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141
Suboptimal Schemes for Atmospheric Data Assimilation Based on the Kalman Filter
, 1994
"... This work is directed toward approximating the evolution of forecast error covariances for data assimilation. We study the performance of different algorithms based on simplification of the standard Kalman filter (KF). These are suboptimal schemes (SOS's) when compared to the KF, which is optim ..."
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Cited by 47 (8 self)
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This work is directed toward approximating the evolution of forecast error covariances for data assimilation. We study the performance of different algorithms based on simplification of the standard Kalman filter (KF). These are suboptimal schemes (SOS's) when compared to the KF, which is optimal for linear problems with known statistics. The SOS's considered here are several versions of optimal interpolation (OI), a scheme for height error variance advection, and a simplified KF in which the full height error covariance is advected. In order to employ a methodology for exact comparison among these schemes we maintain a linear environment, choosing a betaplane shallow water model linearized about a constant zonal flow for the testbed dynamics. Our results show that constructing dynamicallybalanced forecast error covariances, rather than using conventional geostrophicallybalanced ones, is essential for successful performance of any SOS. A posteriori initialization of SOS's to comp...
Quantum walk based search algorithms
 In Proceedings of the 5th Conference on Theory and Applications of Models of Computation
, 2008
"... Abstract. In this survey paper we give an intuitive treatment of the discrete time quantization of classical Markov chains. Grover search and the quantum walk based search algorithms of Ambainis, Szegedy and Magniez et al. will be stated as quantum analogues of classical search procedures. We presen ..."
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Cited by 38 (1 self)
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Abstract. In this survey paper we give an intuitive treatment of the discrete time quantization of classical Markov chains. Grover search and the quantum walk based search algorithms of Ambainis, Szegedy and Magniez et al. will be stated as quantum analogues of classical search procedures. We present a rather detailed description of a somewhat simplified version of the MNRS algorithm. Finally, in the query complexity model, we show how quantum walks can be applied to the following
Gates accept concurrent behavior
 In Proc. 34th Ann. IEEE Symp. on Foundations of Comp. Sci
, 1993
"... We represent concurrent processes as Boolean propositions or gates, cast in the role of acceptors of concurrent behavior. This properly extends other mainstream representations of concurrent behavior such as event structures, yet is defined more simply. It admits an intrinsic notion of duality that ..."
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Cited by 37 (16 self)
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We represent concurrent processes as Boolean propositions or gates, cast in the role of acceptors of concurrent behavior. This properly extends other mainstream representations of concurrent behavior such as event structures, yet is defined more simply. It admits an intrinsic notion of duality that permits processes to be viewed as either schedules or automata. Its algebraic structure is essentially that of linear logic, with its morphisms being consequencepreserving renamings of propositions, and with its operations forming the core of a natural concurrent programming language. 1
Hamiltonian Square Roots of SkewHamiltonian Matrices
, 1997
"... We present a constructive existence proof that every real skewHamiltonian matrix W has a real Hamiltonian square root. The key step in this construction shows how one may bring any such W into a real quasiJordan canonical form via symplectic similarity. We show further that every W has infinitely ..."
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Cited by 26 (9 self)
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We present a constructive existence proof that every real skewHamiltonian matrix W has a real Hamiltonian square root. The key step in this construction shows how one may bring any such W into a real quasiJordan canonical form via symplectic similarity. We show further that every W has infinitely many real Hamiltonian square roots, and give a lower bound on the dimension of the set of all such square roots. AMS subject classification. 65F15 1 Introduction Any matrix X such that X 2 = A is said to be a square root of the matrix A. For general complex matrices A 2 C n\Thetan there exists a welldeveloped although somewhat complicated theory of matrix square roots [7, 14], and a number of algorithms for their effective computation [2, 11]. Similarly for the theory and computation of real square roots for real matrices [10, 14]. By contrast structured square root problems, where both the matrix A and its square root X are required to have some extra (not necessarily the same) spe...
A Discrete Invitation to Quantum Filtering and Feedback Control
, 2009
"... The engineering and control of devices at the quantum mechanical level—such as those consisting of small numbers of atoms and photons—is a delicate business. The fundamental uncertainty that is inherently present at this scale manifests itself in the unavoidable presence of noise, making this a nov ..."
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Cited by 24 (4 self)
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The engineering and control of devices at the quantum mechanical level—such as those consisting of small numbers of atoms and photons—is a delicate business. The fundamental uncertainty that is inherently present at this scale manifests itself in the unavoidable presence of noise, making this a novel field of application for stochastic estimation and control theory. In this expository paper we demonstrate estimation and feedback control of quantum mechanical systems in what is essentially a noncommutative version of the binomial model that is popular in mathematical finance. The model is extremely rich and allows a full development of the theory while remaining completely within the setting of finitedimensional Hilbert spaces (thus avoiding the technical complications of the continuous theory). We introduce discretized models of an atom in interaction with the electromagnetic field, obtain filtering equations for photon counting and homodyne detection, and solve a stochastic control problem using dynamic programming and Lyapunov function methods.
A Rosetta stone for quantum mechanics with an introduction to quantum computation
, 2002
"... Abstract. The purpose of these lecture notes is to provide readers, who have some mathematical background but little or no exposure to quantum mechanics and quantum computation, with enough material to begin reading ..."
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Cited by 23 (10 self)
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Abstract. The purpose of these lecture notes is to provide readers, who have some mathematical background but little or no exposure to quantum mechanics and quantum computation, with enough material to begin reading
1992] Generic bifurcation of Hamiltonian vector fields with symmetry, Nonlinearity 5
, 1992
"... One of the goals of this paper is to describe explicitly the generic movement of eigenvalues through a onetoone resonance in a (linearized) Hamiltonian system. We classify this movement, and hence answer the question of when the collisions are “dangerous ” in the sense of Krein by using a combina ..."
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Cited by 21 (9 self)
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One of the goals of this paper is to describe explicitly the generic movement of eigenvalues through a onetoone resonance in a (linearized) Hamiltonian system. We classify this movement, and hence answer the question of when the collisions are “dangerous ” in the sense of Krein by using a combination of group theory and definiteness properties of the associated quadratic Hamiltonian. For ∗ Research is supported by the Deutsche Forschungsgemeinschaft and by NSF/DARPA DMS
The Unified Learning Paradigm: A Foundation for AI
 In: Artificial Intelligence and Neural Networks: Steps Toward Principled
, 1994
"... Introduction As one of us has already repeatedly stressed ([10], [12], [13], [15]), we believe, together with Hermann von Helmholtz [23], that the central and the most pressing issue confronting cognitive science and artificial intelligence is the development of a satisfactory unified inductive lea ..."
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Cited by 15 (3 self)
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Introduction As one of us has already repeatedly stressed ([10], [12], [13], [15]), we believe, together with Hermann von Helmholtz [23], that the central and the most pressing issue confronting cognitive science and artificial intelligence is the development of a satisfactory unified inductive learning model (see also [5], [34], [43]). Unfortunately, this issue was not perceived to be the central issue by the three leading (and founding) schools of AI, which had a very negative effect on the development of AI up to now. In particular, due only to the difference between the formal models used originally in some areas of AI and pattern recognition, AI had severed practically all ties with pattern recognition, which was very counterproductive to the development of both areas and particularly to AI. 1 With the recent rise of connectionism, this situation has begun to change, which is reflected in the content of the recent AI textbooks ([39], [4
Transition and cancellation in concurrency and branching time
 Mathematical Structures in Computer Science 13(4) (2003
, 2002
"... We review the conceptual development of (true) concurrency and branching time starting from Petri nets and proceeding via Mazurkiewicz traces, pomsets, bisimulation, and event structures up to higher dimensional automata (HDAs), whose acyclic case may be identified with triadic event structures and ..."
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Cited by 14 (1 self)
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We review the conceptual development of (true) concurrency and branching time starting from Petri nets and proceeding via Mazurkiewicz traces, pomsets, bisimulation, and event structures up to higher dimensional automata (HDAs), whose acyclic case may be identified with triadic event structures and triadic Chu spaces. Acyclic HDAs may be understood as the extension of Boolean logic with a third truth value expressing transition. We prove the necessity of such a third value under mild assumptions about the nature of observable events, and show that the expansion of any complete Boolean basis L to L with a third literal �a expressing a = forms an expressively complete basis for the representation of acyclic HDAs. The main contribution is a new event state × of cancellation, sibling to, serving to distinguish a(b + c) from ab + ac while simplifying the extensional definitions of termination �A and sequence AB. We show that every HDAX (acyclic HDA with ×) is representable in the expansion of L to L × with a fourth literal �a expressing a = ×.
Noncontextuality in multipartite entanglement
 J. Phys. A: Math. Gen
, 2005
"... Abstract. We discuss several multiport interferometric preparation and measurement configurations and show that they are noncontextual. Generalizations to the n particle case are discussed. ..."
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Cited by 11 (11 self)
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Abstract. We discuss several multiport interferometric preparation and measurement configurations and show that they are noncontextual. Generalizations to the n particle case are discussed.