We study a two-dimensional spin model obtained by "Higgsing" the rank-2 U(1) lattice gauge theory (LGT) with scalar or vector charges on L_x * L_y square under periodic boundary condition (PBC). There are p degrees of freedom per orbital and three orbitals unit cell in model. The resulting is stabilizer code consisting mutually commuting projectors that are, turn, Higgsing Gauss's law operators...

a r t i c l e i n f o a b s t r a c t Keywords: Saliency Low-rank and sparse analysis Shape feature Structure This paper advocates a novel multi-scale mesh saliency method using the powerful low-rank and sparse analysis in shape feature space. The technical core of our approach is a new shape descriptor that embraces both local geometry information and global structure information in an integra...

Quaternionic representations of Coxeter (reflection) groups of ranks 3 and 4, as well as those of E8, have been used extensively in the literature. The present paper analyses such Coxeter groups in the Clifford Geometric Algebra framework, which affords a simple way of performing reflections and rotations whilst exposing more clearly the underlying geometry. The Clifford approach shows that the...

We theoretically prove that the minimal rank of the interaction between two separated geometry blocks in an integral-equation based analysis of general threedimensional objects, for a prescribed error bound, scales linearly with the electric size of the block diameter. We thus prove the existence of the error-bounded lowrank representation of both surface and volume based integral operators for...

Recall that the rank of a finitely generated group is the minimal number of elements needed to generate it. In [Whi02], M. White proved that the injectivity radius of a closed hyperbolic 3-manifold M is bounded above by some function of rank(π1(M)). Building on a technique that he introduced, we determine the ranks of the fundamental groups of a large class of hyperbolic 3-manifolds fibering ov...

Let ∆ be a rank 2 hyperbolic root system. Then ∆ has generalized Cartan matrix H(a, b) = ( 2 −b −a 2 ) indexed by a, b ∈ Z with ab ≥ 5. If a 6= b, then ∆ is non-symmetric and is generated by one long simple root and one short simple root, whereas if a = b, ∆ is symmetric and is generated by two long simple roots. We prove that if a 6= b, then ∆ contains an infinite family of symmetric rank 2 hy...

We investigate geometric features of the unit ball corresponding to the sum of the nuclear norm of a matrix and the l1 norm of its entries — a common penalty function encouraging joint low rank and high sparsity. As a byproduct of this effort, we develop a calculus (or algebra) of faces for general convex functions, yielding a simple and unified approach for deriving inequalities balancing the ...

This paper presents knowledge-aided space-time adaptive processing (KA-STAP) algorithms that exploit the lowrank dominant clutter and the array geometry properties (LRGP) for airborne radar applications. The core idea is to exploit the fact that the clutter subspace is only determined by the spacetime steering vectors, redwhere the Gram-Schmidt orthogonalization approach is employed to compute ...