Learning to control a complex multistable system.

In this paper the control of a periodically kicked mechanical rotor without gravity in the presence of noise is investigated. In recent work it was demonstrated that this system possesses many competing attracting states and thus shows the characteristics of a complex multistable system. We demonstrate that it is possible to stabilize the system at a desired attracting state even in the presence of high noise level. The control method is based on a recently developed algorithm [S. Gadaleta and G. Dangelmayr, Chaos 9, 775 (1999)] for the control of chaotic systems and applies reinforcement learning to find a global optimal control policy directing the system from any initial state towards the desired state in a minimum number of iterations. Being data-based, the method does not require any information about governing dynamical equations.

Fourier transform infrared microspectroscopic analysis of bones of osteocalcin-deficient mice provides insight into the function of osteocalcin.

Osteocalcin, the gamma-carboxyglutamic acid-containing protein, which in most species is the predominant noncollagenous protein of bone and dentin, has been postulated to play roles in bone formation and remodeling. Recently, genetic studies showed that osteocalcin acts as an inhibitor of osteoblast function. Based on von Kossa staining and measurement of mineral apposition rates in tetracycline-labeled bones, osteocalcin knockout animals were reported to have no detectable alterations in bone mineralization. To test the hypothesis that, in addition to regulating osteoblastic activity, osteocalcin is involved in regulating mineral properties, a more sensitive assay of mineralization, Fourier transform infrared microspectroscopy (FT-IRM) was used to study thin sections of femora of 4-week-, 6-month- (intact and ovariectomized), and 9-month-old wild-type and osteocalcin-knockout mice. FT-IRM spectra provided spatially resolved measures of relative mineral and carbonate contents, and parameters indicative of apatite crystal size and perfection. No differences were detected in the mineral properties of the 4-week-old knockout and wild-type mice indicating that the mineralization process was not altered at this time point. Six-month-old wild-type animals had higher mineral contents (mineral:matrix ratios) in cortical as compared with trabecular bones; mineral contents in knockout and wild-type bones were not different. At each age studied, carbonate:phosphate ratios tended to be greater in the wild-type as compared with knockout animals. Detailed analysis of the phosphate nu1,nu3 vibrations in the spectra from 6-month-old wild-type animals indicated that the crystals were larger/more perfect in the cortical as opposed to the trabecular bones. In contrast, in the knockout animals' bones at 6 months, there were no differences between trabecular and cortical bone in terms of carbonate content or crystallite size and perfection. Spectral parameters of the cortical and trabecular bone of the knockout animals resembled those in the wild-type trabecular bone and differed from wild-type cortical bone. In ovariectomized 6-month-old animals, the mineral content (mineral:matrix ratio) in the wild-type cortices increased from periosteum to endosteum, whereas, in the knockout animals' bones, the mineral:matrix ratio was constant. Ovariectomized knockout cortices had lower carbonate:phosphate ratios than wild-type, and crystallite size and perfection resembled that in wild-type trabeculae, and did not increase from periosteum to endosteum. These spatially resolved data provide evidence that osteocalcin is required to stimulate bone mineral maturation.

Fourier transform infrared spectroscopy of the solution-mediated conversion of amorphous calcium phosphate to hydroxyapatite: new correlations between X-ray diffraction and infrared data.

Fourier Transform infrared spectroscopic analysis of maturing, poorly crystalline hydroxyapatite (HA) formed from the conversion of amorphous calcium phosphate (ACP) at constant pH or variable pH show only subtle changes in the v1, v3 phosphate absorption region (900 cm-1-1200 cm-1). This region is of interest because it can be detected by analysis of mineralized tissue sections using FT-IR microscopy. To evaluate the subtle spectral changes occurring during the maturation, second derivatives of the spectra were calculated. HA formed at constant pH showed little or no variation in the second derivative peak positions with bands occurring at 960 cm-1, 985 cm-1, 1030 cm-1, 1055 cm-1, 1075 cm-1, 1096 cm-1, 1116 cm-1, and 1145 cm-1. These bands can be assigned to molecular vibrations of the phosphate (PO4(3-)) moiety in an apatitic/stoichiometric environment of HA. In contrast, during the early stages of maturation of the HA formed at variable pH, second derivative peak positions occurring at 958 cm-1, 985 cm-1, 1020 cm-1, 1038 cm-1, 1112 cm-1, and 1127 cm-1 shifted in position with maturation, indicating that the environment of the phosphate species is changing as the crystals mature. Peaks at 1020 cm-1, 1038 cm-1, 1112 cm-1, and 1127 cm-1 were attributable to nonstoichiometry and/or the presence of acid phosphate-containing species. This concept was supported by the lower Ca:P molar ratios measured by chemical analysis of the synthetic material made at variable pH. Using the second derivative peak positions as initial input parameters, the v1, v3 phosphate region of the synthetic HAs prepared at constant pH were curve fit. X-ray diffraction patterns of these same materials were also curve fit to calculate the changes in crystallinty (size/perfection) in the c-axis 002 reflection as well as the 102, 210, 211, 112, 300, 202, and 301 planes. Linear regression analysis showed that the changes in the percent area of the underlying bands at 982 cm-1, 999 cm-1, 1030 cm-1, 1075 cm-1, 1096 cm-1, 1116 cm-1, and 1145 cm-1 were correlated with changes in crystallinity in one or more of the reflection planes. It is suggested that a combination of second-derivative and curve-fitting analysis of the v1, v3 phosphate contour allows the most reproducible evaluation of these spectra.

Fourier transform infrared microscopy of calcified turkey leg tendon.

Fourier transform infrared microscopy (FT-IRMS) was used to monitor spatial variations in the quality and quantity of the mineral phase in calcified turkey tendon. Spectral maps were generated by analysis of 50 microns x 50 microns areas within different regions of the tendon. Spectra of the transitional region, where nonmineralized matrix ends and mineralized matrix begins, revealed marked changes in the spectrally determined mineral-to-matrix ratio, whereas regions deeper into the mineralization front showed a relatively constant ratio. Since spectra of EDTA-demineralized matrix were similar to those of nonmineralized matrix, the nonmineralized regions of the tendon were used for spectral subtraction. The broad, relatively featureless contour of the mineral v1, v3 phosphate region (900-1200 cm-1) showed only subtle changes at different stages of mineralization. Second derivatives of these spectra were calculated and compared with those of synthetic, poorly crystalline hydroxyapatite (HA). The peak positions seen in second-derivative spectra of the mineral near the transitional region were within +/- 2 cm-1 of the least mature synthetic HAs whereas spectra of the mineral deeper into the mineralization front were within +/- 2 cm-1 of the most mature synthetic HAs. Spectra from cross- and longitudinal sections at equivalent positions in the tendon, and polarized FT-IRMS data were analyzed to determine the effect of mineral orientation on the parameters used to characterize the mineral. Spectra of cross- and longitudinal sections of the tendon showed no major differences in either the v1, v3 phosphate region or the amide I, II, or III components (1200-1800 cm-1). However, polarized FT-IR spectra revealed dramatic differences in both of these regions. Despite these differences, second-derivative analysis of the v1, v3 regions revealed no significant changes in the positions of the underlying bands used to characterize the environments of the phosphate ion in poorly crystalline HA. The results of this study demonstrate the power of FT-IRMS to monitor spatial variations of the mineral phase in calcified tissue. Also, the incorporation of polarized radiation provides a method capable of assessing the molecular orientation of the mineral phase relative to the collagen matrix.

Polarized FT-IR microscopy of calcified turkey leg tendon.

Polarized Fourier transform infrared microscopy (FT-IRM) was used to assess the orientation of mineral and matrix components of the normally calcified turkey leg tendon. Two groups of tendon, < 16 weeks of age (young) and > 60 weeks of age (old), were analyzed. Linear sequences from calcified, non-calcified, and transitional regions of the tendons were examined. Spectra collected in the "parallel polarization" mode were acquired with the electric vector of the infrared radiation parallel to the collagen fiber axis whereas spectra collected in the "perpendicular polarization" mode were acquired with the electric vector of the infrared radiation perpendicular to this axis. The v2 carbonate (850-890 cm-1) and v1, v3 phosphate (900-1180 cm-1) contours of the tendon mineral as well as the collagen amide I, II, and III bands of the extracellular matrix all displayed marked dichroism. The CO3(2-) ions substituted for PO4(3-) (878 cm-1, type B substitution) in the tendon mineral displayed parallel dichroism while the CO3(2-) ions substituted for OH (871 cm-1, type A substitution) in the tendon mineral displayed perpendicular dichroism. These orientational effects for both sites of carbonate substitution were greater in the older animals. The polarization properties of the v1, v3 phosphate contour were analyzed by use of an empirical anisotropy parameter (A), the value of which monitors the degree of orientation. This index significantly increased in the older animals indicating that aging produces a more highly oriented mineral. The amide I, II, and III contours of the collagen extracellular matrix also exhibited marked dichroism. The amide I component exhibits perpendicular dichroism while the amide II and III components exhibit parallel dichroism. The current study demonstrates the ability of polarized FT-IRM to assess the orientation of the mineral and matrix components of calcified tissue at the microscopic level.