Related papers: Treecode2: The Power of Pluralism. I. Static Tests
We suggest an iterative quantum protocol, allowing to solve optimization problems with a glassy energy landscape. It is based on a periodic cycling around the tricritical point of the many-body localization transition. This ensures that…
I discuss the evolution of the redshift-space bispectrum via perturbation theory (PT) and large high-resolution numerical simulations. At large scales, we give the multipole expansion of the bispectrum in PT, which provides a natural way to…
We present preliminary results on the parallelization of a Tree-Code for evaluating gravitational forces in N-body astrophysical systems. Our HPF/CRAFT implementation on a CRAY T3E machine attained an encouraging speed-up behavior, reaching…
The physics of randomness and regularities for languages (mother tongues) and their lifetimes and family trees and for the second languages are studied in terms of two opposite processes; random multiplicative noise [1], and fragmentation…
In this work, we show new and improved error-correcting properties of folded Reed-Solomon codes and multiplicity codes. Both of these families of codes are based on polynomials over finite fields, and both have been the sources of recent…
We propose a new arithmetic for non-empty rooted unordered trees simply called trees. After discussing tree representation and enumeration, we define the operations of tree addition, multiplication and stretch, prove their properties, and…
We propose a tree-based algorithm for classification and regression problems in the context of functional data analysis, which allows to leverage representation learning and multiple splitting rules at the node level, reducing…
We prove a lower bound on the number of spanning two-forests in a graph, in terms of the number of vertices, edges, and spanning trees. This implies an upper bound on the average cut size of a random two-forest. The main tool is an identity…
A static binary search tree where every search starts from where the previous one ends (lazy finger) is considered. Such a search method is more powerful than that of the classic optimal static trees, where every search starts from the root…
In this paper we present novel algorithmic techniques with a O(H(N)+N/H(N)) time complexity for performing several types of queries and updates on general rooted trees, binary search trees and lists of size N. For rooted trees we introduce…
We extend coupled-cluster theory performed on top of a Slater determinant breaking rotational symmetry to allow for the exact restoration of the angular momentum at any truncation order. The main objective relates to the description of…
The hierarchical and recursive expressive capability of rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. On the other hand, such hierarchical…
A generalization of the Polyakov-Koba-Nielsen-Olesen scaling law of the multiplicity distributions P(n,s) is developed. It states that a suitable change in the normalization point of P(n,s) compensated by a rescaling can restore data…
We develop a general statistical framework for the analysis and inference of large tree-structured data, with a focus on developing asymptotic goodness-of-fit tests. We first propose a consistent statistical model for binary trees, from…
This paper presents a new erasure code called Treeplication designed for distributed recovery of the full information word, while most prior work in coding for distributed storage only supports distributed repair of individual symbols. A…
Despite the impressive growth of the abilities of multilingual language models, such as XLM-R and mT5, it has been shown that they still face difficulties when tackling typologically-distant languages, particularly in the low-resource…
The Pr\"ufer code is a bijection between trees on the vertex set $[n]$ and strings on the set $[n]$ of length $n-2$ (Pr\"ufer strings of order $n$). In this paper we examine the `locality' properties of the Pr\"ufer code, i.e. the effect of…
For a tree Markov random field non-reconstruction is said to hold if as the depth of the tree goes to infinity the information that a typical configuration at the leaves gives about the value at the root goes to zero. The distribution of…
We study the random m-ary search tree model (where m stands for the number of branches of a search tree), an important problem for data storage in computer science, using a variety of statistical physics techniques that allow us to obtain…
Iterative compilation is a widely adopted technique to optimize programs for different constraints such as performance, code size and power consumption in rapidly evolving hardware and software environments. However, in case of statically…