Research
Research
Research
Research
247+ open-access research outputs.
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 …
Autocatalytic cores are minimal units in reaction networks (RNs) responsible for the emergence of autocatalysis. In the absence of explicit catalysis, i.e., when an entity appears both as reactant and…
This paper is intended as a companion to the author's talk "Commutator estimates and mean-field limits for Coulomb/Riesz gases" at the 2025 Journ\'ees \'equations aux d\'eriv\'ees partielles in Aussoi…
The historical quest for unifying the concepts and methods of Chemical Reaction Networks theory (CRNT), Mahematical Epidemiology (ME) and ecology has received increased attention in the last years and…
For a real quadratic field $\mathbb{Q}(\sqrt{d})$, we study the norm-form energy $N = S_\zeta^2 - d \cdot S_L^2$, where $S_\zeta$ and $S_L$ are Lorentzian-weighted zero sums with $w(\rho) = 2/(\tfrac{…
A new tree model is introduced based on ordered trees, by distinguishing exactly one child of each node that \emph{has} children. The basic enumeration leads to a cubic equation of the generating func…
Polynomial functors model systems with interfaces: each polynomial specifies the outputs a system can produce and, for each output, the inputs it accepts. The bicategory $\mathbb{O}\mathbf{rg}$ of dyn…
We consider the enumeration of plane trees (rooted ordered trees) whose vertices are colored according to a specific coloring rule that prescribes which possible pairs of colors can occur as the color…
Adaptive mesh refinement (AMR) is widely used to efficiently resolve localized features in time-dependent partial differential equations (PDEs) by selectively refining and coarsening the mesh. However…
This paper studies the enumeration of seven subclasses of level-$2$ phylogenetic networks under various planarity and structural constraints, including terminal planar, tree-child, and galled networks…
The first purpose of this work is to provide a friendly introduction to the theory of nonautonomous linear systems of ordinary differential equations, the property of exponential dichotomy and its cor…
Banderier, Marchal, and Wallner considered Young tableaux with walls, which are similar to standard Young tableaux, except that local decreases are allowed at some walls. In this work, we prove a conj…
We study the dominion zeta(G), defined as the number of minimum dominating sets of a graph G, and analyze how local forcing and boundary effects control the flexibility of optimal domination in trees.…
In the Chilean local alcohol industry (pisco indus- try), for one liter of alcohol produced 10-15 liters of vinasse as the main wastewater of the process. To comply with industrial waste regulations, …
In the function field setting with a fixed characteristic, it was proven by the second and third authors that the values $\log \big|L\big(\frac12, \chi_D\big)\big|$ as $D$ varies over monic and square…
We improve the range of uniformity in the double-exponential decay of the tail of the distribution established by Lumley~\cite{Lumley} for the quadratic Dirichlet $L$-function $L(1, \chi_D)$ over the …
In the so-called Child-Langmuir law, established since 1911, an electron beam is formed linking two electrodes, which are assumed to be two parallel plates of area $A$, separated to a finite distance …
In 1990, Baker and Montgomery conjectured that $L'(s,\chi_d)$ has $\asymp \log\log |d|$ real zeros in the interval $[1/2,1]$ for almost all fundamental discriminants $d$. The study of these zeros was …
In this article, we study extreme values of quadratic character sums with multiplicative coefficients $\sum_{n \le N}f(n)\chi_d(n)$. For a positive number $N$ within a suitable range, we employ the re…
A normal (phylogenetic) network with $k$ reticulations displays $2^k$ phylogenetic trees. In this paper, we establish an analogous result for tree-child (phylogenetic) networks with no underlying $3$-…
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