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Polynomials as Generators of Minimal Clones

Hajime Machida, Michael Pinsker
2007 Proceedings - International Symposium on Multiple-Value Logic  
A minimal clone is an atom of the lattice of clones. A minimal function is a function which generates a minimal clone.  ...  Starting from binary minimal functions over GF(3), we generalize some of them and obtain binary minimal functions, as polynomials, over GF(k) for any prime k ≥ 3.  ...  In Appendix, we see that there is only one binary monomial on E 3 , x y 2 , which is minimal.  ... 
doi:10.1109/ismvl.2007.41 dblp:conf/ismvl/MachidaP07 fatcat:urdlh5ux4bfbbm6y4xdpay2ybu

Some Observations on Minimal Clones

H. Machida, M. Pinsker
2006 36th International Symposium on Multiple-Valued Logic (ISMVL'06)  
A minimal clone is an atom of the lattice of clones.  ...  Then, we discuss some properties of binary minimal linear polynomials and of binary minimal monomials.  ...  Szczepara [Szc 95] found all minimal clones which are generated by binary functions. However, the determination of all minimal clones in L 4 is not yet settled.  ... 
doi:10.1109/ismvl.2006.39 dblp:conf/ismvl/MachidaP06 fatcat:3om2w724uvdrxdfrcssyghrtvm

Almost associative operations generating a minimal clone [article]

Tamás Waldhauser
2011 arXiv   pre-print
Characterizations of "almost associative" binary operations generating a minimal clone are given for two interpretations of the term "almost associative".  ...  One of them uses the associative spectrum, the other one uses the index of nonassociativity to measure how far an operation is from being associative.  ...  One of the three types where the description of minimal clones is not complete yet is the binary case.  ... 
arXiv:1102.2127v1 fatcat:3xzw7pg2hbhkbml64p3i7zxx44

A survey of clones on infinite sets

Martin Goldstern, Michael Pinsker
2008 Algebra Universalis  
We summarize what we know about the clone lattice on an infinite set and formulate what we consider the most important open problems.  ...  Does there exist a minimal clone with an infinite number of binary operations?  ...  Therefore, finding all minimal operations on X includes finding all minimal operations on all finite sets, and the following seems very ambitious: Problem L. Describe the minimal clones of Cl(X).  ... 
doi:10.1007/s00012-008-2100-2 fatcat:5rrcgbxlhrh3tk3iky3umhis3q

A survey of clones on infinite sets [article]

Martin Goldstern, Michael Pinsker
2008 arXiv   pre-print
Ordering all clones on X by inclusion, one obtains a complete algebraic lattice, called the clone lattice.  ...  A clone on a set X is a set of finitary operations on X which contains all projections and which is moreover closed under functional composition.  ...  Does there exist a minimal clone with an infinite number of binary operations?  ... 
arXiv:math/0701030v2 fatcat:wdh3qqci25bezokpjqyjv5tsmu

Minimal clones with few majority operations [article]

Tamás Waldhauser
2011 arXiv   pre-print
We characterize minimal clones generated by a majority function containing at most seven ternary operations.  ...  Ga luszka which states that if a binary minimal clone contains finitely many nontrivial binary operations all of which are commutative, then there is just one nontrivial binary operation in the clone  ...  Let us note that the binary case is studied in [LP] , where binary minimal clones with at most seven binary operations are determined.  ... 
arXiv:1102.2128v1 fatcat:qefxyljvgvduvgkulmuliizh4m

A Simple PCR Cloning Step to Utilize a Binary Vector for Identification and Characterization of Enhancer Element in Plant Promoters

Dipnarayan Saha, Vajinder Kumar, Sripad Ramachandran Bhat, Ramamurthy Srinivasan
2012 Agricultural Research  
We describe here a simple one-step PCR-based cloning strategy to introduce a 35S CaMV minimal promoter in a binary plant transformation vector pBI101, and utilize the unique features to identify a lateral  ...  Hence, we need to utilize the existing binary plant transformation vectors, such as pBI101, through tedious and timeconsuming restriction enzyme-based cloning steps.  ...  Cloning of Minimal Promoter in pBI101 A binary plant transformation vector pBI-101 (*12.2 kb) [14] consisting of a multiple cloning site (MCS), a promoter-less reporter gene uidA within the T-DNA sequence  ... 
doi:10.1007/s40003-012-0021-y fatcat:fdmkjyalbrdezgqnovpbkbn7yu

Page 4768 of Mathematical Reviews Vol. , Issue 85k [page]

1985 Mathematical Reviews  
A minimal clone on a set S is a clone that contains no nontrivial subclone, that is, it is an atom in the lattice of clones on S. Any minimal clone C is generated by any nontrivial operation in C.  ...  The author explicitly describes all minimal clones on S = {0, 1, 2}. There are 84 such clones and each is a conjugate of exactly one of 24 representative clones.  ... 

Counting Mal'tsev clones on small sets

Andrei A. Bulatov, Paweł M. Idziak
2003 Discrete Mathematics  
Algebra Comput. 9 (1999) 213) has shown that there are only 14 Mal'tsev polynomial clones on a 3 element set and constructed inÿnitely many such clones on a 4 element set.  ...  Here we improve this result by showing that there are, in fact, only countably many Mal'tsev polynomial clones on a 4 element set. A description of all such clones is included.  ...  Claim 10 should be clear, as adding a binary operation m on A to the clone W !  ... 
doi:10.1016/s0012-365x(02)00681-7 fatcat:od4kxfnrvbdmpmnolxdcpxuew4

Monomial clones over $$\mathbb {F}_q$$ F q

Gábor Horváth, Kamilla Kátai-Urbán, Csaba Szabó
2019 Algebra Universalis  
The description of the poset of clones generated by a single binary idempotent monomial over Fq is given by purely number theoretic means. Mathematics Subject Classification. 08A40, 11A07.  ...  In [5] all binary polynomials are given over the field F 3 that generate a minimal clone. A polynomial will be called a minimal polynomial if it generates a minimal clone.  ...  It does not seem feasible to continue along idempotent clones on several variables before understanding all binary monomial clones. Problem 1. Find all binary monomial clones over F q .  ... 
doi:10.1007/s00012-019-0591-7 fatcat:bigpnesivzasliafnyjmtdhwa4

In vitro reconstruction of the Aspergillus (= Emericella) nidulans genome

R. A. Prade, J. Griffith, K. Kochut, J. Arnold, W. E. Timberlake
1997 Proceedings of the National Academy of Sciences of the United States of America  
The physical map is the result of a two-way ordering process, in which clones and probes were ordered simultaneously on a binary DNA͞DNA hybridization matrix.  ...  Compression by elimination of redundant clones resulted in a minimal map, which is a chromosome walk.  ...  Compression of physical maps by elimination of redundant clones results in a minimal map that retains all of the probes and one overlapping clone linking a pair of probes.  ... 
doi:10.1073/pnas.94.26.14564 pmid:9405653 pmcid:PMC25056 fatcat:qqtebjmdozcnpgbadsdb4amg7q

Optimally cloned binary coherent states

C. R. Müller, G. Leuchs, Ch. Marquardt, U. L. Andersen
2017 Physical Review A  
We capitalize this formal connection to analyse the properties of optimally cloned binary coherent states.  ...  Qubits are associated with a two-dimensional Hilbert space and can be illustrated on the Bloch sphere.  ...  Extending previous results for the optimal cloning of binary qubit states to the domain of binary coherent states, we derive the density matrices and the Wigner functions of optimally cloned binary coherent  ... 
doi:10.1103/physreva.96.042311 fatcat:5k2wjeqv65expn53wqsvxzpr3m

Designing Minimal Sorting Networks using a Bio-inspired Technique

Blanca Cecilia López Ramírez, Nareli Cruz Cortés
2015 Journal of Computacion y Sistemas  
SN with a minimal number of comparators results in an optimal manner to sort data; it is a classical NP-hard problem studied for more than 50 years.  ...  In other words, best antibodies receive a higher quantity of clones, meanwhile worst ones create only a small quantity of clones.  ...  That is, each s ∈ S should sort 1 any binary representation of the numbers from 0 to 2 n − 1 (see Theorem Zero-One in Section 2). For that sake the Algorithm 3 is proposed.  ... 
doi:10.13053/cys-18-4-1959 fatcat:2bc3wikjx5foxev3czaew5f4ke

A fast random cost algorithm for physical mapping

Y. Wang, R. A. Prade, J. Griffith, W. E. Timberlake, J. Arnold
1994 Proceedings of the National Academy of Sciences of the United States of America  
Ordering clones from a genomic library into physical maps of whole chromosomes presents a central computational/statIcal problem in genetics.  ...  We compare the ability ofthe random cost algorithm and simulated annealing (7) to minimize the pairwise total linking distance on 20 simulated data sets and 1 real binary hybridization matrix for chromosome  ...  To assess map reliability, first a physical map is assembled as in Fig. 1 from the original binary clone/probe hybridization matrix X by minimizing the pairwise total linking distance with the random  ... 
doi:10.1073/pnas.91.23.11094 pmid:7972016 pmcid:PMC45173 fatcat:miitsycwpjbszl6wadavqfhfxm

Minimal clones generated by majority operations

Tam�s Waldhauser
2000 Algebra Universalis  
The minimal majority functions of the four-element set are determined. 2000 Mathematics Subject Classification. 08A40.  ...  In [4] Post described all clones on a two-element set, in [1] B. Csákány determined the minimal clones of a three-element set. For the four-element case binary minimal clones were described by B.  ...  Conservative minimal majority and binary functions were determined on any finite set by B. Csákány in [2] .  ... 
doi:10.1007/s000120050167 fatcat:ez4adgsxjjht5j6hxir2gvtqh4
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