Strongly non embeddable metric spaces

Enflo constructed a countable metric space that may not be uniformly embedded into any metric space of positive generalized roundness. Dranishnikov, Gong, Lafforgue and Yu modified Enflo's example to construct a locally finite metric space that may not be coarsely embedded into any Hilbert space. In this paper we meld these two examples into one simpler construction. The outcome is a locally finite metric space $(\mathfrak{Z}, \zeta)$ which is strongly non embeddable in the sense that it may not be embedded uniformly or coarsely into any metric space of non zero generalized roundness. Moreover, we show that both types of embedding may be obstructed by a common recursive principle. It follows from our construction that any metric space which is Lipschitz universal for all locally finite metric spaces may not be embedded uniformly or coarsely into any metric space of non zero generalized roundness. Our construction is then adapted to show that the group $\mathbb{Z}_\omega=\bigoplus_{\aleph_0}\mathbb{Z}$ admits a Cayley graph which may not be coarsely embedded into any metric space of non zero generalized roundness. Finally, for each $p \geq 0$ and each locally finite metric space $(Z,d)$, we prove the existence of a Lipschitz injection $f : Z \to \ell_{p}$.Comment: 10 page

Magnetic Bearings at Draper Laboratory

Magnetic bearings, unlike traditional mechanical bearings, consist of a series of components mated together to form a stabilized system. The correct design of the actuator and sensor will provide a cost effective device with low power requirements. The proper choice of a control system utilizes the variables necessary to control the system in an efficient manner. The specific application will determine the optimum design of the magnetic bearing system including the touch down bearing. Draper for the past 30 years has been a leader in all these fields. This paper summarizes the results carried out at Draper in the field of magnetic bearing development. A 3-D radial magnetic bearing is detailed in this paper. Data obtained from recently completed projects using this design are included. One project was a high radial load (1000 pound) application. The second was a high speed (35,000 rpm), low loss flywheel application. The development of a low loss axial magnetic bearing is also included in this paper

Dolichol-linked oligosaccharide selection by the oligosaccharyltransferase in protist and fungal organisms

The dolichol-linked oligosaccharide Glc3Man9GlcNAc2-PP-Dol is the in vivo donor substrate synthesized by most eukaryotes for asparagine-linked glycosylation. However, many protist organisms assemble dolichol-linked oligosaccharides that lack glucose residues. We have compared donor substrate utilization by the oligosaccharyltransferase (OST) from Trypanosoma cruzi, Entamoeba histolytica, Trichomonas vaginalis, Cryptococcus neoformans, and Saccharomyces cerevisiae using structurally homogeneous dolichol-linked oligosaccharides as well as a heterogeneous dolichol-linked oligosaccharide library. Our results demonstrate that the OST from diverse organisms utilizes the in vivo oligo saccharide donor in preference to certain larger and/or smaller oligosaccharide donors. Steady-state enzyme kinetic experiments reveal that the binding affinity of the tripeptide acceptor for the protist OST complex is influenced by the structure of the oligosaccharide donor. This rudimentary donor substrate selection mechanism has been refined in fungi and vertebrate organisms by the addition of a second, regulatory dolichol-linked oligosaccharide binding site, the presence of which correlates with acquisition of the SWP1/ribophorin II subunit of the OST complex

A general and efficient representation of ancestral recombination graphs

As a result of recombination, adjacent nucleotides can have different paths of genetic inheritance and therefore the genealogical trees for a sample of DNA sequences vary along the genome. The structure capturing the details of these intricately interwoven paths of inheritance is referred to as an ancestral recombination graph (ARG). Classical formalisms have focused on mapping coalescence and recombination events to the nodes in an ARG. However, this approach is out of step with some modern developments, which do not represent genetic inheritance in terms of these events or explicitly infer them. We present a simple formalism that defines an ARG in terms of specific genomes and their intervals of genetic inheritance, and show how it generalizes these classical treatments and encompasses the outputs of recent methods. We discuss nuances arising from this more general structure, and argue that it forms an appropriate basis for a software standard in this rapidly growing field.</p

SERT: A Transfomer Based Model for Spatio-Temporal Sensor Data with Missing Values for Environmental Monitoring

Environmental monitoring is crucial to our understanding of climate change, biodiversity loss and pollution. The availability of large-scale spatio-temporal data from sources such as sensors and satellites allows us to develop sophisticated models for forecasting and understanding key drivers. However, the data collected from sensors often contain missing values due to faulty equipment or maintenance issues. The missing values rarely occur simultaneously leading to data that are multivariate misaligned sparse time series. We propose two models that are capable of performing multivariate spatio-temporal forecasting while handling missing data naturally without the need for imputation. The first model is a transformer-based model, which we name SERT (Spatio-temporal Encoder Representations from Transformers). The second is a simpler model named SST-ANN (Sparse Spatio-Temporal Artificial Neural Network) which is capable of providing interpretable results. We conduct extensive experiments on two different datasets for multivariate spatio-temporal forecasting and show that our models have competitive or superior performance to those at the state-of-the-art.Comment: 11 pages, 7 figure

Mechanisms for Controlling HIV-1 Infection: A Gene Therapy Approach

Current anti-retroviral treatment (ART) for HIV-1 is highly effectively at controlling the infection. However, during early infection the virus establishes a latent reservoir, which is not impacted by ART. Any treatment interruption rapidly results in virus rebound from the latent reservoir to pre-therapy levels and thus ART does not constitute an HIV-1 cure. Alternate treatments are currently being explored in the form of gene therapy, following the success of the Berlin patient who has had undetectable virus since 2007. This review will describe the contrasting cure approaches that are currently the focus of multiple studies to control HIV, then focus in on functional cure gene therapy strategies; specifically, epigenetic silencing of HIV-1 by various methods, including RNA-directed transcriptional gene silencing. The various delivery strategies for targeting cells of the latent reservoir will be reviewed and finally, the clinical status and current challenges for ex vivo versus in vivo gene therapy delivery approaches will be discussed

The Use of Cellomics to Study Enterocyte Cytoskeletal Proteins in Coeliac Disease Patients

Coeliac disease is characterised by inflammation of small intestinal mucosa accompanied by abnormal villous architecture. It is now accepted that some patients with positive coeliac serology tests may have minor mucosal lesions that may not be apparent on routine histopathological analysis. The aim of the study was to perform detailed examination of enterocyte morphology and cytoskeletal structures using a high content analysis technology. Duodenal biopsies from 14 untreated and 10 treated coeliac patients and from 20 non-coeliac controls were examined. Tissue sections from six patients (study group subjects) before and after the development of gluten-sensitive enteropathy were also investigated. Immunohistochemical studies were performed on paraffin-embedded sections using an anti-α-tubulin antibody. Significant differences in enterocyte morphology and intracellular cytoskeletal structures were demonstrated in patients with proven coeliac disease and in the study group subjects. These changes were present in study group biopsies before evidence of enteropathy, as assessed by routine microscopy. This is the first study to demonstrate detailed characteristics of enterocyte morphology in coeliac patients using a high content analysis approach. The use of this technology allows a quantitative analysis of enterocyte intracellular structures from routine biopsy material and permits detection of subtle changes that precede the characteristic histological lesion