Tootfinder

A Sierpinski Triangle Data Structure for Efficient Array Value Update and Prefix Sum Calculation
Brent Harrison, Jason Necaise, Andrew Projansky, James D. Whitfield
https://arxiv.org/abs/2403.03990

A Sierpinski Triangle Data Structure for Efficient Array Value Update and Prefix Sum Calculation
The binary indexed tree, or Fenwick tree, is a data structure that can efficiently update values and calculate prefix sums in an array. It allows both of these operations to be performed in $O(\log_2 N)$ time. Here we present a novel data structure resembling the Sierpinski triangle, which accomplishes these operations with the same memory usage in $O(\log_3 N)$ time instead. We show this order to be optimal by making use of a connection to quantum computing.

This https://arxiv.org/abs/2303.03762 has been replaced.
link: https://scholar.google.com/scholar?q=a

New strategy on the existence of a spanning tree without small degree stems
For an integer $k\geq 2$, a spanning tree of a graph without no vertices of degree from $2$ to $k$ is call a {\it $[2,k]$-ST} of the graph. The concept of $[2,k]$-STs is a natural extension of a homeomorphically irreducible spanning tree (or HIST), which has been a well-studied graph-structure. In this paper, we give a new strategy for finding $[2,k]$-STs. By using the strategy, we refine or extend a known degree-sum condition for the existence of a HIST. Furthermore, we also investigate on a d…

This https://arxiv.org/abs/2401.03003 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csSE_…

AST-T5: Structure-Aware Pretraining for Code Generation and Understanding
Large language models (LLMs) have made significant advancements in code-related tasks, yet many LLMs treat code as simple sequences, neglecting its structured nature. We introduce AST-T5, a novel pretraining paradigm that leverages the Abstract Syntax Tree (AST) for enhanced code generation, transpilation, and understanding. Using dynamic programming, our AST-Aware Segmentation retains code structure, while our AST-Aware Span Corruption objective equips the model to reconstruct various code str…

This https://arxiv.org/abs/2211.05690 has been replaced.
link: https://scholar.google.com/scholar?q=a

Robust Model Selection of Gaussian Graphical Models
In Gaussian graphical model selection, noise-corrupted samples present significant challenges. It is known that even minimal amounts of noise can obscure the underlying structure, leading to fundamental identifiability issues. A recent line of work addressing this "robust model selection" problem narrows its focus to tree-structured graphical models. Even within this specific class of models, exact structure recovery is shown to be impossible. However, several algorithms have been developed tha…

This https://arxiv.org/abs/2401.14295 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCL_…

Demystifying Chains, Trees, and Graphs of Thoughts
The field of natural language processing (NLP) has witnessed significant progress in recent years, with a notable focus on improving large language models' (LLM) performance through innovative prompting techniques. Among these, prompt engineering coupled with structures has emerged as a promising paradigm, with designs such as Chain-of-Thought, Tree of Thoughts, or Graph of Thoughts, in which the overall LLM reasoning is guided by a structure such as a graph. As illustrated with numerous exampl…

This https://arxiv.org/abs/2310.19190 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Renewal structure of the Tree Builder Random Walk
In this paper, we study a class of random walks that build their own tree. At each step, the walker attaches a random number of leaves to its current position. The model can be seen as a subclass of the Random Walk in Changing Environments (RWCE) introduced by G. Amir, I. Benjamini, O. Gurel-Gurevich and G. Kozma. We develop a renewal framework for the process analogous to that established by A-S. Sznitman and M. Zerner in the context of RWRE. This provides a more robust foundation for analyzin…

This https://arxiv.org/abs/2306.15984 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Fulkerson duality for modulus of spanning trees and partitions
One of the main properties of modulus on graphs is Fulkerson duality. In this paper, we study Fulkerson duality for spanning tree modulus. We introduce a new notion of Beurling partition, and we identify two important ones, which correspond to the notion of strength and maximum denseness of an arbitrary graph. These special partitions, also give rise to two deflation processes that reveal a hierarchical structure for general graphs. While Fulkerson duality for spanning tree families can be dedu…

This https://arxiv.org/abs/0901.1988 has been replaced.
link: https://scholar.google.com/scholar?q=a<…

Many-Help-One Problem for Gaussian Sources with a Tree Structure on their Correlation
In this paper we consider the separate coding problem for $L+1$ correlated Gaussian memoryless sources. We deal with the case where $L$ separately encoded data of sources work as side information at the decoder for the reconstruction of the remaining source. The determination problem of the rate distortion region for this system is the so called many-help-one problem and has been known as a highly challenging problem. The author determined the rate distortion region in the case where the $L$ so…

This https://arxiv.org/abs/2311.03602 has been replaced.
initial toot: https://mastoxiv.page/@arXi…

Using a Fast Adaptive Function Approximator to calculate Protein-Filament Binding Kinetics
The cytoskeleton, consisting of biopolymer filaments, molecular motors, and passive crosslinking proteins, provides the internal structure of cells that facilitate movement, growth, and cell division. Understanding the microscopic motor-filament kinetics and dynamics is essential for comprehending macroscopic behaviors of reconstituted cytoskeletal assemblies, such as self-organized flow and active stress. In this study, we employ an adaptive fast Chebyshev approximator based on tree search and…

This https://arxiv.org/abs/2403.03391 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

CoRMF: Criticality-Ordered Recurrent Mean Field Ising Solver
We propose an RNN-based efficient Ising model solver, the Criticality-ordered Recurrent Mean Field (CoRMF), for forward Ising problems. In its core, a criticality-ordered spin sequence of an $N$-spin Ising model is introduced by sorting mission-critical edges with greedy algorithm, such that an autoregressive mean-field factorization can be utilized and optimized with Recurrent Neural Networks (RNNs). Our method has two notable characteristics: (i) by leveraging the approximated tree structure …

The Harmonic Descent Chain
David J. Aldous, Svante Janson, Xiaodan Li
https://arxiv.org/abs/2405.05102 https://arxiv.org/pdf/2405.051…

The Harmonic Descent Chain
The decreasing Markov chain on \{1,2,3, \ldots\} with transition probabilities $p(j,j-i) \propto 1/i$ arises as a key component of the analysis of the beta-splitting random tree model. We give a direct and almost self-contained "probability" treatment of its occupation probabilities, as a counterpart to a more sophisticated but perhaps opaque derivation using a limit continuum tree structure and Mellin transforms.

Embracing Uncertainty Flexibility: Harnessing a Supervised Tree Kernel to Empower Ensemble Modelling for 2D Echocardiography-Based Prediction of Right Ventricular Volume
Tuan A. Bohoran, Polydoros N. Kampaktsis, Laura McLaughlin, Jay Leb, Gerry P. McCann, Archontis Giannakidis
https://arxiv.org/abs/2403.03229

Embracing Uncertainty Flexibility: Harnessing a Supervised Tree Kernel to Empower Ensemble Modelling for 2D Echocardiography-Based Prediction of Right Ventricular Volume
The right ventricular (RV) function deterioration strongly predicts clinical outcomes in numerous circumstances. To boost the clinical deployment of ensemble regression methods that quantify RV volumes using tabular data from the widely available two-dimensional echocardiography (2DE), we propose to complement the volume predictions with uncertainty scores. To this end, we employ an instance-based method which uses the learned tree structure to identify the nearest training samples to a target …

Level-Set Percolation of Gaussian Random Fields on Complex Networks
Reimer Kuehn
https://arxiv.org/abs/2404.05503 https://arxiv.org/p…

Level-Set Percolation of Gaussian Random Fields on Complex Networks
We provide an explicit solution of the problem of level-set percolation for multivariate Gaussians defined in terms of weighted graph Laplacians on complex networks. The solution requires an analysis of the heterogeneous micro-structure of the percolation problem, i.e., a self-consistent determination of locally varying percolation probabilities. This is achieved using a cavity or message passing approach. It can be evaluated, both for single large instances of locally tree-like graphs, and in …

This https://arxiv.org/abs/2402.10460 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csDB_…

A survey of LSM-Tree based Indexes, Data Systems and KV-stores
Modern databases typically makes use of the Log Structured Merge-Tree for organizing data in indexes, which is a kind of disk-based data structure. It was proposed to efficiently handle frequent update queries (also called update intensive workloads) databases. In recent years, LSM-Tree has gained popularity and has been adopted by a number of NoSql databases, and key-value stores. Since LSM-Tree was first proposed, researchers and the database community started efforts to improve different com…

This https://arxiv.org/abs/2310.13653 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Optimal Transport for Measures with Noisy Tree Metric
We study optimal transport (OT) problem for probability measures supported on a tree metric space. It is known that such OT problem (i.e., tree-Wasserstein (TW)) admits a closed-form expression, but depends fundamentally on the underlying tree structure over supports of input measures. In practice, the given tree structure may be, however, perturbed due to noisy or adversarial measurements. To mitigate this issue, we follow the max-min robust OT approach which considers the maximal possible dis…

Lower Bounds for the Minimum Spanning Tree Cycle Intersection Problem
Manuel Dubinsky, Kun-Mao Chao, C\'esar Massri, Gabriel Taubin
https://arxiv.org/abs/2404.17428

Lower Bounds for the Minimum Spanning Tree Cycle Intersection Problem
Minimum spanning trees are important tools in the analysis and design of networks. Many practical applications require their computation, ranging from biology and linguistics to economy and telecommunications. The set of cycles of a network has a vector space structure. Given a spanning tree, the set of non-tree edges defines cycles that determine a basis. The intersection of two such cycles is the number of edges they have in common and the intersection number -- denoted $\cap(G)$ -- is the nu…

PASCL: Supervised Contrastive Learning with Perturbative Augmentation for Particle Decay Reconstruction
Junjian Lu, Siwei Liu, Dmitrii Kobylianski, Etienne Dreyer, Eilam Gross, Shangsong Liang
https://arxiv.org/abs/2402.11538

PASCL: Supervised Contrastive Learning with Perturbative Augmentation for Particle Decay Reconstruction
In high-energy physics, particles produced in collision events decay in a format of a hierarchical tree structure, where only the final decay products can be observed using detectors. However, the large combinatorial space of possible tree structures makes it challenging to recover the actual decay process given a set of final particles. To better analyse the hierarchical tree structure, we propose a graph-based deep learning model to infer the tree structure to reconstruct collision events. In…

This https://arxiv.org/abs/2309.08315 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csRO_…

i-Octree: A Fast, Lightweight, and Dynamic Octree for Proximity Search
Establishing the correspondences between newly acquired points and historically accumulated data (i.e., map) through nearest neighbors search is crucial in numerous robotic applications. However, static tree data structures are inadequate to handle large and dynamically growing maps in real-time. To address this issue, we present the i-Octree, a dynamic octree data structure that supports both fast nearest neighbor search and real-time dynamic updates, such as point insertion, deletion, and on-…

This https://arxiv.org/abs/2306.10707 has been replaced.
link: https://scholar.google.com/scholar?q=a

Partial-order Checking with Unfolding for Linear Temporal Properties
Unfolding can tackle the path-explosion problem caused by concurrency. Traditional unfolding generation faces an NP-complete problem when adding events to the unfolding structure, which also exists in the case of verifying linear temporal logic (LTL). The reason is that it is necessary to enumerate possible concurrent event combinations after adding an event. Many state-of-the-art methods optimally explore unfolding-based structure (called event structure) by a tree-like structure, which should…

This https://arxiv.org/abs/2305.15022 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Hierarchical clustering with dot products recovers hidden tree structure
In this paper we offer a new perspective on the well established agglomerative clustering algorithm, focusing on recovery of hierarchical structure. We recommend a simple variant of the standard algorithm, in which clusters are merged by maximum average dot product and not, for example, by minimum distance or within-cluster variance. We demonstrate that the tree output by this algorithm provides a bona fide estimate of generative hierarchical structure in data, under a generic probabilistic gra…

Guide to k-mer approaches for genomics across the tree of life
Katharine M. Jenike, Luc\'ia Campos-Dom\'inguez, Marilou Bodd\'e, Jos\'e Cerca, Christina N. Hodson, Michael C. Schatz, Kamil S. Jaron
https://arxiv.org/abs/2404.01519

Guide to k-mer approaches for genomics across the tree of life
The wide array of currently available genomes display a wonderful diversity in size, composition and structure with many more to come thanks to several global biodiversity genomics initiatives starting in recent years. However, sequencing of genomes, even with all the recent advances, can still be challenging for both technical (e.g. small physical size, contaminated samples, or access to appropriate sequencing platforms) and biological reasons (e.g. germline restricted DNA, variable ploidy lev…

CoRMF: Criticality-Ordered Recurrent Mean Field Ising Solver
Zhenyu Pan, Ammar Gilani, En-Jui Kuo, Zhuo Liu
https://arxiv.org/abs/2403.03391 https://

CoRMF: Criticality-Ordered Recurrent Mean Field Ising Solver
We propose an RNN-based efficient Ising model solver, the Criticality-ordered Recurrent Mean Field (CoRMF), for forward Ising problems. In its core, a criticality-ordered spin sequence of an $N$-spin Ising model is introduced by sorting mission-critical edges with greedy algorithm, such that an autoregressive mean-field factorization can be utilized and optimized with Recurrent Neural Networks (RNNs). Our method has two notable characteristics: (i) by leveraging the approximated tree structure …

A faster algorithm for the construction of optimal factoring automata
Thomas Erlebach, Kleitos Papadopoulos
https://arxiv.org/abs/2404.02354 https://

A faster algorithm for the construction of optimal factoring automata
The problem of constructing optimal factoring automata arises in the context of unification factoring for the efficient execution of logic programs. Given an ordered set of $n$ strings of length $m$, the problem is to construct a trie-like tree structure of minimum size in which the leaves in left-to-right order represent the input strings in the given order. Contrary to standard tries, the order in which the characters of a string are encountered can be different on different root-to-leaf path…

Log-structured merge-tree databases rely on a combination of in-memory buffers and hierarchies of immutable on-disk structures, two cases where a trie data structure is most efficient. Attend Branimir Lambov's talk at this year's Berlin Buzzwords to see how Apache Cassandra uses and benefits from this combination. #bbuzz

A survey of LSM-Tree based Indexes, Data Systems and KV-stores
Supriya Mishra
https://arxiv.org/abs/2402.10460 https://arxiv.org/pdf/…

A survey of LSM-Tree based Indexes, Data Systems and KV-stores
Modern databases typically makes use of the Log Structured Merge-Tree for organizing data in indexes, which is a kind of disk-based data structure. It was proposed to efficiently handle frequent update queries (also called update intensive workloads) databases. In recent years, LSM-Tree has gained popularity and has been adopted by a number of NoSql databases, and key-value stores. Since LSM-Tree was first proposed, researchers and the database community started efforts to improve different com…

This https://arxiv.org/abs/2208.04448 has been replaced.
link: https://scholar.google.com/scholar?q=a

NeuralVDB: High-resolution Sparse Volume Representation using Hierarchical Neural Networks
We introduce NeuralVDB, which improves on an existing industry standard for efficient storage of sparse volumetric data, denoted VDB [Museth 2013], by leveraging recent advancements in machine learning. Our novel hybrid data structure can reduce the memory footprints of VDB volumes by orders of magnitude, while maintaining its flexibility and only incurring small (user-controlled) compression errors. Specifically, NeuralVDB replaces the lower nodes of a shallow and wide VDB tree structure with …

Tree semi-separable matrices: a simultaneous generalization of sequentially and hierarchically semi-separable representations
Nithin Govindarajan, Shivkumar Chandrasekaran
https://arxiv.org/abs/2402.13381

Tree semi-separable matrices: a simultaneous generalization of sequentially and hierarchically semi-separable representations
We present a unification and generalization of sequentially and hierarchically semi-separable (SSS and HSS) matrices called tree semi-separable (TSS) matrices. Our main result is to show that any dense matrix can be expressed in a TSS format. Here, the dimensions of the generators are specified by the ranks of the Hankel blocks of the matrix. TSS matrices satisfy a graph-induced rank structure (GIRS) property. It is shown that TSS matrices generalize the algebraic properties of SSS and HSS matr…

CoRMF: Criticality-Ordered Recurrent Mean Field Ising Solver
Zhenyu Pan, Ammar Gilani, En-Jui Kuo, Zhuo Liu
https://arxiv.org/abs/2403.03391 https://

CoRMF: Criticality-Ordered Recurrent Mean Field Ising Solver
We propose an RNN-based efficient Ising model solver, the Criticality-ordered Recurrent Mean Field (CoRMF), for forward Ising problems. In its core, a criticality-ordered spin sequence of an $N$-spin Ising model is introduced by sorting mission-critical edges with greedy algorithm, such that an autoregressive mean-field factorization can be utilized and optimized with Recurrent Neural Networks (RNNs). Our method has two notable characteristics: (i) by leveraging the approximated tree structure …

This https://arxiv.org/abs/2112.10463 has been replaced.
link: https://scholar.google.com/scholar?q=a

Quasi-Isometries for certain Right-Angled Coxeter Groups
We construct the JSJ tree of cylinders $T_c$ for finitely presented, one-ended, two-dimensional right-angled Coxeter groups (RACGs) splitting over two-ended subgroups in terms of the defining graph of the group, generalizing the visual construction by Dani and Thomas given for hyperbolic RACGs. Additionally, we prove that $T_c$ has two-ended edge stabilizers if and only if the defining graph does not contain a certain subdivided $K_4$. By use of the structure invariant of $T_c$ introduced by Ca…

This https://arxiv.org/abs/2310.01717 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCL_…

Ensemble Distillation for Unsupervised Constituency Parsing
We investigate the unsupervised constituency parsing task, which organizes words and phrases of a sentence into a hierarchical structure without using linguistically annotated data. We observe that existing unsupervised parsers capture differing aspects of parsing structures, which can be leveraged to enhance unsupervised parsing performance. To this end, we propose a notion of "tree averaging," based on which we further propose a novel ensemble method for unsupervised parsing. To improve infer…

A multi-agent model of hierarchical decision dynamics
Paul Kinsler
https://arxiv.org/abs/2404.17477 https://arxiv.org/pdf/2404.17477<…

A multi-agent model of hierarchical decision dynamics
Decision making can be difficult when there are many actors (or agents) who may be coordinating or competing to achieve their various ideas of the optimum outcome. Here I present a simple decision making model with an explicitly hierarchical binary-tree structure, and evaluate how this might cooperate to take actions that match its various evaluations of the uncertain state of the world. Key features of agent behaviour are (a) the separation of its decision making process into three distinct st…

This https://arxiv.org/abs/2311.09522 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csIT_…

Reversed Indexes $\approx$ Values in Wavelet Trees
This work presents a discovery to advance the wisdom in a particular Succinct Data Structure: Wavelet Tree (Grossi, Gupta, and Vitter 2003). The discovery is first made by showing the feasibility of Reversed Indexes = Values: for integers within $[0,2^{N})$, there exists a Wavelet Tree that its compressed indexes can be equivalent to the Leibniz Binary system (Leibniz 1703), with only the bit reversal. Then we show how to strengthen the discovery by generalizing it into Reversed Indexes $\appro…

Stable tree expressions with Omega-classes and Double Ramification cycles
Xavier Blot, Danilo Lewa\'nski, Paolo Rossi, Sergei Shadrin
https://arxiv.org/abs/2403.05190

Stable tree expressions with Omega-classes and Double Ramification cycles
We propose a new system of conjectural relations in the tautological ring of the moduli space of curves involving stable rooted trees with level structure decorated by Hodge and Ω-classes and prove these conjectures in different cases.

Tree-based conditional copula estimation
Francesco Bonacina, Olivier Lopez, Maud Thomas
https://arxiv.org/abs/2403.12565 https://arxi…

Tree-based conditional copula estimation
This paper proposes a regression tree procedure to estimate conditional copulas. The associated algorithm determines classes of observations based on covariate values and fits a simple parametric copula model on each class. The association parameter changes from one class to another, allowing for non-linearity in the dependence structure modeling. It also allows the definition of classes of observations on which the so-called "simplifying assumption" [see Derumigny and Fermanian, 2017] holds re…

Multi-View Active Sensing for Human-Robot Interaction via Hierarchically Connected Tree
Yuanjiong Ying, Xian Huang, Wei Dong
https://arxiv.org/abs/2403.12538

Multi-View Active Sensing for Human-Robot Interaction via Hierarchically Connected Tree
Comprehensive perception of human beings is the prerequisite to ensure the safety of human-robot interaction. Currently, prevailing visual sensing approach typically involves a single static camera, resulting in a restricted and occluded field of view. In our work, we develop an active vision system using multiple cameras to dynamically capture multi-source RGB-D data. An integrated human sensing strategy based on a hierarchically connected tree structure is proposed to fuse localized visual in…

This https://arxiv.org/abs/2304.01823 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The structure of quasi-transitive graphs avoiding a minor with applications to the domino problem
An infinite graph is quasi-transitive if its vertex set has finitely many orbits under the action of its automorphism group. In this paper we obtain a structure theorem for locally finite quasi-transitive graphs avoiding a minor, which is reminiscent of the Robertson-Seymour Graph Minor Structure Theorem. We prove that every locally finite quasi-transitive graph $G$ avoiding a minor has a tree-decomposition whose torsos are finite or planar; moreover the tree-decomposition is canonical, i.e. in…

This https://arxiv.org/abs/2306.14291 has been replaced.
link: https://scholar.google.com/scholar?q=a

Hyp-OW: Exploiting Hierarchical Structure Learning with Hyperbolic Distance Enhances Open World Object Detection
Open World Object Detection (OWOD) is a challenging and realistic task that extends beyond the scope of standard Object Detection task. It involves detecting both known and unknown objects while integrating learned knowledge for future tasks. However, the level of "unknownness" varies significantly depending on the context. For example, a tree is typically considered part of the background in a self-driving scene, but it may be significant in a household context. We argue that this contextual i…

This https://arxiv.org/abs/2207.10923 has been replaced.
link: https://scholar.google.com/scholar?q=a

The coalescent structure of Galton-Watson trees in varying environments
We investigate the genealogy of a sample of $k\geq1$ particles chosen uniformly without replacement from a population alive at large times in a critical discrete-time Galton-Watson process in a varying environment (GWVE). We will show that subject to an explicit deterministic time-change involving only the mean and variances of the varying offspring distributions, the sample genealogy always converges to the same universal genealogical structure; it has the same tree topology as Kingman's coale…

This https://arxiv.org/abs/2404.15990 has been replaced.
link: https://scholar.google.com/scholar?q=a

A mechanism relating the fermionic mass hierarchy to the flavor mixing
Considering the hierarchical structure of fermionic masses and the fermionic flavor mixing puzzles in the Standard Model, we propose to relate them by the see-saw mechanism, i.e. only the third generation of quarks and charged leptons achieve the masses at the tree level, the first two generations achieves masses through the mixings with the third generation, and the neutrinos achieve tiny Majorana masses by the so-called Type-I see-saw mechanism. This new picture at the fermion sector can expl…

This https://arxiv.org/abs/2401.03003 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csSE_…

AST-T5: Structure-Aware Pretraining for Code Generation and Understanding
Large language models (LLMs) have made significant advancements in code-related tasks, yet many LLMs treat code as simple sequences, neglecting its structured nature. We introduce AST-T5, a novel pretraining paradigm that leverages the Abstract Syntax Tree (AST) for enhanced code generation, transpilation, and understanding. Using dynamic programming, our AST-Aware Segmentation retains code structure, while our AST-Aware Span Corruption objective equips the model to reconstruct various code str…

Sandpile groups for cones over trees
Victor Reiner, Dorian Smith
https://arxiv.org/abs/2402.15453 https://arxiv.org/pdf/2402.15453

Sandpile groups for cones over trees
Sandpile groups are a subtle graph isomorphism invariant, in the form of a finite abelian group, whose cardinality is the number of spanning trees in the graph. We study their group structure for graphs obtained by attaching a cone vertex to a tree. For example, it is shown that the number of generators of the sandpile group is at most one less than the number of leaves in the tree. For trees on a fixed number of vertices, the paths and stars are shown to provide extreme behavior, not only for …

This https://arxiv.org/abs/2207.12653 has been replaced.
link: https://scholar.google.com/scholar?q=a

Incremental Measurement of Structural Entropy for Dynamic Graphs
Structural entropy is a metric that measures the amount of information embedded in graph structure data under a strategy of hierarchical abstracting. To measure the structural entropy of a dynamic graph, we need to decode the optimal encoding tree corresponding to the best community partitioning for each snapshot. However, the current methods do not support dynamic encoding tree updating and incremental structural entropy computation. To address this issue, we propose Incre-2dSE, a novel increm…

Bottom-up Rebalancing Binary Search Trees by Flipping a Coin
Gerth St{\o}lting Brodal
https://arxiv.org/abs/2404.08287 https://arxiv.…

Bottom-up Rebalancing Binary Search Trees by Flipping a Coin
Rebalancing schemes for dynamic binary search trees are numerous in the literature, where the goal is to maintain trees of low height, either in the worst-case or expected sense. In this paper we study randomized rebalancing schemes for sequences of $n$ insertions into an initially empty binary search tree, under the assumption that a tree only stores the elements and the tree structure without any additional balance information. Seidel~(2009) presented a top-down randomized insertion algorithm…

This https://arxiv.org/abs/2402.14181 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Grid Minors and Products
Motivated by recent developments regarding the product structure of planar graphs, we study relationships between treewidth, grid minors, and graph products. We show that the Cartesian product of any two connected $n$-vertex graphs contains an $Ω(\sqrt{n})\timesΩ(\sqrt{n})$ grid minor. This result is tight: The lexicographic product (which includes the Cartesian product as a subgraph) of a star and any $n$-vertex tree has no $ω(\sqrt{n})\timesω(\sqrt{n})$ grid minor.

This https://arxiv.org/abs/2301.07704 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Duality in the directed landscape and its applications to fractal geometry
Geodesic coalescence, or the tendency of geodesics to merge together, is a hallmark phenomenon observed in a variety of planar random geometries involving a random distortion of the Euclidean metric. As a result of this, the union of interiors of all geodesics going to a fixed point tends to form a tree-like structure which is supported on a vanishing fraction of the space. Such geodesic trees exhibit intricate fractal behaviour; for instance, while almost every point in the space has only one …

This https://arxiv.org/abs/2402.14181 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Grid Minors and Products
Motivated by recent developments regarding the product structure of planar graphs, we study relationships between treewidth, grid minors, and graph products. We show that the Cartesian product of any two connected $n$-vertex graphs contains an $Ω(\sqrt{n})\timesΩ(\sqrt{n})$ grid minor. This result is tight: The lexicographic product (which includes the Cartesian product as a subgraph) of a star and any $n$-vertex tree has no $ω(\sqrt{n})\timesω(\sqrt{n})$ grid minor.

This https://arxiv.org/abs/2312.14070 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hepp…

Lepton Flavor Violation in Semileptonic Observables
In this paper, we perform a comprehensive study of Lepton Flavor Violation (LFV) in semileptonic transitions in the framework of an Effective Field Theory with general flavor structure. We account for the Renormalization Group Equations (RGEs), which induce non-trivial correlations between the different types of LFV processes. In particular, we show that these loop effects are needed to improve the bounds on several coefficients that are not efficiently constrained at tree level. For illustrati…

This https://arxiv.org/abs/2402.15453 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Sandpile groups for cones over trees
Sandpile groups are a subtle graph isomorphism invariant, in the form of a finite abelian group, whose cardinality is the number of spanning trees in the graph. We study their group structure for graphs obtained by attaching a cone vertex to a tree. For example, it is shown that the number of generators of the sandpile group is at most one less than the number of leaves in the tree. For trees on a fixed number of vertices, the paths and stars are shown to provide extreme behavior, not only for …

This https://arxiv.org/abs/2303.01726 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csDS_…

Tight bounds for the sensitivity of CDAWGs with left-end edits
Compact directed acyclic word graphs (CDAWGs) [Blumer et al. 1987] are a fundamental data structure on strings with applications in text pattern searching, data compression, and pattern discovery. Intuitively, the CDAWG of a string $T$ is obtained by merging isomorphic subtrees of the suffix tree [Weiner 1973] of the same string $T$, thus CDAWGs are a compact indexing structure. In this paper, we investigate the sensitivity of CDAWGs when a single character edit operation (insertion, deletion, …

This https://arxiv.org/abs/2403.03229 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qbi…

Embracing Uncertainty Flexibility: Harnessing a Supervised Tree Kernel to Empower Ensemble Modelling for 2D Echocardiography-Based Prediction of Right Ventricular Volume
The right ventricular (RV) function deterioration strongly predicts clinical outcomes in numerous circumstances. To boost the clinical deployment of ensemble regression methods that quantify RV volumes using tabular data from the widely available two-dimensional echocardiography (2DE), we propose to complement the volume predictions with uncertainty scores. To this end, we employ an instance-based method which uses the learned tree structure to identify the nearest training samples to a target …

This https://arxiv.org/abs/2207.04855 has been replaced.
link: https://scholar.google.com/scholar?q=a

Canonical graph decompositions via coverings
We present a canonical way to decompose finite graphs into highly connected local parts. The decomposition depends only on an integer parameter whose choice sets the intended degree of locality. The global structure of the graph, as determined by the relative position of these parts, is described by a coarser $\it model$. This is a simpler graph determined entirely by the decomposition, not imposed. The model and decomposition are obtained as projections of the tangle-tree structure of a cove…

Grid Minors and Products
Vida Dujmovi\'c, Pat Morin, David Wood, David Worley
https://arxiv.org/abs/2402.14181 https://arxiv.org/…

Grid Minors and Products
Motivated by recent developments regarding the product structure of planar graphs, we study relationships between treewidth, grid minors, and graph products. We show that the Cartesian product of any two connected $n$-vertex graphs contains an $Ω(\sqrt{n})\timesΩ(\sqrt{n})$ grid minor. This result is tight: The lexicographic product (which includes the Cartesian product as a subgraph) of a star and any $n$-vertex tree has no $ω(\sqrt{n})\timesω(\sqrt{n})$ grid minor.

Applying affine urn models to the global profile of hyperrecursive trees
Joshua Sparks
https://arxiv.org/abs/2403.10714 https://arxiv…

Applying affine urn models to the global profile of hyperrecursive trees
Inside the discipline of graph theory exists an extension known as the hypergraph. This generalization of graphs includes vertices along with hyperedges consisting of collections of two or more vertices. One well-studied application of this structure is that of the recursive tree, and we apply its framework within the context of hypergraphs to form hyperrecursive trees, an area that shows promise in network theory. However, when the global profile of these hyperrecursive trees is studied via re…