On the convergence of bumping routes to their limit shapes in the RSK algorithm: numerical experiments

Introduction: The Robinson — Schensted — Knuth (RSK) algorithm transforms a sequence of elements of a linearly ordered set into a pair of Young tableaux P, Q of the same shape. This transformation is based on the process of bumping and inserting elements in tableau P according to special rules. The trajectory formed by all the boxes of the tableau P shifted in the RSK algorithm is called the bumping route. D. Romik and P. Śniady in 2016 obtained an explicit formula for the limit shape of the bumping route, which is determined by its first element. However, the rate of convergence of the bumping routes to the limit shape has not been previously investigated either theoretically or by numerical experiments. Purpose: Carrying out computer experiments to study the dynamics of the bumping routes produced by the RSK algorithm on Young tableaux as their sizes increase. Calculation of statistical means and variances of deviations of bumping routes from their limit shapes in the L2 metric for various values fed to the input of the RSK algorithm. Results: A series of computer experiments have been carried out on Young tableaux, consisting of up to 10 million boxes. We used 300 tableaux of each size. Different input values (0.1, 0.3, 0.5, 0.7, 0.9) were added to each such tableau using the RSK algorithm, and the deviations of the bumping routes built from these values from the corresponding limit shapes were calculated. The graphs of the statistical mean values and variances of these deviations were produced. It is noticed that the deviations decrease in proportion to the fourth root of the tableau size n. An approximation of the dependence of the mean values of deviations on n was obtained using the least squares method.

Gas Chromatographic Fingerprint Analysis for the Comparison of Seized Cannabis Samples

Cannabis sativa L. is widely used as recreational illegal drugs. Illicit Cannabis profiling, comparing seized samples, is challenging due to natural Cannabis heterogeneity. The aim of this study was to use GC–FID and GC–MS herbal fingerprints for intra (within)- and inter (between)-location variability evaluation. This study focused on finding an acceptable threshold to link seized samples. Through Pearson correlation-coefficient calculations between intra-location samples, ‘linked’ thresholds were derived using 95% and 99% confidence limits. False negative (FN) and false positive (FP) error rate calculations, aiming at obtaining the lowest possible FP value, were performed for different data pre-treatments. Fingerprint-alignment parameters were optimized using Automated Correlation-Optimized Warping (ACOW) or Design of Experiments (DoE), which presented similar results. Hence, ACOW data, as reference, showed 54% and 65% FP values (95 and 99% confidence, respectively). An additional fourth root normalization pre-treatment provided the best results for both the GC–FID and GC–MS datasets. For GC–FID, which showed the best improved FP error rate, 54 and 65% FP for the reference data decreased to 24 and 32%, respectively, after fourth root transformation. Cross-validation showed FP values similar as the entire calibration set, indicating the representativeness of the thresholds. A noteworthy improvement in discrimination between seized Cannabis samples could be concluded.

Insight into the secondary imbibition rate of concrete and its relationship with curing time

Long-term capillary imbibition in cementitious materials is relevant to describe their durable behaviour. Many structures are exposed to long-term contact with moisture, such as foundations or wastewater installations. After several weeks, when capillary rise is no longer progressing, a distinguished change in the slope (from the mass gain - fourth root of time relation) is noticed. Primary and secondary imbibition rates (PIR and SIR, respectively) can be obtained from such behaviour. Contrary to the widely investigated PIR, usually defined as the capillary absorption rate, the SIR has been scarcely examined. Data from literature of tests in concrete lasting more than 7 days is very limited. To form a better view of this process, we contrasted values of SIR and porosity (water accessible porosity under vacuum and intrudable porosity by mercury intrusion porosimetry). Moreover, we used statistical inference to evaluate the evolution of the SIR of mixes with different composition and curing age. This paper presents the effect of curing on the SIR and the relation between porosity changes and SIR. Despite the decrease in capillary porosity and intrudable porosity, SIR increases with curing time. This is probably due to a connection between SIR and the increasing C-S-H content with time.

Bilinear pressure diffusion and termination of bilinear flow in a vertically fractured well injecting at constant pressure

This work studies intensively the flow in fractures with finite hydraulic conductivity intersected by a well injecting or producing at constant pressure, either during an injection or production well test or the operation of a production well. Previous investigations showed that for a certain time the reciprocal of flow rate is proportional to the fourth root of time, which is characteristic of the flow regime known as bilinear flow. Using a 2D numerical model, we demonstrated that during the bilinear flow regime the transient propagation of isobars along the fracture is proportional to the fourth root of time. Moreover, we present relations to calculate the termination time of bilinear flow under constant injection or production well pressure as well as an expression for the bilinear hydraulic diffusivity of fractures with finite hydraulic conductivity. To determine the termination of bilinear flow regime, two different methods were used: (a) numerically measuring the transient flow rate in the well and (b) analyzing the propagation of isobars along the fracture. Numerical results show that for low dimensionless fracture conductivities the transition from bilinear flow to another flow regime (e.g., pseudo-radial flow) occurs before the pressure front reaches the fracture tip, and for high dimensionless fracture conductivities it occurs when the pressure front arrives at the fracture tip. Hence, this work complements and advances previous research on the interpretation and evaluation of well test analysis under different reservoir conditions. Our results aim to improve the understanding of the hydraulic diffusion in fractured geologic media, and as a result they can be utilized for the interpretation of hydraulic tests, for example to estimate the fracture length. Highlights. The reciprocal of flow rate is proportional to the fourth root of time. The migration of isobars in the fracture is proportional to the fourth root of time. For low dimensionless fracture conductivities, bilinear flow ends before the pressure front reaches the fracture tip. For high dimensionless fracture conductivities, bilinear flow ends when the pressure front reaches the fracture tip. Isobars accelerate when they approach the fracture tip.

Bilinear pressure diffusion and termination of bilinear flow in a vertically fractured well injecting at constant pressure

This work studies intensively the flow in fractures with finite hydraulic conductivity intersected by a well injecting/producing at constant pressure. Previous investigations showed that for a certain time the reciprocal of flow rate is proportional to the fourth root of time, which is characteristic of the flow regime known as bilinear flow. Using a 2D numerical model, we demonstrated that during the bilinear flow regime the transient propagation of isobars along the fracture is proportional to the fourth root of time. Moreover, we present relations to calculate the termination time of bilinear flow under constant injection or production well pressure, as well as, an expression for the bilinear hydraulic diffusivity of fractures with finite hydraulic conductivity. To determine the termination of bilinear flow regime, two different methods were used: (a) numerically measuring the transient of flow rate in the well and (b) analyzing the propagation of isobars along the fracture. Numerical results show that for low fracture conductivities the transition from bilinear flow to another flow regime occurs before the pressure front reaches the fracture tip and for high fracture conductivities it occurs when the pressure front arrives at the fracture tip. Hence, this work complements and advances previous research on the interpretation and evaluation of well test analysis under different reservoir conditions. Our results aim at improving the understanding of the hydraulic diffusion in fractured geologic media and as a result they can be utilized for the interpretation of hydraulic tests, for example to estimate the fracture length.

On the ancestry of woodrats

We evaluated the fossil record of extinct and extant woodrats, and generated a comprehensive phylogenetic hypothesis of woodrat origins and relationships based on these data. The galushamyinin cricetines are redefined and reclassified as a subtribe of the Neotomini, including Repomys, Miotomodon, Galushamys, Nelsonia, and a new extinct genus with two new species. The geographic distribution of Nelsonia, restricted to montane coniferous forests of western Mexico, suggests that this subtribe was mostly confined to western coniferous ecosystems or similar ecosystems at lower elevation during glacial advances. A second subtribe of the Neotomini includes a new archaic genus and species, Neotoma, Hodomys, and Xenomys. Lindsaymys, a possible neotominin from the late Clarendonian (late Miocene) of California, demonstrates an occlusal morphology consistent with ancestry for the Neotomini, but the presence of a fourth root on M1 is problematic and may preclude the known populations from filling that role. Molars identified as Neotoma sp. from the Hemphillian (latest Miocene or early Pliocene) Rancho el Ocote assemblage of Guanajuato, Mexico, may represent the earliest Xenomys. Extant Neotoma species with a bilobed m3 appear to have originated subsequent to about 2.0 Ma, whereas Hodomys alleni and Xenomys nelsoni likely originated earlier from one or more extinct ancestors with an S-shaped m3.

WHY CONFLICTS OCCUR IN ROADS AND TUNNELS PROJECTS IN NORWAY

Conflicts within the Norwegian construction industry have reached unacceptable levels. The grievance of these disputes, whether it is the number of conflicts or the expense involved in these conflicts, is under discussion. This article examines the reasons for these conflicts in a comprehensive and inclusive manner. Twenty-five respondents with expertise and understanding of most conflicts in the Norwegian construction industry were interviewed. Results from a questionnaire sent to 1799 contractors have also been included in this study. Sixteen reasons for disputes were identified out of which four comprised the root causes. Tender specification and contract understanding came in first followed by “final settlement-payment related”, corroborating previous findings. The third and fourth root causes of conflicts were “low priced contracts” and “changes in projects” respectively. Our findings point to design deficiencies and defective contract plans as significant causes of conflicts, confirming the view of construction experts. The third root cause of conflicts might explicate some aspects of the first and second major causes of disputes. It is also important to mention that though this is the general view, one can also see how every group involved in this study interpret major causes of conflicts. Our findings also point to “communication between clients and contractor”, “carried out quantities” and “client restriction to time extension” as among the chief causes of conflicts, confirming the view of construction experts. Client understanding of contractors’ anxiety and quest for sound contracting process are aspects that Norwegian clients are currently engaging in, for the sake of conflict reduction and prevention in future construction projects.