Incidence varieties in the projectivized kk-th Hodge bundle over curves with rational tails

Over the moduli space of pointed smooth algebraic curves, the projectivized $k$-th Hodge bundle is the space of $k$-canonical divisors. The incidence loci are defined by requiring the $k$-canonical divisors to have prescribed multiplicities at the marked points. We find a recursive description of the closure of the incidence loci in the projectivized $k$-th Hodge bundle over the moduli space of curves with rational tails, and we use it to compute the classes of such loci in all cases when $k=1$, and with few exceptions when $k\geq 2$. The classes are expressed as a linear combination of tautological classes indexed by decorated stable graphs, with coefficients enumerating appropriate weightings of decorated stable graphs. As a consequence, we obtain an explicit expression for some relations in tautological rings of moduli of curves with rational tails.Comment: 67 page

Effective classes in the projectivized k-th Hodge bundle:

Thesis advisor: Dawei ChenWe study the classes of several loci in the projectivization of the k-th Hodge bundle over the moduli space of genus g curves and over the moduli space of genus g curves with n marked points. In particular we consider the class of the closure in the projectivization of the k-th Hodge bundle over the moduli space of genus g curves with n marked points of the codimension n locus where the n marked points are zeros of the k-differential. We compute this class when n=2 and provide a recursive formula for it when n>2. Moreover, when n=1 and k=1,2 we show its rigidity and extremality in the pseudoeffective cone. We also compute the classes of the closures in the projectivization of the k-th Hodge bundle over the moduli space of genus g curves of the loci where the k-differential has a zero at a Brill-Noether special point.Thesis (PhD) — Boston College, 2021.Submitted to: Boston College. Graduate School of Arts and Sciences.Discipline: Mathematics

The cone of Betti tables over three non-collinear points in the plane

We describe the cone of Betti tables of all finitely generated graded modules over the homogeneous coordinate ring of three non-collinear points in the projective plane. We also describe the cone of Betti tables of all finite length modules

Persistent Topology of Syntax

We study the persistent homology of the data set of syntactic parameters of the world languages. We show that, while homology generators behave erratically over the whole data set, non-trivial persistent homology appears when one restricts to specific language families. Different families exhibit different persistent homology. We focus on the cases of the Indo-European and the Niger-Congo families, for which we compare persistent homology over different cluster filtering values. We investigate the possible significance, in historical linguistic terms, of the presence of persistent generators of the first homology. In particular, we show that the persistent first homology generator we find in the Indo-European family is not due (as one might guess) to the Anglo-Norman bridge in the Indo-European phylogenetic network, but is related to the position of Ancient Greek and the Hellenic branch within the network.Comment: 15 pages, 25 jpg figure

Persistent Topology of Syntax

We study the persistent homology of a data set of syntactic parameters of world languages. We show that, while homology generators behave erratically over the whole data set, non-trivial persistent homology appears when one restricts to specific language families. Different families exhibit different persistent homology. We focus on the cases of the Indo-European and the Niger–Congo families, for which we compare persistent homology over different cluster filtering values. The persistent components appear to correspond to linguistic subfamilies, while the meaning, in historical linguistic terms, of the presence of persistent generators of the first homology is more mysterious. We investigate the possible significance of the persistent first homology generator that we find in the Indo-European family. We show that it is not due to the Anglo-Norman bridge (which is a lexical, not syntactic phenomenon), but is related instead to the position of Ancient Greek and the Hellenic branch within the Indo-European phylogenetic network

Essential Oils as Antimicrobial Active Substances in Wound Dressings

Wound dressings for skin lesions, such as bedsores or pressure ulcers, are widely used for many patients, both during hospitalization and in subsequent treatment at home. To improve the treatment and shorten the healing time and, therefore, the cost, numerous types of wound dressings have been developed by manufacturers. Considering certain inconveniences related to the intolerance of some patients to antibiotics and the antimicrobial, antioxidant, and curative properties of certain essential oils, we conducted research by incorporating these oils, based on polyvinyl alcohol/ polyvinyl pyrrolidone (PVA/PVP) biopolymers, into dressings. The objective of this study was to study the potential of a polymeric matrix for wound healing, with polyvinyl alcohol as the main material and polyvinyl pyrrolidone and hydroxypropyl methylcellulose (HPMC) as secondary materials, together with additives (plasticizers poly(ethylene glycol) (PEG) and glycerol), stabilizers (Zn stearate), antioxidants (vitamin A and vitamin E), and four types of essential oils (fennel, peppermint, pine, and thyme essential oils). For all the studied samples, the combining compatibility, antimicrobial, and cytotoxicity properties were investigated. The obtained results demonstrated a uniform morphology for almost all the samples and adequate barrier properties for contact with suppurating wounds. The results show that the obtained samples containing essential oils have a good inhibitory effect on, or antimicrobial properties against, Staphylococcus aureus ATCC 25923, Enterococcus faecalis ATCC 29212, Escherichia coli ATCC 25922, Pseudomonas aeruginosa ATCC 27853, and Candida albicans ATCC 10231. The MTT assay showed that the tested samples were not toxic and did not lead to cell death. The results showed that the essential oils used provide an effective solution as active substances in wound dressings

A Rare Case of Undifferentiated Pleomorphic Cardiac Sarcoma with Inflammatory Pattern

Cardiac undifferentiated pleomorphic sarcoma (UPS) associated with fever and inflammatory response is an extremely rare condition. Herein, we report a rare case of cardiac UPS with unusual clinical presentation and inflammatory response. A 67-year-old male complaining of progressive dyspnea and intermittent fever of unknown cause was referred to our hospital for surgical resection of a left atrial mass. Laboratory analysis showed leukocytosis (26 × 103/μL) and high C-reactive protein (CRP) levels (155.4 mg/L). Hemoculture tests and urine analysis were negative for infection. A contrast chest computed tomography revealed a mass measuring 5.5 × 4.5 cm, occupying the left atrium cavity. The patient underwent surgical excision of the mass, however, surgical margin of the resected tumor could not be evaluated, due to the multifragmented nature of the resection specimen. Postoperative CRP and leukocyte levels normalized, highlighting the relationship between the tumor and the inflammatory status. Early diagnosis is crucial for a proper management and favorable outcome, enabling patients to undergo chemotherapy and achieve complete surgical resection