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16
Constraint Satisfaction Problems with Countable Homogeneous Templates
"... Allowing templates with infinite domains greatly expands the range of problems that can be formulated as a nonuniform constraint satisfaction problem. It turns out that many CSPs over infinite templates can be formulated with templates that are ωcategorical. We survey examples of such problems in ..."
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Cited by 13 (7 self)
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Allowing templates with infinite domains greatly expands the range of problems that can be formulated as a nonuniform constraint satisfaction problem. It turns out that many CSPs over infinite templates can be formulated with templates that are ωcategorical. We survey examples of such problems in temporal and spatial reasoning, infinitedimensional algebra, acyclic colorings in graph theory, artificial intelligence, phylogenetic reconstruction in computational biology, and tree descriptions in computational linguistics. We then give an introduction to the universalalgebraic approach to infinitedomain constraint satisfaction, and discuss how cores, polymorphism clones, and pseudovarieties can be used to study the computational complexity of CSPs with ωcategorical templates. The theoretical results will be illustrated by examples from the mentioned application areas. We close with a series of open problems and promising directions of future research.
Differential arcs and regular types in differential fields
 J. REINE ANGEW. MATH
, 2007
"... We introduce differential arc spaces in analogy to the algebraic arc spaces and show that a differential variety in characteristic zero is determined by its arcs at a point. Using differential arcs, we show that if (K, +, ×, δ1,..., δn) is a differentially closed field of characteristic zero with n ..."
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Cited by 8 (3 self)
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We introduce differential arc spaces in analogy to the algebraic arc spaces and show that a differential variety in characteristic zero is determined by its arcs at a point. Using differential arcs, we show that if (K, +, ×, δ1,..., δn) is a differentially closed field of characteristic zero with n commuting derivations and p ∈ S(K) is a regular type over K, then either p is locally modular or there is a definable subgroup G ≤ (K, +) of the additive group having a regular generic type that is nonorthogonal to p.
ISOMETRY GROUPS OF SEPARABLE METRIC SPACES
"... Abstract. We show that every locally compact Polish group is isomorphic to the isometry group of a proper separable metric space. This answers a question of Gao and Kechris. We also analyze the natural action of the isometry group of a separable ultrametric space on the space. This leads us to a str ..."
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Cited by 1 (1 self)
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Abstract. We show that every locally compact Polish group is isomorphic to the isometry group of a proper separable metric space. This answers a question of Gao and Kechris. We also analyze the natural action of the isometry group of a separable ultrametric space on the space. This leads us to a structure theorem representing an arbitrary separable ultrametric space as a bundle with an ultrametric base and with ultrahomogeneous fibers which are invariant under the action of the isometry group. 1.
Definable sets in algebraically closed valued fields: stable domination and independence
, 2005
"... It is shown that if K is an algebraically closed valued field with valuation ring R, then Th(K) has elimination of imaginaries if sorts are added whose elements are certain cosets in K n of certain definable Rsubmodules of K n (for all n ≥ 1). The proof involves the development of a theory of indep ..."
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Cited by 1 (1 self)
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It is shown that if K is an algebraically closed valued field with valuation ring R, then Th(K) has elimination of imaginaries if sorts are added whose elements are certain cosets in K n of certain definable Rsubmodules of K n (for all n ≥ 1). The proof involves the development of a theory of independence for unary types, which play the role of 1types, followed by an analysis of germs of definable functions from unary sets to the sorts. Contents.
On HighLevel LowLevel Programming
, 2002
"... The current solution for ecient highlevel parallel programming in the industry is to use directives to the compiler. However these directives pose two problems: rst, they are often designed in an ad hoc manner and their subtleties are less easy to understand than the rest of the language; second, ..."
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The current solution for ecient highlevel parallel programming in the industry is to use directives to the compiler. However these directives pose two problems: rst, they are often designed in an ad hoc manner and their subtleties are less easy to understand than the rest of the language; second, the degree of stringency of the directives is not xed, so that evaluating the eciency of the directives he writes is not easy for the programmer. This article proposes a methodology for addressing these issues. The data mapping directives of the language High Performance Fortran are used as an example; in particular, it is shown how the use of formal semantics can help clarify and structure the issues.
BULLETIN (New Series) OF THE
 Bulletin of the American Mathematical Society
, 2006
"... In this paper, we describe some central mathematical problems in medical imaging. The subject has been undergoing rapid changes driven by better hardware and software. Much of the software is based on novel methods utilizing geometric partial di#erential equations in conjunction with standard si ..."
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In this paper, we describe some central mathematical problems in medical imaging. The subject has been undergoing rapid changes driven by better hardware and software. Much of the software is based on novel methods utilizing geometric partial di#erential equations in conjunction with standard signal/image processing techniques as well as computer graphics facilitating man/machine interactions. As part of this enterprise, researchers have been trying to base biomedical engineering principles on rigorous mathematical foundations for the development of software methods to be integrated into complete therapy delivery systems. These systems support the more effective delivery of many imageguided procedures such as radiation therapy, biopsy, and minimally invasive surgery. We will show how mathematics may impact some of the main problems in this area including image enhancement, registration, and segmentation.
LEARNING THROUGH THEORIES
"... This paper builds a decisiontheoretic framework to examine the relationship between language and knowledge. A decision maker describes the world through theories. A theory consists of universal propositions called patterns, and it is formulated in some language. I look at two characteristics of a s ..."
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This paper builds a decisiontheoretic framework to examine the relationship between language and knowledge. A decision maker describes the world through theories. A theory consists of universal propositions called patterns, and it is formulated in some language. I look at two characteristics of a successful theory. A theory is informative if it allows agents to precisely predict outcomes of some process. A theory is brief if it consists of finitely many patterns. The main result of the paper identifies languages for which there is no tradeoff between both characteristics: Any informative theory logically implies a theory that is informative as well as brief. I illustrate the main result on specific problems of reasoning under uncertainty: recommendation problems, binary preferences of a customer, or a stylized example of a chemical research.
Stable embeddedness and NIP
, 2010
"... We give some sufficient conditions for a predicate P in a complete theory T to be “stably embedded”. Let P be P with its “induced ∅definable structure”. The conditions are that P (or rather its theory) is “rosy”, P has NIP in T and that P is stably 1embedded in T. This generalizes a recent result ..."
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We give some sufficient conditions for a predicate P in a complete theory T to be “stably embedded”. Let P be P with its “induced ∅definable structure”. The conditions are that P (or rather its theory) is “rosy”, P has NIP in T and that P is stably 1embedded in T. This generalizes a recent result of Hasson and Onshuus [6] which deals with the case where P is ominimal in T. Our proofs make use of the theory of strict nonforking and weight in NIP theories ([3], [10]). 1 Introduction and
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"... Definable sets in algebraically closed valued fields: elimination of imaginaries. (English summary) J. Reine Angew. Math. 597 (2006), 175–236. In this fundamental paper, the authors shed light on elimination of imaginaries in algebraically closed valued fields. The importance of imaginaries for a be ..."
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Definable sets in algebraically closed valued fields: elimination of imaginaries. (English summary) J. Reine Angew. Math. 597 (2006), 175–236. In this fundamental paper, the authors shed light on elimination of imaginaries in algebraically closed valued fields. The importance of imaginaries for a better understanding of the model theory of any structure cannot be underestimated since they deal with structures interpretable in the given one. Already the techniques of this paper have been applied to other valued fields [T. Mellor, Ann. Pure Appl. Logic 139 (2006), no. 13, 230–279; MR2206257 (2006k:03064)]. An imaginary in a firstorder structure is an equivalence class of a definable equivalence relation. Let T be a multisorted complete firstorder theory; then T is said to have elimination of imaginaries if for any model M of T, any sorts M1,..., Mk in M, any ∅definable set S ⊂ M1 × · · · × Mk and any ∅definable equivalence relation E on S, there is an ∅definable function f from S into a product of sorts such that for any a, b ∈ S we have Eab iff f(a) = f(b). In a way, f(a) acts as a code for the Eclass of a. An oversimplified illustration of this phenomenon is M = C, S = C2 � {(0, 0)}, E(a1, a2)(b1, b2) iff (a1, a2), (b1, b2) define the same line through (0, 0), and f(a1, a2) =
NonStandard Models of Arithmetic: a Philosophical and Historical perspective MSc Thesis (Afstudeerscriptie)
, 2010
"... 1 Descriptive use of logic and Intended models 1 1.1 Standard models of arithmetic.......................... 1 1.2 Axiomatics and Formal theories......................... 3 1.3 Hintikka and the two uses of logic in mathematics.............. 5 ..."
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1 Descriptive use of logic and Intended models 1 1.1 Standard models of arithmetic.......................... 1 1.2 Axiomatics and Formal theories......................... 3 1.3 Hintikka and the two uses of logic in mathematics.............. 5