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Modeling the Process of Speciation Using a Multiscale Framework Including A Posteriori Error Estimates
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| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 2) |
| Halaman | : | 450-475 |
| Abstrak | : | This paper concerns the modeling and numerical simulation of the process of speciation. In particular, given conditions for which one or more speciation events within an ecosystem occur, our aim is to develop the necessary modeling and simulation tools. Care is also taken to establish a solid mathematical foundation on which our modeling framework is built. This is the subject of the first half of the paper. The second half is devoted to developing a multiscale framework for eco-evolutionary modeling, where the relevant scales are that of species and individual/population, respectively. The species level model we employ can be considered as an extension of the classical Lotka--Volterra model, where in addition to the species abundance, the model also governs the evolution of the species mean traits and species trait covariances and in this sense generalizes the purely ecological Lotka--Volterra model to an eco-evolutionary model. Although the model thus allows for evolving species, it does not (by construction) allow for the branching of species, i.e., speciation events. The reason for this is related to that of separate scales; the unit of species is too coarse to capture the fine-scale dynamics of a speciation event. Instead, the branching species should be regarded as a population of individuals moving along a selection of trait axes (i.e., trait-space). For this, we employ a trait-specific population density model governing the dynamics of the population density as a function of evolutionary traits. At this scale there is no a priori definition of species, but both species and speciation may be defined a posteriori as, e.g., local maxima and saddle points of the population density, respectively. Hence, a system of interacting species can be described at the species level, while for branching species a population level description is necessary. Our multiscale framework thus consists of coupling the species and population level models where speciation events are detected in advance and then resolved at the population scale until the branching is complete. Moreover, since the population level model is formulated as a PDE, we first establish the well-posedness in the time-discrete setting and then derive the a posteriori error estimates, which provides a fully computable upper bound on an energy-type error, including also for the case of general smooth distributions (which will be useful for the detection of speciation events). Several numerical tests validate our framework in practice. |
Contact Adapting Electrode Model for Electrical Impedance Tomography
| Pengarang | : | |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 2) |
| Halaman | : | 427-449 |
| Abstrak | : | Electrical impedance tomography is an imaging modality for extracting information on the interior structure of a physical body from boundary measurements of current and voltage. This work studies a new robust way of modeling the contact electrodes used for driving current patterns into the examined object and measuring the resulting voltages. The idea is to not define the electrodes as strict geometric objects on the measurement boundary but only to assume approximate knowledge about their whereabouts and let a boundary admittivity function determine the actual locations of the current inputs. Such an approach enables reconstructing the boundary admittivity, i.e., the locations and strengths of the contacts, at the same time and with analogous methods as the interior admittivity. The functionality of the new model is verified by two-dimensional numerical experiments based on water tank data. |
Nonlinear Ultrasound Imaging Modeled by a Westervelt Equation
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 2) |
| Halaman | : | 408-426 |
| Abstrak | : | We consider the ultrasound imaging problem governed by a nonlinear wave equation of Westervelt type with variable wave speed. We show that the coefficient of nonlinearity can be recovered uniquely from knowledge of the Dirichlet-to-Neumann map. Our proof is based on a second order linearization and the use of Gaussian beam solutions to reduce the problem to the inversion of a weighted geodesic ray transform. We propose an inversion algorithm and report the results of a numerical implementation to solve the nonlinear ultrasound imaging problem in a transmission setting in the frequency domain. |
A Quantification of Long Transient Dynamics
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 2) |
| Halaman | : | 381-407 |
| Abstrak | : | The stability of equilibria and asymptotic behaviors of trajectories are often the primary focuses of mathematical modeling. However, many interesting phenomena that we would like to model, such as the “honeymoon period” of a disease after the onset of mass vaccination programs, are transient dynamics. Honeymoon periods can last for decades and can be important public health considerations. In many fields of science, especially in ecology, there is growing interest in a systematic study of transient dynamics. In this work, we attempt to provide a technical definition of “long transient dynamics” such as the honeymoon period and explain how these behaviors arise in systems of ordinary differential equations. We define a transient center, a point in state space that causes long transient behaviors, and derive some of its properties. In the end, we define reachable transient centers, which are transient centers that can be reached from initializations that do not need to be near the transient center. |
Averaging of a Stochastic Slow-Fast Model for Population Dynamics: Application to the Development of Ovarian Follicles
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 1) |
| Halaman | : | 359-380 |
| Abstrak | : | We analyze a birth, migration, and death stochastic process modeling the dynamics of a finite population, in which individuals transit unidirectionally across successive compartments. The model is formulated as a continuous-time Markov chain, whose transition matrix involves multiscale effects; the whole (or part of the) population affects the rates of individual birth, migration, and death events. Using the slow-fast property of the model, we prove the existence and uniqueness of the limit model in the framework of stochastic singular perturbations. The derivation of the limit model is based on compactness and coupling arguments. The uniqueness is handled by applying the ergodicity theory and studying a dedicated Poisson equation. The limit model consists of an ordinary differential equation ruling the dynamics of the first (slow) compartment, coupled with a quasi-stationary distribution in the remaining (fast) compartments, which averages the contribution of the fast component of the Markov chain on the slow one. We illustrate numerically the convergence and highlight the relevance of dealing with nonlinear event rates for our application in reproductive biology. The numerical simulations involve a simple integration scheme for the deterministic part, coupled with the nested algorithm to sample the quasi-stationary distribution. |
Localization and Delocalization of Ground States of Bose--Einstein Condensates Under Disorder
| Pengarang | : | Robert Altmann |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 1) |
| Halaman | : | 330-358 |
| Abstrak | : | This paper studies the localization behavior of Bose--Einstein condensates in disorder potentials, modeled by a Gross--Pitaevskii eigenvalue problem on a bounded interval. In the regime of weak particle interaction, we are able to quantify exponential localization of the ground state, depending on statistical parameters and the strength of the potential. Numerical studies further show delocalization if we leave the identified parameter range, which is in agreement with experimental data. These mathematical and numerical findings allow the prediction of physically relevant regimes where localization of ground states may be observed experimentally. |
The Dynamics of China-Taiwan Relations and the Possibility of Open Conflict: An Overview
| Pengarang | : | Endah Tarwiyani Yuniar, Fitriani |
| Nama Majalah/Jurnal | : | The Indonesian Quarterly |
| Volume / Edisi | : | 52 (No. 3) |
| Halaman | : | 262-273 |
| Abstrak | : | Abstrak tidak tersedia. |
Economic Growth, Inflationary Pressure, and Post-Pandemic Normalization Efforts
| Pengarang | : | Sylvia Febiandita, Deni Friawan, Ira S. Titiheruw |
| Nama Majalah/Jurnal | : | The Indonesian Quarterly |
| Volume / Edisi | : | 52 (No. 3) |
| Halaman | : | 249-261 |
| Abstrak | : | Abstrak tidak tersedia. |
The Peoples Consultative Assembly (MPR) and the State Policy Outlines (PPHN) in the Post-Fourth Amendment Era of the 1945 Constitution
| Pengarang | : | D. Nicky Fahrizal, Prajna Delfina Dwayne |
| Nama Majalah/Jurnal | : | The Indonesian Quarterly |
| Volume / Edisi | : | 52 (No. 3) |
| Halaman | : | 235-248 |
| Abstrak | : | Abstrak tidak tersedia. |
Regulating Algorithms: The Next Frontier in the Platform Economy Debate
| Pengarang | : | Joanna Octavia |
| Nama Majalah/Jurnal | : | The Indonesian Quarterly |
| Volume / Edisi | : | 52 (No. 3) |
| Halaman | : | 220-234 |
| Abstrak | : | Abstrak tidak tersedia. |