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We consider the phase diagram of the most general SU(4)-symmetric two-site Hamiltonian for a system of two fermions per site (i.e., self-conjugate 6 representation) on the square lattice. It is known that this model hosts magnetic phases breaking SU(4) sym ...
The geodesic flows are studied on real forms of complex semi-simple Lie groups with respect to a left-invariant (pseudo-)Riemannian metric of rigid body type. The Williamson types of the isolated relative equilibria on generic adjoint orbits are determined ...
We consider the problem of finding an optimal transport plan between an absolutely continuous measure and a finitely supported measure of the same total mass when the transport cost is the unsquared Euclidean distance. We may think of this problem as close ...
We study the problem of localizing a configuration of points and planes from the collection of point-to-plane distances. This problem models simultaneous localization and mapping from acoustic echoes as well as the & x201C;structure from sound & x201D; app ...
We present a general theory of Group equivariant Convolutional Neural Networks (G-CNNs) on homogeneous spaces such as Euclidean space and the sphere. Feature maps in these networks represent fields on a homogeneous base space, and layers are equivariant ma ...
The Ebbinghaus illusion is argued to be a product of low-level contour interactions or a higher cognitive comparison process. We examined the effect of grouping on the illusion by manipulating objecthood, i.e., the degree to which an object is a cohesive p ...
We exhibit non-equivariant perturbations of the blowup solutions constructed in [18] for energy critical wave maps into S2. Our admissible class of perturbations is an open set in some sufficiently smooth topology and vanishes near the light co ...
We consider minimizing a nonconvex, smooth function f on a Riemannian manifold M. We show that a perturbed version of Riemannian gradient descent algorithm converges to a second-order stationary point (and hence is able to escape saddle points on the manif ...
DC microgrids often present a hierarchical control architecture, requiring integration of communication layers. This leads to the possibility of malicious attackers disrupting the overall system. Motivated by this application, in this article, we present a ...
Bayesian optimization (BO) recently became popular in robotics to optimize control parameters and parametric policies in direct reinforcement learning due to its data efficiency and gradient-free approach. However, its performance may be seriously compromi ...