Related papers: Jump processes on leaves of multibranching trees
Recently proposed budding tree is a decision tree algorithm in which every node is part internal node and part leaf. This allows representing every decision tree in a continuous parameter space, and therefore a budding tree can be jointly…
The solutions to a large class of semi-linear parabolic PDEs are given in terms of expectations of suitable functionals of a tree of branching particles. A sufficient, and in some cases necessary, condition is given for the integrability of…
We use the theory of motivic integration in order to give a geometric explanation of the behavior of some p-adic integrals.
We describe, in an intrinsic way and using the global chart provided by Ito's parallel transport, a generalisation of the notion of geodesic (as critical path of an energy functional) to diffusion processes on Riemannian manifolds. These…
Decision trees are widely used for non-linear modeling, as they capture interactions between predictors while producing inherently interpretable models. Despite their popularity, performing inference on the non-linear fit remains largely…
In this article, we study a large class of radial probability density functions defined on the p-adic numbers from which it is possible to obtain certain non-archimedean pseudo-differential operators. These operators are associated with…
The segment tree is an extremely versatile data structure. In this paper, a new heap based implementation of segment trees is proposed. In such an implementation of segment tree, the structural information associated with the tree nodes can…
During the last decade, self-affine geometrical properties of many growing aggregates, originated in a wide variety of processes, have been well characterized. However, little progress has been achieved in the search of a unified…
Many algorithms for processing probabilistic networks are dependent on the topological properties of the problem's structure. Such algorithms (e.g., clustering, conditioning) are effective only if the problem has a sparse graph captured by…
We consider a class of jump processes in euclidean space which are associated to a certain non-local symmetric Dirichlet form. We prove a lower bound on the occupation times of sets, and that a support theorem holds for these processes.
A $p$-jump process is a piecewise deterministic Markov process with jumps by a factor of $p$. We prove a limit theorem for such processes on the unit interval. Via duality with respect to probability generating functions, we deduce limiting…
The top tree data structure is an important and fundamental tool in dynamic graph algorithms. Top trees have existed for decades, and today serve as an ingredient in many state-of-the-art algorithms for dynamic graphs. In this work, we give…
Decision trees and systems of decision rules are widely used as classifiers, as a means for knowledge representation, and as algorithms. They are among the most interpretable models for data analysis. The study of the relationships between…
A new tree model is introduced based on ordered trees, by distinguishing exactly one child of each node that \emph{has} children. The basic enumeration leads to a cubic equation of the generating function. The extraction of its coefficients…
Simple stochastic models for phylogenetic trees on species have been well studied. But much paleontology data concerns time series or trees on higher-order taxa, and any broad picture of relationships between extant groups requires use of…
The conception of multi-alphabetical genetics is represented. Matrix forms of the representation of the multi-level system of molecular-genetic alphabets have revealed algebraic properties of this system. These properties are connected with…
Data structures known as $k$-d trees have numerous applications in scientific computing, particularly in areas of modern statistics and data science such as range search in decision trees, clustering, nearest neighbors search, local…
We introduce in this section an Algebraic and Combinatorial approach to the theory of Numbers. The approach rests on the observation that numbers can be identified with familiar combinatorial objects namely rooted trees, which we shall here…
In spatial networks vertices are arranged in some space and edges may cross. When arranging vertices in a 1-dimensional lattice edges may cross when drawn above the vertex sequence as it happens in linguistic and biological networks. Here…
Due to the fact that the numbers of annually published papers have witnessed a linear growth in some citation networks, a geometric model is thus proposed to predict some statistical features of those networks, in which the academic…