Article
Physics, Fluids & Plasmas
Matthieu Mangeat, Heiko Rieger
Summary: This paper investigates the impact of spatial heterogeneity in intracellular transport in living cells on the mean first passage time (MFPT) for Brownian particles, comparing active transport and passive Brownian motion to determine if optimization can be achieved in a two-compartment domain. The study derives asymptotic expressions for MFPT in thin cortex and small escape region limits in two and three dimensions, confirmed by numerical calculations using the finite-element method and stochastic simulations. The analysis reveals the dependence of MFPT on diffusion constants ratio, potential barrier height, and outer shell width, with potential for a minimum value in the latter under specific conditions.
Article
Mathematics, Applied
Medet Nursultanov, William Trad, Leo Tzou
Summary: This paper examines the narrow escape problem of a Brownian particle within a three-dimensional Riemannian manifold under the influence of the force field, and computes an asymptotic expansion of mean sojourn time for Brownian particles. Additionally, a singular structure for the restricted Neumann Green's function is obtained as an auxiliary result.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Physics, Fluids & Plasmas
Vaibhava Srivastava, Alexei Cheviakov
Summary: The narrow escape problem involves calculating the time needed for a Brownian particle to leave a domain with absorbing boundary traps. Direct numerical simulations are used to compute the mean first-passage time values and validate the continuum model based on the Poisson equation. Brownian dynamics simulations are also utilized to study additional features of particle dynamics in narrow escape problems.
Article
Physics, Fluids & Plasmas
Denis S. Grebenkov
Summary: We improve the encounter-based approach for imperfect diffusion-controlled reactions by extending it to a more general setting with a reflecting boundary and escape region. We derive a spectral expansion for the full propagator and investigate the probabilistic interpretations of the associated probability flux density. We also discuss potential applications in chemistry and biophysics.
Article
Mathematics, Interdisciplinary Applications
Kairat Usmanov, Batirkhan Turmetov, Kulzina Nazarova
Summary: This paper introduces integration and differentiation operators connected with fractional conformable derivatives, studies their properties in the class of smooth functions, and introduces a nonlocal analogue of the Laplace operator using generalized involutive transformations. It also studies the solvability of the corresponding nonlocal analogue of the Poisson equation and boundary value problems with fractional conformable derivatives. The existence and uniqueness of solutions are proved, and necessary and sufficient conditions for solvability are obtained, with integral representations of solutions provided.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Applied
Sarafa A. Iyaniwura, Tony Wong, Colin B. Macdonald, Michael J. Ward
Summary: This study focuses on determining the mean first passage time (MFPT) for Brownian particles in a bounded 2-D domain with small absorbing traps, presenting a hybrid asymptotic-numerical approach to predict optimal trap configurations that minimize the average MFPT. The research demonstrates how numerical methods can be effectively implemented to achieve accurate results in various domain shapes.
Article
Mathematics, Applied
Helia Serrano, Ramon F. Alvarez-Estrada, Gabriel F. Calvo
Summary: A variety of cell migration processes across tissue boundaries can be modeled using mean first-passage time (MFPT) in confined domains. This study investigates the MFPT functions T on three-dimensional domains Ω, which satisfy a Poisson-like equation and different boundary conditions on the surface S enclosing Ω. By employing potential theory methods, the calculation of T reduces to solving inhomogeneous linear integral equations with singular kernels on S. The integral equation approach allows for analyzing the MFPT with mixed boundary conditions on a closed spherical surface.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Ali BenAmor
Summary: In this work, necessary and sufficient conditions for defining a Dirichlet-to-Neumann operator via Dirichlet principle in the framework of Hilbert spaces are given. The analysis of singular Dirichlet-to-Neumann operators includes establishing Laurent expansion near singularities and Mittag-Leffler expansion for related quadratic forms. The results obtained are applied to definitively solve the positivity problem of the related semigroup in the framework of Lebesgue spaces.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Physics, Fluids & Plasmas
Adrien Chaigneau, Denis S. Grebenkov
Summary: This article investigates restricted diffusion towards a small partially reactive target in a bounded domain in three and higher-dimensional spaces. An explicit approximation for the principal eigenvalue of the Laplace operator with mixed Robin-Neumann boundary conditions is proposed, which also determines the mean first-reaction time, long-time decay of the survival probability, and overall reaction rate on the target. The relevant lengthscale of the target, which determines its trapping capacity, is identified, and the effect of target anisotropy on the principal eigenvalue is studied.
Article
Mathematics
Virginia Giorno, Amelia G. Nobile
Summary: This article investigates the first-passage time problem for the Feller-type diffusion process, discussing the relations between the first-passage time densities of the Feller process and of the Wiener and the Ornstein-Uhlenbeck processes, and analyzing the asymptotic behavior of the first-passage time density through time-dependent boundaries.
Article
Mathematics, Applied
T. M. Dunster
Summary: Using a differential equation approach, asymptotic expansions were rigorously obtained for Lommel, Weber, Anger-Weber, and Struve functions, as well as Neumann polynomials, each of which is a solution of an inhomogeneous Bessel equation. The approximations involve Airy and Scorer functions, and are uniformly valid for large real order nu and unbounded complex argument z. An interesting complication arises in identifying the Lommel functions with the new asymptotic solutions, requiring consideration of certain sectors of the complex plane and introduction of new forms of Lommel and Struve functions.
STUDIES IN APPLIED MATHEMATICS
(2022)
Article
Mathematics
Calogero Vetro, Francesca Vetro
Summary: In this paper, we demonstrate the existence of at least three weak solutions to a mixed Dirichlet-Neumann boundary value problem for equations driven by the p(z)-Laplace operator. Our approach is variational and relies on three critical points theorems.
MATHEMATISCHE NACHRICHTEN
(2021)
Article
Mathematics
Javier Jimenez-Garrido, Javier Sanz, Gerhard Schindl
Summary: This study explores the surjectivity and right inverses of the asymptotic Borel map in Carleman-Roumieu ultraholomorphic classes defined by regular sequences, building on previous research and emphasizing the significant role of a newly introduced index associated with the sequence. Techniques utilized include regular variation, integral transforms, and characterization results in a half-plane, derived from the study of the surjectivity of the moment mapping in general Gelfand-Shilov spaces.
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
(2021)
Article
Mathematics, Applied
Houry Melkonian, Shingo Takeuchi
Summary: Different types of sinc integrals are studied with the replacement of the standard sine function by the generalised sin(p,q) in two parameters. A notable generalisation of the improper Dirichlet integral is accomplished, along with a surprising generalisation of the identity between the Dirichlet integral and that of the integrand sinc(2). Furthermore, an asymptotically sharpened form of Ball's integral inequality is obtained in terms of two parameters.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics, Applied
Marcela Molina Meyer, Frank Richard Prieto Medina
Summary: In this paper, a pseudospectral method in the disk is presented for solving the Laplace equation and biharmonic equation with various boundary conditions without the need for numerical integration or decoupled systems of ordinary differential equations. The method is demonstrated to have spectral convergence and can be applied to estimate Sherwood numbers and solve Lotka-Volterra systems and nonlinear diffusion problems involving chemical reactions.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Chemistry, Physical
K. Basnayake, D. Holcman
JOURNAL OF CHEMICAL PHYSICS
(2020)
Article
Physics, Multidisciplinary
Suney Toste, David Holcman
Summary: This study derives asymptotic formulas for the mean exit time of the fastest Brownian particle among N identical ones to an absorbing boundary under various initial distributions. The results show a continuous algebraic decay law for the mean exit time, differing from classical Weibull or Gumbel results. Formulas are derived for 1-dimensional and 2-dimensional cases, compared with stochastic simulations, and a discussion on applications in cell biology involving long-tail initial distributions is provided.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2021)
Article
Biochemistry & Molecular Biology
Andrea Papale, David Holcman
Summary: The stability of chromatin loops inside the nucleus is dependent on the balance between binding and unbinding events, with the number of cross-linkers playing a key role. The time scale of loop stability can vary from minutes to the entire cell cycle lifetime as the number of cross-linkers increases.
Article
Biology
A. Tricot, I. M. Sokolov, D. Holcman
Summary: The distribution of voltage in sub-micron cellular domains is poorly understood, especially in terms of maintaining electro-neutrality. Through studying the voltage distribution in a generic domain, it was found that long-range voltage drop changes may have significance in neuronal microcompartments and the activation of voltage-gated channels on the surface membrane.
JOURNAL OF MATHEMATICAL BIOLOGY
(2021)
Article
Multidisciplinary Sciences
U. Dobramysl, D. Holcman
Summary: A computational approach is developed to locate the source of a steady-state gradient of diffusing particles, with a fast numerical scheme accelerating simulation time without computing Brownian trajectories explicitly. Results show that analytical formulae and numerical simulation agree on a large range of parameters for reconstructing the source location, while also investigating the uncertainties and window configurations' influence on source reconstruction. Possible applications for cell navigation in biology are discussed as well.
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2021)
Article
Multidisciplinary Sciences
Kanishka Basnayake, David Mazaud, Lilia Kushnireva, Alexis Bemelmans, Nathalie Rouach, Eduard Korkotian, David Holcman
Summary: The study reveals that replenishment of dendritic spines involves store-operated calcium entry pathway. Key conditions for replenishment without depletion include small amplitude and slow timescale of calcium influx, as well as close proximity between the spine apparatus and plasma membranes. The nanoscale organization of dendritic spines separates replenishment from depletion.
Article
Engineering, Biomedical
Matteo Dora, David Holcman
Summary: This paper proposes a new wavelet-based method for removing artifacts from single-channel EEGs. The method adaptively attenuates artifacts of different nature through data-driven renormalization of wavelet components and demonstrates superior performances on different kinds of artifacts and signal-to-noise levels. The proposed method provides a valuable tool to remove artifacts in real-time EEG applications with few electrodes, such as monitoring in special care units.
IEEE TRANSACTIONS ON NEURAL SYSTEMS AND REHABILITATION ENGINEERING
(2022)
Article
Multidisciplinary Sciences
F. Paquin-Lefebvre, D. Holcman
Summary: This study investigates the diffusion behavior of Brownian particles injected on the surface of a bounded domain, analyzing the distribution of concentration between different windows. The solution is obtained using Green's function techniques and second-order asymptotic analysis, with the results depending on factors such as influx amplitude, diffusion properties, and the geometrical organization of the windows.
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2021)
Article
Biochemical Research Methods
Lou Zonca, David Holcman
Summary: This study investigates how connected neuronal networks contribute to the emergence of the alpha-band, finding that the alpha-band is generated by network behavior near the attractor of the Up-state. By modeling the interaction of excitatory and inhibitory networks, the study shows that short-term plasticity in well-connected neuronal networks can explain the emergence and fragmentation of the alpha-band.
PLOS COMPUTATIONAL BIOLOGY
(2021)
Article
Mathematics, Applied
Lou Zonca, David Holcman
Summary: This study examines the exit time of two-dimensional dynamical systems perturbed by small noise, revealing that the maximum of the probability density function of trajectories is not located at the point attractor and that exiting the basin of attraction does not guarantee full escape. By applying these results to neuronal networks, the study sheds light on bursting events and explains the non-Poissonian long interburst durations observed in neuronal dynamics.
JOURNAL OF NONLINEAR SCIENCE
(2022)
Review
Physics, Condensed Matter
S. Toste, D. Holcman
Summary: The article investigates the switching behavior of stochastic particles between two states and estimates the fastest arrival time through solving Fokker-Planck equations. The results reveal that the fastest particle avoids switching when the switching rates are low, but it switches twice when the diffusion in state 2 is much faster than in state 1.
EUROPEAN PHYSICAL JOURNAL B
(2022)
Article
Mathematics, Applied
Matteo Dora, Stephane Jaffard, David Holcman
Summary: Wavelet quantile normalization (WQN) is a nonparametric algorithm designed to remove transient artifacts from single-channel EEG in real-time while preserving the continuity of monitoring. The algorithm regularizes the signal by transporting the wavelet coefficient distributions of artifacted epochs into a reference distribution. The WQN algorithm preserves the distribution of wavelet coefficients compared to classical wavelet thresholding methods.
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
(2022)
Review
Physics, Multidisciplinary
Ulrich Dobramysl, David Holcman
Summary: Computational methods are powerful and complementary in applied sciences like biology, exploring the gap between molecular and cellular scales. Recent progress includes diffusion modeling, asymptotic analysis, hybrid methods, and simulations for cell sensing and guidance via external gradients. The focus is on reconstructing point source location, estimating uncertainty in source reconstruction, and discussing the impact of window configurations on source position recovery.
REPORTS ON PROGRESS IN PHYSICS
(2022)
Article
Multidisciplinary Sciences
Jurgen Reingruber, Andrea Papale, Stephane Ruckly, Jean-Francois Timsit, David Holcman
Summary: Before vaccines, countries used social restrictions to prevent healthcare system saturation and regain control over COVID-19. Computational approaches are key to efficiently control a pandemic. This study develops a data-driven computational framework to control the pandemic with non-pharmaceutical interventions, using a compartmental model and recalibration based on new data.
Article
Physics, Fluids & Plasmas
F. Paquin-Lefebvre, S. Toste, D. Holcman
Summary: This article introduces the redundancy principle and its application in studying rare events. The authors propose a criterion based on splitting probabilities to estimate large n and obtain explicit computations, which are compared with stochastic simulations. They also provide examples of extreme trajectories with killing in dimension 2 and suggest that optimal trajectories should avoid penetrating inside the killing region for large n. Finally, some applications to cell biology are discussed.
