Exploring multivariate data structures with local principal curves.

A new approach to find the underlying structure of a multidimensional data cloud is proposed, which is based on a localized version of principal components analysis. More specifically, we calculate a series of local centers of mass and move through the data in directions given by the first local principal axis. One obtains a smooth ``local principal curve'' passing through the "middle" of a multivariate data cloud. The concept adopts to branched curves by considering the second local principal axis. Since the algorithm is based on a simple eigendecomposition, computation is fast and easy

Functional Locomotor Morphology of Early Life History Stages of Fishes

Routine activities of early life history stages of fishes occur in an intermediate hydrodynamic environment (as identified by Reynolds numbers), between a zone where drag is linearly dependent on velocity and resistive forces make large contributions to thrust, and a zone where inertial forces dominate except in the boundary layer immediately adjacent to the body surface. Sprint performance carries larvae into this latter zone; thus, locomotor activities important for survival of both larvae and adults occur in the same hydrodynamic environment and similar selective pressures would be expected to influence locomotor morphology of larvae and adults. The simplest framework for evaluating and interpreting development of larvae recognizes the parental form as the developmental terminus and uses adult forms as references to identify similarities and discrepancies in larva structure. Three measures of locomotor structure are used to examine changes during development: (a) the ratio of caudal peduncle depth to maximum body depth, which is small in thunniform fish; (b) a body shape factor, which is small in chaetodontiform fishes; and (c) a transient swimming thrust factor, which is large in esociform fish. Similarities in form are found in yolk‐bearing larvae and are attributed to oxygen demand. Similarities in the pattern of development of larvae directly towards the parental form are found for fusiform species, except for delayed development of the caudal fin in tunas that probably is due to the hydrodynamic regime of the tail. Convergence with parents does not occur during the larva stage of deep‐bodied, compressed species. This is attributed to high drag of compressed forms at low Reynolds numbers and diet differences between larvae and parents. Although this framework is successful in identifying and interpreting problems, comparative studies of form, kinematics, and performance during biologically important activities are essential.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/141928/1/tafs0115.pd

Comparing the states of many quantum systems

We investigate how to determine whether the states of a set of quantum systems are identical or not. This paper treats both error-free comparison, and comparison where errors in the result are allowed. Error-free comparison means that we aim to obtain definite answers, which are known to be correct, as often as possible. In general, we will have to accept also inconclusive results, giving no information. To obtain a definite answer that the states of the systems are not identical is always possible, whereas, in the situation considered here, a definite answer that they are identical will not be possible. The optimal universal error-free comparison strategy is a projection onto the totally symmetric and the different non-symmetric subspaces, invariant under permutations and unitary transformations. We also show how to construct optimal comparison strategies when allowing for some errors in the result, minimising either the error probability, or the average cost of making an error. We point out that it is possible to realise universal error-free comparison strategies using only linear elements and particle detectors, albeit with less than ideal efficiency. Also minimum-error and minimum-cost strategies may sometimes be realised in this way. This is of great significance for practical applications of quantum comparison.Comment: 13 pages, 2 figures. Corrected a misprint on p. 7 and added a few references. Accepted for publication in J Mod Op

Descriptive Studies on Stylized Facts of the German Business Cycle

Thirteen Stylized Facts of the german economy are studied with different descriptive statistical methods. The results of this study are considered with respect to other results from Project B3 "Multivariate Bestimmung und Untersuchung von Konjunkturzyklen"

Boxfishes (Teleostei: Ostraciidae) as a model system for fishes swimming with many fins: kinematics

Swimming movements in boxfishes were much more complex and varied than classical descriptions indicated. At low to moderate rectilinear swimming speeds (<5 TL s^(-1), where TL is total body length), they were entirely median- and paired-fin swimmers, apparently using their caudal fins for steering. The pectoral and median paired fins generate both the thrust needed for forward motion and the continuously varied, interacting forces required for the maintenance of rectilinearity. It was only at higher swimming speeds (above 5 TL s^(-1)), when burst-and-coast swimming was used, that they became primarily body and caudal-fin swimmers. Despite their unwieldy appearance and often asynchronous fin beats, boxfish swam in a stable manner. Swimming boxfish used three gaits. Fin-beat asymmetry and a relatively nonlinear swimming trajectory characterized the first gait (0–1 TL s^(-1)). The beginning of the second gait (1–3 TL s^(-1)) was characterized by varying fin-beat frequencies and amplitudes as well as synchrony in pectoral fin motions. The remainder of the second gait (3–5 TL s^(-1)) was characterized by constant fin-beat amplitudes, varying finbeat frequencies and increasing pectoral fin-beat asynchrony. The third gait (>5 TL s^(-1)) was characterized by the use of a caudal burst-and-coast variant. Adduction was always faster than abduction in the pectoral fins. There were no measurable refractory periods between successive phases of the fin movement cycles. Dorsal and anal fin movements were synchronized at speeds greater than 2.5 TL s^(-1), but were often out of phase with pectoral fin movements

Flow Patterns Around the Carapaces of Rigid-bodied, Multi-propulsor Boxfishes (Teleostei: Ostraciidae)

Boxfishes (Teleostei: Ostraciidae) are rigid-body, multi-propulsor swimmers that exhibit unusually small amplitude recoil movements during rectilinear locomotion. Mechanisms producing the smooth swimming trajectories of these fishes are unknown, however. Therefore, we have studied the roles the bony carapaces of these fishes play in generating this dynamic stability. Features of the carapaces of four morphologically distinct species of boxfishes were measured, and anatomically-exact stereolithographic models of the boxfishes were constructed. Flow patterns around each model were investigated using three methods: 1) digital particle image velocimetry (DPIV), 2) pressure distribution measurements, and 3) force balance measurements. Significant differences in both cross-sectional and longitudinal carapace morphology were detected among the four species. However, results from the three interrelated approaches indicate that flow patterns around the various carapaces are remarkably similar. DPIV results revealed that the keels of all boxfishes generate strong longitudinal vortices that vary in strength and position with angle of attack. In areas where attached, concentrated vorticity was detected using DPIV, low pressure also was detected at the carapace surface using pressure sensors. Predictions of the effects of both observed vortical flow patterns and pressure distributions on the carapace were consistent with actual forces and moments measured using the force balance. Most notably, the three complementary experimental approaches consistently indicate that the ventral keels of all boxfishes, and in some species the dorsal keels as well, effectively generate self-correcting forces for pitching motions—a characteristic that is advantageous for the highly variable velocity fields in which these fishes reside