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 beta--plane shallow water model linearized about a constant zonal flow for the testbed dynamics. Our results show that constructing dynamically--balanced forecast error covariances, rather than using conventional geostrophically--balanced ones, is essential for successful performance of any SOS. A posteriori initialization of SOS's to comp...

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 consequence-preserving renamings of propositions, and with its operations forming the core of a natural concurrent programming language. 1

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

One of the goals of this paper is to describe explicitly the generic movement of eigenvalues through a one-to-one resonance in a (linearized) Hamiltonian sys-tem. 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-

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 counter-productive 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

We present a constructive existence proof that every real skew-Hamiltonian 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 quasi-Jordan 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 well-developed 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...

Abstract. We discuss several multiport interferometric preparation and measurement configurations and show that they are noncontextual. Generalizations to the n particle case are discussed.

. We present bounds on various quantities of interest regarding the central trajectory of a semi-denite program (SDP), where the bounds are functions of Renegar's condition number C(d) and other naturally-occurring quantities such as the dimensions n and m. The condition number C(d) is dened in terms of the data instance d = (A; b; C) for SDP; it is the inverse of a relative measure of the distance of the data instance to the set of ill-posed data instances, that is, data instances for which arbitrary perturbations would make the corresponding SDP either feasible or infeasible. We provide upper and lower bounds on the solutions along the central trajectory, and upper bounds on changes in solutions and objective function values along the central trajectory when the data instance is perturbed and/or when the path parameter dening the central trajectory is changed. Based on these bounds, we prove that the solutions along the central trajectory grow at most linearly and at a rate prop...

Contexts are maximal collections of co-measurable observables “bundled together ” to form a “quasi-classical mini-universe. ” Different notions of contexts are discussed for classical, quantum and generalized urn–automaton systems. PACS numbers: 02.10.-v,02.50.Cw,02.10.Ud

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 = ×.