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Explore symmetry and uniqueness in nonlocal PDEs using variational approaches. Yao Yao discusses recent progress in aggregation-diffusion equations and 2D Euler equations, focusing on steady states and radial symmetry.
Exploring orthogonality sampling methods for electromagnetic inverse scattering problems, focusing on implementation simplicity, noise robustness, and applications in 2D and 3D experimental data.
Explore recent developments in completely integrable nonlinear dispersive PDE, including a priori bounds, orbital stability, well-posedness, and Gibbs distributed initial data dynamics.
Exploring convergence issues in algebraic iterative reconstruction methods for X-ray CT, presenting theoretical results and novel approaches to address non-convergence in limited-angle and limited-data scenarios.
Shape optimization techniques for inverse problems: analyzing piecewise constant models, shape derivatives, and Lagrangian approaches. Applications in electrical impedance tomography and full waveform inversion.
Explore automatic regularization parameter selection in image restoration, focusing on space-invariant blur and Gaussian noise. Learn about residual whiteness principle and its application to various variational models.
Expert panel discusses strategies for Ph.D. success and post-doctoral career paths in academia, industry, and research labs, offering valuable insights for data mining doctoral students.
Exploring neural network performance, normalization effects, and high-dimensional PDE solving using deep learning. Insights on generalization properties and applications in mathematical finance.
Explore analytical aspects of emergent dynamics in collective behavior systems, focusing on alignment dynamics in disconnected flocks and new approaches using topological fractional diffusion and random fluctuations.
Exploring gerrymandering, fairness in redistricting, and the impact of geopolitical geometry on electoral representation through Monte Carlo sampling and mathematical analysis.
Explore the mathematics of genome organization and its impact on gene expression through geometric packing models and deep learning, with insights on 3D genome reconstruction and autoencoder applications in genomics.
Explore Gaussian lower bounds for the Boltzmann equation, examining particle density evolution in gases and conditional estimates for solving global well-posedness challenges in fluid dynamics.
Explore a novel Bregman learning framework for training sparse neural networks, featuring LinBreg, momentum-accelerated, and AdaBreg algorithms, with applications in Neural Architecture Search.
Explore signal recovery using generative priors in imaging, discussing neural network models, recovery guarantees, and applications in compressed sensing and phase retrieval.
Explore innovative methods for handling model errors in inverse problems, focusing on CT reconstruction with uncertain view angles and improving image quality through uncertainty quantification.
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