Tree Research Articles

A Good View for Graph Contrastive Learning.

Due to the success observed in deep neural networks with contrastive learning, there has been a notable surge in research interest in graph contrastive learning, primarily attributed to its superior performance in graphs with limited labeled data. Within contrastive learning, the selection of a "view" dictates the information captured by the representation, thereby influencing the model's performance. However, assessing the quality of information in these views poses challenges, and determining what constitutes a good view remains unclear. This paper addresses this issue by establishing the definition of a good view through the application of graph information bottleneck and structural entropy theories. Based on theoretical insights, we introduce CtrlGCL, a novel method for achieving a beneficial view in graph contrastive learning through coding tree representation learning. Extensive experiments were conducted to ascertain the effectiveness of the proposed view in unsupervised and semi-supervised learning. In particular, our approach, via CtrlGCL-H, yields an average accuracy enhancement of 1.06% under unsupervised learning when compared to GCL. This improvement underscores the efficacy of our proposed method.

A new model construction by making a detour via intuitionistic theories IV: A closer connection between KPω and BI

By combining tree representation of sets with the method introduced in the previous three papers I–III [39,35,37] in the series, we give a new Π21-preserving interpretation of KPωr+(Πn+2-Found)+θ (Kripke–Platek set theory with the foundation schema restricted to Πn+2, and augmented by θ) in Σ11-AC0+(Πn+21-TI)+θ for any Π21 sentence θ, where the language of second order arithmetic is considered as a sublanguage of that of set theory via the standard interpretation. Thus the addition of any Π21 theorem of BI≡Σ11-AC0+(Π∞1-TI) does not increase the consistency strength of KPω. Among such Π21 theorems are several fixed point principles for positive arithmetical operators and ω-model reflection (the cofinal existence of coded ω-models) for theorems of BI. The reader's familiarity to the previous works I–III in the series might help, but is not necessary.

AlignScape, displaying sequence similarity using self-organizing maps.

The current richness of sequence data needs efficient methodologies to display and analyze the complexity of the information in a compact and readable manner. Traditionally, phylogenetic trees and sequence similarity networks have been used to display and analyze sequences of protein families. These methods aim to shed light on key computational biology problems such as sequence classification and functional inference. Here, we present a new methodology, AlignScape, based on self-organizing maps. AlignScape is applied to three large families of proteins: the kinases and GPCRs from human, and bacterial T6SS proteins. AlignScape provides a map of the similarity landscape and a tree representation of multiple sequence alignments These representations are useful to display, cluster, and classify sequences as well as identify functional trends. The efficient GPU implementation of AlignScape allows the analysis of large MSAs in a few minutes. Furthermore, we show how the AlignScape analysis of proteins belonging to the T6SS complex can be used to predict coevolving partners.

Entropy removal of medical diagnostics

Shannon entropy is a core concept in machine learning and information theory, particularly in decision tree modeling. To date, no studies have extensively and quantitatively applied Shannon entropy in a systematic way to quantify the entropy of clinical situations using diagnostic variables (true and false positives and negatives, respectively). Decision tree representations of medical decision-making tools can be generated using diagnostic variables found in literature and entropy removal can be calculated for these tools. This concept of clinical entropy removal has significant potential for further use to bring forth healthcare innovation, such as quantifying the impact of clinical guidelines and value of care and applications to Emergency Medicine scenarios where diagnostic accuracy in a limited time window is paramount. This analysis was done for 623 diagnostic tools and provided unique insights into their utility. For studies that provided detailed data on medical decision-making algorithms, bootstrapped datasets were generated from source data to perform comprehensive machine learning analysis on these algorithms and their constituent steps, which revealed a novel and thorough evaluation of medical diagnostic algorithms.

Explaining neural networks without access to training data

We consider generating explanations for neural networks in cases where the network’s training data is not accessible, for instance due to privacy or safety issues. Recently, Interpretation Nets (I\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {I}$$\\end{document}-Nets) have been proposed as a sample-free approach to post-hoc, global model interpretability that does not require access to training data. They formulate interpretation as a machine learning task that maps network representations (parameters) to a representation of an interpretable function. In this paper, we extend the I\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {I}$$\\end{document}-Net framework to the cases of standard and soft decision trees as surrogate models. We propose a suitable decision tree representation and design of the corresponding I\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {I}$$\\end{document}-Net output layers. Furthermore, we make I\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {I}$$\\end{document}-Nets applicable to real-world tasks by considering more realistic distributions when generating the I\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {I}$$\\end{document}-Net’s training data. We empirically evaluate our approach against traditional global, post-hoc interpretability approaches and show that it achieves superior results when the training data is not accessible.

TooManyCellsInteractive: A visualization tool for dynamic exploration of single-cell data.

As single-cell sequencing technologies continue to advance, the growing volume and complexity of the ensuing data present new analytical challenges. Large cellular populations from single-cell atlases are more difficult to visualize and require extensive processing to identify biologically relevant subpopulations. Managing these workflows is also laborious for technical users and unintuitive for nontechnical users. We present TooManyCellsInteractive (TMCI), a browser-based JavaScript application for interactive exploration of cell populations. TMCI provides an intuitive interface to visualize and manipulate a radial tree representation of hierarchical cell subpopulations and allows users to easily overlay, filter, and compare biological features at multiple resolutions. Here we describe the software architecture and demonstrate how we used TMCI in a pan-cancer analysis to identify unique survival pathways among drug-tolerant persister cells. TMCI will facilitate exploration and visualization of large-scale sequencing data in a user-friendly way. TMCI is freely available at https://github.com/schwartzlab-methods/too-many-cells-interactive. An example tree from data within this article is available at https://tmci.schwartzlab.ca/.

On Normal Subgroups of the Group Representation of the Cayley Tree

Gibbs measure plays an important role in statistical mechanics. On a Cayley tree, for describing periodic Gibbs measures for models in statistical mechanics we need subgroups of the group representation of the Cayley tree. A normal subgroup of the group representation of the Cayley tree keeps the invariance property which is a significant tool in finding Gibbs measures. By this occasion, a full description of normal subgroups of the group representation of the Cayley tree is a significant problem in Gibbs measure theory. For instance, in~[1, 2] a full description of normal subgroups of indices four, six, eight, and ten for the group representation of a Cayley tree is given. The present paper is a generalization of these papers, i.\,e., in this paper, for any odd prime number $p$, we give a characterization of the normal subgroups of indices~$2n$, $n\in\{p, 2p\}$ and $2^i, i\in \mathbb{N},$ of the group representation of the Cayley tree.

Green Urban Scenarios: A Framework for Digital Twin Representation and Simulation for Urban Forests and Their Impact Analysis

Abstract Background Trees are a critical part of urban infrastructure. Cities worldwide are pledging afforestation objectives due to net-zero targets; however, their realisation requires a comprehensive framework that combines science, policy, and practice. Methods The paper presents the Green Urban Scenarios (GUS) framework for designing and monitoring green infrastructures. GUS considers weather, maintenance, tree species, diseases, and spatial distributions of trees to forecast their impacts. The framework uses agent-based modelling (ABM) and simulation paradigm to integrate green infrastructure into a city’s ecological, spatial, economic, and social context. ABM enables the creation of digital twins for urban ecosystems at any level of granularity, including individual trees, to accurately predict their future trajectories. Digital representation of trees is created using a combination of datasets such as earth observations from space, street view images, field surveys, and qualitative descriptions of typologies within existing and future projects. Machine learning and statistical models calibrate biomass growth patterns and carbon release schemes. Results The paper examines various green area typologies, simulating several hypothetical scenarios based on Glasgow’s urban forests. It exhibits the emergence of heterogeneity features of the forests due to interactions among trees. The growth trajectory of trees has a non-linear transition phase toward stable growth in its maturity. Reduced maintenance deteriorates the health of trees leading to lower survival rate and increased CO2emissions, while the stormwater alleviation capacity may differ among species. Conclusions The paper demonstrates how GUS can facilitate policies and maintenance of urban forests with environmental, social, and economic benefits.

Adaptive in-memory representation of decision trees for GPU-accelerated evolutionary induction

Decision trees (DTs) are a type of machine learning technique used for classification and regression problems. They are considered to be a part of explainable artificial intelligence due to their transparent and interpretable nature. The traditional approach in building DTs involves a top-down greedy search, which is usually fast but may result in a sub-optimal solution. An alternative method is evolutionary induction. It allows for more global exploration and can lead to simpler DTs, but it is computationally more expensive. To speed up the induction, different parallel approaches have been considered, with the GPU-based ones being the most efficient.In this paper, we extend the GPU-supported algorithm of DT evolutionary induction to use less memory and time resources. An improved in-memory representation of DTs is introduced, which adapts depending on the tree structure. Two types are possible: compact and complete representations. A compact one is used for DTs that are sparsely filled. It contains only existing tree nodes and therefore the links between parent and child nodes must be explicitly stored (along with the data). On the other hand, a complete representation is applied when the tree levels are densely filled. Then, placeholders for all potential nodes are reserved and the parent position can be easily calculated based on the child’s place (and vice versa). The algorithm switches between the representations based on a density factor of tree filling.To validate our concept, we conducted experiments on both real-life and artificial datasets with varying sizes and dimensions. The results show that the DT in-memory representation affects the time and memory requirements a lot. The most efficient is the adaptive one. It not only speeds up the induction time but also reduces memory requirements (in terms of both transfer and occupancy). As a result, the evolutionary induction of DTs is closer to being competitive with state-of-the-art greedy inducers in terms of computation time.

Innovative method to solve the minimum spanning tree problem: The Dhouib-Matrix-MSTP (DM-MSTP)

The Minimum Spanning Tree problem aims to create a subset of a graph where all the vertices are connected with the minimum edge weights and with no cycle. In this field, an innovative method entitled Dhouib-Matrix-MSTP (DM-MSTP) is designed in this research work with a time complexity independently of the number of edges O(n*log(n)) where n is the number of vertices. DM-MSTP is a constructive algorithm based on a matrix navigation with two new lists (Min-Columns and MST-Path) in order to organize the steering flow. DM-MSTP is composed of four simple steps where the first and the fourth steps are repeated only once, whereas the second and third are reiterated (n-1). For more clarification, a step-by-step application of the proposed method is presented in details. Besides, the performance of DM-MSTP is proved through different examples from the literature including a graph with negative weighted edges and complete graphs from TSP-LIB. Moreover, with a simple modification (Min by Max) the DM-MSTP is tested on the Maximum (Largest) Spanning Tree Problem. Also, DM-MSTP is applied on eight case studies and compared to six methods developed in the literature. All these experimental results in the above different environments show that DM-MSTP can rapidly plan the shortest spanning tree with a stable performance and convivial representation of the optimal tree. Hence, DM-MSTP is developed under Python programming language using Matplotlib and Numpy standard libraries.

Node-depth based Genetic Algorithm to solve Inter-Domain path computation problem

Inter-Domain Path Computation problem under Node-defined Domain Uniqueness Constraint (IDPC-NDU) is an NP-Hard problem that applies to packet routing in multi-domain networks, particularly Hierarchical Path Computation Element (h-PCE) architecture. Its objective is to determine the shortest route between two specified nodes that visit each domain no more than once. In recent years, many proposals have been made to tackle this problem and improve existing algorithms. However, most of these strategies retain a potential weakness that lies in the complex encoding and decoding methods, which consume a lot of computer resources and computation time, especially for large-scale problems. For this reason, this paper introduces an effective Node-depth based Genetic Algorithm (NDEGA) for IDPC-NDU. We propose a novel solution encoding for the problem by using tree representation that helps to satisfy the domain constraint and makes the corresponding solution construction more practical. Instead of conventional encoding techniques, NDEGA is equipped with an improved Node-depth encoding, which is famous for its low time complexity and efficiency for tree problems. Besides, a corresponding decoding method, as well as node-depth search operators, are also well-developed for the problem. To examine the efficiency of NDEGA, we carefully conduct extensive experiments and compare our approach to many competitive baselines on a wide range of synthetic datasets. The empirical results demonstrate that our proposed algorithm significantly outperforms all compared algorithms regarding solution quality, convergence trend, and computation time and obtains the state-of-the-art performance for IDPC-NDU. Notably, our NDEGA achieves 65.17−85.66% solution quality improvement on average compared to the previous approaches while running faster, approximately 50−70 times.

Tree representations of brain structural connectivity via persistent homology.

The brain structural connectome is generated by a collection of white matter fiber bundles constructed from diffusion weighted MRI (dMRI), acting as highways for neural activity. There has been abundant interest in studying how the structural connectome varies across individuals in relation to their traits, ranging from age and gender to neuropsychiatric outcomes. After applying tractography to dMRI to get white matter fiber bundles, a key question is how to represent the brain connectome to facilitate statistical analyses relating connectomes to traits. The current standard divides the brain into regions of interest (ROIs), and then relies on an adjacency matrix (AM) representation. Each cell in the AM is a measure of connectivity, e.g., number of fiber curves, between a pair of ROIs. Although the AM representation is intuitive, a disadvantage is the high-dimensionality due to the large number of cells in the matrix. This article proposes a simpler tree representation of the brain connectome, which is motivated by ideas in computational topology and takes topological and biological information on the cortical surface into consideration. We demonstrate that our tree representation preserves useful information and interpretability, while reducing dimensionality to improve statistical and computational efficiency. Applications to data from the Human Connectome Project (HCP) are considered and code is provided for reproducing our analyses.

Generation matrix: An embeddable matrix representation for hierarchical trees

Starting from the local structures to study hierarchical trees is a common research method. However, the cumbersome analysis and description make the naive method challenging to adapt to the increasingly complex hierarchical tree problems. To improve the efficiency of hierarchical tree research, we propose an embeddable matrix representation for hierarchical trees, called Generation Matrix. It can transform the abstract hierarchical tree into a concrete matrix representation and then take the hierarchical tree as a whole to study, dramatically reducing the research complexity. Mathematical analysis shows that Generation Matrix can simulate various recursive algorithms without accessing local structures and provides a variety of interpretable matrix operations to support the research of hierarchical trees. Applying Generation Matrix to differential privacy hierarchical tree release, we propose a Generation Matrix-based optimally consistent release algorithm (GMC). It provides an exceptionally concise process description so that we can describe its core steps as a simple matrix expression rather than multiple complicated recursive processes like existing algorithms. Our experiments show that GMC takes only a few seconds to complete a release for large-scale datasets with more than 10 million nodes. The calculation efficiency is increased by up to 100 times compared with the state-of-the-art schemes.

A computational growth and remodeling framework for adaptive and maladaptive pulmonary arterial hemodynamics.

Hemodynamic loading is known to contribute to the development and progression of pulmonary arterial hypertension (PAH). This loading drives changes in mechanobiological stimuli that affect cellular phenotypes and lead to pulmonary vascular remodeling. Computational models have been used to simulate mechanobiological metrics of interest, such as wall shear stress, at single time points for PAH patients. However, there is a need for new approaches that simulate disease evolution to allow for prediction of long-term outcomes. In this work, we develop a framework that models the pulmonary arterial tree through adaptive and maladaptive responses to mechanical and biological perturbations. We coupled a constrained mixture theory-based growth and remodeling framework for the vessel wall with a morphometric tree representation of the pulmonary arterial vasculature. We show that non-uniform mechanical behavior is important to establish the homeostatic state of the pulmonary arterial tree, and that hemodynamic feedback is essential for simulating disease time courses. We also employed a series of maladaptive constitutive models, such as smooth muscle hyperproliferation and stiffening, to identify critical contributors to development of PAH phenotypes. Together, these simulations demonstrate an important step toward predicting changes in metrics of clinical interest for PAH patients and simulating potential treatment approaches.

Sparsification of large ultrametric matrices: insights into the microbial Tree of Life

Ultrametric matrices appear in many domains of mathematics and science; nevertheless, they can be large and dense, making them difficult to store and manipulate, unlike large but sparse matrices. In this manuscript, we exploit that ultrametric matrices can be represented as binary trees to sparsify them via an orthonormal base change based on Haar-like wavelets. We show that, with overwhelmingly high probability, only an asymptotically negligible fraction of the off-diagonal entries in random but large ultrametric matrices remain non-zero after the base change; and develop an algorithm to sparsify such matrices directly from their tree representation. We also identify the subclass of matrices diagonalized by the Haar-like wavelets and supply a sufficient condition to approximate the spectrum of ultrametric matrices outside this subclass. Our methods give computational access to a covariance matrix model of the microbiologists’ Tree of Life, which was previously inaccessible due to its size, and motivate introducing a new wavelet-based (beta-diversity) metric to compare microbial environments. Unlike the established metrics, the new metric may be used to identify internal nodes (i.e. splits) in the Tree that link microbial composition and environmental factors in a statistically significant manner.

Deformable Part Region Learning and Feature Aggregation Tree Representation for Object Detection.

Region-based object detection infers object regions for one or more categories in an image. Due to the recent advances in deep learning and region proposal methods, object detectors based on convolutional neural networks (CNNs) have been flourishing and provided promising detection results. However, the accuracy of the convolutional object detectors can be degraded often due to the low feature discriminability caused by geometric variation or transformation of an object. In this article, we propose a deformable part region (DPR) learning in order to allow decomposed part regions to be deformable according to the geometric transformation of an object. Because the ground truth of the part models is not available in many cases, we design part model losses for the detection and segmentation, and learn the geometric parameters by minimizing an integral loss including those part losses. As a result, we can train our DPR network without extra supervision, and make multi-part models deformable according to object geometric variation. Moreover, we propose a novel feature aggregation tree (FAT) so as to learn more discriminative region of interest (RoI) features via bottom-up tree construction. The FAT can learn the stronger semantic features by aggregating part RoI features along the bottom-up pathways of the tree. We also present a spatial and channel attention mechanism for the aggregation between different node features. Based on the proposed DPR and FAT networks, we design a new cascade architecture that can refine detection tasks iteratively. Without bells and whistles, we achieve impressive detection and segmentation results on MSCOCO and PASCAL VOC datasets. Our Cascade D-PRD achieves the 57.9 box AP with the Swin-L backbone. We also provide an extensive ablation study to prove the effectiveness and usefulness of the proposed methods for large-scale object detection.

Strategies and Approaches for Generating Identical Extensive XML Tree Instances

In recent years, XML has become the de facto internet wire language. Data may be organized and given context with the use of XML. A well-organized document facilitates the transformation of raw data into actionable intelligence. In B2B1 applications, the XML data is sent and created. This implies the need for fast query processing on XML data. The processing of XML tree sample queries (XTPQ) that provide an efficient response (also known as sample matching) is a topic of active study in the XML database field.DOM (Parser) may be used to transform an XML document into a tree representation. Extensible Markup Language (XML) query languages like XPath and XQuery use tree samples (twigs) to express query results.XML query processing focuses mostly on effectively locating all instances of twig 1 samples inside an XML database. Numerous techniques for matching such tree samples have been presented in recent years. In this study, we survey recent developments in XTPQ processing. This summary will begin by introducing several algorithms for twig sample matching and then go on to provide some background on holistic techniques to process XTPQ.

Nature Voices in Herman Melville’s Typee: The Cocoa-Nut Trees

The purpose of this study is to examine the representation of cocoa-nut trees in Herman Melville’s Typee: A Peep at Polynesian Life (1846). With the rise of adverse effects of environmental crisis and climate change, calls for action on environment due to its status quo have attracted scholarly attention including the study of literature in lights of environmental humanities. Furthermore, writers have used nature with its diverse elements to contribute into the thematic and narrative structure of their writing. In specific, this study attempts through a close reading of Typee to analyze the cocoa-nut imagery from an ecocritical perspective. It also argues that the narrator’s perception of the cocoa-nut tree has changed over time as a result of his interaction as a white American sailor with the islanders themselves. In other words, the cocoa-nut trees with their multifaceted symbolic representations provide a commentary on the sociopolitical and historical context of the text and reveal the narrator’s endeavors to understand his identity as a 19th century white sailor within non-white and non-Western context. In short, Melville’s Typee centralizes the function of cocoa-nut trees in terms of their textual and contextual significance.

일제하 경성 벚꽃놀이의 식민지적 이중성

The purpose of this paper is to look at the background of the introduction of cherry blossoms in Japanese colonial era and the purpose of the introduction of the Japanese Government-General of Korea from the perspective of colonial use to facilitate rule over Koreans. Through the analysis of primary historical sources such as the newspaper feed of the time and Lee Taejoon's novel, Planted A Flower Tree But, we first looked at how Japanese colonial era cherry blossoms were introduced and why they were introduced, and secondly, we looked at the representation of cherry trees in Lee Taejoon's novel. As a result of the study, cherry blossoms were introduced in Joseon in 1907 and spread through the process of acceptance and resistance. The colonial duality of cherry blossoms can be considered through the relationship between Japanese and wealthy Koreans who embraced cherry blossom viewing and the poor in Gyeongseong, which had no choice but to be alienated from such cherry blossom viewing in the novel.

Tolerant Radon partitions on the all-paths convexity in graphs

In a graph G, the all-paths transit function A(u, v), consists of the set of all vertices in the graph G which lies in some path connecting u and v. Convexity obtained by the all-paths transit function is called all-paths convexity. A partition of a set P of vertices of a graph G into two disjoint non-empty subsets is called a Radon partition if the convex hulls of the subsets intersect. A Radon partition (P0, Q0) of P into nonempty subsets is called t-tolerant Radon partition, if for any set S ⊆ P with | S | ≤ t , the intersection of the convex hulls 〈 P 0 − S 〉 ∩ 〈 Q 0 − S 〉 ≠ ∅ . Here we study the t-tolerant Radon number of G with respect to all-paths convexity. It is the minimum number k such that any collection of k vertices of G has t-tolerant Radon partition. We prove that if G has only one block, then k = 2 t + 2 whenever t ≥ 1 . Finally, we prove that if the block-cut vertex tree representation of G is a path then k = 2 t + 3 , and if the block-cut vertex tree representation of G is a tree that is not a path then k = 2 t + 4 .