We consider a class of `0-regularized linearquadratic (LQ) optimal control problems. This class of problems is obtained by augmenting a penalizing sparsity measure to the cost objective of the standard linear-quadratic regulator (LQR) problem in order to promote sparsity pattern of the state feedback controller. This class of problems is generally NP hard and computationally intractable. First,...

Cocaine, as an indirect dopamine agonist, induces selective behavioral and physiological events such as hyperlocomotion and dopamine release. These changes are considered as consequences of cocaine-induced molecular adaptation such as CREB and c-Fos. Recently, methanolic extracts from licorice was reported to decrease cocaine-induced dopamine release and c-Fos expression in the nucleus accumben...

This paper presents a method for finding an Lqclosest-point to a set of affine subspaces, that is a point for which the sum of the q-th power of orthogonal distances to all the subspaces is minimized, where 1 ≤ q < 2. We give a theoretical proof for the convergence of the proposed algorithm to a unique Lq minimum. The proposed method is motivated by the Lq Weiszfeld algorithm, an extremely simp...

In this paper we consider a nonlinear control design for nonlinear systems by using two-stage formal linearization and twotype LQ controls. The ordinary LQ control is designed on almost linear region around the steady state point. On the other region, another control is derived as follows. This derivation is based on coordinate transformation twice with respect to linearization functions which ...

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Abstract: We consider the problem of aggregating a general collection of affine estimators for fixed design regression. Relevant examples include some commonly used statistical estimators such as least squares, ridge and robust least squares estimators. Dalalyan and Salmon [DS12] have established that, for this problem, exponentially weighted (EW) model selection aggregation leads to sharp orac...

Abstract: Let (W,H,μ) be the classical Wiener space. Assume that U = IW + u is an adapted perturbation of identity, i.e., u : W → H is adapted to the canonical filtration ofW . We give some sufficient analytic conditions on u which imply the invertibility of the map U . In particular it is shown that if u ∈ IDp,1(H) is adapted and if exp( 2‖∇u‖2 − δu) ∈ Lq(μ), where p−1 + q−1 = 1, then IW + u i...

Humane-egalitarian ideals, whose aims are group justice and reducing environmental inequality and privilege, must be tested against reality, as revealed by psychology and other social sciences. Four issues are addressed: the equation between IQ and intelligence, whether group potential is determined by a group's mean IQ, whether the BlackWhite IQ gap is genetic, and the meritocratic thesis that...

Using elementary arguments based on the Fourier transform we prove that for 1 ≤ q < p < ∞ and s ≥ 0 with s > n(1/2 − 1/p), if f ∈ L(R) ∩ Ḣ(R) then f ∈ L(R) and there exists a constant cp,q,s such that ‖f‖Lp ≤ cp,q,s‖f‖ θ Lq,∞‖f‖ 1−θ Ḣs , where 1/p = θ/q+(1− θ)(1/2− s/n). In particular, in R we obtain the generalised Ladyzhenskaya inequality ‖f‖L4 ≤ c‖f‖ 1/2 L2,∞ ‖f‖ 1/2 Ḣ1 . We also show that f...

For fast ε-similarity search, various index structures have been proposed. Yi et al. proposed a concept multimodality support and suggested inequalities by which εsimilarity search by L1, L2 and L∞ norm can be realized. We proposed an extended inequality which allows us to realize ε-similarity search by arbitrary Lp norm using an index based on Lq norm. In these investigations a search radius o...