Toroidal Embeddings and Desingularization

Algebraic geometry is the study of solutions in polynomial equations using objects and shapes. Differential geometry is based on surfaces, curves, and dimensions of shapes and applying calculus and algebra. Desingularizing the singularities of a variety plays an important role in research in algebraic and differential geometry. Toroidal Embedding is one of the tools used in desingularization. Therefore, Toroidal Embedding and desingularization will be the main focus of my project. In this paper, we first provide a brief introduction on Toroidal Embedding, then show an explicit construction on how to smooth a variety with singularity through Toroidal Embeddings

Neuroinspired unsupervised learning and pruning with subquantum CBRAM arrays.

Resistive RAM crossbar arrays offer an attractive solution to minimize off-chip data transfer and parallelize on-chip computations for neural networks. Here, we report a hardware/software co-design approach based on low energy subquantum conductive bridging RAM (CBRAM®) devices and a network pruning technique to reduce network level energy consumption. First, we demonstrate low energy subquantum CBRAM devices exhibiting gradual switching characteristics important for implementing weight updates in hardware during unsupervised learning. Then we develop a network pruning algorithm that can be employed during training, different from previous network pruning approaches applied for inference only. Using a 512 kbit subquantum CBRAM array, we experimentally demonstrate high recognition accuracy on the MNIST dataset for digital implementation of unsupervised learning. Our hardware/software co-design approach can pave the way towards resistive memory based neuro-inspired systems that can autonomously learn and process information in power-limited settings

The role of 39 psoriasis risk variants on age of psoriasis onset.

Recent genome-wide association studies (GWAS) have identified multiple genetic risk factors for psoriasis, but data on their association with age of onset have been marginally explored. The goal of this study was to evaluate known risk alleles of psoriasis for association with age of psoriasis onset in three well-defined case-only cohorts totaling 1,498 psoriasis patients. We selected 39 genetic variants from psoriasis GWAS and tested these variants for association with age of psoriasis onset in a meta-analysis. We found that rs10484554 and rs12191877 near HLA-C and rs17716942 near IFIH1 were associated with age of psoriasis onset with false discovery rate < 0.05. The association between rs17716942 and age of onset was not replicated in a fourth independent cohort of 489 patients (P = 0.94). The imputed HLA-C∗06:02 allele demonstrated a much stronger association with age of psoriasis onset than rs10484554 and rs12191877. We conclude that despite the discovery of numerous psoriasis risk alleles, HLA-C∗06:02 still plays the most important role in determining the age of onset of psoriasis. Larger studies are needed to evaluate the contribution of other risk alleles, including IFIH1, to age of psoriasis onset

The potential of open-access data for flood estimations: uncovering inundation hotspots in Ho Chi Minh City, Vietnam, through a normalized flood severity index

Hydro-numerical models are increasingly important to determine the adequacy and evaluate the effectiveness of potential flood protection measures. However, a significant obstacle in setting up hydro-numerical and associated flood damage models is the tedious and oftentimes prohibitively costly process of acquiring reliable input data, which particularly applies to coastal megacities in developing countries and emerging economies. To help alleviate this problem, this paper explores the usability and reliability of flood models built on open-access data in regions where highly resolved (geo)data are either unavailable or difficult to access yet where knowledge about elements at risk is crucial for mitigation planning. The example of Ho Chi Minh City, Vietnam, is taken to describe a comprehensive but generic methodology for obtaining, processing and applying the required open-access data. The overarching goal of this study is to produce preliminary flood hazard maps that provide first insights into potential flooding hotspots demanding closer attention in subsequent, more detailed risk analyses. As a key novelty, a normalized flood severity index (INFS), which combines flood depth and duration, is proposed to deliver key information in a preliminary flood hazard assessment. This index serves as an indicator that further narrows down the focus to areas where flood hazard is significant. Our approach is validated by a comparison with more than 300 flood samples locally observed during three heavy-rain events in 2010 and 2012 which correspond to INFS-based inundation hotspots in over 73 % of all cases. These findings corroborate the high potential of open-access data in hydro-numerical modeling and the robustness of the newly introduced flood severity index, which may significantly enhance the interpretation and trustworthiness of risk assessments in the future. The proposed approach and developed indicators are generic and may be replicated and adopted in other coastal megacities around the globe

Determination of the Young's modulus of pulsed laser deposited epitaxial PZT thin films

We determined the Young’s modulus of pulsed laser deposited epitaxially grown PbZr0.52Ti0.48O3 (PZT) thin films on microcantilevers by measuring the difference in cantilever resonance frequency before and after deposition. By carefully optimizing the accuracy of this technique, we were able to show that the Young’s modulus of PZT thin films deposited on silicon is dependent on the in-plane orientation, by using cantilevers oriented along the 1 1 0 and 1 0 0 silicon directions. Deposition of thin films on cantilevers affects their flexural rigidity and increases their mass, which results in a change in the resonance frequency. An analytical relation was developed to determine the effective Young’s modulus of the PZT thin films from the shift in the resonance frequency of the cantilevers, measured both before and after the deposition. In addition, the appropriate effective Young’s modulus valid for our cantilevers’ dimensions was used in the calculations that were determined by a combined analytical and finite-element (FE) simulations approach. We took extra care to eliminate the errors in the determination of the effective Young’s modulus of the PZT thin film, by accurately determining the dimensions of the cantilevers and by measuring many cantilevers of different lengths. Over-etching during the release of cantilevers from the handle wafer caused an undercut. Since this undercut cannot be avoided, the effective length was determined and used in the calculations. The Young’s modulus of PZT, deposited by pulsed laser deposition, was determined to be 103.0 GPa with a standard error of ± 1.4 GPa for the 1 1 0 crystal direction of silicon. For the 1 0 0 silicon direction, we measured 95.2 GPa with a standard error of ± 2.0 GPa

Influence of silicon orientation and cantilever undercut on the determination of the Young’s modulus of thin films

The Young’s modulus of thin films can be determined by deposition on a micronsized Si cantilever and measuring the resonance frequency before and after deposition. The accuracy of the method depends strongly on the initial determination of the mechanical properties and dimensions of the cantilever. We discuss the orientation of the cantilever with respect to the Si crystal, and the inevitable undercut of the cantilever caused by process inaccuracies. By finite element modelling we show that the Young’s modulus should be used instead of the analytical plate modulus approximation for the effective Young’s modulus of Si cantilevers used in this work for both the 1 0 0 and 1 1 0 crystal orientation. Cantilever undercut can be corrected by variation of the cantilever length. As an example, the Young’s modulus of PbZr0.52Ti0.48O3 (PZT) thin films deposited by pulsed laser deposition (PLD) was determined to be 99 GPa, with 1.4 GPa standard error

Methods for Integrating Trials and Non-Experimental Data to Examine Treatment Effect Heterogeneity

Estimating treatment effects conditional on observed covariates can improve the ability to tailor treatments to particular individuals. Doing so effectively requires dealing with potential confounding, and also enough data to adequately estimate effect moderation. A recent influx of work has looked into estimating treatment effect heterogeneity using data from multiple randomized controlled trials and/or observational datasets. With many new methods available for assessing treatment effect heterogeneity using multiple studies, it is important to understand which methods are best used in which setting, how the methods compare to one another, and what needs to be done to continue progress in this field. This paper reviews these methods broken down by data setting: aggregate-level data, federated learning, and individual participant-level data. We define the conditional average treatment effect and discuss differences between parametric and nonparametric estimators, and we list key assumptions, both those that are required within a single study and those that are necessary for data combination. After describing existing approaches, we compare and contrast them and reveal open areas for future research. This review demonstrates that there are many possible approaches for estimating treatment effect heterogeneity through the combination of datasets, but that there is substantial work to be done to compare these methods through case studies and simulations, extend them to different settings, and refine them to account for various challenges present in real data