ABSTRACT. We present spectrograph design details and initial radial velocity results from the PRL optical fiberfed high-resolution cross-dispersed echelle spectrograph (PARAS), which has recently been commissioned at the Mount Abu 1.2 m telescope in India. Data obtained as part of the postcommissioning tests with PARAS show velocity precision better than 2 m s À1 over a period of several months on bright RV standard stars. For observations of σ Dra, we report 1:7 m s À1 precision for a period of 7 months, and for HD 9407, we report 2:1 m s À1 over a period of 2 months. PARAS is capable of single-shot spectral coverage of 3800-9500 Å at a resolution of ∼67; 000. The RV results were obtained between 3800 and 6900 Å using simultaneous wavelength calibration with a thorium-argon (ThAr) hollow cathode lamp. The spectrograph is maintained under stable conditions of temperature with a precision of 0.01-0.02°C (rms) at 25.55°C and is enclosed in a vacuum vessel at pressure of 0:1 AE 0:03 mbar. The blaze peak efficiency of the spectrograph between 5000 and 6500 Å, including the detector, is ∼30%; it is ∼25% with the fiber transmission. The total efficiency, including spectrograph, fiber transmission, focal ratio degradation (FRD), and telescope (with 81% reflectivity) is ∼7% in the same wavelength region on a clear night with good seeing conditions. The stable point-spread function (PSF), environmental control, existence of a simultaneous calibration fiber, and availability of observing time make PARAS attractive for a variety of exoplanetary and stellar astrophysics projects. Future plans include testing of octagonal fibers for further scrambling of light and extensive calibration over the entire wavelength range up to 9500 Å using thorium-neon (ThNe) or uranium-neon (UNe) spectral lamps. Thus, we demonstrate how such highly stabilized instruments, even on small aperture telescopes, can contribute significantly to the ongoing radial velocity searches for low-mass planets around bright stars.

Similarity of equations of motion for the classical and quantum trajectories is used to introduce a friction term dependent on the wavefunction phase into the time-dependent Schrödinger equation. The term describes irreversible energy loss by the quantum system. The force of friction is proportional to the velocity of a quantum trajectory. The resulting Schrödinger equation is nonlinear, conserves wavefunction normalization, and evolves an arbitrary wavefunction into the ground state of the system (of appropriate symmetry if applicable). Decrease in energy is proportional to the average kinetic energy of the quantum trajectory ensemble. Dynamics in the high friction regime is suitable for simple models of reactions proceeding with energy transfer from the system to the environment. Examples of dynamics are given for single and symmetric and asymmetric double well potentials.

Pharmacometric modeling establishes causal quantitative relationship between administered dose, tissue exposures, desired and undesired effects and patient’s risk factors. These models are employed to de-risk drug development and guide precision medicine decisions. Recent technological advances rendered collecting real-time and detailed data easy. However, the pharmacometric tools have not been designed to handle heterogeneous, big data and complex models. The estimation methods are outdated to solve modern healthcare challenges. We set out to design a platform that facilitates domain specific modeling and its integration with modern analytics to foster innovation and readiness to data deluge in healthcare.New specialized estimation methodologies have been developed that allow dramatic performance advances in areas that have not seen major improvements in decades. New ODE solver algorithms, such as coefficient-optimized higher order integrators and new automatic stiffness detecting algorithms which are robust to frequent discontinuities, give rise to up to 4x performance improvements across a wide range of stiff and non-stiff systems seen in pharmacometric applications. These methods combine with JIT compiler techniques and further specialize the solution process on the individual systems, allowing statically-sized optimizations and discrete sensitivity analysis via forward-mode automatic differentiation, to further enhance the accuracy and performance of the solving and parameter estimation process. We demonstrate that when all of these techniques are combined with a validated clinical trial dosing mechanism and non-compartmental analysis (NCA) suite, real applications like NLME parameter estimation see run times halved while retaining the same accuracy. Meanwhile in areas with less prior optimization of software, like optimal experimental design, we see orders of magnitude performance enhancements. Together we show a fast and modern domain specific modeling framework which lays a platform for innovation via upcoming integrations with modern analytics.

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Global Sensitivity Analysis (GSA) methods are used to quantify the uncertainty in the output of a model with respect to the parameters. These methods allow practitioners to measure both parameters' individual contributions and the contribution of their interactions to the output uncertainty. GlobalSensitivity.jl is a Julia (Bezanson et al., 2017) package containing implementations of some of the most popular GSA methods. Currently it supports Delta

Recently, Neural Ordinary Differential Equations has emerged as a powerful framework for modeling physical simulations without explicitly defining the ODEs governing the system, but learning them via machine learning. However, the question: "Can Bayesian learning frameworks be integrated with Neural ODE's to robustly quantify the uncertainty in the weights of a Neural ODE?" remains unanswered. In an effort to address this question, we demonstrate the successful integration of Neural ODEs with two methods of Bayesian Inference: (a) The No-U-Turn MCMC sampler (NUTS) and (b) Stochastic Langevin Gradient Descent (SGLD). We test the performance of our Bayesian Neural ODE approach on classical physical systems, as well as on standard machine learning datasets like MNIST, using GPU acceleration. Finally, considering a simple example, we demonstrate the probabilistic identification of model specification in partially-described dynamical systems using universal ordinary differential equations. Together, this gives a scientific machine learning tool for probabilistic estimation of epistemic uncertainties.

Mt. Abu Faint Object Spectrograph and Camera (MFOSC-P) is an in-house developed instrument for Physical Research Laboratory (PRL) 1.2m telescope at Mt. Abu India, commissioned in February 2019. Here we present the first science results derived from the low resolution spectroscopy program of a sample of M Dwarfs carried out during the commissioning run of MFOSC-P between February-June 2019. M dwarfs carry great significance for exoplanets searches in habitable zone and are among the promising candidates for the observatory's several ongoing observational campaigns. Determination of their accurate atmospheric properties and fundamental parameters is essential to constrain both their atmospheric and evolutionary models. In this study, we provide a low resolution (R∼500) spectroscopic catalogue of 80 bright M dwarfs (J<10) and classify them using their optical spectra. We have also performed the spectral synthesis and χ 2 minimisation techniques to determine their fundamental parameters viz. effective temperature and surface gravity by comparing the observed spectra with the most recent BT-Settl synthetic spectra. Spectral type of M dwarfs in our sample ranges from M0 to M5. The derived effective temperature and surface gravity are ranging from 4000 K to 3000 K and 4.5 to 5.5 dex, respectively. In most of the cases, the derived spectral types are in good agreement with previously assigned photometric classification.

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