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Additive partitioning
, 2011
"... This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or sel ..."
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This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier’s archiving and manuscript policies are encouraged to visit:
ON ADDITIVE PARTITIONS OF INTEGERS
, 1978
"... Given a linear recurrence integer sequence U={u,,}, U1 =U1+ u,,, na1, u,=1, uz>ul, we prove that the set of positive integers can be partitioned uniquely into two disjoint subsets such that the sum of any two distinct members from any one set can never be in U. We give a graph theoretic interpr ..."
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Cited by 8 (0 self)
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Given a linear recurrence integer sequence U={u,,}, U1 =U1+ u,,, na1, u,=1, uz>ul, we prove that the set of positive integers can be partitioned uniquely into two disjoint subsets such that the sum of any two distinct members from any one set can never be in U. We give a graph theoretic
Additive Partitions and Continued Fractions
"... . A set S of positive integers is avoidable if there exists a partition of the positive integers into two disjoint sets such that no two distinct integers from the same set sum to an element of S. Much previous work has focused on proving the avoidability of very special sets of integers. We vastly ..."
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Cited by 6 (0 self)
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. A set S of positive integers is avoidable if there exists a partition of the positive integers into two disjoint sets such that no two distinct integers from the same set sum to an element of S. Much previous work has focused on proving the avoidability of very special sets of integers. We vastly
Continued fractions and unique additive partitions
 Ramanujan J
, 1999
"... Abstract. A partition of the positive integers into sets A and B avoids a set S ⊂ N if no two distinct elements in the same part have a sum in S. If the partition is unique, S is uniquely avoidable. For any irrational α> 1, Chow and Long constructed a partition which avoids the numerators of all ..."
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Cited by 4 (0 self)
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Abstract. A partition of the positive integers into sets A and B avoids a set S ⊂ N if no two distinct elements in the same part have a sum in S. If the partition is unique, S is uniquely avoidable. For any irrational α> 1, Chow and Long constructed a partition which avoids the numerators of all
Cluster Ensembles  A Knowledge Reuse Framework for Combining Multiple Partitions
 Journal of Machine Learning Research
, 2002
"... This paper introduces the problem of combining multiple partitionings of a set of objects into a single consolidated clustering without accessing the features or algorithms that determined these partitionings. We first identify several application scenarios for the resultant 'knowledge reuse&ap ..."
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Cited by 603 (20 self)
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This paper introduces the problem of combining multiple partitionings of a set of objects into a single consolidated clustering without accessing the features or algorithms that determined these partitionings. We first identify several application scenarios for the resultant 'knowledge reuse
Additive Partition of the Positive Integers and Generalized Fibonacci Representations
, 1984
"... ..."
The additive partitioning of macroinvertebrate diversity in tropical reservoirs
, 2013
"... Abstract. Understanding the ways in which diversity changes across spatial scales is important for the conservation of biodiversity. The objectives of the present study were (1) to characterise the diversity of aquatic macroinvertebrates in three Brazilian tropical reservoirs and (2) to determine ho ..."
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how the organisms were distributed at different spatial scales, by using a diversity partitioning approach. We compared the diversitypartition results with the null hypothesis that the macroinvertebrate community was uniform across all spatial scales in the study. We expected that differences
Multivariate adaptive regression splines
 The Annals of Statistics
, 1991
"... A new method is presented for flexible regression modeling of high dimensional data. The model takes the form of an expansion in product spline basis functions, where the number of basis functions as well as the parameters associated with each one (product degree and knot locations) are automaticall ..."
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Cited by 700 (2 self)
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) are automatically determined by the data. This procedure is motivated by the recursive partitioning approach to regression and shares its attractive properties. Unlike recursive partitioning, however, this method produces continuous models with continuous derivatives. It has more power and flexibility to model
Fast Folding and Comparison of RNA Secondary Structures (The Vienna RNA Package)
"... Computer codes for computation and comparison of RNA secondary structures, the Vienna RNA package, are presented, that are based on dynamic programming algorithms and aim at predictions of structures with minimum free energies as well as at computations of the equilibrium partition functions and bas ..."
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Cited by 809 (117 self)
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Computer codes for computation and comparison of RNA secondary structures, the Vienna RNA package, are presented, that are based on dynamic programming algorithms and aim at predictions of structures with minimum free energies as well as at computations of the equilibrium partition functions
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