Department of Mathematics
Recent Submissions
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Accelerated ensemble optimization using momentum methods
(Journal article; Peer reviewed, 2024)We investigate the use of various momentum methods in combination with an ensemble approximation of gradients, for accelerated optimization. Although momentum gradient descent methods are popular in machine learning, it ... -
Justification of the Benjamin–Ono equation as an internal water waves model
(Journal article; Peer reviewed, 2024)In this paper, we give the first rigorous justification of the Benjamin-Ono equation: $$\begin{aligned} \hspace{3cm} \partial _t \zeta + (1 - \frac{\gamma }{2}\sqrt{\mu }|\textrm{D}|)\partial _x \zeta + \frac{3{\varepsilon ... -
Intermediate long wave equation in negative Sobolev spaces
(Journal article; Peer reviewed, 2024)We study the intermediate long wave equation (ILW) in negative Sobolev spaces. In particular, despite the lack of scaling invariance, we identify the regularity $s = -\frac 12$ as the critical regularity for ILW with any ... -
ATP dependence of decision-making capacity in a fine-grained model of gene regulatory networks
(Journal article; Peer reviewed, 2024)Cellular decision-making is fundamental to life, from developmental biology to environmental responses and antimicrobial resistance. Many regulatory processes that drive cellular decisions rely on gene expression, which ... -
Real-time ocean wave prediction in time domain with autoregression and echo state networks
(Journal article; Peer reviewed, 2024)This study evaluates the potential of applying echo state networks (ESN) and autoregression (AR) for dynamic time series prediction of free surface elevation for use in wave energy converters (WECs). The performance of ... -
(Uni)rational parametrizations of ℛ g,2 , ℛ g,4 and ℛ g,6 in low genera
(Journal article; Peer reviewed, 2024)The moduli space ℛ g,2n parametrizes double covers of smooth curves of genus g ramified at 2n points. We will prove the (uni)rationality of ℛ g,2 , ℛ g,4 and ℛ g,6 in low genera. -
Particle trajectories in the KP-II equation
(Journal article; Peer reviewed, 2024)In the current work, we consider particle trajectories beneath traveling soliton solutions described by the Kadomtsev–Petiviashvili-II (KP-II) equation, which is a model for small-amplitude water waves in shallow water. ... -
Dynamics of the Collision of Two Nearly Equal Solitary Waves for the Zakharov–Kuznetsov Equation
(Journal article; Peer reviewed, 2024)We study the dynamics of the collision of two solitary waves for the 2 and 3-dimensional Zakharov–Kuznetsov equation, a high-dimensional non-integrable version of the Korteweg-de Vries equation that appears as an asymptotic ... -
Infragravity waves and cross-shore motion–a conceptual study
(Journal article; Peer reviewed, 2024)It is widely known that Infragravity (IG) waves induce cross-shore fluid motion in the nearshore, and multiple recent observational studies have identified IG waves as the dominant factor for a range of nearshore processes ... -
Long time well-posedness and full justification of a Whitham-Green-Naghdi system
(Journal article; Peer reviewed, 2024)We establish the full justification of a ‘‘Whitham-Green-Naghdi’’ system modeling the propagation of surface gravity waves with bathymetry in the shallow water regime. It is an asymptotic model of the water waves equations ... -
Evolution and maintenance of mtDNA gene content across eukaryotes
(Journal article; Peer reviewed, 2024)Across eukaryotes, most genes required for mitochondrial function have been transferred to, or otherwise acquired by, the nucleus. Encoding genes in the nucleus has many advantages. So why do mitochondria retain any genes ... -
Rigorous derivation of weakly dispersive shallow-water models with large amplitude topography variations
(Journal article; Peer reviewed, 2024)We derive rigorously from the water waves equations new irrotational shallow-water models for the propagation of surface waves in the case of uneven topography in horizontal dimensions one and two. The systems are made to ... -
Refining the diffusive compressible Euler model
(Journal article; Peer reviewed, 2024)We revisit the molecular arguments underpinning the diffusive compressible Euler model (proposed in Svärd (2018)), and conclude that a heat diffusive term is not accounted for in the energy equation of the original model. ... -
Identifying codewords in general Reed-Muller codes and determining their weights
(Journal article; Peer reviewed, 2024)Determining the weight distribution of all Reed-Muller codes is a huge and exciting problem that has been around since the sixties. Some progress has been made very recently, but we are still far from a solution. In this ... -
A fixed-stress splitting method for nonlinear poroelasticity
(Journal article; Peer reviewed, 2024)In this paper we consider a nonlinear poroelasticity model that describes the quasi-static mechanical behaviour of a fluid-saturated porous medium whose permeability depends on the divergence of the displacement. Such ... -
A hybrid upwind scheme for two-phase flow in fractured porous media
(Journal article; Peer reviewed, 2024)Simulating the flow of two fluid phases in porous media is a challenging task, especially when fractures are included in the simulation. Fractures may have highly heterogeneous properties compared to the surrounding rock ... -
Acoustic tags versus camera—a case study on feeding behaviour of European seabass in sea cages
(Journal article; Peer reviewed, 2025)Intoduction: With the expansion of the aquaculture industry, the need arises for scalable, reliable, and robust methods to assess fish behaviour in sea cages to guide operational management, which includes feeding optimisation ... -
A hypercubic Mk model framework for capturing reversibility in disease, cancer, and evolutionary accumulation modelling
(Journal article; Peer reviewed, 2025)Motivation Accumulation models, where a system progressively acquires binary features over time, are common in the study of cancer progression, evolutionary biology, and other fields. Many approaches have been developed ... -
Ecological Predictors of Organelle Genome Evolution: Phylogenetic Correlations with Taxonomically Broad, Sparse, Unsystematized Data
(Journal article; Peer reviewed, 2024)Comparative analysis of variables across phylogenetically linked observations can reveal mechanisms and insights in evolutionary biology. As the taxonomic breadth of the sample of interest increases, challenges of data ... -
Models of Hydration Dependent Lymphatic Opening, Interstitial Fluid Flows and Ambipolar Diffusion
(Journal article; Peer reviewed, 2024)Objective A theoretical understanding of fluid exchange and the role of initial lymph formation in tissues through mathematical/physical modeling is lacking. Methods Here, we present three models for tissues rich ...
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