Related papers: Mumford dendrograms and discrete p-adic symmetries

We study the structure of adic curves over an affinoid field of arbitrary rank. In particular, quite analogously to Berkovich geometry we classify points on curves, prove a semistable reduction theorem in the version of Ducros'…

In constrained solution spaces with a huge number of homotopy classes, stand-alone sampling-based kinodynamic planners suffer low efficiency in convergence. Local optimization is integrated to alleviate this problem. In this paper, we…

We extend (scheme-theoretic) Bruhat-Tits theory to quasi-reductive groups i.e. with trivial split unipotent radical over discretely valued henselian non-archimedean fields $K$, whose ring of integers is excellent and residue field is…

For a reductive group $G$ over a discretely valued Henselian field $k$, using valuations of root datum and concave functions, the Bruhat--Tits theory defines an important class of open bounded subgroups of $G(k)$ which are essential objects…

Previously, we proposed a physically-inspired method to construct data points into an effective in-tree (IT) structure, in which the underlying cluster structure in the dataset is well revealed. Although there are some edges in the IT…

While there has been much interest in adapting conventional clustering procedures---and in higher dimensions, persistent homology methods---to directed networks, little is known about the convergence of such methods. In order to even…

Embedding methods such as word embedding have become pillars for many applications containing discrete structures. Conventional embedding methods directly associate each symbol with a continuous embedding vector, which is equivalent to…

Let $K$ be a finite extension of ${\mathbb Q}_p$ and let $X$ be Drinfel'd's symmetric space of dimension $d$ over $K$. Let $\Gamma\subset {\rm SL}_{d+1}(K)$ be a cocompact discrete (torsionfree) subgroup and let…

We study several rigidity properties of $p$-adic local systems on a smooth rigid analytic space $X$ over a $p$-adic field. We prove that the monodromy of the log isocrystal attached to a $p$-adic local system is ''rigid'' along irreducible…

We use the tensor network living on the Bruhat-Tits tree to give a concrete realization of the recently proposed $p$-adic AdS/CFT correspondence (a holographic duality based on the $p$-adic number field $\mathbb{Q}_p$). Instead of assuming…

We construct fast, structure-preserving iterations for computing the sign decomposition of a unitary matrix $A$ with no eigenvalues equal to $\pm i$. This decomposition factorizes $A$ as the product of an involutory matrix $S =…

We describe an algorithm for computing certain quaternionic quotients of the Bruhat-Tits tree for GL2(Qp). As an application, we describe an algorithm to obtain (conjectural) equations for the canonical embedding of Shimura curves.

Presenting p-adic numbers as {\em deformations} of finite fields allows a better understanding of Frobenius lifts and their connection with p-derivations in the sense of Buium \cite{Buium-Main}. In this way "numbers {\em are} functions", as…

Similarity-based Hierarchical Clustering (HC) is a classical unsupervised machine learning algorithm that has traditionally been solved with heuristic algorithms like Average-Linkage. Recently, Dasgupta reframed HC as a discrete…

The recent increase of interest in the graph invariant called tree-depth and in its applications in algorithms and logic on graphs led to a natural question: is there an analogously useful "depth" notion also for dense graphs (say; one…

Algorithms for deriving Huffman codes and the recently developed algorithm for compiling PIFO trees to trees of fixed shape (Mohan et al. 2022) are similar, but work with different underlying algebraic operations. In this paper, we exploit…

The complexity of graph homomorphisms has been a subject of intense study [11, 12, 4, 42, 21, 17, 6, 20]. The partition function $Z_{\mathbf A}(\cdot)$ of graph homomorphism is defined by a symmetric matrix $\mathbf A$ over $\mathbb C$. We…

In this work, we develop a discretisation method for the mixed formulation of the magnetostatic problem supporting arbitrary orders and polyhedral meshes. The method is based on a global discrete de Rham (DDR) sequence, obtained by patching…

The goal of this paper is to offer a new construction of the de Rham-Witt complex of smooth varieties over perfect fields of characteristic $p>0$. We introduce a category of cochain complexes equipped with an endomorphism $F$ of underlying…

We consider the problem of compactly representing the Depth First Search (DFS) tree of a given undirected or directed graph having $n$ vertices and $m$ edges while supporting various DFS related queries efficiently in the RAM with…