32,577 research outputs found
City Focus: A web-based interactive 2D and 3D GIS application to find the best place in a city, using open data and open source software
City Focus is a webbased
interactive 2D and 3D GIS application to find the best place in a city
to live as well as to pass shorter staying. The user can select among different criteria and decide
their importance by assigning weights to each of them. The application provides thematic maps
displaying insights on the places which better fit the user’s preferences. The resulting map is
computed through map algebra by means of Web Coverage Processing Service WCPS provided
by RASDAMAN Database Management System. Data visualization is mainly based on NASA
Web WorldWind opensource
virtual globe. The app exploits exclusively open data as well as
Free and Open Source Software (FOSS) for its implementation by enabling continuous
improvements while minimizing development costs
TheslN-web algebras and dual canonical bases
In this paper, which is a follow-up to [38], I define and study SIN-web algebras, for any N >= 2. For N = 2 these algebras are isomorphic to Khovanov's [22] arc algebras and for N = 3 they are Morita equivalent to the sl(3)-web algebras which I defined and studied together with Pan and Tubbenhauer [34]. The main result of this paper is that the SIN-web algebras are Morita equivalent to blocks of certain level-N cyclotomic KLR algebras, for which I use the categorified quantum skew Howe duality defined in [38]. Using this Morita equivalence and Brundan and Kleshchev's [4] work on cyclotomic KLR-algebras, I show that there exists an isomorphism between a certain space of SIN-webs and the split Grothendieck group of the corresponding SIN-web algebra, which maps the dual canonical basis elements to the Grothendieck classes of the indecomposable projective modules (with a certain normalization of their grading).info:eu-repo/semantics/publishedVersio
The Robinson-Schensted Correspondence and -web Bases
We study natural bases for two constructions of the irreducible
representation of the symmetric group corresponding to : the {\em
reduced web} basis associated to Kuperberg's combinatorial description of the
spider category; and the {\em left cell basis} for the left cell construction
of Kazhdan and Lusztig. In the case of , the spider category is the
Temperley-Lieb category; reduced webs correspond to planar matchings, which are
equivalent to left cell bases. This paper compares the images of these bases
under classical maps: the {\em Robinson-Schensted algorithm} between
permutations and Young tableaux and {\em Khovanov-Kuperberg's bijection}
between Young tableaux and reduced webs.
One main result uses Vogan's generalized -invariant to uncover a close
structural relationship between the web basis and the left cell basis.
Intuitively, generalized -invariants refine the data of the inversion set
of a permutation. We define generalized -invariants intrinsically for
Kazhdan-Lusztig left cell basis elements and for webs. We then show that the
generalized -invariant is preserved by these classical maps. Thus, our
result allows one to interpret Khovanov-Kuperberg's bijection as an analogue of
the Robinson-Schensted correspondence.
Despite all of this, our second main result proves that the reduced web and
left cell bases are inequivalent; that is, these bijections are not
-equivariant maps.Comment: 34 pages, 23 figures, minor corrections and revisions in version
Evaluations of annular Khovanov--Rozansky homology
We describe the universal target of annular Khovanov-Rozansky link homology
functors as the homotopy category of a free symmetric monoidal category
generated by one object and one endomorphism. This categorifies the ring of
symmetric functions and admits categorical analogues of plethystic
transformations, which we use to characterize the annular invariants of Coxeter
braids. Further, we prove the existence of symmetric group actions on the
Khovanov-Rozansky invariants of cabled tangles and we introduce spectral
sequences that aid in computing the homologies of generalized Hopf links.
Finally, we conjecture a characterization of the horizontal traces of Rouquier
complexes of Coxeter braids in other types.Comment: 41 page
Deformations of colored sl(N) link homologies via foams
We generalize results of Lee, Gornik and Wu on the structure of deformed
colored sl(N) link homologies to the case of non-generic deformations. To this
end, we use foam technology to give a completely combinatorial construction of
Wu's deformed colored sl(N) link homologies. By studying the underlying
deformed higher representation theoretic structures and generalizing the
Karoubi envelope approach of Bar-Natan and Morrison we explicitly compute the
deformed invariants in terms of undeformed type A link homologies of lower rank
and color.Comment: 64 pages, many figure
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