W{\cal W} algebras are L∞_\infty algebras

It is shown that the closure of the infinitesimal symmetry transformations underlying classical ${\cal W}$ algebras give rise to L$_\infty$ algebras with in general field dependent gauge parameters. Therefore, the class of well understood ${\cal W}$ algebras provides highly non-trivial examples of such strong homotopy Lie-algebras. We develop the general formalism for this correspondence and apply it explicitly to the classical ${\cal W}_3$ algebra.Comment: 15 pages; v2: typos corrected, minor change

Cardy Algebras, Sewing Constraints and String-Nets

In \cite{Schweigert:2019zwt} it was shown how string-net spaces for the Cardy bulk algebra in the Drinfeld center $\mathsf{Z}(\mathsf{C})$ of a modular tensor category $\mathsf{C}$ give rise to a consistent set of correlators. We extend their results to include open-closed world sheets and allow for more general field algebras, which come in the form of $(\mathsf{C}|\mathsf{Z}(\mathsf{C}))$-Cardy algebras. To be more precise, we show that a set of fundamental string-nets with input data from a $(\mathsf{C}|\mathsf{Z}(\mathsf{C}))$-Cardy algebra gives rise to a solution of the sewing constraints formulated in \cite{Kong_2014} and that any set of fundamental string-nets solving the sewing constraints determine a $(\mathsf{C}|\mathsf{Z}(\mathsf{C}))$-Cardy algebra up to isomorphism. Hence we give an alternative proof of the results in \cite{Kong_2014} in terms of string-nets.Comment: 36 pages, lots of figures, v3: minor change

Algebraic constructions related to quantum field theories

Quantum field theory is the main technical tool in understanding modern theoretical high energy physics. After nearly a century of quantum field theory its mathematics remains mysterious, though. A firm grip on the mathematics of quantum field theory seems ever more desirable since the upcoming of string theory with its rich and challenging mathematical structure. Among the best understood quantum field theories are two dimensional rational quantum field theories. In this work we contribute to a better mathematical understanding of such theories by providing a mathematically rigorous but intuitive description in terms of string-net models. Heuristically string-net models give a Feynman diagram framework for rational conformal field theories on all genus $g$ surfaces. We prove a uniqueness and existence result for open-closed rational conformal field theories with fixed boundary condition making extensive use of the category theory underlying string-nets. Secondly, we give a construction of consistent correlators in rational conformal field theories with arbitrary topological defects and symmetry preserving boundary conditions using string-nets. As a proof of principle we compute torus and annulus partition functions in the string-net framework, thereby reproducing established results. Compared to earlier categorical approaches the use of string-nets almost completely avoids three dimensional considerations, rendering the use of categorical tools very intuitive. The second part of the thesis deals with homotopy algebras and their appearance in quantum field theories. Roughly speaking every consistent classical field theory having some gauge freedom produces a strong homotopy Lie algebra through the Batalin Vilkovisky formalism. Hence by studying strong homotopy Lie algebras (or $L_\infty$ algebras) one can learn something about field theories. The first result presented in that direction is a theorem closing every skewsymmetric bilinear bracket on a vector space into a finite term $L_\infty$ algebra. This is a generalization of the $L_\infty$ structure of the Courant algebroid. The second result is a theorem relating quasi-isomorphisms of $L_\infty$ algebras to Seiberg-Witten maps, linking the mathematics of homotopy algebras closer to physical notions

Mechanisms, Potential Therapies, and the Role of TGF-β in the Formation of Scars

Scarring is the inevitable outcome of wound healing. This review looks at some of the underlying mechanisms of this complex process with the aim of identifying targets for therapeutic manipulation that could result in reduced scarring or even scarless wound repair. Fetal wounds are shown to heal without scars primarily due to low levels of TGF-β1 and TGF-β2 and high levels of TGF-β3 as compared to adult wounds which heal with scars. Abnormal excessive scarring in keloid and hypertrophic scars are also attributed to TGF-β. Clinical manipulation of TGF-β ratios showed promise as a therapeutic means of controlling scar formation. The effect of the COX enzyme and PGE2 levels remains controversial and more research is needed to understand the exact roles these molecules play in the wound healing process before they can be exploited in a clinical settin

Development of a Quality Improvement Initiative to Screen for Postpartum Depression

Postpartum depression (PPD) is a mood disorder affecting approximately 20% of women within 6 months of delivery. Untreated PPD diminishes a woman\u27s functioning and may result in short and long-term consequences for her infant. Screening with evidence-based tools can identify prenatal and postpartum women at risk for PPD, ensure early treatment, and limit adverse maternal and infant effects. Using Rosswurm and Larrabee\u27s evidence-based practice model, a multidisciplinary team of 7 key stakeholders, including directors and a nurse from the departments of OB/GYN, Pediatrics, and Primary Care, a psychiatrist specializing in women\u27s health, and a member of nursing leadership, formed to guide the project. The purpose of the project was to develop a quality improvement initiative to promote antenatal and postnatal screening for PPD in the practice setting that lacked an evidence-based tool. As a federally qualified health center, the practice setting serves an ethnically and racially diverse population, particularly at risk for PPD. Project team members evaluated and graded current literature using the Johns Hopkins Evidence-Based Practice Rating Scale. The Edinburgh Postnatal Depression Scale (EPDS) was introduced and a policy and procedure developed to guide PPD screening. A formative evaluation of the policy and procedure using the AGREE instrument validated development. Project team members strongly agreed to use the EPDS as a PPD screening tool in the clinic population. A summative evaluation supported DNP student leadership of the project. The project has increased awareness of PPD and screening in the practice setting and, focused on improvements in the lives of women, infants, and their families