Linking rivers to the rock record: Channel patterns and paleocurrent circular variance

Alluvial rivers are the most important agents of sediment transport in continental basins, whose fluvial deposits enclose information related to the time when rivers were active. In order to extract the most information from fluvial deposits in the sedimentary record, it is imperative to quantify the natural variability of channel patterns at the global scale, explore what controls may influence their development, and investigate whether channel pattern information is preserved in the alluvial plains in order to develop tools for recognizing them in the sedimentary record. By surveying 361 reaches of modern alluvial rivers with available water discharge data at a global scale, we present a quantitative channel pattern classification based on sinuosity and channel count index applicable to the recognition in the rock record. A continuum of channel patterns ranging from high-sinuosity single channel to lowsinuosity multichannels is documented, along with the proportion of depositional elements in their alluvial plains and their conditions of occurrence. Preserved barforms in the alluvial plains of these rivers are used to infer and quantify paleoflow directions at the channel-belt scale and result in ranges of paleocurrent circular variance that may lead to channel pattern identification in the rock record. Data from this work indicate that the recognition of channel patterns may be used to predict paleogeographic features such as the scale of drainage basin area and discharge, slope, and annual discharge regimes.

Effect of Preconditioning and Stress Relaxation on Local Collagen Fiber Re-Alignment: Inhomogeneous Properties of Rat Supraspinatus Tendon

Repeatedly and consistently measuring the mechanical properties of tendon is important but presents a challenge. Preconditioning can provide tendons with a consistent loading history to make comparisons between groups from mechanical testing experiments. However, the specific mechanisms occurring during preconditioning are unknown. Previous studies have suggested that microstructural changes, such as collagen fiber re-alignment, may be a result of preconditioning. Local collagen fiber re-alignment is quantified throughout tensile mechanical testing using a testing system integrated with a polarized light setup, consisting of a backlight, 90 deg-offset rotating polarizer sheets on each side of the test sample, and a digital camera, in a rat supraspinatus tendon model, and corresponding mechanical properties are measured. Local circular variance values are compared throughout the mechanical test to determine if and where collagen fiber re-alignment occurred. The inhomogeneity of the tendon is examined by comparing local circular variance values, optical moduli and optical transition strain values. Although the largest amount of collagen fiber re-alignment was found during preconditioning, significant re-alignment was also demonstrated in the toe and linear regions of the mechanical test. No significant changes in re-alignment were seen during stress relaxation. The insertion site of the supraspinatus tendon demonstrated a lower linear modulus and a more disorganized collagen fiber distribution throughout all mechanical testing points compared to the tendon midsubstance. This study identified a correlation between collagen fiber re-alignment and preconditioning and suggests that collagen fiber re-alignment may be a potential mechanism of preconditioning and merits further investigation. In particular, the conditions necessary for collagen fibers to re-orient away from the direction of loading and the dependency of collagen reorganization on its initial distribution must be examined.

SUBWORD OCCURRENCES, PARIKH MATRICES AND LYNDON IMAGES

We investigate the number of occurrences of a word u as a (scattered) subword of a word w. The notion of a Parikh matrix, recently introduced, is a basic tool in this investigation. In general, several words are associated with a Parikh matrix. The ambiguity can be resolved by associating a unique word called the Lyndon image to each Parikh matrix. In this paper we will investigate properties of Lyndon images and the corresponding questions of ambiguity. We give an exhaustive characterization in the case of a binary alphabet. Our main results in the general case deal with the comparison of unambiguous words and Lyndon images, algorithms for constructing Lyndon images, as well as classes of words with the same Parikh matrix, obtained by circular variance.