The Max-Cut Decision Tree: Improving on the Accuracy and Running Time of Decision Trees

Decision trees are a widely used method for classification, both by themselves and as the building blocks of multiple different ensemble learning methods. The Max-Cut decision tree involves novel modifications to a standard, baseline model of classification decision tree construction, precisely CART Gini. One modification involves an alternative splitting metric, maximum cut, based on maximizing the distance between all pairs of observations belonging to separate classes and separate sides of the threshold value. The other modification is to select the decision feature from a linear combination of the input features constructed using Principal Component Analysis (PCA) locally at each node. Our experiments show that this node-based localized PCA with the novel splitting modification can dramatically improve classification, while also significantly decreasing computational time compared to the baseline decision tree. Moreover, our results are most significant when evaluated on data sets with higher dimensions, or more classes; which, for the example data set CIFAR-100, enable a 49% improvement in accuracy while reducing CPU time by 94%. These introduced modifications dramatically advance the capabilities of decision trees for difficult classification tasks.Comment: 12 pages, 8 figures, 5 table

Reservoir Study and Facies Analysis of the Big Clifty Sandstone in South Central Kentucky

The Big Clifty (Jackson) Sandstone Member of the Golconda Formation is the most important of the Mississippian (Chesterian) heavy-oil reservoirs in the southeastern Illinois Basin. Heavy oil reservoirs, or asphalt rock deposits, have been studied extensively in south central and western Kentucky, and ~2 billion barrels of original oil in place (OOIP) have been proposed to occur in the Big Clifty Sandstone. Despite high OOIP estimates, heterogeneities in the reservoir negatively impact the production of heavy oil deposits. Heterogeneities related to depositional facies changes are poorly understood in the Big Clifty Sandstone of Kentucky, where it has been mostly described as a 60-120 feet thick sandstone unit. In some locations, the Big Clifty occurs as two distinct sand bodies with intercalated mud-rich units and, most typically, with the greatest clay- and silt-rich units present between sandstone bodies. Questions exist as to how such muddy facies occur in the reservoir. This study couples sedimentary facies analysis with sequence stratigraphy to assess how lithological factors affect the occurrence of petroleum in Big Clifty reservoirs. Multiple datasets were integrated to develop a depositional model for lithologic facies observed in this study. Datasets include core, exposure descriptions, petrographic analysis, bitumen concentrations, electrical resistivity tomography (ERT), and borehole geophysical analysis. This study occurred in Logan, Warren, and Butler counties, with emphasis on an active asphalt-rock mine in Logan County. Surface geophysical methods aided in demarcating Chesterian limestones, sandstone bodies and, in particular, highly resistive heavy-oil laden Big Clifty channel bodies. In Warren County, located E-NE of the Stampede Mine, the Big Clifty coalesces into a single amalgamated sandstone channel or a series of superimposed stacked channels as observed in outcrop along Indian Creek at McChesney Field Station and at Jackson’s Orchard. In these locations, the tidal influence is subtle with large-scale trough cross bedding dominating, and the contact on the Beech Creek Limestone is sharp. Facies changes related to the environment of deposition greatly impact the quality of heavy-oil reservoirs and must be taken into consideration during exploration and siting of asphalt rock mines

Recursion relations and branching rules for simple Lie algebras

The branching rules between simple Lie algebras and its regular (maximal) simple subalgebras are studied. Two types of recursion relations for anomalous relative multiplicities are obtained. One of them is proved to be the factorized version of the other. The factorization property is based on the existence of the set of weights $\Gamma$ specific for each injection. The structure of $\Gamma$ is easily deduced from the correspondence between the root systems of algebra and subalgebra. The recursion relations thus obtained give rise to simple and effective algorithm for branching rules. The details are exposed by performing the explicit decomposition procedure for $A_{3} \oplus u(1) \to B_{4}$ injection.Comment: 15p.,LaTe

A Demographic Model of an Endangered Florida Native Bromeliad (Tillandsia utriculata)

The large, long-lived, epiphytic bromeliad Tillandsia utriculata is currently listed as state-endangered in Florida due to significant population reduction from predation by an invasive weevil, Metamasius callizona. We have developed a novel demographic model of a population of T. utriculata in Myakka River State Park (MRSP) in Sarasota, Florida using a stage-structured matrix model. Analysis of the model revealed conditions for population viability over a variety of parameter scenarios. Model analysis showed that without weevil predation the minimum germination rate required for population viability is low (4–16%), and that given a viable population at structural equilibrium we would expect to find 15 cm in flower or post-flowering each year. Additionally, the model presented here provides a basis for further analyses which explore specific conservation strategies

Arthroscopic Latarjet Learning Curve: Operating Time Decreases After 25 Cases

PURPOSE: To demonstrate the learning curve associated with the arthroscopic Latarjet procedure and create a timetable to proficiency. METHODS: Using retrospective data of a single surgeon, consecutive patients who had an arthroscopic Latarjet procedure performed between December 2015 and May 2021 were initially reviewed for inclusion in the study. Patients were excluded if medical data were insufficient for accurate surgical time record, their surgery was transitioned to open or minimally invasive, or if their surgery was performed in conjunction with a second procedure for a separate issue. All surgeries were performed on an outpatient basis and sports participation was the most common reason for initial glenohumeral dislocation. RESULTS: Fifty-five patients were identified. Of these, 51 met the inclusion criteria. Analysis of operative times for all 51 procedures demonstrated that proficiency with the arthroscopic Latarjet procedure was obtained after 25 cases. This number was determined by 2 methods using statistical analysis (P \u3c .05). The average operative time over the course of the first 25 cases was 105.68 minutes and beyond 25 cases was 82.41 minutes. Male gender was seen in 86.3 percent of the patients. The average age of the patients was 28.6 years old. CONCLUSIONS: With continued transition towards bony augmentation procedures for addressing glenoid bone deficiency there is an increasing demand for the arthroscopic bony glenoid reconstruction procedures including the Latarjet procedure. It is a challenging procedure with a substantial initial learning curve. For a skilled arthroscopist there is a significant decrease in overall surgical time after the first 25 cases. CLINICAL RELEVANCE: The arthroscopic Latarjet procedure has advantages over the open Latarjet approach; however, it is controversial because it is technically challenging. It is important for surgeons to understand when they can expect to be proficient with the arthroscopic approach

Arthroscopic Latarjet Learning Curve: Operating Time Decreases After 25 Cases

PURPOSE: To demonstrate the learning curve associated with the arthroscopic Latarjet procedure and create a timetable to proficiency. METHODS: Using retrospective data of a single surgeon, consecutive patients who had an arthroscopic Latarjet procedure performed between December 2015 and May 2021 were initially reviewed for inclusion in the study. Patients were excluded if medical data were insufficient for accurate surgical time record, their surgery was transitioned to open or minimally invasive, or if their surgery was performed in conjunction with a second procedure for a separate issue. All surgeries were performed on an outpatient basis and sports participation was the most common reason for initial glenohumeral dislocation. RESULTS: Fifty-five patients were identified. Of these, 51 met the inclusion criteria. Analysis of operative times for all 51 procedures demonstrated that proficiency with the arthroscopic Latarjet procedure was obtained after 25 cases. This number was determined by 2 methods using statistical analysis (P \u3c .05). The average operative time over the course of the first 25 cases was 105.68 minutes and beyond 25 cases was 82.41 minutes. Male gender was seen in 86.3 percent of the patients. The average age of the patients was 28.6 years old. CONCLUSIONS: With continued transition towards bony augmentation procedures for addressing glenoid bone deficiency there is an increasing demand for the arthroscopic bony glenoid reconstruction procedures including the Latarjet procedure. It is a challenging procedure with a substantial initial learning curve. For a skilled arthroscopist there is a significant decrease in overall surgical time after the first 25 cases. CLINICAL RELEVANCE: The arthroscopic Latarjet procedure has advantages over the open Latarjet approach; however, it is controversial because it is technically challenging. It is important for surgeons to understand when they can expect to be proficient with the arthroscopic approach

Single-cell profiling of human megakaryocyte-erythroid progenitors identifies distinct megakaryocyte and erythroid differentiation pathways

Background Recent advances in single-cell techniques have provided the opportunity to finely dissect cellular heterogeneity within populations previously defined by “bulk” assays and to uncover rare cell types. In human hematopoiesis, megakaryocytes and erythroid cells differentiate from a shared precursor, the megakaryocyte-erythroid progenitor (MEP), which remains poorly defined. Results To clarify the cellular pathway in erythro-megakaryocyte differentiation, we correlate the surface immunophenotype, transcriptional profile, and differentiation potential of individual MEP cells. Highly purified, single MEP cells were analyzed using index fluorescence-activated cell sorting and parallel targeted transcriptional profiling of the same cells was performed using a specifically designed panel of genes. Differentiation potential was tested in novel, single-cell differentiation assays. Our results demonstrate that immunophenotypic MEP comprise three distinct subpopulations: “Pre-MEP,” enriched for erythroid/megakaryocyte progenitors but with residual myeloid differentiation capacity; “E-MEP,” strongly biased towards erythroid differentiation; and “MK-MEP,” a previously undescribed, rare population of cells that are bipotent but primarily generate megakaryocytic progeny. Therefore, conventionally defined MEP are a mixed population, as a minority give rise to mixed-lineage colonies while the majority of cells are transcriptionally primed to generate exclusively single-lineage output. Conclusions Our study clarifies the cellular hierarchy in human megakaryocyte/erythroid lineage commitment and highlights the importance of using a combination of single-cell approaches to dissect cellular heterogeneity and identify rare cell types within a population. We present a novel immunophenotyping strategy that enables the prospective identification of specific intermediate progenitor populations in erythro-megakaryopoiesis, allowing for in-depth study of disorders including inherited cytopenias, myeloproliferative disorders, and erythromegakaryocytic leukemias