Data-driven discovery of coordinates and governing equations

The discovery of governing equations from scientific data has the potential to transform data-rich fields that lack well-characterized quantitative descriptions. Advances in sparse regression are currently enabling the tractable identification of both the structure and parameters of a nonlinear dynamical system from data. The resulting models have the fewest terms necessary to describe the dynamics, balancing model complexity with descriptive ability, and thus promoting interpretability and generalizability. This provides an algorithmic approach to Occam's razor for model discovery. However, this approach fundamentally relies on an effective coordinate system in which the dynamics have a simple representation. In this work, we design a custom autoencoder to discover a coordinate transformation into a reduced space where the dynamics may be sparsely represented. Thus, we simultaneously learn the governing equations and the associated coordinate system. We demonstrate this approach on several example high-dimensional dynamical systems with low-dimensional behavior. The resulting modeling framework combines the strengths of deep neural networks for flexible representation and sparse identification of nonlinear dynamics (SINDy) for parsimonious models. It is the first method of its kind to place the discovery of coordinates and models on an equal footing.Comment: 25 pages, 6 figures; added acknowledgment

Inhibition of Poly(ADP-Ribose) polymerase enhances the toxicity of 131I-Metaiodobenzylguanidine/Topotecan combination therapy to cells and xenografts that express the noradrenaline transporter

Targeted radiotherapy using [131I]meta-iodobenzylguanidine ([131I]MIBG) has produced remissions in some neuroblastoma patients. We previously reported that combining [131I]MIBG with the topoisomerase I (Topo-I) inhibitor topotecan induced long-term DNA damage and supra-additive toxicity to NAT-expressing cells and xenografts. This combination treatment is undergoing clinical evaluation. This present study investigated the potential of PARP-1 inhibition, in vitro and in vivo, to further enhance [131I]MIBG/topotecan efficacy

Application of the Gaussian mixture model in pulsar astronomy -- pulsar classification and candidates ranking for {\it Fermi} 2FGL catalog

Machine learning, algorithms to extract empirical knowledge from data, can be used to classify data, which is one of the most common tasks in observational astronomy. In this paper, we focus on Bayesian data classification algorithms using the Gaussian mixture model and show two applications in pulsar astronomy. After reviewing the Gaussian mixture model and the related Expectation-Maximization algorithm, we present a data classification method using the Neyman-Pearson test. To demonstrate the method, we apply the algorithm to two classification problems. Firstly, it is applied to the well known period-period derivative diagram, where we find that the pulsar distribution can be modeled with six Gaussian clusters, with two clusters for millisecond pulsars (recycled pulsars) and the rest for normal pulsars. From this distribution, we derive an empirical definition for millisecond pulsars as $\frac{\dot{P}}{10^{-17}} \leq3.23(\frac{P}{100 \textrm{ms}})^{-2.34}$. The two millisecond pulsar clusters may have different evolutionary origins, since the companion stars to these pulsars in the two clusters show different chemical composition. Four clusters are found for normal pulsars. Possible implications for these clusters are also discussed. Our second example is to calculate the likelihood of unidentified \textit{Fermi} point sources being pulsars and rank them accordingly. In the ranked point source list, the top 5% sources contain 50% known pulsars, the top 50% contain 99% known pulsars, and no known active galaxy (the other major population) appears in the top 6%. Such a ranked list can be used to help the future follow-up observations for finding pulsars in unidentified \textit{Fermi} point sources.Comment: 9 pages, 4 figures, accepted by MNRA

Intake Characteristics of Diploid and Tetraploid Perennial Ryegrass Varieties when Grazed by Simmental x Holstein Yearling Heifers Under Rotational Stocking Management

Orr et al. (2003) measured large differences in dry matter (DM) intake rate between 15 intermediate-heading perennial ryegrass varieties when they were continuously stocked with sheep and subsequently explored the extent to which, for 5 of these varieties, these differences could be explained by chemical and morphological traits (Orr et al., 2004a) which could be targeted in grass breeding programmes. Here, four of the 15 varieties, which within ploidy had low or high intake characteristics when grazed by sheep, were rotationally stocked with cattle and intake and sward factors were measured