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Polynomials as Generators of Minimal Clones

2007
*
Proceedings - International Symposium on Multiple-Value Logic
*

A

doi:10.1109/ismvl.2007.41
dblp:conf/ismvl/MachidaP07
fatcat:urdlh5ux4bfbbm6y4xdpay2ybu
*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*. ...##
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Some Observations on Minimal Clones

2006
*
36th International Symposium on Multiple-Valued Logic (ISMVL'06)
*

A

doi:10.1109/ismvl.2006.39
dblp:conf/ismvl/MachidaP06
fatcat:3om2w724uvdrxdfrcssyghrtvm
*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. ...##
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Almost associative operations generating a minimal clone
[article]

2011
*
arXiv
*
pre-print

Characterizations of "almost associative"

arXiv:1102.2127v1
fatcat:3xzw7pg2hbhkbml64p3i7zxx44
*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. ...##
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A survey of clones on infinite sets

2008
*
Algebra Universalis
*

We summarize what we know about the

doi:10.1007/s00012-008-2100-2
fatcat:5rrcgbxlhrh3tk3iky3umhis3q
*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). ...##
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A survey of clones on infinite sets
[article]

2008
*
arXiv
*
pre-print

Ordering all

arXiv:math/0701030v2
fatcat:wdh3qqci25bezokpjqyjv5tsmu
*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? ...##
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Minimal clones with few majority operations
[article]

2011
*
arXiv
*
pre-print

We characterize

arXiv:1102.2128v1
fatcat:qefxyljvgvduvgkulmuliizh4m
*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. ...##
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A Simple PCR Cloning Step to Utilize a Binary Vector for Identification and Characterization of Enhancer Element in Plant Promoters

2012
*
Agricultural Research
*

We describe here a simple

doi:10.1007/s40003-012-0021-y
fatcat:fdmkjyalbrdezgqnovpbkbn7yu
*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 ...##
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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*. ...##
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Counting Mal'tsev clones on small sets

2003
*
Discrete Mathematics
*

Algebra Comput. 9 (1999) 213) has shown that there are only 14 Mal'tsev polynomial

doi:10.1016/s0012-365x(02)00681-7
fatcat:od4kxfnrvbdmpmnolxdcpxuew4
*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 ! ...##
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Monomial clones over $$\mathbb {F}_q$$ F q

2019
*
Algebra Universalis
*

The description of the poset of

doi:10.1007/s00012-019-0591-7
fatcat:bigpnesivzasliafnyjmtdhwa4
*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 . ...##
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In vitro reconstruction of the Aspergillus (= Emericella) nidulans genome

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

doi:10.1073/pnas.94.26.14564
pmid:9405653
pmcid:PMC25056
fatcat:qqtebjmdozcnpgbadsdb4amg7q
*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. ...##
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Optimally cloned binary coherent states

2017
*
Physical Review A
*

We capitalize this formal connection to analyse the properties of optimally

doi:10.1103/physreva.96.042311
fatcat:5k2wjeqv65expn53wqsvxzpr3m
*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 ...##
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Designing Minimal Sorting Networks using a Bio-inspired Technique

2015
*
Journal of Computacion y Sistemas
*

SN with a

doi:10.13053/cys-18-4-1959
fatcat:2bc3wikjx5foxev3czaew5f4ke
*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. ...##
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A fast random cost algorithm for physical mapping

1994
*
Proceedings of the National Academy of Sciences of the United States of America
*

Ordering

doi:10.1073/pnas.91.23.11094
pmid:7972016
pmcid:PMC45173
fatcat:miitsycwpjbszl6wadavqfhfxm
*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 ...##
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Minimal clones generated by majority operations

2000
*
Algebra Universalis
*

The

doi:10.1007/s000120050167
fatcat:ez4adgsxjjht5j6hxir2gvtqh4
*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] . ...
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