This paper proposes a control theoretic formulation and a controller design method for the feature-based visual servoing with redundant features. The linear time-invariant (LTI) formulation copes with the redundant features and provides a simple framework for controller design. The proposed linear quadratic (LQ) method can deal with the redundant features, which is important because the previou...

Artin's celebrated conjecture on primitive roots (Artin [l, p. viii], Hasse [2], Hooley [3]) suggests the following Conjecture. Let S' be a set of rational primes. For each q£-S, let Lq be an algebraic number field of degree n(q). For every square-f ree integer k, divisible only by primes of S, define Lk to be the composite of all Lq, q\ k, and denote n{k) =deg(Ljb/0). Assume that 2 * l/n(k) co...

Sparse learning has recently received increasing attention in many areas including machine learning, statistics, and applied mathematics. The mixed-norm regularization based on the l1/lq norm with q > 1 is attractive in many applications of regression and classification in that it facilitates group sparsity in the model. The resulting optimization problem is, however, challenging to solve due t...

Let 1 < p ≤ q < +∞ and let v, w be weights on (0,+∞) satisfying: (?) v(x)xis equivalent to a non-decreasing function on (0,+∞) for some ρ ≥ 0; [w(x)x] ≈ [v(x)x] for all x ∈ (0,+∞). We prove that if the averaging operator (Af)(x) := 1 x R x 0 f(t) dt, x ∈ (0,+∞), is bounded from the weighted Lebesgue space Lp((0,+∞); v) into the weighted Lebesgue space Lq((0,+∞);w), then there exists ε0 ∈ (0, p−...

We apply the recently developed duality methods based on information relaxations to the classic linear quadratic (LQ) control problem. We derive two dual optimal penalties for the LQ problem when the control space is unconstrained. These two penalties, which are derived using value function and gradient methods, respectively, may be used to evaluate sub-optimal policies for constrained LQ probl...

One approach to improving efficiency of protein and nitrogen use for optimal productivity in dairy heifers is to provide adequate levels of protein with differing rumen degradabilities. The objective of this experiment was to determine effects of manipulating RDP in diets of dairy heifers precision fed low- and high-quality forage. Eight rumen-cannulated Holstein heifers (448 ± 19 kg BW) were r...

We present a formula for the Fourier transforms of order statistics in Rn showing that all these Fourier transforms are equal up to a constant multiple outside the coordinate planes in Rn. For a1 ≥ ... ≥ an ≥ 0 and q > 0, denote by lw,q the n-dimensional Lorentz space with the norm ‖(x1, ..., xn)‖ = (a1(x∗1) q + ...+ an(x∗n) q)1/q, where (x 1 , ..., x∗n) is the non-increasing permutation of the...

The aim of this study was to examine the applicability of the linear-quadratic (LQ) model to single and fractionated irradiation in EMT6 cells. First, the α/β ratio of the cells was determined from single-dose experiments, and a biologically effective dose (BED) for 20 Gy in 10 fractions (fr) was calculated. Fractional doses yielding the same BED were calculated for 1-, 2-, 3-, 4-, 5-, 7-, 15- ...

A semidefinite relaxation σ(Γ) for the problem of finding the maximum number κ(Γ) of edges in a complete bipartite subgraph of a bipartite graph Γ = (V1 ∪ V2, E) is considered. For a large class of graphs, the relaxation is better than the LP-relaxation described in [9]. It is shown that σ(Γ) is bounded from above by the Lovász theta function θ(LQ(Γ)) of the graph LQ(Γ) related to the line grap...

Given a dictionary of Mn initial estimates of the unknown true regression function, we aim to construct linearly aggregated estimators that target the best performance among all the linear combinations under a sparse q-norm (0 ≤ q ≤ 1) constraint on the linear coefficients. Besides identifying the optimal rates of aggregation for these lq-aggregation problems, our multi-directional (or adaptive...