Existence Theorem for Periodic Solutions of Higher Order Nonlinear Differential Equations

AbstractWe study the existence of periodic solutions to differential equations of the formL(x)+g(t,x,x′,…,x(m))=f(t) withL(x)=x(m)+am−1x(m−1)+···+a1x′

Prediction of Supernova Rates in Known Galaxy-galaxy Strong-lens Systems

We propose a new strategy of finding strongly-lensed supernovae (SNe) by monitoring known galaxy-scale strong-lens systems. Strongly lensed SNe are potentially powerful tools for the study of cosmology, galaxy evolution, and stellar populations, but they are extremely rare. By targeting known strongly lensed starforming galaxies, our strategy significantly boosts the detection efficiency for lensed SNe compared to a blind search. As a reference sample, we compile the 128 galaxy-galaxy strong-lens systems from the Sloan Lens ACS Survey (SLACS), the SLACS for the Masses Survey, and the Baryon Oscillation Spectroscopic Survey Emission-Line Lens Survey. Within this sample, we estimate the rates of strongly-lensed Type Ia SN (SNIa) and core-collapse SN (CCSN) to be $1.23 \pm 0.12$ and $10.4 \pm 1.1$ events per year, respectively. The lensed SN images are expected to be widely separated with a median separation of 2 arcsec. Assuming a conservative fiducial lensing magnification factor of 5 for the most highly magnified SN image, we forecast that a monitoring program with a single-visit depth of 24.7 mag (5$\sigma$ point source, $r$ band) and a cadence of 5 days can detect 0.49 strongly-lensed SNIa event and 2.1 strongly-lensed CCSN events per year within this sample. Our proposed targeted-search strategy is particularly useful for prompt and efficient identifications and follow-up observations of strongly-lensed SN candidates. It also allows telescopes with small field of views and limited time to efficiently discover strongly-lensed SNe with a pencil-beam scanning strategy.Comment: 14 pages, 5 figures, ApJ in pres

Conditional Generation of Medical Images via Disentangled Adversarial Inference

Synthetic medical image generation has a huge potential for improving healthcare through many applications, from data augmentation for training machine learning systems to preserving patient privacy. Conditional Adversarial Generative Networks (cGANs) use a conditioning factor to generate images and have shown great success in recent years. Intuitively, the information in an image can be divided into two parts: 1) content which is presented through the conditioning vector and 2) style which is the undiscovered information missing from the conditioning vector. Current practices in using cGANs for medical image generation, only use a single variable for image generation (i.e., content) and therefore, do not provide much flexibility nor control over the generated image. In this work we propose a methodology to learn from the image itself, disentangled representations of style and content, and use this information to impose control over the generation process. In this framework, style is learned in a fully unsupervised manner, while content is learned through both supervised learning (using the conditioning vector) and unsupervised learning (with the inference mechanism). We undergo two novel regularization steps to ensure content-style disentanglement. First, we minimize the shared information between content and style by introducing a novel application of the gradient reverse layer (GRL); second, we introduce a self-supervised regularization method to further separate information in the content and style variables. We show that in general, two latent variable models achieve better performance and give more control over the generated image. We also show that our proposed model (DRAI) achieves the best disentanglement score and has the best overall performance.Comment: Published in Medical Image Analysi

Whole blueberry protects pancreatic beta-cells in diet-induced obese mouse

Background Blueberry is rich in bioactive substances and possesses powerful antioxidant potential, which can protect against oxidant-induced and inflammatory cell damage and cytotoxicity. The aim of this study was to determine how blueberry affects glucose metabolism and pancreatic β-cell proliferation in high fat diet (HFD)-induced obese mice. Methods Wild type male mice at age of 4 weeks received two different kinds of diets: high-fat diet (HFD) containing 60% fat or modified HFD supplemented with 4% (wt:wt) freeze-dried whole blueberry powder (HFD + B) for 14 weeks. A separate experiment was performed in mice fed with low-fat diet (LFD) containing 10% fat or modified LFD + B supplemented with 4% (wt:wt) freeze-dried whole blueberry powder. The metabolic parameters including blood glucose and insulin levels, glucose and insulin tolerances were measured. Results Blueberry-supplemented diet significantly increased insulin sensitivity and glucose tolerance in HFD + B mice compared to HFD mice. However, no difference was observed in blood glucose and insulin sensitivity between LFD + B and LFD mice. In addition, blueberry increased β-cell survival and prevented HFD-induced β-cell expansion. The most important finding was the observation of presence of small scattered islets in blueberry treated obese mice, which may reflect a potential role of blueberry in regenerating pancreatic β-cells. Conclusions Blueberry-supplemented diet can prevent obesity-induced insulin resistance by improving insulin sensitivity and protecting pancreatic β-cells. Blueberry supplementation has the potential to protect and improve health conditions for both type 1 and type 2 diabetes patients

Addax: A fast, private, and accountable ad exchange infrastructure

This paper proposes Addax, a fast, verifiable, and private online ad exchange. When a user visits an ad-supported site, Addax runs an auction similar to those of leading exchanges; Addax requests bids, selects the winner, collects payment, and displays the ad to the user. A key distinction is that bids in Addax’s auctions are kept private and the outcome of the auction is publicly verifiable. Addax achieves these properties by adding public verifiability to the affine aggregatable encodings in Prio (NSDI’17) and by building an auction protocol out of them. Our implementation of Addax over WAN with hundreds of bidders can run roughly half the auctions per second as a non-private and non-verifiable exchange, while delivering ads to users in under 600 ms with little additional bandwidth requirements. This efficiency makes Addax the first architecture capable of bringing transparency to this otherwise opaque ecosystem

The BOSS Emission-Line Lens Survey. III. : Strong Lensing of Lyα\alpha Emitters by Individual Galaxies

We introduce the Baryon Oscillation Spectroscopic Survey (BOSS) Emission-Line Lens Survey (BELLS) for GALaxy-Ly$\alpha$ EmitteR sYstems (BELLS GALLERY) Survey, which is a Hubble Space Telescope program to image a sample of galaxy-scale strong gravitational lens candidate systems with high-redshift Ly$\alpha$ emitters (LAEs) as the background sources. The goal of the BELLS GALLERY Survey is to illuminate dark substructures in galaxy-scale halos by exploiting the small-scale clumpiness of rest-frame far-UV emission in lensed LAEs, and to thereby constrain the slope and normalization of the substructure-mass function. In this paper, we describe in detail the spectroscopic strong-lens selection technique, which is based on methods adopted in the previous Sloan Lens ACS (SLACS) Survey, BELLS, and SLACS for the Masses Survey. We present the BELLS GALLERY sample of the 21 highest-quality galaxy--LAE candidates selected from $\approx 1.4 \times 10^6$ galaxy spectra in the BOSS of the Sloan Digital Sky Survey III. These systems consist of massive galaxies at redshifts of approximately 0.5 strongly lensing LAEs at redshifts from 2--3. The compact nature of LAEs makes them an ideal probe of dark substructures, with a substructure-mass sensitivity that is unprecedented in other optical strong-lens samples. The magnification effect from lensing will also reveal the structure of LAEs below 100 pc scales, providing a detailed look at the sites of the most concentrated unobscured star formation in the universe. The source code used for candidate selection is available for download as a part of this release.Comment: 14 pages, 5 figures, accepted for publication in the ApJ (ApJ, 824, 86). Minor edits to match the ApJ published versio