The Optimal Solution of a Non-Convex State-Dependent LQR Problem and Its Applications

This paper studies a Non-convex State-dependent Linear Quadratic Regulator (NSLQR) problem, in which the control penalty weighting matrix in the performance index is state-dependent. A necessary and sufficient condition for the optimal solution is established with a rigorous proof by Euler-Lagrange Equation. It is found that the optimal solution of the NSLQR problem can be obtained by solving a Pseudo-Differential-Riccati-Equation (PDRE) simultaneously with the closed-loop system equation. A Comparison Theorem for the PDRE is given to facilitate solution methods for the PDRE. A linear time-variant system is employed as an example in simulation to verify the proposed optimal solution. As a non-trivial application, a goal pursuit process in psychology is modeled as a NSLQR problem and two typical goal pursuit behaviors found in human and animals are reproduced using different control weighting . It is found that these two behaviors save control energy and cause less stress over Conventional Control Behavior typified by the LQR control with a constant control weighting , in situations where only the goal discrepancy at the terminal time is of concern, such as in Marathon races and target hitting missions.     

Optimal Sequence of Irinotecan and Oxaliplatin-Based Regimens in Metastatic Colorectal Cancer: A Population-Based Observational Study

The optimal sequence of irinotecan and oxaliplatin-based regimens for metastatic colorectal cancer remains unclear. We conducted a population-based observational study by retrospectively reviewing records from Taiwan’s National Health Insurance Research Database to explore this issue. Patients aged ≥20 years with metastatic colorectal cancer newly diagnosed between 2004 and 2008 (n = 9490) were enrolled in current study. Among these 9490 patients, 3895 patients (41.04%) did not receive any chemotherapy within the first three months after catastrophic illness registration. Patients who received best supportive care were older and had higher Charlson comorbidity indexes and incidences of comorbidities than those who received irinotecan-based regimens, oxaliplatin-based regimens, and 5-fluorouracil/capecitabine alone. Patients who received irinotecan followed by oxaliplatin-based regimens and those who received the reverse sequence were further stratified into arm A (n = 542) and arm B (n = 1156), respectively. The median first time to next treatment was not significantly different between arm A and arm B (210 days vs. 196 days; p = 0.17). However, the median second time to next treatment was longer in arm A than in arm B (155 days vs. 123 days; p = 0.006), which translated into a better overall survival (487 days vs. 454 days; p = 0.02). The crossover rate was higher in arm A than in arm B (47.84% vs. 41.61%; p<0.001). Multivariate Cox regression analyses showed that overall survival was comparable between the two chemotherapy sequences (p = 0.27). Our study suggested that irinotecan followed by oxaliplatin-based regimens might be a better chemotherapy treatment option for metastatic colorectal cancer than the reverse sequence given the higher crossover rate and potential overall survival benefit.     

Rice G protein γ subunit qPE9-1 modulates root elongation for phosphorus uptake by involving 14-3-3 protein OsGF14b and plasma membrane H+-ATPase

Heterotrimeric G protein is involved in plant growth and development, while the role of rice (Oryza sativa) G protein γ subunit qPE9-1 in response to low-phosphorus (LP) conditions remains unclear. The gene expression of qPE9-1 was significantly induced in rice roots under LP conditions. Rice varieties carrying the qPE9-1 allele showed a stronger primary root response to LP than the varieties carrying the qpe9-1 allele (mutant of the qPE9-1 allele). Transgenic rice plants with the qPE9-1 allele had longer primary roots and higher P concentrations than those with the qpe9-1 allele under LP conditions. The plasma membrane (PM) H⁺-ATPase was important for the qPE9-1-mediated response to LP. Furthermore, OsGF14b, a 14-3-3 protein that acts as a key component in activating PM H⁺-ATPase for root elongation, is also involved in the qPE9-1 mediation. Moreover, the overexpression of OsGF14b in WYJ8 (carrying the qpe9-1 allele) partially increased primary root length under LP conditions. Experiments using R18 peptide (a 14-3-3 protein inhibitor) showed that qPE9-1 is important for primary root elongation and H⁺ efflux under LP conditions by involving the 14-3-3 protein. In addition, rhizosheath weight, total P content, and the rhizosheath soil Olsen-P concentration of qPE9-1 lines were higher than those of qpe9-1 lines under soil drying and LP conditions. These results suggest that the G protein γ subunit qPE9-1 in rice plants modulates root elongation for phosphorus uptake by involving the 14-3-3 protein OsGF14b and PM H⁺-ATPase, which is required for rice P use.     

Dextrorphan: an antagonist for phencyclidine receptors

Radio-binding assay, bioassay and HPLC detection were used to observe the antagonistic effects of dextrorphan on PCP's actions. Dextrorphan displayed high affinity to PCP receptor in the rabbit mesenteric blood vessels. It had weak PCP-like bioactivity, but could antagonize PCP's action dose-dependently in vitro study with the rabbit ear artery preparation and shifted the dose-response curve of PCP to the right. After PCP administration, the content of norepinephrine in the vascular bath medium was increased, which was reversed by dextrorphan. Thus suggests that dextrorphan is an antagonist with very mild agonistic action for PCP receptors.     

The effect of berbamine derivatives on activated Ca2+-stimulated Mg2+-dependent ATPase in erythrocyte membranes.

Ca2+-stimulated Mg2+-dependent ATPase (Ca2+ + Mg2+-ATPase) stimulated by calmodulin, by partial proteolysis or by oleic acid in erythrocyte membranes was inhibited by various derivatives of the naturally occurring alkaloid berbamine. The ability of these derivatives to inhibit trypsin-activated Ca2+ + Mg2+-ATPase correlated well with their ability to inhibit the calmodulin-stimulated enzyme. Inhibition of the trypsin-activated Ca2+ + Mg2+-ATPase by O-4-(ethoxybutyl)berbamine (EBB) was competitive with respect to ATP. The Ki for inhibition was about 8 microM. These results suggest that the binding site of EBB on the activated Ca2+ + Mg2+-ATPase may bear structural similarity to that on calmodulin, and may be closely related to the ATP-binding site on the enzyme.