arXiv subjects

Niall M. Mangan

Publications and source records attributed to Niall M. Mangan.

12 recordsLinked to original sources

arXiv2026

Discovering a low-dimensional temperature control architecture across animals

Hibernation is an adaptation to extreme environmental seasonality that has been studied for almost 200 years, but our understanding of the underlying physiological system remains lacking due to the partially observed nature of the system. During hibernation, small mammals, such as the Arctic ground squirrel, exhibit dramatic oscillations in body temperature, typically one of the only physiological states measured, of up to 40 $^{\circ}$C. These spikes are known as interbout arousals and typically occur 10-20 times throughout hibernation. The physiological process that drives interbout arousals is unknown, but two distinct macro-scale mechanisms have been hypothesized. Using model selection for partially observed systems and classical dynamical systems theory, we are able to differentiate between these two hypotheses using only body temperature data recorded from a free-ranging Arctic ground squirrel, and show that our model can capture the broad features of the observed seasonal physiological transitions. We then modify our discovered physiological model of Arctic ground squirrel to include internally-encoded environmental information and find that we can qualitatively match body temperature data recorded from a wide range of species, including a bird, a shrew, and a bear, which also dynamically modulate body temperature. Our results suggest that a low-dimensional, environmentally sensitive core regulator could control body temperature across a diverse range of species -- a new understanding of the physiological organization across species. While the findings presented here are applicable to thermophysiology, the general modeling procedure is applicable to time series data collected from partially observed biological, chemical, physical, mechanical, and cosmic systems for which the goal is to elucidate the underlying mechanism or control structure.

physics.bio-ph↗

arXiv2026

SODAs: Sparse Optimization for the Discovery of Differential and Algebraic Equations

Differential-algebraic equations (DAEs) integrate ordinary differential equations (ODEs) with algebraic constraints, providing a fundamental framework for developing models of dynamical systems characterized by timescale separation, conservation laws, and physical constraints. While sparse optimization has revolutionized model development by allowing data-driven discovery of parsimonious models from a library of possible equations, existing approaches for dynamical systems assume DAEs can be reduced to ODEs by eliminating variables before model discovery. This assumption limits the applicability of such methods for DAE systems with unknown constraints and time scales. We introduce Sparse Optimization for Differential-Algebraic Systems (SODAs), a data-driven method for the identification of DAEs in their explicit form. By discovering the algebraic and dynamic components sequentially without prior identification of the algebraic variables, this approach leads to a sequence of convex optimization problems. It has the advantage of discovering interpretable models that preserve the structure of the underlying physical system. To this end, SODAs improves numerical stability when handling high correlations between library terms, caused by near-perfect algebraic relationships, by iteratively refining the conditioning of the candidate library. We demonstrate the performance of our method on biological, mechanical, and electrical systems, showcasing its robustness to noise in both simulated time series and real-time experimental data.

math.DS↗

arXiv2026

Uncertainty Quantification of Bacterial Microcompartment Permeability

Salmonella expresses bacterial microcompartments (MCPs) upon 1,2-propanediol exposure. MCPs are nanoscale protein-bound shells that encase enzymes for the cofactor-dependent 1,2-propanediol metabolism. They are hypothesized to limit exposure to the toxic intermediate, propionaldehyde, decrease cofactor involvement in competing reactions, and enhance flux. We construct a mass-action mathematical model of purified MCPs and calibrate parameters to measured metabolite concentrations. We constrain mass-action kinetic parameters to previously estimated Michaelis-Menten parameters. We identified two distinct fits with different dynamics in the pathway product, propionate, but similar goodness of fit. Across fits, we inferred that the MCP 1,2-propanediol and propionaldehyde permeability should be greater than 10^{-6} and 10^{-8} m/s, respectively. Our results identify parameter ranges consistent with prevailing theories that MCPs impose preferential diffusion to 1,2-propanediol over propionaldehyde, and sequester toxic propionaldehyde away from the cell cytosol. The bimodality of the posterior distribution arises from bimodality in the estimated coenzyme-A (CoA) permeability and inhibition rates. The MCP permeability to CoA was inferred to be either less than 10^{-8.8} m/s or greater than 10^{-7.3} m/s. In a high CoA permeability environment with low rates of CoA inhibition, enzymes produced metabolites by recycling (NAD+)/(NADH). In a low CoA permeability environment with high rates of CoA inhibition, enzymes required external NAD+/H to produce metabolites. Dynamics are consistent with prevailing hypotheses about MCP function to sequester toxic propionaldehyde, and additional collection of data points between 6 and 24 hours or characterization of enzyme inhibition rates could further reduce uncertainty and provide better permeability estimates.

q-bio.QM↗

arXiv2026

Explicit complex time integrators for stiff problems

Most numerical methods for time integration use real-valued time steps. Complex time steps, however, can provide an additional degree of freedom, as we can select the magnitude of the time step in both the real and imaginary directions. We show that specific paths in the complex time plane lead to expanded stability regions, providing clear computational advantages for complex-valued systems. In particular, we highlight the Schrödinger equation, for which complex time integrators can be uniquely optimal. Furthermore, we demonstrate that these benefits extend to certain classes of real-valued stiff systems by coupling complex time steps with the Projective Integration method.

math.NA↗

arXiv2025

Practical indistinguishability in a gene regulatory network inference problem, a case study

Determining mechanistic models of gene regulation, especially underlying phenotypic variation, is a central goal of both mathematical biology and modern evolutionary biology. However, several challenges, involving both common characteristics of experimental data and the model development process, remain that limit the discovery of general principles. Even the highest-quality experimental data come with challenges. There are always sources of noise, a limit to how often we can measure the system in time, and it is impossible to measure all the relevant states that participate in the full underlying complexity. Additionally, there are usually sources of uncertainty in the underlying biological mechanisms, which give rise to multiple competing model structures. We walk through a case study involving inference of a regulatory network structure involved in a developmental decision in the nematode, \textit{Pristonchus pacificus}. In this study, we fit 13,824 distinct regulatory network models to gene expression data from three experimental conditions to determine which regulatory features are supported by the data. We discover \textit{model sets}, or collections of models with shared regulatory network features that best fit the data, for each of the three experiments we considered, and identify a regulatory network in the intersection of the three model sets. This model describes the data across the experimental conditions and exhibits a high degree of positive regulation and interconnectivity between the key regulators, \textit{eud-1}, \textit{sult-1}, and \textit{nhr-40}. While the biological results are specific to the molecular biology of development in \textit{Pristonchus pacificus}, the comparative modeling framework introduced here can be applied to other systems of gene regulation in an evolutionary developmental context.

q-bio.MN↗

arXiv2025

Data Analysis and Modeling for Transitioning Between Laboratory Methods for Detecting SARS-CoV-2 in Wastewater

Wastewater surveillance has proven to be a useful tool to monitor pathogens such as SARS-CoV-2 as it is a nonintrusive way to survey the potential disease burden of the population contributing to a sewershed. With the expansion of this field since the beginning of the COVID-19 pandemic, laboratory methods to process wastewater and quantify pathogen nucleic acid levels have improved as technologies changed, efforts expanded in size and scope, and supply chain issues were resolved. Maintaining data continuity is crucial for labs undergoing method transitions to accurately assess infectious disease levels over time and compare measured RNA concentrations to public health data. Despite the dynamic nature of laboratory methods and the necessity to ensure uninterrupted data, to our knowledge there has not been a study that unites two datasets from different lab methods for pathogen quantification from environmental samples. Here, we describe a lab transition from SARS-CoV-2 RNA quantification using a low-throughput, manual filtration-based wastewater concentration and RNA extraction followed by qPCR to a high-throughput, automated magnetic bead-based concentration and extraction followed by dPCR. During the two-month transition period, wastewater samples from across the Chicago metropolitan area were processed with both methods in parallel. We evaluated a variety of regression models to relate the RNA measurements from both methods and found a log-log model was most appropriate after removing outliers and discrepancy points to improve model performance. We also evaluated the consequences of assigning values to samples that were below the detection limit. Our study demonstrates that data continuity can be maintained throughout a transition of laboratory methods if there is a sufficient period of overlap between the methods for an appropriate model to be constructed to relate the datasets.

q-bio.QM↗

arXiv2022

Walking into the complex plane to "order" better time integrators

Most numerical methods for time integration use real time steps. Complex time steps provide an additional degree of freedom, as we can select the magnitude of the step in both the real and imaginary directions. By time stepping along specific paths in the complex plane, integrators can gain higher orders of accuracy or achieve expanded stability regions. We show how to derive these paths for explicit and implicit methods, discuss computational costs and storage benefits, and demonstrate clear advantages for complex-valued systems like the Schrodinger equation. We also explore how complex time stepping also allows us to break the Runge-Kutta order barrier, enabling 5th order accuracy using only five function evaluations for real-valued differential equations.

math.NA↗

arXiv2019

Frequency comb generation at 800nm in waveguide array quantum well diode lasers

A traveling wave model for a semiconductor diode laser based on quantum wells is presented as well as a comprehensive theoretical model of the lasing dynamics produced by the intensity discrimination of the nonlinear mode-coupling in a waveguide array. By leveraging a recently developed model for the detailed semiconductor gain dynamics, the temporal shaping effects of the nonlinear mode-coupling induced by the waveguide arrays can be characterized. Specifically, the enhanced nonlinear pulse shaping provided by the waveguides are capable of generating stable frequency combs wavelength of 800 nm in a GaAs device, a parameter regime not feasible for stable combline generation using a single waveguide. Extensive numerical simulations showed that stable waveform generation could be achieved and optimized by an appropriate choice of the linear waveguide coupling coefficient, quantum well depth, and the input currents to the first and second waveguides. The model provides a first demonstration that a compact, efficient and robust on-chip comb source can be produced in GaAs.

physics.optics↗

arXiv2018

Framework for systematic flow manipulation by wind and hydrokinetic energy turbine arrays

Wind and hydrokinetic energy turbines are often constrained to locations where the available energy is limited by the operation of the turbines themselves. In two-dimensions, we describe how an array can manipulate the steady flow, redirecting more fluid kinetic energy to itself. Two computational examples of turbine arrays present solutions of the Navier-Stokes equations to illustrate the feasibility of flow manipulation, and motivate an idealized model. Using inviscid fluid dynamics, we underscore the relation between bound vorticity and flow deflection, and between free vorticity and energy extraction. To understand and design flow manipulations that increase the kinetic energy incident on the turbines, we consider an idealized deflector-turbine array constrained to a line segment, acting as an internal flow-boundary. We impose profiles of bound and shed vorticity on this segment by parameterizing the flow deflection and the wake deficit, respectively, and analyze the resulting flow using inviscid fluid dynamics. We find that the power extracted by the array is the product of two components: (i) the deflected kinetic energy incident on the array, and (ii) the array efficiency, both of which vary with deflection strength. The array efficiency, or its ability to extract a fraction of the incident energy, decreases slightly with increasing deflection from about 57\% at weak deflection to 39\% at high deflection. This decrease is outweighed by increasing incident kinetic energy with deflection, resulting in monotonically improved power extraction, thus highlighting the benefits from flow deflection.

physics.flu-dyn↗

arXiv2017

Traveling Wave Model for Frequency Comb Generation in Single Section Quantum Well Diode Lasers

We present a traveling wave model for a semiconductor diode laser based on quantum wells. The gain model is carefully derived from first principles and implemented with as few phenomeno- logical constants as possible. The transverse energies of the quantum well confined electrons are discretized to automatically capture the effects of spectral and spatial hole burning, gain asym- metry, and the linewidth enhancement factor. We apply this model to semiconductor optical amplifiers and single-section phase-locked lasers. We are able to reproduce the experimental re- sults. The calculated frequency modulated comb shows potential to be a compact, chip-scale comb source without additional external components.

physics.optics↗

arXiv2017

Model selection for dynamical systems via sparse regression and information criteria

We develop an algorithm for model selection which allows for the consideration of a combinatorially large number of candidate models governing a dynamical system. The innovation circumvents a disadvantage of standard model selection which typically limits the number candidate models considered due to the intractability of computing information criteria. Using a recently developed sparse identification of nonlinear dynamics algorithm, the sub-selection of candidate models near the Pareto frontier allows for a tractable computation of AIC (Akaike information criteria) or BIC (Bayes information criteria) scores for the remaining candidate models. The information criteria hierarchically ranks the most informative models, enabling the automatic and principled selection of the model with the strongest support in relation to the time series data. Specifically, we show that AIC scores place each candidate model in the {\em strong support}, {\em weak support} or {\em no support} category. The method correctly identifies several canonical dynamical systems, including an SEIR (susceptible-exposed-infectious-recovered) disease model and the Lorenz equations, giving the correct dynamical system as the only candidate model with strong support.

physics.data-an↗

arXiv2016

Inferring biological networks by sparse identification of nonlinear dynamics

Inferring the structure and dynamics of network models is critical to understanding the functionality and control of complex systems, such as metabolic and regulatory biological networks. The increasing quality and quantity of experimental data enable statistical approaches based on information theory for model selection and goodness-of-fit metrics. We propose an alternative method to infer networked nonlinear dynamical systems by using sparsity-promoting $\ell_1$ optimization to select a subset of nonlinear interactions representing dynamics on a fully connected network. Our method generalizes the sparse identification of nonlinear dynamics (SINDy) algorithm to dynamical systems with rational function nonlinearities, such as biological networks. We show that dynamical systems with rational nonlinearities may be cast in an implicit form, where the equations may be identified in the null-space of a library of mixed nonlinearities including the state and derivative terms; this approach applies more generally to implicit dynamical systems beyond those containing rational nonlinearities. This method, implicit-SINDy, succeeds in inferring three canonical biological models: Michaelis-Menten enzyme kinetics, the regulatory network for competence in bacteria, and the metabolic network for yeast glycolysis.

math.DS↗