Sparse recovery on Euclidean Jordan algebras

This paper is concerned with the problem of sparse recovery on Euclidean Jordan algebra (SREJA), which includes the sparse signal recovery problem and the low-rank symmetric matrix recovery problem as special cases. We introduce the notions of restricted isometry property (RIP), null space property (NSP), and s-goodness for linear transformations in s-SREJA, all of which provide sufficient conditions for s-sparse recovery via the nuclear norm minimization on Euclidean Jordan algebra. Moreover, we show that both the s-goodness and the NSP are necessary and sufficient conditions for exact s-sparse recovery via the nuclear norm minimization on Euclidean Jordan algebra. Applying these characteristic properties, we establish the exact and stable recovery results for solving SREJA problems via nuclear norm minimization

Orbits of triples in the Shilov boundary of a bounded symmetric domain

Let ${\cal D}$ be a bounded symmetric domain of tube type, $S$ its Shilov boundary, and $G$ the neutral component of its group of biholomorphic transforms. We classify the orbits of $G$ in the set $S\times S\times S$

A regularized smoothing Newton method for symmetric cone complementarity problems

This paper extends the regularized smoothing Newton method in vector complementarity problems to symmetric cone complementarity problems (SCCP), which includes the nonlinear complementarity problem, the second-order cone complementarity problem, and the semidefinite complementarity problem as special cases. In particular, we study strong semismoothness and Jacobian nonsingularity of the total natural residual function for SCCP. We also derive the uniform approximation property and the Jacobian consistency of the Chen–Mangasarian smoothing function of the natural residual. Based on these properties, global and quadratical convergence of the proposed algorithm is established

Workshop on Harmonic Oscillators

Proceedings of a workshop on Harmonic Oscillators held at the College Park Campus of the University of Maryland on March 25 - 28, 1992 are presented. The harmonic oscillator formalism is playing an important role in many branches of physics. This is the simplest mathematical device which can connect the basic principle of physics with what is observed in the real world. The harmonic oscillator is the bridge between pure and applied physics

Microlocal Analysis of Quantum Fields on Curved Spacetimes

These lecture notes give an exposition of microlocal analysis methods in the study of Quantum Field Theory on curved spacetimes. We concentrate on free fields and the corresponding quasi-free states and mainly on Klein-Gordon fields

Microlocal Analysis of Quantum Fields on Curved Spacetimes

International audienceThese lecture notes give an exposition of microlocal analysis methods in the study of Quantum Field Theory on curved spacetimes. We concentrate on free fields and the corresponding quasi-free states and mainly on Klein-Gordon fields

Twisted Holography: The Examples of 4d and 5d Chern-Simons Theories

Twisted holography is a duality between a twisted supergravity, and a twisted supersymmetric gauge theory living on the D-branes in the supergravity. The main objectives of this duality is the comparison between the algebra of observables in the bulk twisted supergravity and the algebra of observables in the boundary twisted supersymmetric gauge theory. In this thesis, two example of the twisted holography duality are explored. The bulk theory for the first example is the 4d topological-holomorphic Chern-Simons theory, which is expected to be dual to 2d BF theory with line defects. The algebra of observables in the 2d BF theory is computed by two methods: perturbation theory (Feynman diagrams), and phase space quantization. By holography duality this algebra is expected to be isomorphic to the algebra of bulk-boundary scattering process, and the latter is computed in this thesis using perturbative method. The bulk theory for the second example is the 5d topological-holomorphic Chern-Simons theory, which is expected to be dual to the large-N limit of a family of 1d quantum mechanics built from the ADHM quivers. The generators and relations of the large-N limit algebra of observables in the 1d quantum mechanics are studied from algebraic point view. By holography duality, this algebra is expected to be the algebra of observables on the universal line defect coupled to the 5d Chern-Simons theory, and some nontrivial relations of the latter algebra are computed in this thesis using perturbative method. The surface defects and various fusion process between line and surface defects are also explored