Smoothed Analysis of Tensor Decompositions

Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and tensors analogs of much of the matrix algebra toolkit are unlikely to exist because of hardness results. Efficient decomposition in the overcomplete case (where rank exceeds dimension) is particularly challenging. We introduce a smoothed analysis model for studying these questions and develop an efficient algorithm for tensor decomposition in the highly overcomplete case (rank polynomial in the dimension). In this setting, we show that our algorithm is robust to inverse polynomial error -- a crucial property for applications in learning since we are only allowed a polynomial number of samples. While algorithms are known for exact tensor decomposition in some overcomplete settings, our main contribution is in analyzing their stability in the framework of smoothed analysis. Our main technical contribution is to show that tensor products of perturbed vectors are linearly independent in a robust sense (i.e. the associated matrix has singular values that are at least an inverse polynomial). This key result paves the way for applying tensor methods to learning problems in the smoothed setting. In particular, we use it to obtain results for learning multi-view models and mixtures of axis-aligned Gaussians where there are many more "components" than dimensions. The assumption here is that the model is not adversarially chosen, formalized by a perturbation of model parameters. We believe this an appealing way to analyze realistic instances of learning problems, since this framework allows us to overcome many of the usual limitations of using tensor methods.Comment: 32 pages (including appendix

A Spectral Algorithm with Additive Clustering for the Recovery of Overlapping Communities in Networks

This paper presents a novel spectral algorithm with additive clustering designed to identify overlapping communities in networks. The algorithm is based on geometric properties of the spectrum of the expected adjacency matrix in a random graph model that we call stochastic blockmodel with overlap (SBMO). An adaptive version of the algorithm, that does not require the knowledge of the number of hidden communities, is proved to be consistent under the SBMO when the degrees in the graph are (slightly more than) logarithmic. The algorithm is shown to perform well on simulated data and on real-world graphs with known overlapping communities.Comment: Journal of Theoretical Computer Science (TCS), Elsevier, A Para\^itr

Bongard-LOGO: A New Benchmark for Human-Level Concept Learning and Reasoning

Humans have an inherent ability to learn novel concepts from only a few samples and generalize these concepts to different situations. Even though today's machine learning models excel with a plethora of training data on standard recognition tasks, a considerable gap exists between machine-level pattern recognition and human-level concept learning. To narrow this gap, the Bongard Problems (BPs) were introduced as an inspirational challenge for visual cognition in intelligent systems. Albeit new advances in representation learning and learning to learn, BPs remain a daunting challenge for modern AI. Inspired by the original one hundred BPs, we propose a new benchmark Bongard-LOGO for human-level concept learning and reasoning. We develop a program-guided generation technique to produce a large set of human-interpretable visual cognition problems in action-oriented LOGO language. Our benchmark captures three core properties of human cognition: 1) context-dependent perception, in which the same object may have disparate interpretations given different contexts; 2) analogy-making perception, in which some meaningful concepts are traded off for other meaningful concepts; and 3) perception with a few samples but infinite vocabulary. In experiments, we show that the state-of-the-art deep learning methods perform substantially worse than human subjects, implying that they fail to capture core human cognition properties. Finally, we discuss research directions towards a general architecture for visual reasoning to tackle this benchmark

Bongard-LOGO: A New Benchmark for Human-Level Concept Learning and Reasoning

Humans have an inherent ability to learn novel concepts from only a few samples and generalize these concepts to different situations. Even though today's machine learning models excel with a plethora of training data on standard recognition tasks, a considerable gap exists between machine-level pattern recognition and human-level concept learning. To narrow this gap, the Bongard problems (BPs) were introduced as an inspirational challenge for visual cognition in intelligent systems. Despite new advances in representation learning and learning to learn, BPs remain a daunting challenge for modern AI. Inspired by the original one hundred BPs, we propose a new benchmark Bongard-LOGO for human-level concept learning and reasoning. We develop a program-guided generation technique to produce a large set of human-interpretable visual cognition problems in action-oriented LOGO language. Our benchmark captures three core properties of human cognition: 1) context-dependent perception, in which the same object may have disparate interpretations given different contexts; 2) analogy-making perception, in which some meaningful concepts are traded off for other meaningful concepts; and 3) perception with a few samples but infinite vocabulary. In experiments, we show that the state-of-the-art deep learning methods perform substantially worse than human subjects, implying that they fail to capture core human cognition properties. Finally, we discuss research directions towards a general architecture for visual reasoning to tackle this benchmark.Comment: 22 pages, NeurIPS 202

Formulation and In-Vitro Evaluation of Gastroretentive Expandable Film of Nateglinide

The present work was based on the development and characterization of unfolding type gastro retentive dosage form appropriate for the controlled release of Nateglinide (NAT), a drug with a narrow therapeutic window. Gastroretentive films were formulated using hydroxypropyl methylcellulose (HPMC) as a film-forming agent, and polyethylene glycol 400 (PEG) as a plasticizer. The drug-loaded polymer film of hydroxypropyl methylcellulose (HPMC) as a film-forming agent and polyethylene glycol 400 (PEG) as a plasticizer was folded into hard gelatin capsules. The prepared films were evaluated for several parameters like physical appearance, surface texture, weight variation, thickness, folding endurance, swelling index, tensile strength, unfolding behavior, drug content, and In vitro drug release studies. Drug and polymers were found to be compatible as revealed by Fourier transform infrared spectroscopy (FTIR) study revealed uniform dispersion of NAT in polymeric matrices. The best release for gastroretentive film was shown by formulation F19 (HPMC 15cps and PEG 400). Formulation F19 exhibited a good appearance, better mechanical strength with acceptable flexibility. Formulation F19 was given 90% NAT release after 12 hr, 95.15±0.18% drug content, and found to be stable.  The results indicate that the unfolding type gastro retentive drug delivery system offers a suitable and practical approach for the prolonged release of drug over an extended period and thus oral bioavailability, efficacy, and patient compliance is improved

Score-based Diffusion Models in Function Space

Diffusion models have recently emerged as a powerful framework for generative modeling. They consist of a forward process that perturbs input data with Gaussian white noise and a reverse process that learns a score function to generate samples by denoising. Despite their tremendous success, they are mostly formulated on finite-dimensional spaces, e.g. Euclidean, limiting their applications to many domains where the data has a functional form such as in scientific computing and 3D geometric data analysis. In this work, we introduce a mathematically rigorous framework called Denoising Diffusion Operators (DDOs) for training diffusion models in function space. In DDOs, the forward process perturbs input functions gradually using a Gaussian process. The generative process is formulated by integrating a function-valued Langevin dynamic. Our approach requires an appropriate notion of the score for the perturbed data distribution, which we obtain by generalizing denoising score matching to function spaces that can be infinite-dimensional. We show that the corresponding discretized algorithm generates accurate samples at a fixed cost that is independent of the data resolution. We theoretically and numerically verify the applicability of our approach on a set of problems, including generating solutions to the Navier-Stokes equation viewed as the push-forward distribution of forcings from a Gaussian Random Field (GRF).Comment: 26 pages, 7 figure

Cytotoxicity and antibacterial activity of gold-supported cerium oxide nanoparticles

BACKGROUND: Cerium oxide nanoparticles (CeO(2)) have been shown to be a novel therapeutic in many biomedical applications. Gold (Au) nanoparticles have also attracted widespread interest due to their chemical stability and unique optical properties. Thus, decorating Au on CeO(2) nanoparticles would have potential for exploitation in the biomedical field. METHODS: In the present work, CeO(2) nanoparticles synthesized by a chemical combustion method were supported with 3.5% Au (Au/CeO(2)) by a deposition-precipitation method. The as-synthesized Au, CeO(2), and Au/CeO(2) nanoparticles were evaluated for antibacterial activity and cytotoxicity in RAW 264.7 normal cells and A549 lung cancer cells. RESULTS: The as-synthesized nanoparticles were characterized by X-ray diffraction, scanning and transmission electron microscopy, and ultraviolet-visible measurements. The X-ray diffraction study confirmed the formation of cubic fluorite-structured CeO(2) nanoparticles with a size of 10 nm. All synthesized nanoparticles were nontoxic towards RAW 264.7 cells at doses of 0–1,000 μM except for Au at >100 μM. For A549 cancer cells, Au/CeO(2) had the highest inhibitory effect, followed by both Au and CeO(2) which showed a similar effect at 500 and 1,000 μM. Initial binding of nanoparticles occurred through localized positively charged sites in A549 cells as shown by a shift in zeta potential from positive to negative after 24 hours of incubation. A dose-dependent elevation in reactive oxygen species indicated that the pro-oxidant activity of the nanoparticles was responsible for their cytotoxicity towards A549 cells. In addition, cellular uptake seen on transmission electron microscopic images indicated predominant localization of nanoparticles in the cytoplasmic matrix and mitochondrial damage due to oxidative stress. With regard to antibacterial activity, both types of nanoparticles had the strongest inhibitory effect on Bacillus subtilis in monoculture systems, followed by Salmonella enteritidis, Escherichia coli, and Staphylococcus aureus, while, in coculture tests with Lactobacillus plantarum, S. aureus was inhibited to a greater extent than the other bacteria. CONCLUSION: Gold-supported CeO(2) nanoparticles may be a potential nanomaterial for in vivo application owing to their biocompatible and antibacterial properties

Laparoscopy in management of appendicitis in high-, middle-, and low-income countries: a multicenter, prospective, cohort study.

BACKGROUND: Appendicitis is the most common abdominal surgical emergency worldwide. Differences between high- and low-income settings in the availability of laparoscopic appendectomy, alternative management choices, and outcomes are poorly described. The aim was to identify variation in surgical management and outcomes of appendicitis within low-, middle-, and high-Human Development Index (HDI) countries worldwide. METHODS: This is a multicenter, international prospective cohort study. Consecutive sampling of patients undergoing emergency appendectomy over 6 months was conducted. Follow-up lasted 30 days. RESULTS: 4546 patients from 52 countries underwent appendectomy (2499 high-, 1540 middle-, and 507 low-HDI groups). Surgical site infection (SSI) rates were higher in low-HDI (OR 2.57, 95% CI 1.33-4.99, p = 0.005) but not middle-HDI countries (OR 1.38, 95% CI 0.76-2.52, p = 0.291), compared with high-HDI countries after adjustment. A laparoscopic approach was common in high-HDI countries (1693/2499, 67.7%), but infrequent in low-HDI (41/507, 8.1%) and middle-HDI (132/1540, 8.6%) groups. After accounting for case-mix, laparoscopy was still associated with fewer overall complications (OR 0.55, 95% CI 0.42-0.71, p < 0.001) and SSIs (OR 0.22, 95% CI 0.14-0.33, p < 0.001). In propensity-score matched groups within low-/middle-HDI countries, laparoscopy was still associated with fewer overall complications (OR 0.23 95% CI 0.11-0.44) and SSI (OR 0.21 95% CI 0.09-0.45). CONCLUSION: A laparoscopic approach is associated with better outcomes and availability appears to differ by country HDI. Despite the profound clinical, operational, and financial barriers to its widespread introduction, laparoscopy could significantly improve outcomes for patients in low-resource environments. TRIAL REGISTRATION: NCT02179112

Dry Needling for Spine Related Disorders: a Scoping Review

Introduction/Background: The depth and breadth of research on dry needling (DN) has not been evaluated specifically for symptomatic spine related disorders (SRD) from myofascial trigger points (TrP), disc, nerve and articular structures not due to serious pathologies. Current literature appears to support DN for treatment of TrP. Goals of this review include identifying research published on DN treatment for SRD, sites of treatment and outcomes studied. Methods: A scoping review was conducted following Levac et al.’s five part methodological framework to determine the current state of the literature regarding DN for patients with SRD. Results: Initial and secondary search strategies yielded 55 studies in the cervical (C) region (71.43%) and 22 in the thoracolumbar-pelvic (TLP) region (28.57%). Most were randomized controlled trials (60% in C, 45.45% in TLP) and clinical trials (18.18% in C, 22.78% in TLP). The most commonly treated condition was TrP for both the C and TLP regions. In the C region, DN was provided to 23 different muscles, with the trapezius as treatment site in 41.88% of studies. DN was applied to 31 different structures in the TLP region. In the C region, there was one treatment session in 23 studies (41.82%) and 2–6 treatments in 25 (45.45%%). For the TLP region, one DN treatment was provided in 8 of the 22 total studies (36.36%) and 2–6 in 9 (40.9%). The majority of experimental designs had DN as the sole intervention. For both C and TLP regions, visual analogue scale, pressure pain threshold and range of motion were the most common outcomes. Conclusion: For SRD, DN was primarily applied to myofascial structures for pain or TrP diagnoses. Many outcomes were improved regardless of diagnosis or treatment parameters. Most studies applied just one treatment which may not reflect common clinical practice. Further research is warranted to determine optimal treatment duration and frequency. Most studies looked at DN as the sole intervention. It is unclear whether DN alone or in addition to other treatment procedures would provide superior outcomes. Functional outcome tools best suited to tracking the outcomes of DN for SRD should be explored.https://doi.org/10.1186/s12998-020-00310-

Identification of the traditional and non-traditional sulfate-reducing bacteria associated with corroded ship hull

Pitting corrosion due to microbial activity is the most severe type of corrosion that occurs in ship hull. Since biogenic sulfide produced by sulfate-reducing bacteria (SRB) is involved in the acceleration of pitting corrosion of marine vessels, so it is important to collect information about SRB community involved in maritime vessel failure. We investigated the SRB community on corroded hull portion of the ship. With the use of common cultural method and 16S rDNA sequencing, ten bacteria with sulfate reduction ability were isolated and identified. They belonged to both traditional (Desulfovibrio, Desulfotomaculum) and non-traditional (Citrobacter) sulfate-reducing bacteria. All the isolates were able to produce a high amount of sulfide. However, only traditional isolates were showing the amplification for the SRB-specific gene, dsrAB. Further studies on corrosion potential of these two groups of bacteria showed that in spite of high sulfide and biofilm production by non-traditional SRB, they are less aggressive towards the mild steel compare to the traditional group