Fractal dimension for Inhomogeneous graph-directed attractors

In this paper, we define inhomogeneous Graph-Directed (GD) separation conditions for a given inhomogeneous GD Iterated Function Systems (IFS), and estimate the upper box dimension of attractors by the dimension of the condensation set and associated Mauldin-Williams graph dimension. Following some work of Fraser, we also estimate the lower box dimension of attractors generated by inhomogeneous GDIFS. In the end, we shed few lights on the continuity of dimensions for the attractors of inhomogeneous GDIFS.Comment: 14 pages, 1 figur

The Genealogy of Ideology: Predicting Agreement and Persuasive Memes in the U.S. Courts of Appeals

We employ machine learning techniques to identify common characteristics and features from cases in the US courts of appeals that contribute in determining dissent. Our models were able to predict vote alignment with an average F1 score of 73%, and our results show that the length of the opinion, the number of citations in the opinion, and voting valence, are all key factors in determining dissent. These results indicate that certain high level characteristics of a case can be used to predict dissent. We also explore the influence of dissent using seating patterns of judges, and our results show that raw counts of how often two judges sit together plays a role in dissent. In addition to the dissents, we analyze the notion of memetic phrases occurring in opinions - phrases that see a small spark of popularity but eventually die out in usage - and try to correlate them to dissent

The Genealogy of Ideology: Predicting Agreement and Persuasive Memes in the U.S. Courts of Appeals

We employ machine learning techniques to identify common characteristics and features from cases in the US courts of appeals that contribute in determining dissent. Our models were able to predict vote alignment with an average F1 score of 73%, and our results show that the length of the opinion, the number of citations in the opinion, and voting valence, are all key factors in determining dissent. These results indicate that certain high level characteristics of a case can be used to predict dissent. We also explore the influence of dissent using seating patterns of judges, and our results show that raw counts of how often two judges sit together plays a role in dissent. In addition to the dissents, we analyze the notion of memetic phrases occurring in opinions - phrases that see a small spark of popularity but eventually die out in usage - and try to correlate them to dissent

Estimation of Serum Levels of Heavy Metals in Patients with Chronic Invasive Fungal Rhinosinusitis Before the COVID-19 Era: A Pilot Study

Objective:Various metals play role in the survival and pathogenesis of the invasive fungal disease. The objectives of this study were to compare the levels of heavy metals in patients with chronic invasive fungal rhinosinusitis (CIFR) and healthy controls, and to analyze their role in disease outcome.Methods:Twenty-three patients (15 with invasive mucormycosis and 8 with invasive aspergillosis, Group 1), and 14 healthy controls (Group 2) were recruited. Blood samples were collected from each group into ion-free tubes and analyzed for serum levels of Nickel (Ni), Copper (Cu), Zinc (Zn), Gallium (Ga), Arsenic (As), Selenium (Se), Rubidium (Rb), Strontium (Sr), Cadmium (Cd), and Lead (Pb). The final outcome of the patients during their hospital stay was categorized clinico-radiologically as improved or worsened, or death.Results:The levels of all metals were higher in Group 1 except for As and Pb. However, the differences in Cu (p=0.0026), Ga (p=0.002), Cd (p=0.0027), and Pb (p=0.0075) levels were significant. Higher levels of Zn (p=0.009), Se (p=0.020), and Rb (p=0.016) were seen in the invasive aspergillosis subgroup. Although Zn (p=0.035), As (p=0.022), and Sr (p=0.002) levels were higher in patients with improved outcome, subgroup analysis showed no differences.Conclusion:The levels of some heavy metals in CIFR significantly differ from those of the general population and also vary with the type of the disease and its outcome. These levels may not have a direct effect on the outcome of the patient, but they do play a role in the pathogenesis of the invading fungus

Synthesis of H2BK120ub in Mammalian Nuclei Using a Novel Method to Chemically Modify Chromatin

Histone post-translational modifications (PTMs) play a key regulatory role in the eukaryotic cell. Consequently, aberrant PTM levels are implicated in developmental disorders, neurodegenerative diseases, and carcinogenesis. However, there are considerable barriers to studying molecular interactions and functions of histone PTMs with traditional biological tools. In vitro analyses using chemically-defined nucleosomes have provided exceptional insight into the mechanistic functions of histone PTMs, partially filling the methodological void by isolating specific biochemical phenomena for study. Nonetheless, this approach is limited due to the inherent reduction of biological complexity. Indeed, there is a need for techniques providing the precise control of chemistry within complex biological systems. In this study, we have developed one such approach that uses protein trans-splicing (PTS) to chemically join expressed and synthetic histone fragments together on native chromatin via the autocatalytic activity of naturally split inteins. Specifically, we demonstrate that PTS can be used to generate lysine-120 ubiquitinated histone H2B (H2Bub) in isolated mammalian nuclei in a time- controlled manner. This PTM is intimately involved in active gene transcription, DNA damage repair, and DNA replication, rendering it an important focus of epigenetic inquiry. As a preliminary study, we have attempted to interrogate known histone crosstalk pathways using semisynthetic H2Bub in nucleo. This work provides a model for the molecular interrogation of histone PTM interactions within biochemically complex systems, a useful technology for epigenetics research using chemical tools