Related papers: On the boundary components of central streams in t…
Foliations on the space of $p$-divisible groups were studied by Oort in 2004. In his theory, special leaves called central stream play an important role. In this paper, we give a complete classification of the boundary components of the…
In this paper, for any pair $(\zeta, \xi)$ of Newton polygons with $\zeta \prec \xi$, we construct a concrete specialization from the minimal $p$-divisible group of $\xi$ to the minimal $p$-divisible group of $\zeta$ by a beautiful…
This paper analyses the finer structure of Newton strata in loop groups. These can be decomposed into so-called central leaves. We define them, and determine their global geometric structure. We then study the closure of central leaves,…
The comprehensive characterization of the structure of complex networks is essential to understand the dynamical processes which guide their evolution. The discovery of the scale-free distribution and the small world property of real…
This is the second article in a series that aims at classifying partial sections of flows, that is a general family of transverse surfaces. In this part, we classify partial cross-sections for all continuous flows, in the spirit of…
Consider all moduli points corresponding with polarized abelian varieties in characteristic p such that the associated quasi-polarized p-divisible group is geometrically isomorphic with a given one. This defines a subset C of the moduli…
Let a planar algebraic curve $C$ be defined over a valuation field by an equation $F(x,y)=0$. Valuations of the coefficients of $F$ define a subdivision of the Newton polygon $\Delta$ of the curve $C$. If a given point $p$ is of…
New elementary, self-contained proofs are presented for the topological and the smooth classification theorems of linear flows on finite-dimensional normed spaces. The arguments, and the examples that accompany them, highlight the…
We classify singular foliations admitting a given leaf and a given transverse singular foliation.
We define new differential structures on the Wasserstein spaces $\mathcal{W}_p(M)$ for $p > 2$ and a general Riemannian manifold $(M,g)$. We consider a very general and possibly degenerate second order partial differential flow equation…
The structure of a river network may be seen as a discrete set of nested sub-networks built out of individual stream segments. These network components are assigned an integral stream order via a hierarchical and discrete ordering method.…
We develop a theory of arithmetic Newton polygons of higher order, that provides the factorization of a separable polynomial over a $p$-adic field, together with relevant arithmetic information about the fields generated by the irreducible…
Two natural foliations, guided by area and perimeter, of the configurations spaces of planar polygons are considered and the topology of their leaves is investigated in some detail. In particular, the homology groups and the homotopy type…
We study the convergence of graphs consisting of finitely many internal rays for degenerating Newton maps. We state a sufficient condition to guarantee the convergence. As an application, we investigate the boundedness of hyperbolic…
Subject of research is complex networks and network systems. The network system is defined as a complex network in which flows are moved. Classification of flows in the network is carried out on the basis of ordering and continuity. It is…
Various modifications of decision trees have been extensively used during the past years due to their high efficiency and interpretability. Tree node splitting based on relevant feature selection is a key step of decision tree learning, at…
Classic measures of graph centrality capture distinct aspects of node importance, from the local (e.g., degree) to the global (e.g., closeness). Here we exploit the connection between diffusion and geometry to introduce a multiscale…
We study continuous analogues of "vitality" for discrete network flows/paths, and consider problems related to placing segment barriers that have highest impact on a flow/path in a polygonal domain. This extends the graph-theoretic notion…
In this paper, we study the dynamics of Newton maps for arbitrary polynomials. Let $p$ be an arbitrary polynomial with at least three distinct roots, and $f$ be its Newton map. It is shown that the boundary $\partial B$ of any immediate…
Oort-Zink proved that a $p$-divisible group over a normal base in characteristic $p$ with constant Newton polygon is isogenous to a $p$-divisible group admitting a slope filtration. In this paper, we generalize this result to log…