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| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Ilmu dan Budaya |
| Volume / Edisi | : | VIII-4, JANUARI (No. 4) |
| Halaman | : | 256-268 |
| Abstrak | : | - |
The Combinatorial Code and the Graph Rules of Dale Networks
| Pengarang | : | Nikola Milicevic, Vladimir Itskov |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 84 (No. 6) |
| Halaman | : | 2522-2544 |
| Abstrak | : | We describe the combinatorics of equilibria and steady states of neurons in threshold-linear networks that satisfy Dale’s law. The combinatorial code of a Dale network is characterized in terms of two conditions: (i) a condition on the network connectivity graph, and (ii) a spectral condition on the synaptic matrix. We find that in the weak coupling regime the combinatorial code depends only on the connectivity graph, and not on the particulars of the synaptic strengths. Moreover, we prove that the combinatorial code of a weakly coupled network is a sublattice, and we provide a learning rule for encoding a sublattice in a weakly coupled excitatory network. In the strong coupling regime we prove that the combinatorial code of a generic Dale network is intersection-complete and is therefore a convex code, as is common in some sensory systems in the brain. |
The Spiritual Heritage Of Women
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Ilmu dan Budaya |
| Volume / Edisi | : | VIII-4, JANUARI (No. 4) |
| Halaman | : | 250-255 |
| Abstrak | : | - |
Continuous and Discrete Baroclinic Modes in Continuously Varying Stratification
| Pengarang | : | Rachel Robey, Ian Grooms |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 84 (No. 6) |
| Halaman | : | 2502-2521 |
| Abstrak | : | We study the behavior of baroclinic modes in a continuously stratified fluid and their discrete representation in a layer model. The modes are shown to rapidly approach simple sinusoidal behavior under a Charney-coordinate transform. We propose a corresponding grid scheme to near-optimally preserve the oscillating structure in the discrete modes. The discrete modal representation and analysis are relevant for quasi-geostrophic models and are also shown to apply to the primitive equations using a common discretization scheme. |
Exact and Approximate Solutions for Elastic Interactions in a Nematic Liquid Crystal
| Pengarang | : | Thomas G. J. Chandler, Saverio E. Spagnolie |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 84 (No. 6) |
| Halaman | : | 2476-2501 |
| Abstrak | : | Anisotropic fluids appear in a diverse array of systems, from liquid crystal displays to bacterial swarms, and are characterized by orientational order. Large colloidal particles immersed in such environments disturb the medium’s orientational order, resulting in a stored elastic energy within the bulk. As a consequence, multiple immersed bodies interact at equilibrium through fluid-mediated forces and torques, which depend on the bodies’ positions, orientations, and shapes. We provide the equilibrium configuration of a model nematic liquid crystal with multiple immersed bodies or inclusions in two dimensions, as well as the associated body forces, torques, and surface tractions. A complex variables approach is taken which leans on previous work by Crowdy [Solving Problems in Multiply Connected Domains, SIAM, Philadelphia, 2020] for describing solutions with multiply connected domains. Free periods of a complex director field, which correspond to topological defect positioning and net topological charge, are determined numerically to minimize a global stored elastic energy, including a contribution of a weak (finite) anchoring strength on the body surfaces. Finally, a general, analytical description of two-body far-field interactions is provided, along with examples using two cylindrical inclusions of arbitrary position and size, and two triangles of arbitrary position and orientation. |
On the Convergence Analysis of One-Shot Inversion Methods
| Pengarang | : | Marcella Bonazzoli, Houssem Haddar, Tuan-Anh Vu |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 84 (No. 6) |
| Halaman | : | 2440-2475 |
| Abstrak | : | When an inverse problem is solved by a gradient-based optimization algorithm, the corresponding forward and adjoint problems, which are introduced to compute the gradient, can be also solved iteratively. The idea of iterating at the same time on the inverse problem unknown and on the forward and adjoint problem solutions yields the concept of one-shot inversion methods. We are especially interested in the case where the inner iterations for the direct and adjoint problems are incomplete, that is, stopped before achieving a high accuracy on their solutions. Here, we focus on general linear inverse problems and generic fixed-point iterations for the associated forward problem. We analyze variants of the so-called multistep one-shot methods, in particular semi-implicit schemes with a regularization parameter. We establish sufficient conditions on the descent step for convergence by studying the eigenvalues of the block matrix of the coupled iterations. Several numerical experiments are provided to illustrate the convergence of these methods in comparison with the classical gradient descent, where the forward and adjoint problems are solved exactly by a direct solver instead. We observe that very few inner iterations are enough to guarantee good convergence of the inversion algorithm, even in the presence of noisy data. |
Kedudukan dan Tugas Pemuda dalam Menghadapi Zaman Baru
| Pengarang | : | Alisjahbana, S. Takdir |
| Nama Majalah/Jurnal | : | Ilmu dan Budaya |
| Volume / Edisi | : | VIII-4, JANUARI (No. 4) |
| Halaman | : | 242-249 |
| Abstrak | : | - |
Analytic Shape Recovery of an Elastic Inclusion from Elastic Moment Tensors
| Pengarang | : | Daehee Cho, Mikyoung Lim |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 84 (No. 6) |
| Halaman | : | 2417-2439 |
| Abstrak | : | In this paper, we present an analytic noniterative approach for recovering a planar isotropic elastic inclusion embedded in an unbounded medium from the elastic moment tensors (EMTs), which are coefficients for the multipole expansion of a field perturbation caused by the inclusion. EMTs contain information about the inclusion’s material and geometric properties, and, as is well known, the inclusion can be approximated by a disk from leading-order EMTs. We define the complex contracted EMTs as the linear combinations of EMTs where the expansion coefficients are given from complex-valued background polynomial solutions. By using the layer potential technique for the Lamé system and the theory of conformal mapping, we derive explicit asymptotic formulas in terms of the complex contracted EMTs for the shape of the inclusion, treating the inclusion as a perturbed disk. These formulas lead us to an analytic noniterative algorithm for elastic inclusion reconstruction using EMTs. We perform numerical experiments to demonstrate the validity and limitations of our proposed method. |
The Diffusive Ultrasound-Modulated Bioluminescence Tomography with Partial Data and Uncertain Optical Parameters
| Pengarang | : | Tianyu Yang, Yang Yang |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 84 (No. 6) |
| Halaman | : | 2393-2416 |
| Abstrak | : | The paper studies an imaging problem in the diffusive ultrasound-modulated bioluminescence tomography (UMBLT) with partial boundary measurement in an anisotropic medium. Assuming plane-wave modulation, we transform the imaging problem to an inverse problem with internal data and derive a reconstruction procedure to recover the bioluminescent source. Subsequently, an uncertainty quantification (UQ) estimate is established to assess the robustness of the reconstruction. To facilitate practical implementation, we discretize the diffusive model using the staggered grid scheme, resulting in a discrete formulation of the UMBLT inverse problem. A discrete reconstruction procedure is then presented along with a discrete UQ estimate. Finally, the reconstruction procedure is quantitatively validated through numerical examples to demonstrate the efficacy and reliability of the proposed approach and estimates. |
Electro-Osmotic Flow within Multilayer Microfluidic Structures and an Algebraic Framework for Hydrodynamic Cloaking and Shielding
| Pengarang | : | Lingzheng Kong, Liyan Zhu, Youjun Deng, Hongyu Liu |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 84 (No. 6) |
| Halaman | : | 2365-2392 |
| Abstrak | : | Multilayer structures are ubiquitous in constructing microfluidic devices for manipulating fluids to realize various frontier applications, including energy harvesting and invisibility cloaking. In this study, we develop a mathematical framework for analyzing electro-osmotic flow (EOF) within multilayer microfluidic structures. These structures are formed by Hele–Shaw configurations, with cross-sectional shapes that are concentric disks or confocal ellipses, and each layer is filled with a fluid material characterized by a zeta potential. The number of layers can vary, and the zeta potentials in each layer may differ. By dynamically adjusting the zeta potential, the multilayer EOF structure can effectively manipulate fluids without requiring metamaterials in microfluidic devices. Considering the impingement of an arbitrary nonuniform incident field on the multilayer structure, we first establish the representation formula of the solution of the coupled system using the layer potential techniques, and then the concept of contracted hydrodynamic Generalized Polarization Tensors (GPTs) is defined by multipolar expansion. Utilizing Fourier series and spectral theory, we derive a closed-form solution for the coupled system in the control region with multilayer concentric disks or confocal ellipses. This framework provides a convenient algebraic approach for studying hydrodynamic cloaking and shielding in multilayer structures, laying the groundwork for various microfluidic applications. |