33,077 research outputs found
K-theoretic crystals for set-valued tableaux of rectangular shapes
In earlier work with C. Monical (2018), we introduced the notion of a
K-crystal, with applications to K-theoretic Schubert calculus and the study of
Lascoux polynomials. We conjectured that such a K-crystal structure existed on
the set of semistandard set-valued tableaux of any fixed rectangular shape.
Here, we establish this conjecture by explicitly constructing the K-crystal
operators. As a consequence, we establish the first combinatorial formula for
Lascoux polynomials when is a multiple of a
fundamental weight as the sum over flagged set-valued tableaux. Using this
result, we then prove corresponding cases of conjectures of Ross-Yong (2015)
and Monical (2016) by constructing bijections with the respective combinatorial
objects.Comment: 20 pages, 2 figures; changed the statement of Conjecture 6.
Spatial database implementation of fuzzy region connection calculus for analysing the relationship of diseases
Analyzing huge amounts of spatial data plays an important role in many
emerging analysis and decision-making domains such as healthcare, urban
planning, agriculture and so on. For extracting meaningful knowledge from
geographical data, the relationships between spatial data objects need to be
analyzed. An important class of such relationships are topological relations
like the connectedness or overlap between regions. While real-world
geographical regions such as lakes or forests do not have exact boundaries and
are fuzzy, most of the existing analysis methods neglect this inherent feature
of topological relations. In this paper, we propose a method for handling the
topological relations in spatial databases based on fuzzy region connection
calculus (RCC). The proposed method is implemented in PostGIS spatial database
and evaluated in analyzing the relationship of diseases as an important
application domain. We also used our fuzzy RCC implementation for fuzzification
of the skyline operator in spatial databases. The results of the evaluation
show that our method provides a more realistic view of spatial relationships
and gives more flexibility to the data analyst to extract meaningful and
accurate results in comparison with the existing methods.Comment: ICEE201
Harvesting systems for steep terrain in the Italian Alps: state of the art and future prospects
Steep slope forest operations in Central Europe and in particular in the Alps are strongly related to the adoption of the cable-based harvesting system, even if innovative ground-based harvesting system, even if innovative ground-based harvesting systems have been proposed in the last years. In this context, the present works aim to acquire a thorough knowledge of yarding technologies used by the logging companies of the central Italian Alps, to evaluate their professionality in steep slope forest operations, and to predict the potential diffusion of innovative steep slope harvesting systems in the area. The results show a large number of logging companies (106) working with cable-based systems and in particular with four different standing skyline yarding technologies. The analysis of professionality in using cable cranes shows big differences between the companies. In particular, it identifies a consistent group of companies with a highly mechanized machinery fleet and high skills and experience in steep slope forest operations. These enterprises evidence a still limited potential diffusion of the innovative ground-based harvesting systems in the area, even if it is theoretically possible according to the GIS analysis of morphology and forest road networ
Mod-two cohomology of symmetric groups as a Hopf ring
We compute the mod-2 cohomology of the collection of all symmetric groups as
a Hopf ring, where the second product is the transfer product of Strickland and
Turner. We first give examples of related Hopf rings from invariant theory and
representation theory. In addition to a Hopf ring presentation, we give
geometric cocycle representatives and explicitly determine the structure as an
algebra over the Steenrod algebra. All calculations are explicit, with an
additive basis which has a clean graphical representation. We also briefly
develop related Hopf ring structures on rings of symmetric invariants and end
with a generating set consisting of Stiefel-Whitney classes of regular
representations v2. Added new results on varieties which represent the
cocycles, a graphical representation of the additive basis, and on the Steenrod
algebra action. v3. Included a full treatment of invariant theoretic Hopf
rings, refined the definition of representing varieties, and corrected and
clarified references.Comment: 31 pages, 6 figure
- …