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 $L_{w\lambda}$ when $\lambda$ 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