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Weak solutions arise naturally in the study of the Navier-Stokes and Euler equations both from an abstract regularity/blow-up perspective and from physical theories of turbulence. This thesis studies the structure and size of singular set of such weak solu ...
In the recent years, Deep Neural Networks (DNNs) have managed to succeed at tasks that previously appeared impossible, such as human-level object recognition, text synthesis, translation, playing games and many more. In spite of these major achievements, o ...
We show that isogeometric Galerkin discretizations of eigenvalue problems related to the Laplace operator subject to any standard type of homogeneous boundary conditions have no outliers in certain optimal spline subspaces. Roughly speaking, these optimal ...
We prove the bigness of the Chow-Mumford line bundle associated to a Q-Gorenstein family of log Fano varieties of maximal variation with uniformly K-stable general geometric fibers. This result generalizes a theorem of Codogni and Patakfalvi to the logarit ...
Polynomial Networks (PNs) have demonstrated promising performance on face and image recognition recently. However, robustness of PNs is unclear and thus obtaining certificates becomes imperative for enabling their adoption in real-world applications. Exist ...
We introduce a family of neural quantum states for the simulation of strongly interacting systems in the presence of spatial periodicity. Our variational state is parametrized in terms of a permutationally invariant part described by the Deep Sets neural-n ...
The celebrated PCP Theorem states that any language in NP can be decided via a verifier that reads O(1) bits from a polynomially long proof. Interactive oracle proofs (IOP), a generalization of PCPs, allow the verifier to interact with the prover for multi ...
The Arctic environment is transforming rapidly due to climate change, which induces several feedback processes such as retreating sea ice, changing atmospheric transport patterns and cloud formation. In addition, more local pollution due to shipping and re ...
Owing in large part to the advent of integrated biphoton frequency combs, recent years have witnessed increased attention to quantum information processing in the frequency domain for its inherent high dimensionality and entanglement compatible with fiber- ...
Electroadhesion is a versatile and controllable adhesion mechanism that has been used extensively in robotics. Soft electroadhesion embodies electrostatic adhesion in soft materials and is required for shape-adaptive and safe grasping of curved objects and ...
