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Inverse Design of Multiple-Input Multiple-Output Perfectly-Matched Metamaterials

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Inverse Design of Multiple-Input Multiple-Output Perfectly-M...

International Review of Progress in Applied Computational Electromagnetics (ACES)

作者： Shrey Thakkar Jorge Ruiz-Garcia Luke Szymanski Gurkan Gok Anthony Grbic Department of Electrical Engineering and Computer Science University of Michigan Ann Arbor USA MIT Lincoln Laboratory Lexington USA RTX Technology Research Centre East Hartford USA

ISBN: (数字)9781733509671

ISBN: (纸本)9798350362978

Inverse design has been applied to a variety of complex electromagnetic structures including multifunctional and multiple-input multiple-output (MIMO) devices, where analytical design methods are limiting. We have previously reported on the inverse design of single-input, single-output Perfectly-Matched Metamaterials (PMMs). PMMs are inhomogeneous, anisotropic 2D metamaterials composed of unit cells that remain impedance-matched to each other and the surroundings under all excitations. PMMs rely primarily on refractive effects and exhibit broadband operation. This work presents the inverse design of a compact MIMO device based on PMMs: a 2D beamformer with prescribed amplitude and phase profiles that exhibits zero scan loss.

关键词： Limiting Design methodology Anisotropic Nonhomogeneous media Computational electromagnetics Metamaterials Broadband communication

Bounds on the ground state energy of quantum p-spin Hamiltonians

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arXiv 2024年

作者： Anschuetz, Eric R. Gamarnik, David Kiani, Bobak T. Institute for Quantum Information and Matter Caltech Walter Burke Institute for Theoretical Physics Caltech MIT Center for Theoretical Physics MIT United States Operations Research Center Statistics and Data Science Center Sloan School of Management MIT United States John A. Paulson School of Engineering and Applied Sciences Department of Electrical Engineering and Computer Science MIT Harvard United States

We consider the problem of estimating the ground state energy of quantum p-local spin glass random Hamiltonians, the quantum analogues of widely studied classical spin glass models. Our main result shows that the maximum energy achievable by product states has a well-defined limit (for even p) as n → ∞ and is Eproduct∗ = √2 log p in the limit of large p. This value is interpreted as the maximal energy of a much simpler so-called Random Energy Model, widely studied in the setting of classical spin glasses. The proof of the limit existing follows from an extension of Fekete’s Lemma after we demonstrate near super-additivity of the (normalized) quenched free energy. The proof of the value follows from a second moment method on the number of states achieving a given energy when restricting to an ǫ-net of product states. Furthermore, we relate the maximal energy achieved over all states to a p-dependent constant γ (p), which is defined by the degree of violation of a certain asymptotic independence ansatz over graph matchings. We show that the maximal energy achieved by all states E∗ (p) in the limit of large n is at most pγ (p)Eproduct∗ . We also prove using Lindeberg’s interpolation method that the limiting E∗ (p) is robust with respect to the choice of the randomness and, for instance, also applies to the case of sparse random Hamiltonians. This robustness in the randomness extends to a wide range of random Hamiltonian models including SYK and random quantum max-cut. Copyright © 2024, The Authors. All rights reserved.

关键词： Hamiltonians

SGD learning on neural networks: leap complexity and saddle-to-saddle dynamics

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arXiv 2023年

作者： Abbe, Emmanuel Boix-Adserà, Enric Misiakiewicz, Theodor Mathematics Institute EPFL Switzerland Department of Electrical Engineering and Computer Science MIT United States Department of Statistics Stanford University United States

We investigate the time complexity of SGD learning on fully-connected neural networks with isotropic data. We put forward a complexity measure, the leap, which measures how "hierarchical" target functions are. For d-dimensional uniform Boolean or isotropic Gaussian data, our main conjecture states that the time complexity to learn a function f with low-dimensional support is Θ˜(dmax(Leap(f),2)). We prove a version of this conjecture for a class of functions on Gaussian isotropic data and 2-layer neural networks, under additional technical assumptions on how SGD is run. We show that the training sequentially learns the function support with a saddle-to-saddle dynamic. Our result departs from [ABM22] by going beyond leap 1 (merged-staircase functions), and by going beyond the mean-field and gradient flow approximations that prohibit the full complexity control obtained here. Finally, we note that this gives an SGD complexity for the full training trajectory that matches that of Correlational Statistical Query (CSQ) lower-bounds. Copyright © 2023, The Authors. All rights reserved.

关键词： Complex networks

Graph Neural Tangent Kernel: Convergence on Large Graphs

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arXiv 2023年

作者： Krishnagopal, Sanjukta Ruiz, Luana Dept. of Electrical Engineering and Computer Science United States Dept. of Mathematics UCLA United States MIT CSAIL United States

Graph neural networks (GNNs) achieve remarkable performance in graph machine learning tasks but can be hard to train on large-graph data, where their learning dynamics are not well understood. We investigate the training dynamics of large-graph GNNs using graph neural tangent kernels (GNTKs) and graphons. In the limit of large width, optimization of an overparametrized NN is equivalent to kernel regression on the NTK. Here, we investigate how the GNTK evolves as another independent dimension is varied: the graph size. We use graphons to define limit objects—graphon NNs for GNNs, and graphon NTKs for GNTKs—, and prove that, on a sequence of graphs, the GNTKs converge to the graphon NTK. We further prove that the spectrum of the GNTK, which is related to the directions of fastest learning which becomes relevant during early stopping, converges to the spectrum of the graphon NTK. This implies that in the large-graph limit, the GNTK fitted on a graph of moderate size can be used to solve the same task on the large graph, and to infer the learning dynamics of the large-graph GNN. These results are verified empirically on node regression and classification tasks. © 2023, CC BY.

关键词： Dynamics

Geometric Graph Filters and Neural Networks: Limit Properties and Discriminability Trade-offs

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arXiv 2023年

作者： Wang, Zhiyang Ruiz, Luana Ribeiro, Alejandro Department of Electrical and Systems Engineering University of Pennsylvania PA United States Computer Science & Artificial Intelligence Laboratory MIT MA United States

This paper studies the relationship between a graph neural network (GNN) and a manifold neural network (MNN) when the graph is constructed from a set of points sampled from the manifold, thus encoding geometric information. We consider convolutional MNNs and GNNs where the manifold and the graph convolutions are respectively defined in terms of the Laplace-Beltrami operator and the graph Laplacian. Using the appropriate kernels, we analyze both dense and moderately sparse graphs. We prove non-asymptotic error bounds showing that convolutional filters and neural networks on these graphs converge to convolutional filters and neural networks on the continuous manifold. As a byproduct of this analysis, we observe an important trade-off between the discriminability of graph filters and their ability to approximate the desired behavior of manifold filters. We then discuss how this trade-off is ameliorated in neural networks due to the frequency mixing property of nonlinearities. We further derive a transferability corollary for geometric graphs sampled from the same manifold. We validate our results numerically on a navigation control problem and a point cloud classification task. © 2023, CC0.

关键词： Graph neural networks

Modulating cell-free DNA biology as the next frontier in liquid biopsies

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Trends in Cell Biology 2025年第6期35卷 459-469页

作者： Tabrizi, Shervin Martin-Alonso, Carmen Xiong, Kan Bhatia, Sangeeta N. Adalsteinsson, Viktor A. Love, J. Christopher Koch Institute for Integrative Cancer Research Massachusetts Institute of Technology Cambridge MA United States Broad Institute of MIT and Harvard Cambridge MA United States Department of Radiation Oncology Mass General Brigham Boston MA United States Harvard Medical School Boston MA United States Harvard-MIT Division of Health Sciences and Technology Institute for Medical Engineering and Science Massachusetts Institute of Technology Cambridge MA United States Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology Cambridge MA United States Wyss Institute at Harvard University Boston MA United States Howard Hughes Medical Institute Cambridge MA United States Department of Chemical Engineering Massachusetts Institute of Technology Cambridge MA United States

Technical advances over the past two decades have enabled robust detection of cell-free DNA (cfDNA) in biological samples. Yet, higher clinical sensitivity is required to realize the full potential of liquid biopsies. This opinion article argues that to overcome current limitations, the abundance of informative cfDNA molecules – such as circulating tumor DNA (ctDNA) – collected in a sample needs to increase. To accomplish this, new methods to modulate the biological processes that govern cfDNA production, trafficking, and clearance in the body are needed, informed by a deeper understanding of cfDNA biology. Successful development of such methods could enable a major leap in the performance of liquid biopsies and vastly expand their utility across the spectrum of clinical care. © 2024 Elsevier Ltd

关键词： biomarkers cfDNA clearance cfDNA shedding ctDNA

Randomized probe imaging through deep K-learning

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Randomized probe imaging through deep K-learning

Computational Optical Sensing and Imaging, COSI 2021 - Part of OSA Imaging and Applied Optics Congress 2021

作者： Guo, Zhen Levitan, Abraham Barbastathis, George Comin, Riccardo Department of Electrical Engineering and Computer Science MIT CambridgeMA02139 United States Department of Physics MIT CambridgeMA02139 United States Department of Mechanical Engineering MIT CambridgeMA02139 United States

Iterative phase retrieval algorithms are time-consuming. To accelerate reconstructions for Randomized Probe Imaging (RPI), we propose deep k-learning, a neural network with attention to frequency. The associated compu... 详细信息

ISBN: (纸本)9781557528209

关键词： Probes

Electrostatic Microfiltration Enriches Low-abundance Bacteria and Improves Downstream Detection 26

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Electrostatic Microfiltration Enriches Low-abundance Bacteri...

26th International Conference on Miniaturized Systems for Chemistry and Life sciences, MicroTAS 2022

作者： Liu, Yaoping Raymond, Joshua Wu, Xiaolin Springs, Stacy L. Lu, Timothy K. Yu, Hanry Han, Jongyoon 138602 Singapore United States Department of Electrical Engineering and Computer Science United States Department of Biological Engineering MIT CambridgeMA02139 United States A*STAR Singapore Department of physiology and WisDM Mechanobiology Institute National University of Singapore Singapore

ISBN: (纸本)9781733419048

It is challenging to detect low-abundance bacteria from large-volume raw samples or huge backgrounds. This work proposes electrostatic microfiltration as effective sample preparation for bacteria enrichment to improve the downstream detection. The Ca-alginate gel was used for positive charge modification on the microfilter surface to capture negatively-charged bacteria. The enriched bacteria was detected via digital loop-mediated isothermal amplification (dLAMP). Capture efficiency@87.8±21.0%, enrichment factor>20, and detection improvement@36.9±9.4× (compared to centrifugation) in samples (1 mL) of ~104 CFU bacteria at a throughput≥1 mL/min were demonstrated so far, with potential to improve towards even lower abundances from larger volumes. © 2022 MicroTAS 2022 - 26th International Conference on Miniaturized Systems for Chemistry and Life sciences. All rights reserved.

关键词： Bacteria

Controllable multi-level switching of optical phase change materials via microheater temperature profile engineering

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Controllable multi-level switching of optical phase change m...

2024 Conference on Lasers and Electro-Optics, CLEO 2024

作者： Sun, Hongyi Lian, Chuanyu Vásquez-Aza, Francis Huang, Yi-Siou Vitale, Steven A. Takeuchi, Ichiro Hu, Juejun Youngblood, Nathan Pavlidis, Georges Ríos Ocampo, Carlos A. Department of Materials Science & Engineering University of Maryland College ParkMD20742 United States Institute for Research in Electronics and Applied Physics University of Maryland College ParkMD20742 United States Department of Mechanical Engineering University of Connecticut StorrsCT06269 United States Advanced Materials and Microsystems Group MIT Lincoln Laboratory LexingtonMA02139 United States Quantum Materials Center Department of Physics University of Maryland College ParkMD20742 United States Department of Materials Science & Engineering MIT CambridgeMA02139 United States Electrical & Computer Engineering Department The University of Pittsburgh PittsburghPA15213 United States

ISBN: (纸本)9781957171395

We demonstrate doped-silicon-on-insulator microheaters with triangle-like temperature profiles. Such devices control the hotspot size and temperature and, thus, the area that undergoes amorphization or crystallization in optical phase-change materials, leading to controllable multilevel, nonvolatile response. © Optica Publishing Group 2024 © 2024 The Author(s)

关键词： Optical materials