The Asymptotic Cone of Teichm\"uller Space: Thickness and Divergence

We study the Asymptotic Cone of Teichm\"uller space equipped with the Weil-Petersson metric. In particular, we provide a characterization of the canonical finest pieces in the tree-graded structure of the asymptotic cone of Teichm\"uller space along the same lines as a similar characterization for right angled Artin groups by Behrstock-Charney and for mapping class groups by Behrstock-Kleiner-Minksy-Mosher. As a corollary of the characterization, we complete the thickness classification of Teichm\"uller spaces for all surfaces of finite type, thereby answering questions of Behrstock-Drutu, Behrstock-Drutu-Mosher, and Brock-Masur. In particular, we prove that Teichm\"uller space of the genus two surface with one boundary component (or puncture) can be uniquely characterized in the following two senses: it is thick of order two, and it has superquadratic yet at most cubic divergence. In addition, we characterize strongly contracting quasi-geodesics in Teichm\"uller space, generalizing results of Brock-Masur-Minsky. As a tool, we develop a complex of separating multicurves, which may be of independent interest.Comment: This paper comprises the main portion of the author's doctoral thesis, 54 page

Machine Learning Approaches for Principle Prediction in Naturally Occurring Stories

Value alignment is the task of creating autonomous systems whose values align with those of humans. Past work has shown that stories are a potentially rich source of information on human values; however, past work has been limited to considering values in a binary sense. In this work, we explore the use of machine learning models for the task of normative principle prediction on naturally occurring story data. To do this, we extend a dataset that has been previously used to train a binary normative classifier with annotations of moral principles. We then use this dataset to train a variety of machine learning models, evaluate these models and compare their results against humans who were asked to perform the same task. We show that while individual principles can be classified, the ambiguity of what "moral principles" represent, poses a challenge for both human participants and autonomous systems which are faced with the same task.Comment: Nahian and Frazier contributed equally to this wor

Bridging the Gap between Cosmic Dawn and Reionization favors Faint Galaxies-dominated Models

It has been claimed that traditional models struggle to explain the tentative detection of the 21\,cm absorption trough centered at $z\sim17$ measured by the EDGES collaboration. On the other hand, it has been shown that the EDGES results are consistent with an extrapolation of a declining UV luminosity density, following a simple power-law of deep Hubble Space Telescope observations of $4 < z < 9$ galaxies. We here explore the conditions by which the EDGES detection is consistent with current reionization and post-reionization observations, including the neutral hydrogen fraction at $z\sim6$--$8$, Thomson scattering optical depth, and ionizing emissivity at $z\sim5$. By coupling a physically motivated source model derived from radiative transfer hydrodynamic simulations of reionization to a Markov Chain Monte Carlo sampler, we find that it is entirely possible to reconcile the high-redshift (cosmic dawn) and low-redshift (reionization) existing constraints. In particular, we find that high contribution from low-mass halos along with high photon escape fractions are required to simultaneously reproduce cosmic dawn and reionization constraints. Our analysis further confirms that low-mass galaxies produce a flatter emissivity evolution, which leads to an earlier onset of reionization with gradual and longer duration, resulting in a higher optical depth. While our faint-galaxies dominated models successfully reproduce the measured globally averaged quantities over the first one billion years, they underestimate the late redshift-instantaneous measurements in efficiently star-forming and massive systems. We show that our (simple) physically-motivated semi-analytical prescription produces consistent results with the (sophisticated) state-of-the-art \thesan radiation-magneto-hydrodynamic simulation of reionization.Comment: 14 pages, 6 figures. Accepted for publication in ApJ. Comments are welcom

Multiple Simultaneous Threats Detection in Distributed Systems

This research examines a simultaneous threats detection system for distributed systems that uses a hybrid identification fusion model. This hybrid model is comprised of mathematical and statistical data fusion engines: Dempster-Shafer, Extended Dempster-Shafer, and Generalised Evidential Processing (GEP). The simultaneous threats detection system produced threat detection rates of 56% using Dempster-Shafer whilst Extended Dempster-Shafer and Generalised Evidential Processing (GEP) achieved 80% and 95% threat detection rate. Thus, the simultaneous threats detection system can improve threat detection rates by 39% (i.e. 95% - 56%) simply by adopting a more effective hybrid fusion model. In terms of efficiency and performance, the comparison of the three inference engines of the simultaneous threats detection system showed that Generalised Evidential Processing is a better data fusion model than Dempster-Shafer or Extended Dempster-Shafer. In addition, the set cover packing technique was used as a middle-tier data fusion tool to determine the reduced size groups of the threat data. Set cover provided significant improvement and reduced the threat population from 2,272 to 295. This helped to minimise the complexity of evidential processing, and therefore reduced the cost and time taken to determine the combined probability mass of the multiple simultaneous threats detection system. This technique is particularly relevant to online and internet-dependent applications, including portals

Microcephaly with a disproportionate hippocampal reduction, stem cell loss and neuronal lipid droplet symptoms in Trappc9 KO mice

Mutations of the human TRAFFICKING PROTEIN PARTICLE COMPLEX SUBUNIT 9 (TRAPPC9) cause a neurodevelopmental disorder characterised by microcephaly and intellectual disability. Trappc9 constitutes a subunit specific to the intracellular membrane-associated TrappII complex. The TrappII complex interacts with Rab11 and Rab18, the latter being specifically associated with lipid droplets (LDs). Here we used non-invasive imaging to characterise Trappc9 knock-out (KO) mice as a model of the human hereditary disorder. KOs developed postnatal microcephaly with many grey and white matter regions being affected. In vivo magnetic resonance imaging (MRI) identified a disproportionately stronger volume reduction in the hippocampus, which was associated with a significant loss of Sox2-positive neural stem and progenitor cells. Diffusion tensor imaging indicated a reduced organisation or integrity of white matter areas. Trappc9 KOs displayed behavioural abnormalities in several tests related to exploration, learning and memory. Trappc9-deficient primary hippocampal neurons accumulated a larger LD volume per cell following Oleic Acid stimulation, and the coating of LDs by Perilipin-2 was much reduced. Additionally, Trappc9 KOs developed obesity, which was significantly more severe in females than in males. Our findings indicate that, beyond previously reported Rab11-related vesicle transport defects, dysfunctions in LD homeostasis might contribute to the neurobiological symptoms of Trappc9 deficiency

Microcephaly with a disproportionate hippocampal reduction, stem cell loss and neuronal lipid droplet symptoms in Trappc9 KO mice

Mutations of the humanTRAFFICKING PROTEIN PARTICLE COMPLEX SUBUNIT 9(TRAPPC9) cause a neurodevelopmental disorder characterised by microcephaly and intellectual disability. Trappc9 constitutes a subunit specific to the intracellular membrane-associated TrappII complex. The TrappII complex interacts with Rab11 and Rab18, the latter being specifically associated with lipid droplets (LDs). Here we used non-invasive imaging to characteriseTrappc9knock-out (KO) mice as a model of the human hereditary disorder. KOs developed postnatal microcephaly with many grey and white matter regions being affected.In vivoMRI identified a disproportionately stronger volume reduction in the hippocampus, which was associated with a significant loss of Sox2-positive neural stem and progenitor cells. Diffusion Tensor imaging indicated a reduced organisation or integrity of white matter areas.Trappc9KOs displayed behavioural abnormalities in several tests related to exploration, learning and memory. Trappc9-deficient primary hippocampal neurons accumulated a larger LD volume per cell following Oleic Acid stimulation, and the coating of LDs by Perilipin-2 was much reduced. Additionally,Trappc9KOs developed obesity, which was significantly more severe in females than in males. Our findings indicate that, beyond previously reported Rab11-related vesicle transport defects, dysfunctions in LD homeostasis might contribute to the neurobiological symptoms of Trappc9 deficiency.</jats:p