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Quantum gravity and minimum length,”
- International Journal of Modern Physics A,
, 1995
"... Abstract The existence of a fundamental scale, a lower bound to any output of a position measurement, seems to be a model-independent feature of quantum gravity. In fact, different approaches to this theory lead to this result. The key ingredients for the appearance of this minimum length are quant ..."
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Cited by 44 (0 self)
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Abstract The existence of a fundamental scale, a lower bound to any output of a position measurement, seems to be a model-independent feature of quantum gravity. In fact, different approaches to this theory lead to this result. The key ingredients for the appearance of this minimum length
Segmentation by Minimum Length Encoding
- 10th ICPR, NJ
, 1990
"... A digitized waveform is approximated by segments whose total description length is minimal for a given error bonnd. This approximation can be computed efficiently, and can be used for segmentation. The method is also shown to be applicable for segmentation and edge detection in gray level and range ..."
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Cited by 3 (0 self)
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A digitized waveform is approximated by segments whose total description length is minimal for a given error bonnd. This approximation can be computed efficiently, and can be used for segmentation. The method is also shown to be applicable for segmentation and edge detection in gray level
ON RANDOM MINIMUM LENGTH SPANNING TREES
- COMBINATORICA 9 (4) (1989) 363---374
, 1989
"... We extend and strengthen the result hat, in the complete graph K, with independent random edge-lengths uniformly distributed on [0, I], the expected length of the minimum spanning tree tends to s as n ~--. In particular, ifK. is replaced by the complete bipartite graph Kn. ~ then there is a correspo ..."
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Cited by 12 (1 self)
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We extend and strengthen the result hat, in the complete graph K, with independent random edge-lengths uniformly distributed on [0, I], the expected length of the minimum spanning tree tends to s as n ~--. In particular, ifK. is replaced by the complete bipartite graph Kn. ~ then there is a
Minimum Length from First Principles
, 2008
"... We show that no device or gedanken experiment is capable of measuring a distance less than the Planck length. By ”measuring a distance less than the Planck length” we mean, technically, resolve the eigenvalues of the position operator to within that accuracy. The only assumptions in our argument are ..."
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We show that no device or gedanken experiment is capable of measuring a distance less than the Planck length. By ”measuring a distance less than the Planck length” we mean, technically, resolve the eigenvalues of the position operator to within that accuracy. The only assumptions in our argument
Minimum length cutoff in inflation and uniqueness of the action,” Phys
- Rev. D 71 (2005) 023503 [arXiv:astro-ph/0410139]. – 14 – E. Komatsu et al. [WMAP Collaboration], “Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations:Cosmological Interpretation,” arXiv:0803.0547 [astro-ph
"... According to most inflationary models, fluctuations that are of cosmological size today started out much smaller than any plausible cutoff length such as the string or Planck lengths. It has been shown that this could open an experimental window for testing models of the short-scale structure of spa ..."
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Cited by 8 (0 self)
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minimum length uncertainty principle. We find that the usual strategy for determining the initial conditions faces an unexpected difficulty because it involves reformulating the action and discarding a boundary term: we find that actions that normally differ merely by a boundary term can differ
Counting words of minimum length in an automorphic orbit, in preparation
"... Abstract. Let u be a cyclic word in a free group Fn of finite rank n that has the minimum length over all cyclic words in its automorphic orbit, and let N(u) be the cardinality of the set {v: |v | = |u | and v = φ(u) for some φ ∈ AutFn}. In this paper, we prove that N(u) is bounded by a polynomial ..."
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Cited by 9 (2 self)
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Abstract. Let u be a cyclic word in a free group Fn of finite rank n that has the minimum length over all cyclic words in its automorphic orbit, and let N(u) be the cardinality of the set {v: |v | = |u | and v = φ(u) for some φ ∈ AutFn}. In this paper, we prove that N(u) is bounded by a polynomial
What is the Minimum Length of a Non-Extendable Lace?
"... A family fC 1 ; : : : ; C n g of pairwise distinct, non-overlapping, congruent circles in the plane form a lace provided C i touches C i+1 for all i = 1; : : : ; n \Gamma 1. If, additionally, C n touches C 1 , the lace is named a loop. A lace (loop) fC 1 ; : : : ; C n g is called extendable if it ..."
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if it is properly contained in another lace (respectively, loop). In the paper various problems and results on minimum lengths of non-extendable laces and loops are discussed. Key words. Finite packing, circles, plane. AMS subject classification. 52C15 1 Main Problems and Results According to [1], a family of n
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