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7,306
The axon hillock and the initial segment
 In preparation
, 1968
"... Axon hillocks and initial segments have been recognized and studied in electron micrographs of a wide variety of neurons. In all multipolar neurons the fine structure of the initial segment has the same pattern, whether or not the axon is ensheathed in myelin. The internal structure of the initial s ..."
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Cited by 19 (2 self)
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Axon hillocks and initial segments have been recognized and studied in electron micrographs of a wide variety of neurons. In all multipolar neurons the fine structure of the initial segment has the same pattern, whether or not the axon is ensheathed in myelin. The internal structure of the initial
Lattice initial segments of the hyperdegrees
, 2009
"... We affirm a conjecture of Sacks [1972] by showing that every countable distributive lattice is isomorphic to an initial segment of the hyperdegrees, Dh. In fact, we prove that every sublattice of any hyperarithmetic lattice (and so, in particular, every countable, locally finite lattice) is isomorph ..."
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We affirm a conjecture of Sacks [1972] by showing that every countable distributive lattice is isomorphic to an initial segment of the hyperdegrees, Dh. In fact, we prove that every sublattice of any hyperarithmetic lattice (and so, in particular, every countable, locally finite lattice
Initial Segments of the Lattice of ... Classes
, 1999
"... The study of the lattice E of computably enumerable sets under inclusion has been one of the central tasks of computability theory since the 1960's. We investigate initial segments of the lattice L of \Pi 0 1 classes (of sets) under inclusion and we compare this lattice with E . It was recent ..."
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The study of the lattice E of computably enumerable sets under inclusion has been one of the central tasks of computability theory since the 1960's. We investigate initial segments of the lattice L of \Pi 0 1 classes (of sets) under inclusion and we compare this lattice with E
On Initial Segments of Computable Linear Orders
, 1997
"... We show there is a computable linear order with a # 0 2 initial segment that is not isomorphic to any computable linear order. ..."
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Cited by 9 (2 self)
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We show there is a computable linear order with a # 0 2 initial segment that is not isomorphic to any computable linear order.
RESOLUTE SEQUENCES IN INITIAL SEGMENT COMPLEXITY
"... Abstract. We study infinite sequences whose initial segment complexity is invariant under effective insertions of blocks of zeros inbetween their digits. Surprisingly, such resolute sequences may have nontrivial initial segment complexity. In fact, we show that they occur in many well known classes ..."
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Abstract. We study infinite sequences whose initial segment complexity is invariant under effective insertions of blocks of zeros inbetween their digits. Surprisingly, such resolute sequences may have nontrivial initial segment complexity. In fact, we show that they occur in many well known
Combining Initial Segments of Lists
 ALT
, 2011
"... We propose a new way to build a combined list from K base lists, each containing N items. A combined list consists of top segments of various sizes from each base list so that the total size of all top segments equals N. A sequence of item requests is processed and the goal is to minimize the total ..."
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Cited by 2 (0 self)
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We propose a new way to build a combined list from K base lists, each containing N items. A combined list consists of top segments of various sizes from each base list so that the total size of all top segments equals N. A sequence of item requests is processed and the goal is to minimize the total
Definability of Initial Segments
"... In any nonstandard model of Peano arithmetic, the standard part is not first order definable. But we show that in some model the standard part is definable as the unique solution of a formula ϕ(P), where P is a unary predicate variable. 1 ..."
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In any nonstandard model of Peano arithmetic, the standard part is not first order definable. But we show that in some model the standard part is definable as the unique solution of a formula ϕ(P), where P is a unary predicate variable. 1
On initial segment complexity and degrees of randomness
 Trans. Amer. Math. Soc
"... Abstract. One approach to understanding the fine structure of initial segment complexity was introduced by Downey, Hirschfeldt and LaForte. They define X ≤K Y to mean that (∀n) K(X ↾ n) ≤ K(Y ↾ n) +O(1). The equivalence classes under this relation are the Kdegrees. We prove that if X ⊕ Y is 1rand ..."
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Cited by 38 (8 self)
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Abstract. One approach to understanding the fine structure of initial segment complexity was introduced by Downey, Hirschfeldt and LaForte. They define X ≤K Y to mean that (∀n) K(X ↾ n) ≤ K(Y ↾ n) +O(1). The equivalence classes under this relation are the Kdegrees. We prove that if X ⊕ Y is 1
Region Competition: Unifying Snakes, Region Growing, and Bayes/MDL for Multiband Image Segmentation
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1996
"... We present a novel statistical and variational approach to image segmentation based on a new algorithm named region competition. This algorithm is derived by minimizing a generalized Bayes/MDL criterion using the variational principle. The algorithm is guaranteed to converge to a local minimum and c ..."
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Cited by 774 (20 self)
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We present a novel statistical and variational approach to image segmentation based on a new algorithm named region competition. This algorithm is derived by minimizing a generalized Bayes/MDL criterion using the variational principle. The algorithm is guaranteed to converge to a local minimum
Initial Segment Complexities of Randomness Notions
"... Abstract. Schnorr famously proved that MartinLöfrandomness of a sequence A can be characterised via the complexity of A’s initial segments. Nies, Stephan and Terwijn as well as independently Miller showed that Kolmogorov randomness coincides with MartinLöf randomness relative to the halting pro ..."
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Abstract. Schnorr famously proved that MartinLöfrandomness of a sequence A can be characterised via the complexity of A’s initial segments. Nies, Stephan and Terwijn as well as independently Miller showed that Kolmogorov randomness coincides with MartinLöf randomness relative to the halting
Results 1  10
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7,306