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Sakhalin taimen, Hucho perryi, is one of the largest freshwater fish in Japan, where it is close to extinction because of indiscriminate fishing, water pollution, and river construction. Interpretable ecological information about the species, however, is scarce. We examined the migration history of H. perryi by analysis of strontium (Sr) content in fish scales using inductively coupled plasma mass spectrometry and Sr distributions associated with ridges (growth lines) in the scales, with micro-beam scanning PIXE (micro-PIXE) analyses. Sr levels in the scales of H. perryi collected along the Sarufutsu coast were higher than those of salmonid collected at Shumarinai, a freshwater lake. Micro-PIXE line analyses showed that the scale Sr values of the Shumarinai Lake samples remained consistently low from the edge toward the core of the scales. The Sr values from the Sarufutsu coast samples remained relatively high from the edge toward the core; Sr levels from second to fourth position from the edge were about ten times higher than the mean levels of Shumarinai Lake samples. These results suggested that H. perryi from the Sarufutsu Coast had experienced the marine environment.

Sr is an indicator used in studies on fish migration. In this study, the Sr profiles of ridges, which are growth lines in fish scales, in Sakhalin taimen (Hucho perryi) were examined by micro-PIXE analysis. Sakhalin taimen were reared under freshwater conditions for six months. The ridges that formed during the rearing experiment were subjected to PIXE spot analysis. This analysis was performed in a 5 X 5 μm² area in the center region of each ridge of the scale section, and the Sr levels were calculated using the thin-section standard. The mean Sr concentration in the ridges was 428± 48 μg/g. The quantitative PIXE spot analysis successfully provided Sr profiles for the scale corresponding to ridge formation.

Orthogonal Fourier–Mellin (OFM) moments have better feature representation capabilities, and are more robust to image noise than the conventional Zernike moments and pseudo-Zernike moments. However, OFM moments have not been extensively used as feature descriptors since they do not possess scale invariance. This paper discusses the drawbacks of the existing methods of extracting OFM moments, and proposes an improved OFM moments. A part of the theory, which proves the improved OFM moments possesses invariance of rotation and scale, is given. The performance of the improved OFM moments is experimentally examined using trademark images, and the invariance of the improved OFM moments is shown to have been greatly improved over the current methods.

Image registration is an essential step in many image processing applications that need visual information from multiple images for comparison, integration or analysis. Recently researchers have introduced image registration techniques using the log-polar transform (LPT) for its rotation and scale invariant properties. However, there are two major problems with the LPT based image registration method: inefficient sampling point distribution and high computational cost in the matching procedure. Motivated by the success of LPT based approach, we propose a novel pre-shifted logarithmic spiral (PSLS) approach that distributes the sampling point more efficiently, robust to translation, scale, and rotation. By pre-shifting the sampling point by π/n_θ radian, the total number of samples in the angular direction can be reduced by half. This yields great reduction in computational load in the matching process. Translation between the registered images is recovered with the new search scheme using Gabor feature extraction to accelerate the localization procedure. Experiments on real images demonstrate the effectiveness and robustness of the proposed approach for registering images that are subjected to scale, rotation and translation.

We derive a sum rule that constrains the scale based decomposition of the trajectories of finite systems of particles. The sum rule reflects a tradeoff between the finer and larger scale collective degrees of freedom. For short duration trajectories, where acceleration is irrelevant, the sum rule can be related to the moment of inertia and the kinetic energy (times a characteristic time squared). Thus, two nonequilibrium systems that have the same kinetic energy and moment of inertia can, when compared to each other, have different scales of behavior, but if one of them has larger scales of behavior than the other, it must compensate by also having smaller scales of behavior. In the context of coherence or correlation, the larger scale of behavior corresponds to the collective motion, while the smaller scales of behavior correspond to the relative motion of correlated particles. For longer duration trajectories, the sum rule includes the full effective moment of inertia of the system in space-time with respect to an external frame of reference, providing the possibility of relating the class of systems that can exist in the same space-time domain.

We discuss the role of scale dependence of entropy/complexity and its relationship to component interdependence. The complexity as a function of scale of observation is expressed in terms of subsystem entropies for a system having a description in terms of variables that have the same a priori scale. The sum of the complexity over all scales is the same for any system with the same number of underlying degrees of freedom (variables), even though the complexity at specific scales differs due to the organization/interdependence of these degrees of freedom. This reflects a tradeoff of complexity at different scales of observation. Calculation of this complexity for a simple frustrated system reveals that it is possible for the complexity to be negative. This is consistent with the possibility that observations of a system that include some errors may actually cause, on average, negative knowledge, i.e. incorrect expectations.

A wavelet-based forecasting method for time series is introduced. It is based on a multiple resolution decomposition of the signal, using the redundant "à trous" wavelet transform which has the advantage of being shift-invariant.

The result is a decomposition of the signal into a range of frequency scales. The prediction is based on a small number of coefficients on each of these scales. In its simplest form it is a linear prediction based on a wavelet transform of the signal. This method uses sparse modelling, but can be based on coefficients that are summaries or characteristics of large parts of the signal. The lower level of the decomposition can capture the long-range dependencies with only a few coefficients, while the higher levels capture the usual short-term dependencies.

We show the convergence of the method towards the optimal prediction in the autoregressive case. The method works well, as shown in simulation studies, and studies involving financial data.

In the present study, a statistical strength model is proposed, which aims at describing how the strength of geometrically irregular honeycomb material is affected by the scale. Hence, the samples are designed based on the selected geometrical irregularity and the number of the cells/scale. Simulation experiments are conducted on these samples under different loading combinations. The experiment results are linked to possible failure mechanisms in order to obtain the critical loads which are expressed in terms of cumulative distribution functions. The discrete distribution data of the critical loads are then fitted to analyze the effect of scale on different strength percentiles by virtue of the least squares function and closed quadric surface fitting. Eventually, the outcome is expressed in terms of ellipsoid surface representing the honeycomb material strength in three-dimensional stress space.

For each Baumslag-Solitar group BS(m, n) (m, n ∊ 𝕫 \ {0}), a totally disconnected, locally compact group, G_{m, n}, is constructed so that BS(m, n) is identified with a dense subgroup of G_{m, n}. The scale function on G_{m, n}, a structural invariant for the topological group, is seen to distinguish the parameters m and n to the extent that the set of scale values is