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Continuum Limit of Spin Dynamics on Two Dimensional Hexagonal Lattice
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| Pengarang | : | Mengjia Bai, Jingrun Chen, Zhiwei Sun, Yun Wang |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 85 (No. 4) |
| Halaman | : | 1856-1880 |
| Abstrak | : | This study investigates the continuum limit of spin dynamics on a two-dimensional hexagonal lattice, with a focus on the atomistic spin system in C?r?C?l3, which exhibits topologically nontrivial meron structures. We analyze the discrete Landau–Lifshitz–Gilbert (LLG) equation and establish its weak convergence to the continuum LLG equation as the lattice constant approaches zero. To address the challenges posed by the hexagonal lattice’s symmetry breaking, we develop novel multistep difference quotients and generalize Ladyzhenskaya’s interpolation operators to hexagonal lattice. Our main result demonstrates the weak convergence of the discrete spin dynamics to the continuum model, supported by rigorous energy estimates and a priori bounds. This work provides a mathematical foundation for understanding spin dynamics in hexagonal lattice systems and offers tools for analyzing weak convergence in other atomistic nonlinear problems. |
The Role of Higher-Order Self Dynamics in Neural Dynamical Networks: Preserving Memory Capacity and Enhancing Retrieval Basin
| Pengarang | : | Weichen Fu, Zhuchun Li, Wei Lin, Xiaoxue Zhao |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 85 (No. 4) |
| Halaman | : | 1834-1855 |
| Abstrak | : | Networks of coupled Kuramoto-type oscillators have been proposed as models of associative memory. In this paper, we design a model for neural dynamical networks by incorporating higher-order self-dynamics. This system is not invariant under global phase translation, which makes it more direct to link phases and patterns. We present a unified approach for error-free retrieval in the pattern retrieval problem with an arbitrary set of standard patterns. We find that this model preserves the memory capacity, simultaneously enhancing the basin for error-free retrieval. More practically, we propose a strategy for the retrieval problems with grayscale and even colorful images. |
Mathematical Justifications of Dipolar Resonances with Hard Inclusions Embedded in a Soft Elastic Material
| Pengarang | : | Hongjie Li, Jun Zou |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 85 (No. 4) |
| Halaman | : | 1810-1833 |
| Abstrak | : | The current study is motivated by the work [Z. Liu, et al., Science, 289 (2000), pp. 1734–1736], which investigated the incorporation of hard inclusions into a soft elastic matrix (HISE) to achieve a negative mass density through some subwavelength dipolar resonances. This work offers a comprehensive and mathematically rigorous justification of the subwavelength dipolar resonances within the HISE structure. First, an explicit formula for computing the resonant frequencies for arbitrarily shaped hard inclusions is derived for the first time. Then it is shown that the resonances are generated by the high contrast in Lamé parameters between different materials, while the subwavelength nature of the resonances is attributed to the significant disparities in material densities. Furthermore, the wave fields inside the hard inclusion are derived explicitly when the frequencies of the incident wave are located within different regimes. In addition, the dipolar characterization of the resonances is justified. To validate our findings, we study resonant phenomena within a spherical geometry via two methods. One is to apply the results derived in this work for arbitrarily shaped hard inclusions. The other is through directly solving the original model system. The investigation within the spherical geometry offers not only an alternative method to calculate resonant frequencies, but also a confirmation of the results presented in this work. |
Mathematical Analysis of Resonances for an Array of Subwavelength Annular Holes and Its Application in Superresolution Imaging
| Pengarang | : | Jiaxin Zhou, Junshan Lin, Wangtao Lu, Hai Zhang |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 85 (No. 4) |
| Halaman | : | 1785-1809 |
| Abstrak | : | This work presents a mathematical analysis of resonances for an array of subwavelength coaxial annular holes and a new superresolution imaging approach using the resonant structure. By employing a multiscale analytical framework based on a combination of the integral equation in the exterior domain and the waveguide mode expansion inside the small three-dimensional holes, we derive asymptotic expansions of complex-valued scattering resonances for the underlying subwavelength structure and analyze the electromagnetic field amplification at the resonant frequencies. In particular, it is shown that the resonant modes oscillate on a subwavelength scale in the near field if the annular holes are placed close to each other. By leveraging this observation, we develop a novel superresolution imaging approach that utilizes resonant modes through the subwavelength resonant structure as they illuminate patterns and present a numerical reconstruction algorithm to solve the underlying inverse problem. Numerical examples show that a tenfold improvement can be achieved in image resolution with the new imaging method. |
Personalized Recommendation Based on Evolutionary Multi-Objective Optimization
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | IEEE Computational intelligence |
| Volume / Edisi | : | 10 (No. 1) |
| Halaman | : | 52-62 |
| Abstrak | : | Traditional recommendation techniques in recommender systems mainly focus on improving recommendation accuracy. However, personalized recommendation, which considers the multiple needs of users and can make both accurate and diverse recommendations, is more suitable for modern recommender systems. In this paper, the task of personalized recommendation is modeled as a multi-objective optimization problem. A multiobjective recommendation model is proposed. The proposed model maximizes two conflicting performance metrics termed as accuracy and diversity. The accuracy is evaluated by the probabilistic spreading method, while the diversity is measured by recommendation coverage. The proposed MOEA-based recommendation method can simultaneously provide multiple recommendations for multiple users in only one run. Our experimental results demonstrate the effectiveness of the proposed algorithm. Comparison experiments also indicate that the proposed algorithm can make more diverse yet accurate recommendations. |
Employing Type-2 Fuzzy Logic Systems in the Efforts to Realize Ambient Intelligent Environments
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | IEEE Computational intelligence |
| Volume / Edisi | : | 10 (No. 1) |
| Halaman | : | 44-51 |
| Abstrak | : | Ambient Intelligence (Aml) is an emerging vision that aims to realize intelligent environments which are sensitive and responsive to the users' needs and behaviors. This paper presents an insight on the benefits that type-2 Fuzzy Logic Systems (FLSs) can offer towards the efforts to realize Ambient Intelligent Environments (AIEs). We will introduce research results from the Scaleup project showing different type-2 FLSs based applications in AIEs. Such applications include intelligent machine vision systems, blending real and virtual realities over dispersed geographical areas and allowing natural communication between the AIE and humans. |
Efficient Heuristics for Profit Optimization of Virtual Cloud Brokers
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | IEEE Computational intelligence |
| Volume / Edisi | : | 10 (No. 1) |
| Halaman | : | 33-43 |
| Abstrak | : | This article introduces a new kind of broker for cloud computing, whose business relies on outsourcing virtual machines (VMs) to its customers. More specifically, the broker owns a number of reserved instances of different VMs from several cloud providers and offers them to its customers in an on-demand basis, at cheaper prices than those of the cloud providers. The essence of the business resides in the large difference in price between ondemand and reserved VMs. We define the Virtual Machine Planning Problem, an optimization problem to maximize the profit of the broker. We also propose a number of efficient smart heuristics (seven two-phase list scheduling heuristics and a reordering local search) to allocate a set of VM requests from customers into the available pre-booked ones, that maximize the broker earnings. We perform experimental evaluation to analyze the profit and quality of service metrics for the resulting planning, including a set of 400 problem instances that account for realistic workloads and scenarios using real data from cloud providers. |
Bring Your Own Learner! A Cloud-Based, Data-Parallel Commons for Machine Learning
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | IEEE Computational intelligence |
| Volume / Edisi | : | 10 (No. 1) |
| Halaman | : | 20-32 |
| Abstrak | : | We introduce FCUBE, a cloud-based framework that enables machine learning researchers to contribute their learners to its community-shared repository. FCUBE exploits data parallelism in lieu of algorithmic parallelization to allow its users to efficiently tackle large data problems automatically. It passes random subsets of data generated via resampling to multiple learners that it executes simultaneously and then it combines their model predictions with a simple fusion tech- nique. It is an example of what we have named a Bring Your Own Learner model. It allows multiple machine learning researchers to contribute algorithms in a plug-and-play style. We contend that the Bring Your Own Learner model signals a design shift in cloud-based machine learning infrastructure because it is capable of executing anyone's supervised machine learning algorithm. We demonstrate FCUBE executing five different learners contributed by three different machine learning groups on a 100 node deployment on Amazon E?2. They collectively solve a publicly available classification prob- lem trained with 11 million exemplars from the Higgs dataset. |
Computational Intelligence for Cloud Computing
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | IEEE Computational intelligence |
| Volume / Edisi | : | 10 (No. 1) |
| Halaman | : | 18 |
| Abstrak | : | - |
CIS Publication Spotlight
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | IEEE Computational intelligence |
| Volume / Edisi | : | 10 (No. 1) |
| Halaman | : | 16-17 |
| Abstrak | : | - |