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.     

Natal recruitment and adult retention in a population of nine-banded armadillos

Nine-banded armadillosDasypus novemcinctus Linnaeus, 1758 are interesting in part because (a) they give birth to litters of genetically identical quadruplets, and (b) the species’ range has expanded rapidly throughout the southern United States during the last 150 years, suggesting substantial dispersal of individuals. Using data from 7 field seasons between 1992 and 1999, we examined the extent of juvenile recruitment and retention of adults in a population of armadillos from northern Florida. There were no sex differences in the likelihood of recruitment or most attributes of male and female recruits at any age. In the few cases where more than one littermate was recruited into the population, siblings were significantly more widely dispersed as adults than they were as juveniles, thus limiting opportunities for interaction among clonal siblings. There was some evidence that recruits ranged more widely than other individuals, suggesting recruits may have been searching for suitable sites to establish themselves. Recruits were heavier than non-recruits as both juveniles and yearlings, which may have aided in establishing a home range, but recruits were lighter than other animals as adults. Overall, slightly less than 50% of armadillos first captured as adults were never seen in a subsequent year, suggesting these individuals may have been transients. However, some adults remained in the population for multiple years, moving very little from the area where they were first sighted. As with recruits, there were no sex differences in the likelihood of adults being retained in the population nor in the attributes of retained males and females. Retained animals exhibited more extensive anatomical damage and moved farther between successive sightings within years than did non-residents. Adults were more likely to be retained in the population than juveniles were to be recruited, and retained adults were older, heavier, and exhibited more extensive anatomical damage than did recruits. Our data seem to indicate a population characterized by limited recruitment of juveniles (particularly of clonemates) and an adult population exhibiting considerable turnover from year to year, but with a core of individuals who are long-term residents.     

Endocrine changes before and after weaning in response to boar exposure and altered suckling in sows

Eighteen sows (6 primiparous and 12 multiparous) were allotted randomly within parity to two lactational treatments: litter separation (LS; 6 h/day) plus boar exposure (BE; 1 h/day; N = 14) beginning 8 days before weaning (4 weeks) and no LS + no BE (controls; N = 4). Blood was collected from all sows via indwelling venous catheters at 20-min intervals for 5 h on Days -1, 0, 1, 2 and 3 from start of treatment. Control sows and those exposed to LS + BE not exhibiting oestrus during lactation were resampled on Days -1, 0, 1 and 2 from weaning. All 10 multiparous sows receiving LS + BE exhibited oestrus during lactation, whereas none of the 4 primiparous sows exposed to LS + BE or the 2 control multiparous and 2 control primiparous sows exhibited lactational oestrus. Overall concentrations of LH in serum were higher (P less than 0.05) in sows receiving LS + BE than in control sows during lactation, whereas overall FSH was higher (P less than 0.05) in primiparous than multiparous sows. Number and amplitude of pulses of LH were greater (P less than 0.05) for treated primiparous than multiparous sows during lactation. Oestradiol-17 beta increased (P less than 0.05) in sows during LS + BE and was higher (P less than 0.01) in multiparous sows of this group than control multiparous or treated primiparous sows. Preweaning concentrations of cortisol and progesterone in serum were higher (P less than 0.05) in treated than control sows for multiparous and primiparous animals. In sows resampled at weaning, the number of pulses of LH was greater (P less than 0.05) in treated primiparous than in control sows. Postweaning concentrations of FSH in serum were unaffected by preweaning treatments. It was concluded that (1) litter separation and boar exposure increased basal and pulsatile secretion of LH in multiparous and primiparous sows; (2) lack of ovarian follicular development and oestradiol secretion may preclude expression of oestrus in primiparous sows during lactation, despite elevated concentrations of FSH and LH in serum; and (3) if elevated concentrations of cortisol and progesterone inhibit the onset of oestrous cycles, in response to litter separation and boar exposure during lactation, the effect is limited to primiparous sows.     

Analysis of the interaction of antibodies with immunoglobulin idiotypes on neoplastic B lymphocytes: implications for immunotherapy

We have examined the reactions of a panel of nine monoclonal anti-idiotype antibodies with the surface immunoglobulin in situ on guinea pig L2C leukemic lymphocytes. Equilibrium binding constants were shown to range between 10(7) and 10(8) M-1 for univalent Fab' gamma fragments and between 10(8) and 10(9) M-1 for intact IgG. Saturation of the cell surface binding sites was achieved with 2.9 X 10(5) Fab' gamma molecules/cell and 1.2 X 10(5) IgG molecules/cell for each antibody, a result that is consistent with a bivalent mode of interaction for the IgG. Despite these overall similarities in binding characteristics antibodies showed striking differences in their ability to clear Ig from the cell surface by antigenic modulation in vitro. This suggested differences in the readiness with which the antibodies cross-linked neighboring surface Ig molecules. Such an interpretation was supported by differences in the times required to achieve bivalent binding at 0 degree C, and in the rates at which labeled antibody dissociated from the cell surface in the presence or absence of an excess of unlabeled antibody. The data are consistent with there being two functionally distinct types of anti-idiotype antibody: those that form predominantly intra-Ig bridges, with each antibody Fab being linked to an Fab on one target molecule ("monogamous" binding) and not favoring modulation; and those that form predominantly inter-Ig bridges ("bigamous" binding) and favor modulation. The nature of interaction is presumably dictated by the orientation of the particular idiotope concerned. This distinction could be of great importance in the therapeutic use of anti-idiotype to ablate B cell neoplasms.