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Canonical representation genetic programming

2009
*
Proceedings of the first ACM/SIGEVO Summit on Genetic and Evolutionary Computation - GEC '09
*

When the search space consists

doi:10.1145/1543834.1543914
dblp:conf/gecco/WoodwardB09
fatcat:ljidrgczpnhyziaxq47dvsaa44
*of**canonical**representations*it is called a*canonical*search space, and when Genetic Programming is applied to this search space, it is called*Canonical**Representation*Genetic ... It is argued that, if a search space can be constructed where only unique*representations**of*a function are permitted, then this will be more successful than employing multiple*representations*. ... Primitive Set {+, −, * , /} ∪ {1} Given {+, −, * , /} ∪ {1}, we can generate*rational**numbers*.*Rational**numbers*, as we have seen, have a*number**of**canonical**representations*. ...##
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Free actions of finite groups on rational homology 3-spheres

2000
*
Topology and its Applications
*

We show that any finite group can act freely on a

doi:10.1016/s0166-8641(98)00116-3
fatcat:nxmw33g25rag7mjh4tps4cyx6m
*rational*homology 3-sphere. ... The*number**of*times a*simple*module appears (up to isomorphism) in a decomposition*of*M into*simple*submodules is independent*of*the decomposition [2, p. 440 ]. ... If we consider the decompositions*of*both sides into*simple*submodules and compare the*number**of*times each*simple*module appears, we deduce that ker(i * ) ∼ = Im(i * ) ∼ = (L G ) k . ...##
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Page 4001 of Mathematical Reviews Vol. , Issue 2000f
[page]

2000
*
Mathematical Reviews
*

This paper presents the character tables for the irreducible

*rational**representations**of*SL(2, p”) for all values*of*the prime p and exponent n. ...*of*V®”", so the problem*of*calculating the Kazhdan-Lusztig polynomials is a special case*of*the problem*of*calculating the*canonical*basis in a tensor power*of*the funda- mental*representation**of*U,sl ...##
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LCF: A Lexicographic Binary Representation of the Rationals
[chapter]

1996
*
J.UCS The Journal of Universal Computer Science
*

in the

doi:10.1007/978-3-642-80350-5_41
fatcat:3bok4cu4mrb7tnfxwn23g72moa
*representation**of*any reasonably sized*rational**number*. ... Worst case*representation*-induced precision loss for any real*number*by a xed length*representable**number**of*the system is shown to be at most 19*of*bit word length, with no precision loss whatsoever induced ... Acknowledgements This paper reports some previously unpublished results presented as part*of*an invited talk entitled "*Rational**Number*Systems and Arithmetic", given by the rst author at the symposium ...##
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A McKay Correspondence in Positive Characteristic
[article]

2022
*
arXiv
*
pre-print

In dimension 2, we establish simultaneous resolutions

arXiv:2207.06286v1
fatcat:k56czlrhtbd73j2zllygl6nc5u
*of*singularities*of*these*canonical*lifts via G-Hilbert schemes. ... We discuss linearly reductive quotient singularities and*canonical*lifts over the ring*of*Witt vectors. ... In this case, the*number**of*isomorphism classes*of**simple**representations*is equal to the*number**of*conjugacy classes. ...##
###
Euler and algebraic geometry

2007
*
Bulletin of the American Mathematical Society
*

In section 1, we reach a major open problem

doi:10.1090/s0273-0979-07-01178-0
fatcat:faenzkrkv5fnthovcirdagixga
*of*algebraic geometry: which*representations**of*the fundamental group are summands*of*the cohomology*of*some family*of*algebraic varieties? ... from*rational*curves, and not only in a negative way. ... in all the*rational**numbers*t. ...##
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Dibaryons as canonically quantized biskyrmions
[article]

2000
*
arXiv
*
pre-print

The ground state

arXiv:nucl-th/0011063v1
fatcat:n6y7k5c2cjeszhcplvxj53i5iq
*of*the skyrmion with baryon*number*2 is axially symmetric, and is well approximated by a*simple**rational*map, which represents a direct generalization*of*Skyrme's hedgehog ansatz for the ... If the Lagrangian density is*canonically*quantized this configuration may support excitations that lie close and possible below the threshold for pion decay, and therefore describe dibaryons. ... Research supported in part by the Academy*of*Finland by grants No. 43982 and 44903. ...##
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Page 2054 of Mathematical Reviews Vol. , Issue 90D
[page]

1990
*
Mathematical Reviews
*

(S @ k)) be the

*canonical*/-adic*representation*(/ a prime*number*). Then the*canonical*map NS(S @, k) @z Q; — H?(S @, k)(1)4°'™) is an isomorphism (NS = Néron-Severi group). ... Surfaces*of*type K 3 over*number*fields, and /-adic*representations*. (Russian) Izv. Akad. Nauk SSSR Ser. Mat. 52 (1988), no. 6, 1252-1271, 1328; translation in Math. ...##
###
Page 2802 of Mathematical Reviews Vol. , Issue 97E
[page]

1997
*
Mathematical Reviews
*

The

*canonical*local height is given in terms*of*a local integral*of*a*simple*polynomial function over the complete curve. ... The paper under review provides and discusses bounds for the*number**of*Q-*rational*elliptic curves with good reduction outside*of*a finite set S*of**rational*primes. ...##
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Representation, simplification and display of fractional powers of rational numbers in computer algebra
[article]

2013
*
arXiv
*
pre-print

Simplification

arXiv:1302.2169v1
fatcat:gzvoeosmyvd4pftng32dq4oj6i
*of*fractional powers*of*positive*rational**numbers*and*of*sums, products and powers*of*such*numbers*is taught in beginning algebra. ... Since they are such a restricted subset*of*algebraic*numbers*, it might seem that good simplification*of*them must already be implemented in all widely used computer algebra systems. ... One way to make it*canonical*is: Whenever an input or a tentative result is a*rational**number*times a fractional power*of*a*rational**number*: 1. ...##
###
On Laguerre Series

1940
*
Proceedings of the National Academy of Sciences of the United States of America
*

*of*like elements in the

*canonical*(basis)

*representation*

*of*integers

*of*the ring. 4. ... The passage from

*simple*to compound systems in the ring

*of*

*rational*integers depends only on the existence

*of*a G. C. D. for

*rational*integers. ...

##
###
Compound Multiplicative Diophantine Systems

1940
*
Proceedings of the National Academy of Sciences of the United States of America
*

*of*like elements in the

*canonical*(basis)

*representation*

*of*integers

*of*the ring. 4. ... The passage from

*simple*to compound systems in the ring

*of*

*rational*integers depends only on the existence

*of*a G. C. D. for

*rational*integers. ...

##
###
The rational invariants of the tame quivers

1980
*
Inventiones Mathematicae
*

Let n, be the

doi:10.1007/bf01390253
fatcat:rr4io2k46nakvke3a7richlhri
*number**of**simple*regular*representations*in ~,. Let V = V~|174 ~ be a direct sum decomposition with V i indecomposable. ... We denote by n t the*number**of**simple*regular*representations*in ~t-We will also have to consider the special quiver A=o~ (which has an oriented cycle). ... Using again the multiplicativity*of*F on extensions, one sees immediately, that for any regular*representation*((p~.,,) we find a*representation*(~.,) in ...##
###
Page 665 of American Mathematical Society. Bulletin of the American Mathematical Society Vol. 50, Issue 9
[page]

1944
*
American Mathematical Society. Bulletin of the American Mathematical Society
*

Let S[n, g(x) ]=>02",e(3)/p*, where the summation is over

*numbers*prime to p, and p is a*rational*prime. ... The question*of*the invariance*of*the*representation*is discussed in the case (1). ...##
###
REPRESENTATIONS OF THE COMMUTATION RELATIONS

1954
*
Proceedings of the National Academy of Sciences of the United States of America
*

The

doi:10.1073/pnas.40.7.622
pmid:16589534
pmcid:PMC528006
fatcat:7fo2vl75zfcs7k3plbk4twlwcm
*canonical**representation*is the only one for which the*number**of*particles operator 2 ak*ak exists. Letting M be concentrated on a Ar, we obtain a translated*canonical**representation*. ... Let A denote the set*of*"*rational*" sequences, i.e., those with only a finite*number**of*components different from zero. ...
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