Gaussian processes with built-in dimensionality reduction: Applications in high-dimensional uncertainty quantification

Uncertainty quantification (UQ) tasks, such as model calibration, uncertainty propagation, and optimization under uncertainty, typically require several thousand evaluations of the underlying computer codes. To cope with the cost of simulations, one replaces the real response surface with a cheap surrogate based, e.g., on polynomial chaos expansions, neural networks, support vector machines, or Gaussian processes (GP). However, the number of simulations required to learn a generic multivariate response grows exponentially as the input dimension increases. This curse of dimensionality can only be addressed, if the response exhibits some special structure that can be discovered and exploited. A wide range of physical responses exhibit a special structure known as an active subspace (AS). An AS is a linear manifold of the stochastic space characterized by maximal response variation. The idea is that one should first identify this low dimensional manifold, project the high-dimensional input onto it, and then link the projection to the output. If the dimensionality of the AS is low enough, then learning the link function is a much easier problem than the original problem of learning a high-dimensional function. The classic approach to discovering the AS requires gradient information, a fact that severely limits its applicability. Furthermore, and partly because of its reliance to gradients, it is not able to handle noisy observations. The latter is an essential trait if one wants to be able to propagate uncertainty through stochastic simulators, e.g., through molecular dynamics codes. In this work, we develop a probabilistic version of AS which is gradient-free and robust to observational noise. Our approach relies on a novel Gaussian process regression with built-in dimensionality reduction. In particular, the AS is represented as an orthogonal projection matrix that serves as yet another covariance function hyper-parameter to be estimated from the data. To train the model, we design a two-step maximum likelihood optimization procedure that ensures the orthogonality of the projection matrix by exploiting recent results on the Stiefel manifold, i.e., the manifold of matrices with orthogonal columns. The additional benefit of our probabilistic formulation, is that it allows us to select the dimensionality of the AS via the Bayesian information criterion. We validate our approach by showing that it can discover the right AS in synthetic examples without gradient information using both noiseless and noisy observations. We demonstrate that our method is able to discover the same AS as the classical approach in a challenging one-hundred-dimensional problem involving an elliptic stochastic partial differential equation with random conductivity. Finally, we use our approach to study the effect of geometric and material uncertainties in shock propagation in a one dimensional granular system

Accuracy and reliability of ultrasound estimation of fetal weight in women with a singleton term pregnancy

Background: Prenatal estimation of birth-weight is of utmost importance to predict the mode of delivery. This is also an important parameter of antenatal care. This study was conducted to evaluate the accuracy of estimated fetal weight by ultrasound, compared with actual birth weight.Methods: This was a prospective and comparative study comprising 110 pregnant women at term. Patients who had their sonography done within 7 days from date of delivery were included. Fetal weight was estimated by Hadlock 2 formula, the software of which was preinstalled in ultrasound-machine. The estimated fetal weight was compared to the post-delivery birth-weight. The Pearson's correlation coefficient was used and the accuracy of sonographic fetal weight estimation was evaluated using mean error, mean absolute error, mean percentage error, mean absolute percentage error and proportion of estimates within 10% of actual birth weight.Results: Mean estimated and actual birth weights were 3120.8±349.4 gm and 3088.2±404.5 g respectively. There was strong positive correlation between estimated fetal weight and actual birth weight (r = 0.58, p<0.001). The mean percentage error and mean absolute percentage error of ultrasound fetal weight estimations were 1.96±11.8% and 8.7±8.2% respectively. The percentage of estimates within ±10% of the actual birth weight was found to be 67.3%. In 23% of the cases, ultrasound overestimated the birth weight. In 13% of the cases, ultrasound underestimated the birth weight.Conclusions: There was strong positive correlation between actual and sonographically estimated fetal weight. So, ultrasonography can be considered as useful tool for estimating the fetal weight for improving the perinatal outcome

Surgical management of supracondylar femur fracture using rush pinning technique in dogs

Supracondylar femur fracture in twelve dogs were managed using rush pinning technique. Post-operative radiographs displayed good anatomical alignment and reduction of fracture fragments without any pin migration. All the eight dogs showed normal gait without any limp on last reappraisal day. Rush pinning yielded good clinical outcomes in the management of supracondylar femur fractures with minimum complications

Properties of Light Flavour Baryons in Hypercentral quark model

The light flavour baryons are studied within the quark model using the hyper central description of the three-body system. The confinement potential is assumed as hypercentral coulomb plus power potential ($hCPP_\nu$) with power index $\nu$. The masses and magnetic moments of light flavour baryons are computed for different power index, $\nu$ starting from 0.5 to 1.5. The predicted masses and magnetic moments are found to attain a saturated value with respect to variation in $\nu$ beyond the power index $\nu>$ 1.0. Further we computed transition magnetic moments and radiative decay width of light flavour baryons. The results are in good agreement with known experimental as well as other theoretical models.Comment: Accepted in Pramana J. of Physic

Preduodenal portal vein: A recipe for disaster during laparoscopic cholecystectomy

We had encountered a very rare congenital anomaly of a preduodenal portal vein while doing laparoscopic cholecystectomy. More significant in our case is that this preduodenal vein is hiding behind omental adhesions with the gallbladder. We want to raise awareness about this very rare anomaly. Recognition and knowledge of this anomaly will prevent the potential of a serious operative misadventure

Influencing users for paper recycling using an E-commerce website

Currently, the most used promotional strategy for paper recycling includes Mail, Ads, Posters, Articles, etc. We are taking an E-commerce website that will be built upon the ideology of recycling as a candidate for being the best tool for the promotion of paper recycling among this generation among its potential impact on carbon footprint reduction. In this paper we will be comparing various statistics regarding the trends of searches and the current state of recycling in different regions of our country. We will also conduct a survey among colleagues for their habits and their current contributions. We will also be comparing different literature related to our topic. We have found that there is significant potential for a website and it has many supportive statistics with it. An E-commerce website with modern retention techniques can also bring awareness to the young masses in this cause. Big tech companies are currently competing with each other using computer science for the attention of the masses. Bringing this attention to the current most important scenarios can be so much impactful

Social Implications of Graphics Processing Units

A Graphics Processing Unit (GPU) is a processor deemed as a complete replacement of CPUs for intensive computational purposes. Due to the constant improvements in speed and number of flops, GPUs have led to many technological breakthroughs in medical research, database enhancement, military computations, etc. With GPUs being used more and more in our day-to-day life for general purpose computations, the role they play on our society have become significant. This project is pertaining to the societal impacts of GPUs

Multiparametric magnetic resonance imaging-transrectal ultrasound fusion biopsies increase the rate of cancer detection in populations with a low incidence of prostate cancer

Purpose: To prospectively evaluate the diagnostic yield of multiparametric magnetic resonance imaging (mpMRI)-fusion, transrectal ultrasound (TRUS)-guided prostate biopsies for detection of prostate cancer in an Asian population with a low incidence of prostate cancer. Materials and Methods: A total of 131 males with suspected prostate cancer were recruited to undergo fusion biopsy with the Artemis prostate fusion biopsy device (Eigen, Grass Valley, CA, USA). All patients underwent standard 12-core systematic biopsies in addition to biopsies targeted at the mpMRI-identified abnormal regions. Yield from the standard cores was compared with that from the targeted cores. Gleason scores of 4+3 or higher were considered significant. Results: The mean age of the patients was 63.54±7.96 years and the mean prostate-specific antigen value was 9.75±5.35 ng/mL. A total of 36 patients had cancer, of which 3 (8.3%) were detected only on standard cores and 3 (8.3%) only on targeted cores. Of the clinically significant cancers (n=30), targeted biopsy detected a higher number (28/30, 93.3%) than standard biopsy (21/30, 70.0%). A total of 6 of 8 cancers (75.0%) that were insignificant on standard biopsy were upgraded to significant cancer on targeted cores. Conclusions: Eight percent of cancers were detected only on MRI-TRUS fusion-targeted biopsies, whereas the method upgraded more than two-thirds of insignificant cancers to significant cancers. Fusion biopsies thus provide incremental information over standard TRUS biopsies in the diagnosis of significant prostate cancer in populations with a low incidence of prostate cancer

Development and characterization of microwave processed cast iron joint

The feasibility of joining cast iron through novel microwave heating using susceptor (i.e. microwave hybrid heating), is carried out in present work. The joints were developed in domestic microwave applicator at 2.45 GHz frequency and 900 W. Nickel based powder slurry was placed between the faying surfaces for obtaining the joint. The detailed mechanism of joining through microwaves has been explained by using suitable illustrations. The microwave processed joint was characterized by using scanning electron microscopy, energy dispersive X-ray spectroscopy and X-ray diffraction for microstructure analysis and study of developed inter-metallic phases. Results revealed that uniform and dense joint of 0.5 mm thickness were obtained. Obtained joints revealed metallurgical bonding of nickel powder with faying surfaces of base metal. This metallurgical bonding resulted into wavy interface and this was due to dilution of the base metal along the joint region. The EDS analysis confirms the uniform distribution of elements in the joint region and SEM results revealed that some porosity (in the range of 1.5–1.88%) was observed in the joint region. Tensile strength of microwave joined cast iron was ∼90% of the base metal strength. This was due to the development of high strength intermetallics and presence of nickel metal in the joint region. Microhardness at joint region was 201.7 ± 18 HV and 315 ± 10 HV along HAZ, whereas microhardness of bulk cast iron was 184 ± 4 HV. Microwave processed samples fractured along the HAZ region. Keywords: Joining, Microwave heating, Microstructure, Microhardness, Porosity measuremen

Prevention and management of ventilator-associated pneumonia: A survey on current practices by intensivists practicing in the Indian subcontinent

Implementation of evidence-based guidelines to prevent and manage ventilator-associated pneumonia (VAP) in the clinical setting may not be adequate. We aimed to assess the implementation of selected VAP prevention strategies, and to learn how VAP is managed by the intensivists practicing in the Indian Subcontinent. Three hundred 10-point questionnaires were distributed during an International Critical Care Conferenceheld at New Delhi in 2009. A total of 126 (42%) questionnaires distributed among delegates from India, Nepal and Sri Lanka were analyzed. Majority (96.8%) reported using VAP bundles with a high proportion including head elevation (98.4%), chlorhexidine mouthcare (83.3%), stress ulcer prophylaxis (96.8%), heat and moisture exchangers (HME, 92.9%), early weaning (94.4%), and hand washing (97.6%) as part of their VAP bundle. Use of subglottic secretion drainage (SSD, 45.2%) and closed suction systems (CSS, 74.6%) was also reported by many intensivists, whereas use of selective gut decontamination was reported by only 22.2%. Commonest method for sampling was endotracheal suction by 68.3%. Gram negative organisms were reported to be the most commonly isolated. Majority (39.7%) reported using proton pump inhibitors for stress ulcer prophylaxis and 84.1% believed that VAP contributed to increased mortality. De-escalating therapy was considered in patients responding to treatment by 57.9% and 65.9% considered adding empirical methicillin resistant Staphylococcus aureus (MRSA)coverage, while 63.5% considered adding nebulized antibiotics in certain high-risk patients. There was good concordance regarding VAP prophylaxis among the intensivists with a majority adhering to evidence-based guidelines. We could identify certain issues like the choice of agent for stress ulcer prophylaxis, use of HME filters, SSD and CSS, where there still exists some practice variability and opportunities for improvement