We give a decomposition of triply rooted trees into three doubly rooted trees. This leads to a combinatorial interpretation of an identity conjectured by Lacasse in the study of the PAC-Bayesian machine learning theory, and proved by Younsi by using the Hurwitz identity on multivariate Abel polynomials. Let [n] = {1, 2, . . . , n}. We also give a bijection between the set of functions from [n +...

we report a rare case of a two-rooted maxillary central incisor, stressing the importance of three-dimensional imaging in treatment planning and conservative approach of management. endodontic treatment of this central incisor was carried out with a successful outcome.

In this paper we present duplication-free tableau calculi for three propositional intermediate interpolable logics, namely the logic characterized by rooted Kripke models with depth two at most, the logic characterized by rooted Kripke models with two final elements at most and depth two at most and the logic characterized by rooted Kripke models with a final element at most (also known as Jank...

Prefetching constitutes a valuable tool toward the goal of efficient Web surfing. As result, estimating amount resources that need to be preloaded during surfer's browsing becomes an important task. In this regard, prefetching can modeled as two-player combinatorial game (Fomin et al. (2014) [6] ), where surfer and marker alternately play on given graph (representing graph). During its turn, ch...