepts of almost local observables and energy-momentum transfer (or Arveson spectrum) from relativistic QFT to the lattice setting. The Lieb-Robinson bound, which is the crucial substitute of strict locality from relativistic QFT, underlies all our constructions. Our results hold, in particular, in the Ising model in strong transverse magnetic fields

Convergence and monotonicity of the hormone levels in a hormone-based content delivery system

The practical significance of bio-inspired, self-organising methods is rapidly increasing due to their robustness, adaptability and capability of handling complex tasks in a dynamically changing environment. Our aim is to examine an artificial hormone system that was introduced in order to deliver multimedia content in dynamic networks. The artificial hormone algorithm proved to be an efficient approach to solve the problem during the experimental evaluations. In this paper we focus on the theoretical foundation of its goodness. We show that the hormone levels converge to a limit at each node in the typical cases. We form a series of theorems on convergence with different conditions which are built on each other by starting with a specific base case and then we consider more general, practically relevant cases. The theorems are proved by exploiting the analogy between the Markov chains and the artificial hormone system. We examine spatial and temporal monotonicity of the hormone levels as well and give sufficient conditions on monotonic increase

05431 Abstracts Collection -- Deduction and Applications

From 23.10.05 to 28.10.05, the Dagstuhl Seminar 05431 ``Deduction and Applications\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Evidence and explanation in Cicero's On Divination

In this paper, I examine Cicero’s oft-neglected De Divinatione, a dialogue investigating the legitimacy of the practice of divination. First, I offer a novel analysis of the main arguments for divination given by Quintus, highlighting the fact that he employs two logically distinct argument forms. Next, I turn to the first of the main arguments against divination given by Marcus. Here I show, with the help of modern probabilistic tools, that Marcus’ skeptical response is far from the decisive, proto-naturalistic assault on superstition that it is sometimes portrayed to be. Then, I offer an extended analysis of the second of the main arguments against divination given by Marcus. Inspired by Marcus’ second main argument, I formulate, explicate, and defend a substantive principle of scientific methodology that I call the “Ciceronian Causal-Nomological Requirement” (CCR). Roughly, this principle states that causal knowledge is essential for relying on correlations in predictive inference. Although I go on to argue that Marcus’ application of the CCR in his debate with Quintus is dialectically inadequate, I conclude that De Divinatione deserves its place in Cicero’s philosophical corpus, and that ultimately, its significance for the history and philosophy of science ought to be recognized

Fermat, Leibniz, Euler, and the gang: The true history of the concepts of limit and shadow

Fermat, Leibniz, Euler, and Cauchy all used one or another form of approximate equality, or the idea of discarding "negligible" terms, so as to obtain a correct analytic answer. Their inferential moves find suitable proxies in the context of modern theories of infinitesimals, and specifically the concept of shadow. We give an application to decreasing rearrangements of real functions.Comment: 35 pages, 2 figures, to appear in Notices of the American Mathematical Society 61 (2014), no.

Adaptable processes

We propose the concept of adaptable processes as a way of overcoming the limitations that process calculi have for describing patterns of dynamic process evolution. Such patterns rely on direct ways of controlling the behavior and location of running processes, and so they are at the heart of the adaptation capabilities present in many modern concurrent systems. Adaptable processes have a location and are sensible to actions of dynamic update at runtime; this allows to express a wide range of evolvability patterns for concurrent processes. We introduce a core calculus of adaptable processes and propose two verification problems for them: bounded and eventual adaptation. While the former ensures that the number of consecutive erroneous states that can be traversed during a computation is bound by some given number k, the latter ensures that if the system enters into a state with errors then a state without errors will be eventually reached. We study the (un)decidability of these two problems in several variants of the calculus, which result from considering dynamic and static topologies of adaptable processes as well as different evolvability patterns. Rather than a specification language, our calculus intends to be a basis for investigating the fundamental properties of evolvable processes and for developing richer languages with evolvability capabilities