IA Scholar Query: Generalized k-tuple colorings of cycles and other graphs.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgSun, 18 Sep 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440MARRS: A Framework for multi-objective risk-aware route recommendation using Multitask-Transformer
https://scholar.archive.org/work/xr5f5qibkfg6rgczqf7iuzd6xq
One of the most significant map services in navigation applications is route recommendation. However, most route recommendation systems only recommend trips based on time and distance, impacting quality-of-experience and route selection. This paper introduces a novel framework, namely MARRS, a multi-objective route recommendation system based on heterogeneous urban sensing open data (i.e., crime, accident, traffic flow, road network, meteorological, calendar event, and point of interest distributions). We introduce a wide, deep, and multitask-learning (WD-MTL) framework that uses a transformer to extract spatial, temporal, and semantic correlation for predicting crime, accident, and traffic flow of particular road segment. Later, for a particular source and destination, the adaptive epsilon constraint technique is used to optimize route satisfying multiple objective functions. The experimental results demonstrate the feasibility of figuring out the safest and efficient route selection.Bhumika, Debasis Daswork_xr5f5qibkfg6rgczqf7iuzd6xqSun, 18 Sep 2022 00:00:00 GMTNon-kissing complexes and tau-tilting for gentle algebras
https://scholar.archive.org/work/xefhjt4czzfr3lorskorfmoutq
We interpret the support τ-tilting complex of any gentle bound quiver as the non-kissing complex of walks on its blossoming quiver. Particularly relevant examples were previously studied for quivers defined by a subset of the grid or by a dissection of a polygon. We then focus on the case when the non-kissing complex is finite. We show that the graph of increasing flips on its facets is the Hasse diagram of a congruence-uniform lattice. Finally, we study its 𝐠-vector fan and prove that it is the normal fan of a non-kissing associahedron.Yann Palu, Vincent Pilaud, Pierre-Guy Plamondonwork_xefhjt4czzfr3lorskorfmoutqWed, 14 Sep 2022 00:00:00 GMTBayesian Tensor Factorized Vector Autoregressive Models for Inferring Granger Causality Patterns from High-Dimensional Multi-subject Panel Neuroimaging Data
https://scholar.archive.org/work/ctqfre3ktngfthyuhtt4dtzqd4
Understanding the dynamics of functional brain connectivity patterns using noninvasive neuroimaging techniques is an important focus in human neuroscience. Vector autoregressive (VAR) processes and Granger causality analysis (GCA) have been extensively used for this purpose. While high-resolution multi-subject neuroimaging data are routinely collected now-a-days, the statistics literature on VAR models has remained heavily focused on small-to-moderate dimensional problems and single-subject data. Motivated by these issues, we develop a novel Bayesian random effects panel VAR model for multi-subject high-dimensional neuroimaging data. We begin with a single-subject model that structures the VAR coefficients as a three-way tensor, then reduces the dimensions by applying a Tucker tensor decomposition. A novel sparsity-inducing shrinkage prior allows data-adaptive rank and lag selection. We then extend the approach to a novel random effects model for multi-subject data that carefully avoids the dimensions getting exploded with the number of subjects but also flexibly accommodates subject-specific heterogeneity. We design a Markov chain Monte Carlo algorithm for posterior computation. Finally, GCA with posterior false discovery control is performed on the posterior samples. The method shows excellent empirical performance in simulation experiments. Applied to our motivating functional magnetic resonance imaging study, the approach allows the directional connectivity of human brain networks to be studied in fine detail, revealing meaningful but previously unsubstantiated cortical connectivity patterns.Jingjing Fan, Kevin Sitek, Bharath Chandrasekaran, Abhra Sarkarwork_ctqfre3ktngfthyuhtt4dtzqd4Wed, 14 Sep 2022 00:00:00 GMTString Diagram Rewrite Theory II: Rewriting with Symmetric Monoidal Structure
https://scholar.archive.org/work/2njpyhl4cnctlbkq3yyrs5ssia
Symmetric monoidal theories (SMTs) generalise algebraic theories in a way that make them suitable to express resource-sensitive systems, in which variables cannot be copied or discarded at will. In SMTs, traditional tree-like terms are replaced by string diagrams, topological entities that can be intuitively thoughts as diagrams of wires and boxes. Recently, string diagrams have become increasingly popular as a graphical syntax to reason about computational models across diverse fields, including programming language semantics, circuit theory, quantum mechanics, linguistics, and control theory. In applications, it is often convenient to implement the equations appearing in SMTs as rewriting rules. This poses the challenge of extending the traditional theory of term rewriting, which has been developed for algebraic theories, to string diagrams. In this paper, we develop a mathematical theory of string diagram rewriting for SMTs. Our approach exploits the correspondence between string diagram rewriting and double pushout (DPO) rewriting of certain graphs, introduced in the first paper of this series. Such a correspondence is only sound when the SMT includes a Frobenius algebra structure. In the present work, we show how an analogous correspondence may be established for arbitrary SMTs, once an appropriate notion of DPO rewriting (which we call convex) is identified. As proof of concept, we use our approach to show termination of two SMTs of interest: Frobenius semi-algebras and bialgebras.Filippo Bonchi, Fabio Gadducci, Aleks Kissinger, Pawel Sobocinski, Fabio Zanasiwork_2njpyhl4cnctlbkq3yyrs5ssiaWed, 14 Sep 2022 00:00:00 GMTNeutrosophic k-Number
https://scholar.archive.org/work/ymw3bowjrzcybkqidjm2g4zuvm
Also, some studies and researches about neutrosophic graphs, are proposed as books in following by Henry Garrett (2022) which is indexed by Google Scholar and has more than 300 readers in Scribd. [Ref] Henry Garrett, (2022). "Beyond Neutrosophic Graphs", Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grand- view Heights, Ohio 43212 United States. ISBN: 978-1-59973-725-6 (http://fs.unm.edu/BeyondNeutrosophicGraphs.pdf). And in following by Henry Garrett (2022) which is indexed by Google Scholar and has more than 1000 readers in Scribd. [Ref] Henry Garrett, (2022). "Neutrosophic Duality", Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. ISBN: 978-1-59973-743-0 (http://fs.unm.edu/NeutrosophicDuality.pdf).Henry Garrettwork_ymw3bowjrzcybkqidjm2g4zuvmWed, 14 Sep 2022 00:00:00 GMTGeometric models for the derived categories of Ginzburg algebras of n-angulated surfaces via local-to-global principles
https://scholar.archive.org/work/ukanqnp26jejflpkdbcgis3udm
We relate the derived category of a relative Ginzburg algebra of an n-angulated surface to the geometry of the surface. Results include the description of a subset of the objects in the derived category in terms of curves in the surface and their Homs in terms of intersection. By using the description of these derived categories as the global sections of perverse schobers, we arrive at the geometric model through gluing local data. Most results also hold for the perverse schobers defined over any commutative ring spectrum. As an application of the geometric model in the case n=3, we match some Ext-groups in the derived categories of these relative Ginzburg algebras and the extended mutation matrices of a class of cluster algebras with coefficients, associated to multi-laminated marked surfaces by Fomin-Thurston. Finally, we also consider a modified version of the perverse schober for triangulated surfaces with punctures.Merlin Christwork_ukanqnp26jejflpkdbcgis3udmWed, 14 Sep 2022 00:00:00 GMTA Review and Roadmap of Deep Learning Causal Discovery in Different Variable Paradigms
https://scholar.archive.org/work/2wzo2fn5zncqncsi2h6cuo2ydq
Understanding causality helps to structure interventions to achieve specific goals and enables predictions under interventions. With the growing importance of learning causal relationships, causal discovery tasks have transitioned from using traditional methods to infer potential causal structures from observational data to the field of pattern recognition involved in deep learning. The rapid accumulation of massive data promotes the emergence of causal search methods with brilliant scalability. Existing summaries of causal discovery methods mainly focus on traditional methods based on constraints, scores and FCMs, there is a lack of perfect sorting and elaboration for deep learning-based methods, also lacking some considers and exploration of causal discovery methods from the perspective of variable paradigms. Therefore, we divide the possible causal discovery tasks into three types according to the variable paradigm and give the definitions of the three tasks respectively, define and instantiate the relevant datasets for each task and the final causal model constructed at the same time, then reviews the main existing causal discovery methods for different tasks. Finally, we propose some roadmaps from different perspectives for the current research gaps in the field of causal discovery and point out future research directions.Hang Chen, Keqing Du, Xinyu Yang, Chenguang Liwork_2wzo2fn5zncqncsi2h6cuo2ydqWed, 14 Sep 2022 00:00:00 GMTTrace Moments of the Sample Covariance Matrix with Graph-Coloring
https://scholar.archive.org/work/73cpada6uvbkxj6eff2crgq2te
Let S_p,n denote the sample covariance matrix based on n independent identically distributed p-dimensional random vectors in the null-case. The main result of this paper is an expansion of trace moments and power-trace covariances of S_p,n simultaneously for both high- and low-dimensional data. To this end we develop a graph theory oriented ansatz of describing trace moments as weighted sums over colored graphs. Specifically, explicit formulas for the highest order coefficients in the expansion are deduced by restricting attention to graphs with either no or one cycle. The novelty is a color-preserving decomposition of graphs into a tree-structure and their seed graphs, which allows for the identification of Euler circuits from graphs with the same tree-structure but different seed graphs. This approach may also be used to approximate the mean and covariance to even higher degrees of accuracy.Ben Deitmarwork_73cpada6uvbkxj6eff2crgq2teTue, 13 Sep 2022 00:00:00 GMTStochastic pedestrian models for autonomous vehicles
https://scholar.archive.org/work/4f6lofvmrvhxbld6ywopeosj6y
This dissertation addresses the modeling of pedestrians in dynamic and urban environments interacting with autonomous vehicles. The collision avoidance system of an autonomous vehicle has contrary safety and effi- ciency requirements. On the one hand, there might be collisions in following a risky driving policy. On the other hand, a safe driving policy might bring the passenger very slow to the target to prevent all kinds of risks. The au- tonomous vehicle does not know or perceive all relevant information, such as the unknown intention and the environmental and situational factors influencing the pedestrian's behavior. There is a resulting decision dilemma for autonomous vehicles between road safety for all road users and efficient motion planning in environments with vulnerable road users. There also exists a lack of knowledge by predicting the future movements of pedestri- ans, where one could compute worst-case reachable state-sets. The areas of possible reach sets could get very large. An autonomous vehicle is not allowed to drive into these areas, making motion planning inefficient. The adaption to real-world scenarios is not trivial. The decision-making process in motion planning is challenging due to the enormous variety of situations and the uncertainty of predicting future human movements with absolute certainty. There is a potential risk of accidents in adapting and predicting human locomotion. These problems influence the trust and acceptance of autonomous vehicles with additional technological and legal challenges. This dissertation aims not to ensure total safety because of pedestrians' technical and diverse physical, cognitive, situational, and environmental complexity. This work uses a new method that combines machine learning with reachability analysis (resulting in an adaptive funnel, hull, or belief set computation). Machine learning adapts the reachability analysis to current situations. Therefore adaptive reachability analysis and corresponding mo- tion planning are presented and evaluated i [...]Michael Hartmannwork_4f6lofvmrvhxbld6ywopeosj6yTue, 13 Sep 2022 00:00:00 GMTSoftware-Hardware Codesign for Efficient In-Memory Regular Pattern Matching
https://scholar.archive.org/work/yevofpvxwvawdefyut7rbtoavq
Regular pattern matching is used in numerous application domains, including text processing, bioinformatics, and network security. Patterns are typically expressed with an extended syntax of regular expressions that include the computationally challenging construct of bounded iteration or counting, which describes the repetition of a pattern a fixed number of times. We develop a design for a specialized in-memory hardware architecture for NFA execution that integrates counter and bit vector elements. The design is inspired by the theoretical model of nondeterministic counter automata (NCA). A key feature of our approach is that we statically analyze regular expressions to determine bounds on the amount of memory needed for the occurrences of counting. The results of this analysis are used by a regex-to-hardware compiler in order to make an appropriate selection of counter or bit vector elements. We evaluate the performance of our hardware implementation on a simulator based on circuit parameters collected by SPICE simulation using a TSMC 28nm process. We find the usage of counter and bit vector quickly outperforms unfolding solutions by orders of magnitude with small counting quantifiers. Experiments concerning realistic workloads show up to 76% energy reduction and 58% area reduction in comparison to traditional in-memory NFA processors.Lingkun Kong, Qixuan Yu, Agnishom Chattopadhyay, Alexis Le Glaunec, Yi Huang, Konstantinos Mamouras, Kaiyuan Yangwork_yevofpvxwvawdefyut7rbtoavqTue, 13 Sep 2022 00:00:00 GMTAutomated detection of pronunciation errors in non-native English speech employing deep learning
https://scholar.archive.org/work/ovpm5jerkrbkretr3di2grcocy
Despite significant advances in recent years, the existing Computer-Assisted Pronunciation Training (CAPT) methods detect pronunciation errors with a relatively low accuracy (precision of 60% at 40%-80% recall). This Ph.D. work proposes novel deep learning methods for detecting pronunciation errors in non-native (L2) English speech, outperforming the state-of-the-art method in AUC metric (Area under the Curve) by 41%, i.e., from 0.528 to 0.749. One of the problems with existing CAPT methods is the low availability of annotated mispronounced speech needed for reliable training of pronunciation error detection models. Therefore, the detection of pronunciation errors is reformulated to the task of generating synthetic mispronounced speech. Intuitively, if we could mimic mispronounced speech and produce any amount of training data, detecting pronunciation errors would be more effective. Furthermore, to eliminate the need to align canonical and recognized phonemes, a novel end-to-end multi-task technique to directly detect pronunciation errors was proposed. The pronunciation error detection models have been used at Amazon to automatically detect pronunciation errors in synthetic speech to accelerate the research into new speech synthesis methods. It was demonstrated that the proposed deep learning methods are applicable in the tasks of detecting and reconstructing dysarthric speech.Daniel Korzekwawork_ovpm5jerkrbkretr3di2grcocyTue, 13 Sep 2022 00:00:00 GMTOnline Algorithms with Lookaround
https://scholar.archive.org/work/dosd4c67l5hqzohusswxgfkusm
In this work, we give a unifying view of locality in four settings: distributed algorithms, sequential greedy algorithms, dynamic algorithms, and online algorithms. We introduce a new model of computing, called the online-LOCAL model: the adversary reveals the nodes of the input graph one by one, in the same way as in classical online algorithms, but for each new node the algorithm can also inspect its radius-T neighborhood before choosing the output. Instead of looking ahead in time, we have the power of looking around in space. We compare the online-LOCAL model with three other models: the LOCAL model of distributed computing, where each node produces its output based on its radius-T neighborhood, its sequential counterpart SLOCAL, and the dynamic-LOCAL model, where changes in the dynamic input graph only influence the radius-T neighborhood of the point of change. SLOCAL and dynamic-LOCAL models are sandwiched between LOCAL and online-LOCAL models, with LOCAL being the weakest and online-LOCAL the strongest model. In this work, we seek to answer the following question: is the online-LOCAL model strictly stronger than the LOCAL model when we look at graph algorithms for solving locally checkable labeling problems (LCLs)? First, we show that for LCL problems in paths, cycles, and rooted trees, all four models are roughly equivalent: the locality of any LCL problem falls in the same broad class - O(log^* n), Θ(log n), or n^Θ(1) - in all four models. In particular, prior work on the LOCAL model directly generalizes to all four models. Second, we show that this equivalence does not hold in two-dimensional grids. We show that the locality of the 3-coloring problem is O(log n) in the online-LOCAL model, while it is known to be Ω(√(n)) in the LOCAL model.Amirreza Akbari, Navid Eslami, Henrik Lievonen, Darya Melnyk, Joona Särkijärvi, Jukka Suomelawork_dosd4c67l5hqzohusswxgfkusmMon, 12 Sep 2022 00:00:00 GMTMending Partial Solutions with Few Changes
https://scholar.archive.org/work/jjjpn3e7o5gczhnh2men6s43fy
In this paper, we study the notion of mending, i.e. given a partial solution to a graph problem, we investigate how much effort is needed to turn it into a proper solution. For example, if we have a partial coloring of a graph, how hard is it to turn it into a proper coloring? In prior work (SIROCCO 2022), this question was formalized and studied from the perspective of mending radius: if there is a hole that we need to patch, how far do we need to modify the solution? In this work, we investigate a complementary notion of mending volume: how many nodes need to be modified to patch a hole? We focus on the case of locally checkable labeling problems (LCLs) in trees, and show that already in this setting there are two infinite hierarchies of problems: for infinitely many values 0 < α≤ 1, there is an LCL problem with mending volume Θ(n^α), and for infinitely many values k ≥ 1, there is an LCL problem with mending volume Θ(log^k n). Hence the mendability of LCL problems on trees is a much more fine-grained question than what one would expect based on the mending radius alone. We define three variants of the theme: (1) existential mending volume, i.e., how many nodes need to be modified, (2) expected mending volume, i.e., how many nodes we need to explore to find a patch if we use randomness, and (3) deterministic mending volume, i.e., how many nodes we need to explore if we use a deterministic algorithm. We show that all three notions are distinct from each other, and we analyze the landscape of the complexities of LCL problems for the respective models.Darya Melnyk, Jukka Suomela, Neven Villaniwork_jjjpn3e7o5gczhnh2men6s43fyMon, 12 Sep 2022 00:00:00 GMTSpinorial Games and Synaptic Economics
https://scholar.archive.org/work/owy6xa2v3bcx3muopa5kiug5hm
Projections from the study of the human universe onto the study of the self-organizing brain are herein leveraged to address certain concerns raised in latest neuroscience research, namely (i) the extent to which neural codes are multidimensional; (ii) the functional role of neural dark matter; (iii) the challenge to traditional theoretical frameworks posed by the needs for accurate interpretation of large-scale neural recordings linking brain and behavior. On the grounds of (hyper-)self-duality under (hyper-)mirror supersymmetry, inter-relativistic principles are introduced, whose consolidation, as pillars of a network- and game-theoretical construction, is conducive to (i) the reproduction of core experimental observations on neural coding in the self-organizing brain, in connection with behavior; (ii) a proof that the instantaneous geometric dimensionality of neural (co-)representations of a spontaneous (co-)behavioral state is at most 16, unidirectionally; (iii) spinor (co-)representations, as the latent building blocks of self-organizing cortical circuits subserving (co-)behavioral states; (iv) an early crystallization of pertinent multidimensional synaptic (co-)architectures, whereby Lorentz (co-)partitions are in principle verifiable; and, ultimately, (v) potentially inverse insights into matter-antimatter asymmetry.Sofia Karamintziouwork_owy6xa2v3bcx3muopa5kiug5hmMon, 12 Sep 2022 00:00:00 GMTOn the M2-Brane Index on Noncommutative Crepant Resolutions
https://scholar.archive.org/work/ctts5nlb5vho5jsa7cct4tlqlm
On certain M-theory backgrounds which are a circle fibration over a smooth Calabi-Yau, the quantum theory of M2 branes can be studied in terms of the K-theoretic Donaldson-Thomas theory on the threefold. We extend this relation to noncommutative crepant resolutions. In this case the threefold develops a singularity and classical smooth geometry is replaced by the algebra of paths of a certain quiver. K-theoretic quantities on the quiver representation moduli space can be computed via toric localization and result in certain rational functions of the toric parameters. We discuss in particular the case of the conifold and certain orbifold singularities.Michele Ciraficiwork_ctts5nlb5vho5jsa7cct4tlqlmSun, 11 Sep 2022 00:00:00 GMTInducibility in the hypercube
https://scholar.archive.org/work/337sqo2gcba4xlfhkndvdtjnga
Let Q_d be the hypercube of dimension d and let H and K be subsets of the vertex set V(Q_d), called configurations in Q_d. We say that K is an exact copy of H if there is an automorphism of Q_d which sends H onto K. Let n≥ d be an integer, let H be a configuration in Q_d and let S be a configuration in Q_n. We let λ(H,d,n) be the maximum, over all configurations S in Q_n, of the fraction of sub-d-cubes R of Q_n in which S∩ R is an exact copy of H, and we define the d-cube density λ(H,d) of H to be the limit as n goes to infinity of λ(H,d,n). We determine λ(H,d) for several configurations in Q_3 and Q_4 as well as for an infinite family of configurations. There are strong connections with the inducibility of graphs.John Goldwasser, Ryan Hansenwork_337sqo2gcba4xlfhkndvdtjngaSat, 10 Sep 2022 00:00:00 GMTA capacitated multi-vehicle covering tour problem on a road network and its application to waste collection
https://scholar.archive.org/work/yzms4fp4ffdlvfmec5zxzkvkwa
In most Swiss municipalities, a curbside system consisting of heavy trucks stopping at almost each household is used for non-recoverable waste collection. Due to the many stops of the trucks, this strategy causes high fuel consumption, emissions and noise. These effects can be alleviated by reducing the number of stops performed by collection vehicles. One possibility consists of locating collection points throughout the municipality such that residents bring their waste to their most preferred location. The optimization problem consists of selecting a subset of candidate locations to place the points such that each household disposes the waste at the most preferred location. Provided that the underlying road network is available, we refer to this optimization problem as the capacitated multi-vehicle covering tour problem on a road network (Cm-CTP-R). We introduce two mixed-integer linear programming (MILP) formulations: a road-network-based formulation that exploits the sparsity of the network and a customer-based formulation typically used in vehicle routing problems (VRP). To solve large instances, we propose a two-phased heuristic approach that addresses the two subproblems the Cm-CTP-R is built on: a set covering problem to select the locations and a split-delivery VRP to determine the routes. Computational experiments on both small and real-life instances show that the road-network-based formulation is better suited. Furthermore, the proposed heuristic provides good solutions with optimality gaps below 0.5% and 3.5% for 75% of the small and real-life instances respectively and is able to find better solutions than the exact method for many real-life instances.V. Fischer, M. Pacheco Paneque, A. Legrain, R. Bürgywork_yzms4fp4ffdlvfmec5zxzkvkwaThu, 08 Sep 2022 00:00:00 GMTThe Polyhedral Tree Complex
https://scholar.archive.org/work/pl2hlerhlbhzvnwfmosn5ihqaq
The tree complex is a simplicial complex defined in recent work of Belk, Lanier, Margalit, and Winarski with natural applications to mapping class groups and complex dynamics. In this article, we connect this setting with the study of certain convex polytopes: associahedra and cyclohedra. Specifically, we describe a characterization of these polytopes using planar embeddings of trees and show that the tree complex is the barycentric subdivision of a polyhedral cell complex for which the cells are products of associahedra and cyclohedra.Michael Doughertywork_pl2hlerhlbhzvnwfmosn5ihqaqThu, 08 Sep 2022 00:00:00 GMTPlanarizing Graphs and their Drawings by Vertex Splitting
https://scholar.archive.org/work/cwbm5bksqnewzcqghgyadfas4i
The splitting number of a graph G=(V,E) is the minimum number of vertex splits required to turn G into a planar graph, where a vertex split removes a vertex v ∈ V, introduces two new vertices v_1, v_2, and distributes the edges formerly incident to v among its two split copies v_1, v_2. The splitting number problem is known to be NP-complete. In this paper we shift focus to the splitting number of graph drawings in ℝ^2, where the new vertices resulting from vertex splits can be re-embedded into the existing drawing of the remaining graph. We first provide a non-uniform fixed-parameter tractable (FPT) algorithm for the splitting number problem (without drawings). Then we show the NP-completeness of the splitting number problem for graph drawings, even for its two subproblems of (1) selecting a minimum subset of vertices to split and (2) for re-embedding a minimum number of copies of a given set of vertices. For the latter problem we present an FPT algorithm parameterized by the number of vertex splits. This algorithm reduces to a bounded outerplanarity case and uses an intricate dynamic program on a sphere-cut decomposition.Martin Nöllenburg and Manuel Sorge and Soeren Terziadis and Anaïs Villedieu and Hsiang-Yun Wu and Jules Wulmswork_cwbm5bksqnewzcqghgyadfas4iThu, 08 Sep 2022 00:00:00 GMTEnumerative and Distributional Results for d-combining Tree-Child Networks
https://scholar.archive.org/work/wrz62w5c2bawzfbgnovsi3555m
Tree-child networks are one of the most prominent network classes for modeling evolutionary processes which contain reticulation events. Several recent studies have addressed counting questions for bicombining tree-child networks in which every reticulation node has exactly two parents. We extend these studies to d-combining tree-child networks where every reticulation node has now d≥ 2 parents, and we study one-component as well as general tree-child networks. Moreover, we also give results on the distributional behavior of shape parameters (e.g., number of reticulation nodes, Sackin index) of a network which is drawn uniformly at random from the set of all tree-child networks with the same number of leaves. We show phase transitions depending on d, leading to normal, Bessel, Poisson, and degenerate distributions. Some of our results are new even in the bicombining case.Yu-Sheng Chang, Michael Fuchs, Hexuan Liu, Michael Wallner, Guan-Ru Yuwork_wrz62w5c2bawzfbgnovsi3555mThu, 08 Sep 2022 00:00:00 GMT