Related papers: Recursive PGFs for BSTs and DSTs
P2P computing lifts taxing issues in various areas of computer science. The largely used decentralized unstructured P2P systems are ad hoc in nature and present a number of research challenges. In this paper, we provide a comprehensive…
Recursive Neural Networks are non-linear adaptive models that are able to learn deep structured information. However, these models have not yet been broadly accepted. This fact is mainly due to its inherent complexity. In particular, not…
Certain families of combinatorial objects admit recursive descriptions in terms of generating trees: each node of the tree corresponds to an object, and the branch leading to the node encodes the choices made in the construction of the…
This paper investigates the problem of determining a binary-valued function through a sequence of strategically selected queries. The focus is an algorithm called Generalized Binary Search (GBS). GBS is a well-known greedy algorithm for…
Tackling simulation optimization problems with non-convex objective functions remains a fundamental challenge in operations research. In this paper, we propose a class of random search algorithms, called Regular Tree Search, which…
Fitting generative models to sequential data typically involves two recursive computations through time, one forward and one backward. The latter could be a computation of the loss gradient (as in backpropagation through time), or an…
Decision theories offer principled methods for making choices under various types of uncertainty. Algorithms that implement these theories have been successfully applied to a wide range of real-world problems, including materials and drug…
Let $V(k)$ denote the waiting time, the number of trials needed to get a consecutive $k$ ones. We propose recurrence algorithms for the probability distribution function (pdf) and the probability generating function (pgf) of $V(k)$ in…
Additive tree functionals allow to represent the cost of many divide-and-conquer algorithms. We give an invariance principle for such tree functionals for the Catalan model (random tree uniformly distributed among the full binary ordered…
Inferences in directed acyclic graphs associated with probability sets and probability intervals are NP-hard, even for polytrees. In this paper we focus on such inferences, and propose: 1) a substantial improvement on Tessems A / R…
For random matrices with tree-like structure there exists a recursive relation for the local Green functions whose solution permits to find directly many important quantities in the limit of infinite matrix dimensions. The purpose of this…
Many developments in Mathematics involve the computation of higher order derivatives of Gaussian density functions. The analysis of univariate Gaussian random variables is a well-established field whereas the analysis of their multivariate…
Recursive formulas extending some known $_{2}F_{1}$ and $_{3}F_{2}$ summation formulas by using contiguous relations have been obtained. On the one hand, these recursive equations are quite suitable for symbolic and numerical evaluation by…
We derive recursions for the probability distribution of random sums by computer algebra. Unlike the well-known Panjer-type recursions, they are of finite order and thus allow for computation in linear time. This efficiency is bought by the…
In this paper, we consider a possible representation of a DNA sequence in a quaternary tree, in which on can visualize repetitions of subwords. The CGR-tree turns a sequence of letters into a digital search tree (DST), obtained from the…
The BRST structure of polynomial Poisson algebras is investigated. It is shown that Poisson algebras provide non trivial models where the full BRST recursive procedure is needed. Quadratic Poisson algebras may already be of arbitrarily high…
We initiate the study of tree structures in the context of scenario-based robust optimization. Specifically, we study Binary Search Trees (BSTs) and Huffman coding, two fundamental techniques for efficiently managing and encoding data based…
In this paper we study different algorithms for backward stochastic differential equations (BSDE in short) basing on random walk framework for 1-dimensional Brownian motion. Implicit and explicit schemes for both BSDE and reflected BSDE are…
This paper presents a permutation binary neural network characterized by local binary connection, global permutation connection, and the signum activation function. The dynamics is described by a difference equation of binary state…
This paper provides a unifying view of a wide range of problems of interest in machine learning by framing them as the minimization of functionals defined on the space of probability measures. In particular, we show that generative…