arXiv subjects

Mark Jones

Publications and source records attributed to Mark Jones.

At least 19 recordsLinked to original sources

arXiv2026

Metropolis-Hastings Sampling of Phylogenetic Networks: Correcting for Symmetries

In phylogenetics, Metropolis-Hastings methods are commonly used to sample phylogenetic trees or networks, for example from Bayesian posteriors. These methods generally use transitions that distinguish all nodes involved, and thus require fully labelled representations of phylogenetic networks. We argue that sampling leaf-labelled phylogenetic networks demands a correction for the number of fully labelled representatives of a leaf-labelled network, or, equivalently, for its internal symmetry. Without correction, there is a danger of undersampling networks with internal symmetries. We show that this correction can be realized by a quotient construction on the Metropolis-Hastings Markov chain, which, in practice, requires the calculation of the size of the network's automorphism group. Using $\mu$-vectors, we show that the automorphism group is trivial for orchard networks, and thus also for tree-child networks and trees. This implies that a correction for symmetry is not needed when sampling only from such network classes. More generally, using our Python implementation of the algorithms in this paper, we show that using $\mu$-vectors can significantly speed up calculations of automorphism group sizes and thus of Metropolis-Hastings sampling of leaf-labelled networks.

cs.DM↗

arXiv2026

Maximizing All-Paths Phylogenetic Diversity: Parameterized Approaches for Networks

Phylogenetic Diversity (PD) is a fundamental measure of biodiversity, originally defined on phylogenetic trees and widely used in conservation biology. Phylogenetic trees are often generalised to directed acyclic graphs, called phylogenetic networks. As such, a corresponding generalization of PD is needed. A natural generalization to edge-weighted phylogenetic networks is the all-paths measure, where the diversity of a set S of species (taxa) is defined as the total weight of all edges that lie on a path from the root to at least one species in S. While maximizing PD on trees can be solved in polynomial time, the corresponding problem on networks is NP-hard and difficult to approximate. We undertake a systematic parameterized complexity study of the Max-All-Paths-PD (MapPD) problem. We establish W[2]-hardness when parameterized by the number of species that are included in a solution, and W[1]-hardness for the number of species that are excluded. On the positive side, we show that the problem is fixed-parameter tractable with respect to the threshold of diversity and the acceptable loss of diversity. We further analyze how the network's proximity to a tree influences algorithmic behavior and present single-exponential fixed-parameter algorithms when parameterized by the number of reticulations and by the treewidth of the underlying graph. Finally, we present a polynomial kernelization for MapPD with respect to the number of reticulation edges.

cs.DS↗

arXiv2026

Proximity Measures for Classes of Phylogenetic Networks

Phylogenetic networks are used to represent the evolutionary history of species. Due to biological interpretations and computational advantages, researchers have focused on restricted classes of phylogenetic networks, such as tree-child, orchard, and tree-based. These classes capture different notions of tree-likeness: tree-child networks require every internal vertex to have a taxon reachable by a tree path, orchard networks are trees with horizontal arcs (for modelling histories rife with horizontal gene transfers), and tree-based networks are trees with additional (not-necessarily horizontal) arcs. A natural question to ask is ``how far is a given network from belonging to a particular class?'' This motivates the study of proximity measures, which measure the minimum number of graph modifications required to transform a network into one belonging to a particular class. In this paper, we consider three proximity measures based on leaf addition, valid arc deletion, and arc deletion. We study pairwise comparability of the proximity measures, prove complexity results, and derive extremal bounds for the classes of tree, tree-child, orchard, and tree-based networks.

math.CO↗

arXiv2026

Tree Containment Parameterized by Scanwidth

TREE CONTAINMENT is a central decision problem in mathematical phylogenetics, asking whether a given rooted phylogenetic tree is embeddable in ("displayed by") a given rooted phylogenetic network. While the problem is NP-complete for general networks, many algorithmic advances have relied on structural parameters that capture how "tree-like" a network is. In this paper we investigate TREE CONTAINMENT under the structural parameter scanwidth, a directed width measure generalizing popular parameters measuring tree-likeness of phylogenetic networks. We first present a parameterized algorithm that solves the problem in $O(4^{k + k\log{k}} n + nm^2)$ time, where $n$ and $m$ are the numbers of nodes and arcs in the network and $k$ is the width of a given tree-extension. Complementing this upper bound, we prove a matching lower bound under the Exponential-Time Hypothesis (ETH), showing that there is no algorithm for TREE CONTAINMENT that runs in $2^{o(c\log{c})} n^{O(1)}$ time, even on binary inputs, where $c$ is the directed cutwidth of the input network, which upper-bounds the scanwidth $k$.

cs.DS↗

arXiv2026

Average-Tree Phylogenetic Diversity Parameterized by Scanwidth and Invisibility

We investigate parameterized algorithms for computing the average-tree phylogenetic diversity (APD) in rooted phylogenetic networks, studying the problem under different structural parameters that capture the deviation of a network from a tree. Our primary parameter is the scanwidth, a measure of the tree-likeness of a given directed acyclic graph. We show that a subset of taxa with maximum APD can be found in polynomial time in phylogenetic networks of scanwidth at most 2, but becomes NP-hard in networks of scanwidth 3. Further, we design an algorithm that computes the APD of a given set of taxa in O(2^sw n) time, where sw denotes the scanwidth and n the number of taxa in the input network. Finally, we give a linear-time algorithm for computing the APD of a given set of taxa if the network induced by these taxa is reticulation-visible. We generalize this algorithm to still run in polynomial time if each biconnected component of the induced network has only constantly many invisible reticulations.

cs.DS↗

arXiv2026

A Class of Unrooted Phylogenetic Networks Inspired by the Properties of Rooted Tree-Child Networks

A directed phylogenetic network is tree-child if every non-leaf vertex has a child that is not a reticulation. As a class of directed phylogenetic networks, tree-child networks are very useful from a computational perspective. For example, several computationally difficult problems in phylogenetics become tractable when restricted to tree-child networks. At the same time, the class itself is rich enough to contain quite complex networks. Furthermore, checking whether a directed network is tree-child can be done in polynomial time. In this paper, we seek a class of undirected phylogenetic networks that is rich and computationally useful in a similar way to the class tree-child directed networks. A natural class to consider for this role is the class of tree-child-orientable networks which contains all those undirected phylogenetic networks whose edges can be oriented to create a tree-child network. However, we show here that recognizing such networks is NP-hard, even for binary networks, and as such this class is inappropriate for this role. Towards finding a class of undirected networks that fills a similar role to directed tree-child networks, we propose new classes called $q$-cuttable networks, for any integer $q\geq 1$. We show that these classes have many of the desirable properties, similar to tree-child networks in the rooted case, including being recognizable in polynomial time, for all $q\geq 1$. Towards showing the computational usefulness of the class, we show that the NP-hard problem Tree Containment is polynomial-time solvable when restricted to $q$-cuttable networks with $q\geq 3$.

math.CO↗

arXiv2026

The BigBite Calorimeter for the Super Bigbite Spectrometer Program at Jefferson Lab

We report features of the design, construction, installation, and performance of the BigBite Calorimeter (BBCal), a lead-glass electromagnetic calorimeter constructed as part of the BigBite Spectrometer (BBS), which served as the electron arm for the Super Bigbite Spectrometer (SBS) program of high-precision neutron electromagnetic form factor measurements in Hall A at Jefferson Lab. As a total-absorption calorimeter, BBCal provided the primary electron trigger for BBS, detecting (quasi-) elastically scattered electrons in the 1-4 GeV energy range with an energy resolution of approximately 6.2%, position resolution of 1.2 cm, and timing resolution of 0.5 ns.

physics.ins-det↗

arXiv2025

Bounds on the sequence length sufficient to reconstruct binary level-$1$ phylogenetic networks under the CFN model

Phylogenetic trees and networks are graphs used to model evolutionary relationships, with trees representing strictly branching histories and networks allowing for events in which lineages merge, called reticulation events. While the question of data sufficiency has been studied extensively in the context of trees, it remains largely unexplored for networks. In this work we take a first step in this direction by establishing bounds on the amount of genomic data required to reconstruct binary level-$1$ semi-directed phylogenetic networks, which are binary networks in which reticulation events are indicated by directed edges, all other edges are undirected, and cycles are vertex-disjoint. For this class, methods have been developed recently that are statistically consistent. Roughly speaking, such methods are guaranteed to reconstruct the correct network assuming infinitely long genomic sequences. Here we consider the question whether networks from this class can be uniquely and correctly reconstructed from finite sequences. Specifically, we present an inference algorithm that takes as input genetic sequence data, and demonstrate that the sequence length sufficient to reconstruct the correct network with high probability, under the CFN model of evolution, scales logarithmically, polynomially, or polylogarithmically with the number of taxa, depending on the parameter regime. As part of our contribution, we also present novel inference rules for quartet data in the semi-directed phylogenetic network setting.

q-bio.PE↗

arXiv2025

Public Goods Games in Directed Networks with Constraints on Sharing

In a public goods game, every player chooses whether or not to buy a good that all neighboring players will have access to. We consider a setting in which the good is indivisible, neighboring players are out-neighbors in a directed graph, and there is a capacity constraint on their number, k, that can benefit from the good. This means that each player makes a two-pronged decision: decide whether or not to buy and, conditional on buying, choose which k out-neighbors to share access. We examine both pure and mixed Nash equilibria in the model from the perspective of existence, computation, and efficiency. We perform a comprehensive study for these three dimensions with respect to both sharing capacity (k) and the network structure (the underlying directed graph), and establish sharp complexity dichotomies for each.

cs.GT↗

arXiv2025

Parameterized Algorithms for Diversity of Networks with Ecological Dependencies

For a phylogenetic tree, the phylogenetic diversity of a set A of taxa is the total weight of edges on paths to A. Finding small sets of maximal diversity is crucial for conservation planning, as it indicates where limited resources can be invested most efficiently. In recent years, efficient algorithms have been developed to find sets of taxa that maximize phylogenetic diversity either in a phylogenetic network or in a phylogenetic tree subject to ecological constraints, such as a food web. However, these aspects have mostly been studied independently. Since both factors are biologically important, it seems natural to consider them together. In this paper, we introduce decision problems where, given a phylogenetic network, a food web, and integers k, and D, the task is to find a set of k taxa with phylogenetic diversity of at least D under the maximize all paths measure, while also satisfying viability conditions within the food web. Here, we consider different definitions of viability, which all demand that a "sufficient" number of prey species survive to support surviving predators. We investigate the parameterized complexity of these problems and present several fixed-parameter tractable (FPT) algorithms. Specifically, we provide a complete complexity dichotomy characterizing which combinations of parameters - out of the size constraint k, the acceptable diversity loss D, the scanwidth of the food web, the maximum in-degree in the network, and the network height h - lead to W[1]-hardness and which admit FPT algorithms. Our primary methodological contribution is a novel algorithmic framework for solving phylogenetic diversity problems in networks where dependencies (such as those from a food web) impose an order, using a color coding approach.

cs.DS↗

arXiv2025

Evaluating the performance of Bayesian cumulative logistic models in randomised controlled trials: a simulation study

Background: The proportional odds (PO) model is the most common analytic method for ordinal outcomes in randomised controlled trials. While parameter estimates obtained under departures from PO can be interpreted as an average odds ratio, they can obscure differing treatment effects across the distribution of the ordinal categories. Extensions to the PO model exist and this work evaluates their performance under deviations to the PO assumption. Methods: We evaluated the bias, coverage and mean square error of four modeling approaches for ordinal outcomes via Monte Carlo simulation. Specifically, independent logistic regression models, the PO model, and constrained and unconstrained partial proportional odds (PPO) models were fit to simulated ordinal outcome data. The simulated data were designed to represent a hypothetical two-arm randomised trial under a range of scenarios. Additionally, we report on a case study; an Australasian COVID-19 Trial that adopted multiple secondary ordinal endpoints. Results: The PO model performed best when the data are generated under PO, as expected, but can result in bias and poor coverage in the presence of non-PO, particularly with increasing effect size and number of categories. The odds ratios (ORs) estimated using the unconstrained PPO and separate logistic regression models in the presence of non-PO had negligible bias and good coverage across most scenarios. The unconstrained PPO model under-performed when there was sparse data within some categories. Conclusions: While the PO model is effective when PO holds, the unconstrained and constrained PPO and logistic regression models provide unbiased and efficient estimates under non-PO conditions.

stat.ME↗

arXiv2025

Evaluating the effect of different non-informative prior specifications on the Bayesian proportional odds model in randomised controlled trials: a simulation study

Background: Ordinal outcomes combine multiple distinct ordered patient states into a single endpoint and are commonly analysed using proportional odds (PO) models in clinical trials. When using a Bayesian approach, it is not obvious what the influence of a 'non-informative' prior is in the analysis of a fixed design or on early stopping decisions in adaptive designs. Methods: This study compares different non-informative prior specifications for the Bayesian PO model in the context of both a two-arm trial with a fixed design and an adaptive design with an early stopping rule. We conducted an extensive simulation study, varying the effect size, sample size, number of categories and distribution of the control arm probabilities. Results: Our findings indicate that the choice of prior specification can introduce bias in the estimation of the treatment effect, particularly when control arm probabilities are right-skewed. The R-square prior specification resulted in the smallest bias and increased the likelihood of appropriately stopping early when there was a treatment effect. However, this specification exhibited larger biases when control arm probabilities were U-shaped when there was an early stopping rule. Dirichlet priors with concentration parameters close to zero resulted in the smallest bias when probabilities were right-skewed in the control arm, but were more likely to inappropriately stop early for superiority when there was no treatment effect and an early stopping rule. Conclusions: The specification of non-informative priors in Bayesian adaptive trials with ordinal outcomes has implications for treatment effect estimation and early stopping decisions. We recommend the careful selection of priors that consider the possible distribution of control arm probabilities and that sensitivity analyses to the prior be conducted.

stat.ME↗

arXiv2025

Characterizing semi-directed phylogenetic networks and their multi-rootable variants

In evolutionary biology, phylogenetic networks are graphs that provide a flexible framework for representing complex evolutionary histories that involve reticulate evolutionary events. Recently phylogenetic studies have started to focus on a special class of such networks called semi-directed networks. These graphs are defined as mixed graphs that can be obtained by de-orienting some of the arcs in some rooted phylogenetic network, that is, a directed acyclic graph whose leaves correspond to a collection of species and that has a single source or root vertex. However, this definition of semi-directed networks is implicit in nature since it is not clear when a mixed-graph enjoys this property or not. In this paper, we introduce novel, explicit mathematical characterizations of semi-directed networks, and also multi-semi-directed networks, that is, mixed graphs that can be obtained from directed phylogenetic networks that may have more than one root. In addition, through extending foundational tools from the theory of rooted networks into the semi-directed setting - such as cherry picking sequences, omnians, and path partitions - we characterize when a (multi-)semi-directed network can be obtained by de-orienting some rooted network that is contained in one of the well-known classes of tree-child, orchard, tree-based or forest-based networks. These results address structural aspects of (multi-)semi-directed networks and pave the way to improved theoretical and computational analyses of such networks, for example, within the development of algebraic evolutionary models that are based on such networks.

q-bio.PE↗

arXiv2024

New Measurements of the Deuteron to Proton F2 Structure Function Ratio

Nucleon structure functions, as measured in lepton-nucleon scattering, have historically provided a critical observable in the study of partonic dynamics within the nucleon. However, at very large parton momenta it is both experimentally and theoretically challenging to extract parton distributions due to the probable onset of non-perturbative contributions and the unavailability of high precision data at critical kinematics. Extraction of the neutron structure and the d-quark distribution have been further challenging due to the necessity of applying nuclear corrections when utilizing scattering data from a deuteron target to extract free neutron structure. However, a program of experiments has been carried out recently at the energy-upgraded Jefferson Lab electron accelerator aimed at significantly reducing the nuclear correction uncertainties on the d-quark distribution function at large partonic momentum. This allows leveraging the vast body of deuterium data covering a large kinematic range to be utilized for d-quark parton distribution function extraction. We present new data from experiment E12-10-002 carried out in Jefferson Lab Hall C on the deuteron to proton cross-section ratio at large BJorken-x. These results significantly improve the precision of existing data, and provide a first look at the expected impact on quark distributions extracted from global parton distribution function fits.

hep-ex↗

arXiv2024

A Simple 4-Approximation Algorithm for Maximum Agreement Forests on Multiple Unrooted Binary Trees

We present a simple 4-approximation algorithm for computing a maximum agreement forest of multiple unrooted binary trees. This algorithm applies LP rounding to an extension of a recent ILP formulation of the maximum agreement forest problem on two trees by Van Wersch al. We achieve the same approximation ratio as the algorithm of Chen et al. but our algorithm is extremely simple. We also prove that no algorithm based on the ILP formulation by Van Wersch et al. can achieve an approximation ratio of $4 - \varepsilon$, for any $\varepsilon > 0$, even on two trees. To this end, we prove that the integrality gap of the ILP approaches 4 as the size of the two input trees grows.

cs.DS↗

arXiv2024

Reconstructing semi-directed level-1 networks using few quarnets

Semi-directed networks are partially directed graphs that model evolution where the directed edges represent reticulate evolutionary events. We present an algorithm that reconstructs binary $n$-leaf semi-directed level-1 networks in $O( n^2)$ time from its quarnets (4-leaf subnetworks). Our method assumes we have direct access to all quarnets, yet uses only an asymptotically optimal number of $O(n \log n)$ quarnets. When the network is assumed to contain no triangles, our method instead relies only on four-cycle quarnets and the splits of the other quarnets. A variant of our algorithm works with quartets rather than quarnets and we show that it reconstructs most of a semi-directed level-1 network from an asymptotically optimal $O(n \log n)$ of the quartets it displays. Additionally, we provide an $O(n^3)$ time algorithm that reconstructs the tree-of-blobs of any binary $n$-leaf semi-directed network with unbounded level from $O(n^3)$ splits of its quarnets.

q-bio.PE↗

arXiv2024

When are quarnets sufficient to reconstruct semi-directed phylogenetic networks?

Phylogenetic networks are graphs that are used to represent evolutionary relationships between different taxa. They generalize phylogenetic trees since for example, unlike trees, they permit lineages to combine. Recently, there has been rising interest in semi-directed phylogenetic networks, which are mixed graphs in which certain lineage combination events are represented by directed edges coming together, whereas the remaining edges are left undirected. One reason to consider such networks is that it can be difficult to root a network using real data. In this paper, we consider the problem of when a semi-directed phylogenetic network is defined or encoded by the smaller networks that it induces on the 4-leaf subsets of its leaf set. These smaller networks are called quarnets. We prove that semi-directed binary level-2 phylogenetic networks are encoded by their quarnets, but that this is not the case for level-3. In addition, we prove that the so-called blob tree of a semi-directed binary network, a tree that give the coarse-grained structure of the network, is always encoded by the quarnets of the network. These results are relevant for proving the statistical consistency of programs that are currently being developed for reconstructing phylogenetic networks from practical data, such as the recently developed Squirrel software tool.

q-bio.PE↗

arXiv2024

A Wild Sheep Chase Through an Orchard

Orchards are a biologically relevant class of phylogenetic networks as they can describe treelike evolutionary histories augmented with horizontal transfer events. Moreover, the class has attractive mathematical characterizations that can be exploited algorithmically. On the other hand, undirected orchard networks have hardly been studied yet. Here, we prove that deciding whether an undirected, binary phylogenetic network is an orchard -- or equivalently, whether it has an orientation that makes it a rooted orchard -- is NP-hard. For this, we introduce a new characterization of undirected orchards which could be useful for proving positive results.

q-bio.PE↗