This paper considers the problem of finding a controller for a discrete time linear periodically time-varying system with structured parametric uncertainty which achieves robust ‘2 semi-norm performance (the equivalent of robust H2 norm performance for time-varying systems). This problem is shown to be a generalization of a guaranteed cost control problem when the structure of the uncertainty i...

Many practical applications such as gene expression analysis, multi-task learning, image recognition, signal processing, and medical data analysis pursue a sparse solution for the feature selection purpose and particularly favor the nonzeros evenly distributed in different groups. The exclusive sparsity norm has been widely used to serve to this purpose. However, it still lacks systematical stu...

Introduction: L1 norm constrained reconstruction/compressed sensing techniques [1, 2] have recently been proposed to accelerate data acquisitions in MRI by acquiring fewer data in k-space. Image artifacts due to k-space undersampling are resolved by minimizing L1 norm of the sparse image estimate while preserving fidelity to the acquired data. Using an L1 norm constraint exploits implicit spars...

For structured estimation problems with atomic norms, recent advances in the literature express sample complexity and estimation error bounds in terms of certain geometric measures, in particular Gaussian width of the unit norm ball, Gaussian width of a spherical cap induced by a tangent cone, and a restricted norm compatibility constant. However, given an atomic norm, bounding these geometric ...

Orthodontists commonly specify the alignment of the teeth and jaws by means of a set of k angles and their relationship with each other. Each individual can thus be visualized as a point in k-dimensional space. Individuals regarded as having an ideal occlusion and well-balanced face, form a cloud of points that is termed the 'norm' population. Individuals far from the cloud require orthodontic ...

Weinberger in 1973 has shown that under the Generalized Riemann Hypothesis for Dedekind zeta functions, an algebraic number field with infinite unit group is Euclidean if and only if it is a principal ideal domain. Using a method recently introduced by us, we give two examples of cubic fields which are Euclidean but not norm–Euclidean. Let R be the ring of integers of an algebraic number field ...

The largest volume ratio of a given convex body $K \subset \mathbb R^n$ is defined as $$ \mathrm{lvr}(K):= \mathrm {sup}\_{L R^n} {vr}(K,L), where the sup runs over all bodies $L$. We prove following sharp lower bound: c \sqrt{n} \leq \mathrm{lvr}(K), for every $K$ (where $c > 0$ an absolute constant). This result improves former best known bound, order $\sqrt{{n}/{\log \log(n)}}$. also study e...

A normed vector space is a real or complex vector space in which a norm has been defined. Formally, one says that a normed vector space is a pair (V, ∥ · ∥) where V is a vector space over K and ∥ · ∥ is a norm in V , but then one usually uses the usual abuse of language and refers to V as being the normed space. Sometimes (frequently?) one has to consider more than one norm at the same time; th...

Let (G, u) be an Archimedean norm-complete dimension group with order-unit. Continuing a previous paper, we study intervals (i.e., nonempty upward directed lower subsets) of G which are closed with respect to the canonical norm of (G, u). In particular, we establish a canonical one-to-one correspondence between closed intervals of G and certain affine lower semicontinuous functions on the state...