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New results in linear filtering and prediction theory
 TRANS. ASME, SER. D, J. BASIC ENG
, 1961
"... A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary sta ..."
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statistics. The variance equation is closely related to the Hamiltonian (canonical) differential equations of the calculus of variations. Analytic solutions are available in some cases. The significance of the variance equation is illustrated by examples which duplicate, simplify, or extend earlier results
Infinite Gammoids: Minors and Duality
, 2015
"... This sequel to Afzali Borujeni et. al. (2015) considers minors and duals of infinite gammoids. We prove that the class of gammoids defined by digraphs not containing a certain type of substructure, called an outgoing comb, is minorclosed. Also, we prove that finiterank minors of gammoids are gammo ..."
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This sequel to Afzali Borujeni et. al. (2015) considers minors and duals of infinite gammoids. We prove that the class of gammoids defined by digraphs not containing a certain type of substructure, called an outgoing comb, is minorclosed. Also, we prove that finiterank minors of gammoids
Structure in minorclosed classes of matroids
 Surveys in Combinatorics 2013, London Math. Soc. Lecture Notes 409
, 2013
"... This paper gives an informal introduction to structure theory for minorclosed classes of matroids representable over a fixed finite field. The early sections describe some historical results that give evidence that welldefined structure exists for members of such classes. In later sections we desc ..."
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This paper gives an informal introduction to structure theory for minorclosed classes of matroids representable over a fixed finite field. The early sections describe some historical results that give evidence that welldefined structure exists for members of such classes. In later sections we
A powerdomain construction
 SIAM J. OF COMPUTING
, 1976
"... We develop a powerdomain construction, [.], which is analogous to the powerset construction and also fits in with the usual sum, product and exponentiation constructions on domains. The desire for such a construction arises when considering programming languages with nondeterministic features or p ..."
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Cited by 234 (15 self)
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in an elementwise fashion. In the general case they are given the coarsest ordering consistent, in an appropriate sense, with the ordering given in the discrete case. We then find a restricted class of algebraic inductive partial orders which is closed under [. as well as the sum, product and exponentiation
Classification of Kleinian groups
, 1974
"... We present here a complete classification of those Kleinian groups which have an invariant region of discontinuity and which, in their action on hyperbolic 3space, have a finitesided fundamental polyhedron. This classification is complete in the same sense that finitelygenerated Fuchsian groups o ..."
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Cited by 208 (5 self)
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(defined using quasiconformal mappings) of any one group in the class; this deformation space can be parametrized as a complex manifold. Our results can also be regarded as a classification of all uniformizations of any finite Riemann surface (i.e., a closed Riemann surface from which a finite number
Asymptotic properties of some minorclosed classes of graphs
, 2013
"... Abstract. Let A be a minorclosed class of labelled graphs, and let Gn be a random graph sampled uniformly from the set of nvertex graphs of A. When n is large, what is the probability that Gn is connected? How many components does it have? How large is its biggest component? Thanks to the work of ..."
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Abstract. Let A be a minorclosed class of labelled graphs, and let Gn be a random graph sampled uniformly from the set of nvertex graphs of A. When n is large, what is the probability that Gn is connected? How many components does it have? How large is its biggest component? Thanks to the work
Some Existentially Closed Graphs
"... We give a characterization of the existentially closed models and pregeneric models of the theory of planar graphs and graphs without K 3;3  minor. We show that there are 2 @0 countable existentially closed models in these classes and that all are elementary equivalent, though there are no model ..."
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We give a characterization of the existentially closed models and pregeneric models of the theory of planar graphs and graphs without K 3;3  minor. We show that there are 2 @0 countable existentially closed models in these classes and that all are elementary equivalent, though there are no model
The Nielsen realization problem
 Bull. Amer. Math. Soc
, 1980
"... If M is a closed, oriented 2manifold of genus g> 2, then it admits many hyperbolic metrics (metrics of constant curvature 1). In special cases such a metric possesses a nontrivial group of symmetries, of isometries to itself. The group of isometries of a closed hyperbolic manifold is always fin ..."
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finite and the only isometry isotopic to the identity is the identity itself. Thus a group of symmetries of a hyperbolic surface determines an isomorphic finite subgroup of the group of isotopy classes of diffeomorphisms of M. The purpose of this paper is to announce a positive solution to the Nielsen
Duality for Some Categories of Coalgebras
 Algebra Universalis
, 2001
"... A contravariant duality is constructed between the category of coalgebras of a given signature, and a category of Boolean algebras with operators, including modal operators corresponding to state transitions in coalgebras, and distinguished elements abstracting the sets of states defined by observab ..."
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Cited by 3 (1 self)
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by observable equations. This duality is used to give a new proof that a class of coalgebras is definable by Boolean combinations of observable equations if it is closed under disjoint unions, domains and images of coalgebraic morphisms, and ultrafilter enlargements. The proof reduces the problem to a direct
Logical limit laws for minorclosed classes of graphs
, 2014
"... Let G be an addable, minorclosed class of graphs. We prove that the zeroone law holds in monadic secondorder logic (MSO) for the random graph drawn uniformly at random from all connected graphs in G on n vertices, and the convergence law in MSO holds if we draw uniformly at random from all graphs ..."
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Let G be an addable, minorclosed class of graphs. We prove that the zeroone law holds in monadic secondorder logic (MSO) for the random graph drawn uniformly at random from all connected graphs in G on n vertices, and the convergence law in MSO holds if we draw uniformly at random from all
Results 1  10
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1,116