A Dynamically Adaptive Sparse Grid Method for Quasi-Optimal Interpolation of Multidimensional Analytic Functions

In this work we develop a dynamically adaptive sparse grids (SG) method for quasi-optimal interpolation of multidimensional analytic functions defined over a product of one dimensional bounded domains. The goal of such approach is to construct an interpolant in space that corresponds to the "best $M$-terms" based on sharp a priori estimate of polynomial coefficients. In the past, SG methods have been successful in achieving this, with a traditional construction that relies on the solution to a Knapsack problem: only the most profitable hierarchical surpluses are added to the SG. However, this approach requires additional sharp estimates related to the size of the analytic region and the norm of the interpolation operator, i.e., the Lebesgue constant. Instead, we present an iterative SG procedure that adaptively refines an estimate of the region and accounts for the effects of the Lebesgue constant. Our approach does not require any a priori knowledge of the analyticity or operator norm, is easily generalized to both affine and non-affine analytic functions, and can be applied to sparse grids build from one dimensional rules with arbitrary growth of the number of nodes. In several numerical examples, we utilize our dynamically adaptive SG to interpolate quantities of interest related to the solutions of parametrized elliptic and hyperbolic PDEs, and compare the performance of our quasi-optimal interpolant to several alternative SG schemes

Deep Reinforcement Learning for Concentric Tube Robot Control with a Goal-Based Curriculum

Concentric Tube Robots (CTRs), a type of continuum robot, are a collection of concentric, pre-curved tubes composed of super elastic nickel titanium alloy. CTRs can bend and twist from the interactions between neighboring tubes causing the kinematics and therefore control of the end-effector to be very challenging to model. In this paper, we develop a control scheme for a CTR end-effector in Cartesian space with no prior kinematic model using a deep reinforcement learning (DRL) approach with a goal-based curriculum reward strategy. We explore the use of curricula by changing the goal tolerance through training with constant, linear and exponential decay functions. Also, relative and absolute joint representations as a way of improving training convergence are explored. Quantitative comparisons for combinations of curricula and joint representations are performed and the exponential decay relative approach is used for training a robust policy in a noise-induced simulation environment. Compared to a previous DRL approach, our new method reduces training time and employs a more complex simulation environment. We report mean Cartesian errors of 1.29 mm and a success rate of 0.93 with a relative decay curriculum. In path following, we report mean errors of 1.37 mm in a noise-induced path following task. Albeit in simulation, these results indicate the promise of using DRL in model free control of continuum robots and CTRs in particular

OPTIMAL WEIGHT AND DIALYSIS DOSE IN PATIENTS ON PERIODIC HEMODIALYSIS

Small patients tend to be better dialyzed than large ones. We analyzed the delivered dose of dialysis in two groups of patients - group A, body weight over 50 kg (n-39, m:f=28:l; 57,4 8,3 kg) and group B, body weight under 50 kg (n=15, m:f=6:9; 45,4 3,4 kg). We calculated KT/V and Time Average Concentration of urea (TAC) using two-pool method for urea kinetic modeling. The patients from group Ð’ had a higher KT/V urea =1,35 0,25 (p < 0,05) and lower TAC =13,7 2,72 (p < 0,05) with a shorter dialysis time. Mean serum protein and albumin levels for a year did not differ

Spectral observations of X Persei: Connection between H-alpha and X-ray emission

We present spectroscopic observations of the Be/X-ray binary X Per obtained during the period 1999 - 2018. Using new and published data, we found that during "disc-rise" the expansion velocity of the circumstellar disc is 0.4 - 0.7 km/s. Our results suggest that the disc radius in recent decades show evidence of resonant truncation of the disc by resonances 10:1, 3:1, and 2:1, while the maximum disc size is larger than the Roche lobe of the primary and smaller than the closest approach of the neutron star. We find correlation between equivalent width of H-alpha emission line ($W\alpha$) and the X-ray flux, which is visible when $15 \: \AA \: < W\alpha \le 40 \: \AA$. The correlation is probably due to wind Roche lobe overflow.Comment: Accepted for publication in Astronomy & Astrophysic

Connection between orbital modulation of H-alpha and gamma-rays in the Be/X-ray binary LSI+61303

We studied the average orbital modulation of various parameters (gamma-ray flux, H-alpha emission line, optical V band brightness) of the radio- and gamma-ray emitting Be/X-ray binary LSI+61303. Using the Spearman rank correlation test, we found highly significant correlations between the orbital variability of the equivalent width of the blue hump of the H-alpha and Fermi-LAT flux with a Spearman p-value 2e-5, and the equivalent widths ratio EW_B/EW_R and Fermi-LAT flux with p-value 9e-5. We also found a significant anti-correlation between Fermi-LAT flux and V band magnitude with p-value 7.10^{-4}. All these correlations refer to the average orbital variability, and we conclude that the H-alpha and gamma-ray emission processes in LSI+61303 are connected. The possible physical scenario is briefly discussed.Comment: accepted as a Letter in Astronomy and Astrophysic

ULTRASOUND AND COMPUTED TOMOGRAPHY IN LIVER HEMANGIOMAS

No abstrac