311 research outputs found
Non-Koszulness of operads and positivity of Poincaré series
We prove that the operad of mock partially associative -ary algebras is not Koszul, as conjectured by the second and the third author in 2009, and utilise Zeilberger’s algorithm for hypergeometric summation to demonstrate that non-Koszulness of that operad for n = 8 cannot be established by hunting for negative coefficients in the inverse of its Poincaré series
Helmintiaaside esinemine Tartu piirkonna lastepäevakodude lastel ja seda mõjutavad tegurid
https://www.ester.ee/record=b1294681*es
Coadjoint Orbits of Lie Algebras and Cartan Class
We study the coadjoint orbits of a Lie algebra in terms of Cartan class. In fact, the tangent space to a coadjoint orbit O(α) at the point α corresponds to the characteristic space associated to the left invariant form α and its dimension is the even part of the Cartan class of α. We apply this remark to determine Lie algebras such that all the nontrivial orbits (nonreduced to a point) have the same dimension, in particular when this dimension is 2 or 4. We determine also the Lie algebras of dimension 2n or 2n+1 having an orbit of dimension 2n
Global alignment of protein-protein interaction networks by graph matching methods
Aligning protein-protein interaction (PPI) networks of different species has
drawn a considerable interest recently. This problem is important to
investigate evolutionary conserved pathways or protein complexes across
species, and to help in the identification of functional orthologs through the
detection of conserved interactions. It is however a difficult combinatorial
problem, for which only heuristic methods have been proposed so far. We
reformulate the PPI alignment as a graph matching problem, and investigate how
state-of-the-art graph matching algorithms can be used for that purpose. We
differentiate between two alignment problems, depending on whether strict
constraints on protein matches are given, based on sequence similarity, or
whether the goal is instead to find an optimal compromise between sequence
similarity and interaction conservation in the alignment. We propose new
methods for both cases, and assess their performance on the alignment of the
yeast and fly PPI networks. The new methods consistently outperform
state-of-the-art algorithms, retrieving in particular 78% more conserved
interactions than IsoRank for a given level of sequence similarity.
Availability:http://cbio.ensmp.fr/proj/graphm\_ppi/, additional data and codes
are available upon request. Contact: [email protected]: Preprint versio
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Soft topographic map for clustering and classification of bacteria
In this work a new method for clustering and building a
topographic representation of a bacteria taxonomy is presented. The method is based on the analysis of stable parts of the genome, the so-called “housekeeping genes”. The proposed method generates topographic maps of the bacteria taxonomy, where relations among different
type strains can be visually inspected and verified. Two well known DNA alignement algorithms are applied to the genomic sequences. Topographic maps are optimized to represent the similarity among the sequences according to their evolutionary distances. The experimental analysis is carried out on 147 type strains of the Gammaprotebacteria
class by means of the 16S rRNA housekeeping gene. Complete sequences of the gene have been retrieved from the NCBI public database. In the experimental tests the maps show clusters of homologous type strains and present some singular cases potentially due to incorrect classification
or erroneous annotations in the database
The partially alternating ternary sum in an associative dialgebra
The alternating ternary sum in an associative algebra, , gives rise to the partially alternating ternary sum in an
associative dialgebra with products and by making the
argument the center of each term: . We use computer algebra to determine the polynomial identities in
degree satisfied by this new trilinear operation. In degrees 3 and 5 we
obtain and ; these identities define a new variety of partially alternating ternary
algebras. We show that there is a 49-dimensional space of multilinear
identities in degree 7, and we find equivalent nonlinear identities. We use the
representation theory of the symmetric group to show that there are no new
identities in degree 9.Comment: 14 page
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