All Outputs (133)

Normalisation of Action Potential Data Recorded with Sharp Electrodes Maximises Its Utility for Model Development (2022)
Conference Proceeding
Barral, Y. S. H., Polonchuk, L., R. Mirams, G., Clerx, M., Page, G., Sweat, K., …Gavaghan, D. J. (2022). Normalisation of Action Potential Data Recorded with Sharp Electrodes Maximises Its Utility for Model Development. In Computing in Cardiology 2022. https://doi.org/10.22489/cinc.2022.356

In silico models of cardiomyocyte electrophysiology describe the various ionic currents and fluxes that lead to the formation of action potentials (APs). Experimental data used to create such models can be recorded in adult human cardiac trabeculae u... Read More about Normalisation of Action Potential Data Recorded with Sharp Electrodes Maximises Its Utility for Model Development.

Modelling the Effect of Intracellular Calcium in the Rundown of L-Type Calcium Current (2022)
Conference Proceeding
Agrawal, A., Clerx, M., Wang, K., Polonchuk, L., Gavaghan, D. J., & Mirams, G. R. (2022). Modelling the Effect of Intracellular Calcium in the Rundown of L-Type Calcium Current. In 2022 Computing in Cardiology (CinC). https://doi.org/10.22489/CinC.2022.051

The L-type calcium current (ICaL) is a key current of the heart playing an important role in the contraction of the cardiomyocyte. Patch-clamp recordings of ionic currents can be associated with a reduction of the current magnitude with time (termed... Read More about Modelling the Effect of Intracellular Calcium in the Rundown of L-Type Calcium Current.

Integrality of twisted L-values of elliptic curves (2022)
Journal Article
Wiersema, H., & Wuthrich, C. (2022). Integrality of twisted L-values of elliptic curves. Documenta Mathematica, 27, 2041-2066. https://doi.org/10.25537/dm.2022v27.2041-2066

Under suitable, fairly weak hypotheses on an elliptic curve E/Q and a primitive non-trivial Dirichlet character χ, we show that the algebraic L-value L (E, χ) at s = 1 is an algebraic integer. For instance, for semistable curves L (E, χ) is integral... Read More about Integrality of twisted L-values of elliptic curves.

Slepian eigenvalues as tunnelling rates (2022)
Journal Article
Creagh, S. C., & Gradoni, G. (2023). Slepian eigenvalues as tunnelling rates. Annals of Physics, 449, Article 169204. https://doi.org/10.1016/j.aop.2022.169204

We calculate the eigenvalues of an integral operator associated with Prolate Spheroidal Wave Functions (or Slepian functions) by interpreting them as tunnelling probabilities in an analogous quantum problem. Doing so allows us to extend a well-known... Read More about Slepian eigenvalues as tunnelling rates.

Likelihood-Free Dynamical Survival Analysis applied to the COVID-19 epidemic in Ohio (2022)
Journal Article
Klaus, C., Wascher, M., KhudaBukhsh, W. R., & Rempała, G. A. (2023). Likelihood-Free Dynamical Survival Analysis applied to the COVID-19 epidemic in Ohio. Mathematical Biosciences and Engineering, 20(2), 4103-4127. https://doi.org/10.3934/mbe.2023192

The Dynamical Survival Analysis (DSA) is a framework for modeling epidemics based on mean field dynamics applied to individual (agent) level history of infection and recovery. Recently, the DSA method has been shown to be an effective tool in analyzi... Read More about Likelihood-Free Dynamical Survival Analysis applied to the COVID-19 epidemic in Ohio.

On the maximum dual volume of a canonical Fano polytope (2022)
Journal Article
Balletti, G., Kasprzyk, A. M., & Nill, B. (2022). On the maximum dual volume of a canonical Fano polytope. Forum of Mathematics, Sigma, 10, Article e109. https://doi.org/10.1017/fms.2022.93

We give an upper bound on the volume vol(P*) of a polytope P* dual to a d-dimensional lattice polytope P with exactly one interior lattice point, in each dimension d. This bound, expressed in terms of the Sylvester sequence, is sharp, and is achieved... Read More about On the maximum dual volume of a canonical Fano polytope.

A continuum framework for phase field with bulk-surface dynamics (2022)
Journal Article
Espath, L. (2023). A continuum framework for phase field with bulk-surface dynamics. Partial Differential Equations and Applications, 4, Article 1. https://doi.org/10.1007/s42985-022-00218-8

This continuum mechanical theory aims at detailing the underlying rational mechanics of dynamic boundary conditions proposed by Fischer et al. (Phys Rev Lett 79:893, 1997), Goldstein et al. (Phys D Nonlinear Phenom 240:754–766, 2011), and Knopf et al... Read More about A continuum framework for phase field with bulk-surface dynamics.

GPT4 : The Ultimate Brain (2022)
Working Paper
Adesso, G. GPT4 : The Ultimate Brain

We introduce a powerful general probabilistic theory, GPT4, that extends classical and quantum theories to include higher-dimensional probabilistic models. GPT4 results from the four-fold integration of GPT in physics (Generalized Probabilistic T... Read More about GPT4 : The Ultimate Brain.

Adjoint-aided inference of Gaussian process driven differential equations (2022)
Conference Proceeding
Gahungu, P., Lanyon, C. W., Álvarez, M. A., Smith, M. T., & Wilkinson, R. D. (2022). Adjoint-aided inference of Gaussian process driven differential equations. In S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, & A. Oh (Eds.), Advances in Neural Information Processing Systems 35 (NeurIPS 2022)

Linear systems occur throughout engineering and the sciences, most notably as differential equations. In many cases the forcing function for the system is unknown, and interest lies in using noisy observations of the system to infer the forcing, as w... Read More about Adjoint-aided inference of Gaussian process driven differential equations.

Cauchy-Dirichlet problems for the porous medium equation (2022)
Journal Article
Bowen, M., King, J. R., & Witelski, T. P. (2023). Cauchy-Dirichlet problems for the porous medium equation. Discrete and Continuous Dynamical Systems - Series A, 43(3&4), 1143-1174. https://doi.org/10.3934/dcds.2022182

We consider the porous medium equation subject to zero-Dirichlet conditions on a variety of two-dimensional domains, namely strips, slender domains and sectors, allowing us to capture a number of different classes of behaviours. Our focus is on inter... Read More about Cauchy-Dirichlet problems for the porous medium equation.

Shape and Structure Preserving Differential Privacy (2022)
Presentation / Conference
Soto, C., Bharath, K., Reimherr, M., & Slavkovic, A. (2022, November). Shape and Structure Preserving Differential Privacy. Poster presented at Thirty-sixth Conference on Neural Information Processing Systems (NeurIPS 2022), New Orleans, USA

It is common for data structures such as images and shapes of 2D objects to be represented as points on a manifold. The utility of a mechanism to produce sanitized differentially private estimates from such data is intimately linked to how compatible... Read More about Shape and Structure Preserving Differential Privacy.

The two-process model for sleep–wake regulation: A nonsmooth dynamics perspective (2022)
Journal Article
Şaylı, M., Skeldon, A. C., Thul, R., Nicks, R., & Coombes, S. (2023). The two-process model for sleep–wake regulation: A nonsmooth dynamics perspective. Physica D: Nonlinear Phenomena, 444, Article 133595. https://doi.org/10.1016/j.physd.2022.133595

Since its inception four decades ago the two-process model introduced by Borbély has provided the conceptual framework to explain sleep–wake regulation across many species, including humans. At its core, high level notions of circadian and homeostati... Read More about The two-process model for sleep–wake regulation: A nonsmooth dynamics perspective.

Neural Control of Discrete Weak Formulations: Galerkin, Least Squares & Minimal-Residual Methods with Quasi-Optimal Weights (2022)
Journal Article
Brevis, I., Muga, I., & van der Zee, K. G. (2022). Neural Control of Discrete Weak Formulations: Galerkin, Least Squares & Minimal-Residual Methods with Quasi-Optimal Weights. Computer Methods in Applied Mechanics and Engineering, 402, Article 115716. https://doi.org/10.1016/j.cma.2022.115716

There is tremendous potential in using neural networks to optimize numerical methods. In this paper, we introduce and analyse a framework for the neural optimization of discrete weak formulations, suitable for finite element methods. The main idea of... Read More about Neural Control of Discrete Weak Formulations: Galerkin, Least Squares & Minimal-Residual Methods with Quasi-Optimal Weights.

BV quantization of dynamical fuzzy spectral triples (2022)
Journal Article
Gaunt, J., Nguyen, H., & Schenkel, A. (2022). BV quantization of dynamical fuzzy spectral triples. Journal of Physics A: Mathematical and Theoretical, 55(47), Article 474004. https://doi.org/10.1088/1751-8121/aca44f

This paper provides a systematic study of gauge symmetries in the dynamical fuzzy spectral triple models for quantum gravity that have been proposed by Barrett and collaborators. We develop both the classical and the perturbative quantum BV formalism... Read More about BV quantization of dynamical fuzzy spectral triples.

Mathematical Models of Chiral Symmetry-breaking – A Review of General Theories, and Adiabatic Approximations of the APED System (2022)
Journal Article
Diniz, P. C., Wattis, J. A., & Da Costa, F. P. (2022). Mathematical Models of Chiral Symmetry-breaking – A Review of General Theories, and Adiabatic Approximations of the APED System. Origins of Life and Evolution of Biospheres, 52(4), 183-204. https://doi.org/10.1007/s11084-022-09631-w

We review the literature surrounding chiral symmetry-breaking in chemical systems, with a focus on understanding the mathematical models underlying these chemical processes. We comment in particular on the toy model of Sandars, Viedma’s crystal grind... Read More about Mathematical Models of Chiral Symmetry-breaking – A Review of General Theories, and Adiabatic Approximations of the APED System.

In silico evidence for the utility of parsimonious root phenotypes for improved vegetative growth and carbon sequestration under drought (2022)
Journal Article
Schäfer, E. D., Ajmera, I., Farcot, E., Owen, M. R., Band, L. R., & Lynch, J. P. (2022). In silico evidence for the utility of parsimonious root phenotypes for improved vegetative growth and carbon sequestration under drought. Frontiers in Plant Science, 13, Article 1010165. https://doi.org/10.3389/fpls.2022.1010165

Drought is a primary constraint to crop yields and climate change is expected to increase the frequency and severity of drought stress in the future. It has been hypothesized that crops can be made more resistant to drought and better able to sequest... Read More about In silico evidence for the utility of parsimonious root phenotypes for improved vegetative growth and carbon sequestration under drought.

L-Series of Harmonic Maass Forms and a Summation Formula for Harmonic Lifts (2022)
Journal Article
Diamantis, N., Lee, M., Raji, W., & Rolen, L. (2023). L-Series of Harmonic Maass Forms and a Summation Formula for Harmonic Lifts. International Mathematics Research Notices, 2023(18), 15729-15765. https://doi.org/10.1093/imrn/rnac310

We introduce an L-series associated with harmonic Maass forms and prove their functional equations. We establish converse theorems for these L-series and, as an application, we formulate and prove a summation formula for the holomorphic part of a har... Read More about L-Series of Harmonic Maass Forms and a Summation Formula for Harmonic Lifts.

On isotropic and numerical equivalence of cycles (2022)
Journal Article
Vishik, A. (2022). On isotropic and numerical equivalence of cycles. Selecta Mathematica (New Series), 29(1), Article 8. https://doi.org/10.1007/s00029-022-00812-z

We study the conjecture claiming that, over a flexible field, isotropic Chow groups coincide with numerical Chow groups (with Fp-coefficients). This conjecture is essential for understanding the structure of the isotropic motivic category and that of... Read More about On isotropic and numerical equivalence of cycles.

Hypergraphon mean field games (2022)
Journal Article
Cui, K., KhudaBukhsh, W. R., & Koeppl, H. (2022). Hypergraphon mean field games. Chaos, 32(11), Article 113129. https://doi.org/10.1063/5.0093758

We propose an approach to modeling large-scale multi-agent dynamical systems allowing interactions among more than just pairs of agents using the theory of mean field games and the notion of hypergraphons, which are obtained as limits of large hyperg... Read More about Hypergraphon mean field games.

The Leydig cell biomarker INSL3 as a predictor of age-related morbidity: Findings from the EMAS cohort (2022)
Journal Article
Ivell, R., Heng, K., Severn, K., Antonio, L., Bartfai, G., Casanueva, F. F., …Anand-Ivell, R. (2022). The Leydig cell biomarker INSL3 as a predictor of age-related morbidity: Findings from the EMAS cohort. Frontiers in Endocrinology, 13, Article 1016107. https://doi.org/10.3389/fendo.2022.1016107

Background: Insulin-like peptide 3 (INSL3) is a constitutive hormone secreted in men by the mature Leydig cells of the testes. It is an accurate biomarker for Leydig cell functional capacity, reflecting their total cell number and differentiation sta... Read More about The Leydig cell biomarker INSL3 as a predictor of age-related morbidity: Findings from the EMAS cohort.