Focusing on the groundbreaking work of women in mathematics past, present, and future, Springer's Association for Women in Mathematics Series presents the latest research and proceedings of conferences worldwide organized by the Association for Women in Mathematics (AWM). All works are peer-reviewed to meet the highest standards of scientific literature, while presenting topics at the cutting edge of pure and applied mathematics, as well as in the areas of mathematical education and history. Since its inception in 1971, The Association for Women in Mathematics has been a non-profit organization designed to help encourage women and girls to study and pursue active careers in mathematics and the mathematical sciences and to promote equal opportunity and equal treatment of women and girls in the mathematical sciences. Currently, the organization represents more than 3000 members and 200 institutions constituting a broad spectrum of the mathematical community, in the United States and around the world.
Peritoneal metastasis (PM) is a debilitating consequence of multiple cancers. As cancer cells lose tonic signaling related to attachment dependence, critical morphologic shifts result in alteration of the transcriptome. Identifying key genes associated with this transformation may lead to targeted therapies for this devastating complication. TC71, CHLA9, PANC1, YOU and HEYA8 cell lines were grown as tumor spheroids in polyHEMA coated plates. Temporal profiling of transcriptomic alterations over 72 hrs was used to develop a comprehensive PM model. We identified transcriptomic outliers using Gaussian mixtures model clustering to identify drivers of spheroid formation. Outliers were validated in The Cancer Genome Atlas (TCGA) and an ovarian tissue microarray (TMA) and by modulation in ovarian cancer models in vitro and in peritoneal xenograft models. Outlier analysis of PM genes identified the gene TXNIP and the TORC signaling as central to PM. Ovarian cancer spheroids isolated from patient ascites had significantly higher TXNIP than their attached counterparts (p = 0.047). TXNIP levels predicted progression-free (log-rank p = 0.026) survival in stage 1/2 ovarian cancer and overall survival (log rank p = 0.047) in stage 3/4 ovarian cancer. In vitro, TXNIP silencing was associated with increased mTOR signaling and enhanced spheroid development which could be overcome by TAK228, a TORC1/2 inhibitor. Similarly, in vivo peritoneal xenograft models of carcinomatosis were prevented by TAK228. PM is driven by TXNIP-associated TORC1/2 signaling. This work provides the first evidence that TORC1/2 inhibition may prevent PM.
Placental chorionic surface vascular networks (PCSVNs) are essential high-capacitance, low-resistance distribution and drainage networks, and are hence important to placental function and to fetal and newborn health. It was hypothesized that variations in the PCSVN structure may reflect both the overall effects of genetic and environmentally regulated variations in branching morphogenesis within the conceptus and the fetus’s vital organs. A critical step in PCSVN analysis is the extraction of blood vessel structure, which has only been done manually through a laborious process, making studies in large cohorts and applications in clinical settings nearly impossible. The large variation in the shape, color, and texture of the placenta presents significant challenges to both machine and human to accurately extract PCSVNs. To increase the visibility of the vessels, colored paint can be injected into the vascular networks of placentas, allowing PCSVNs to be manually traced with a high level of accuracy.This paper provides a proof-of-concept study to explain the geometric differences between manual tracings of paint-injected and un-manipulated PCSVNs under the framework of a shape-context model. Under this framework, paint-injected and un-manipulated tracings of PCSVNs can be matched with nearly 100% accuracy. The implication of our results is that the manual tracing protocol yields faithful PCSVN representations modulo a set of affine transformations, making manual tracing a reliable method for studying PCSVNs. Our work provides assurance to a new pre-processing approach for studying vascular networks by ways of dye-injection in medical imaging problems.
The purpose of this article is to study directed collapsibility of directed Euclidean cubical complexes. One application of this is in the nontrivial task of verifying the execution of concurrent programs. The classical definition of collapsibility involves certain conditions on a pair of cubes of the complex. The direction of the space can be taken into account by requiring that the past links of vertices remain homotopy equivalent after collapsing. We call this type of collapse a link-preserving directed collapse. In this paper, we give combinatorially equivalent conditions for preserving the topology of the links, allowing for the implementation of an algorithm for collapsing a directed Euclidean cubical complex. Furthermore, we give conditions for when link-preserving directed collapses preserve the contractability and connectedness of directed path spaces, as well as examples when link-preserving directed collapses do not preserve the number of connected components of the path space between the minimum and a given vertex.
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