The spectral characteristics of dextran, labeled with fluorescein, depend upon pH. We have loaded the lysosomes of mouse peritoneal macrophages with this fluorescence probe and used it to measure the intralysosomal pH under various conditions. The pH of the medium has no effect on the intralysosomal pH. Weakly basic substances in the medium cause a concentration-dependent increase in the intralysosomal pH. However, the concentration of base necessary to produce a significant change in the intralysosomal pH varies over a wide range for different bases. The active form of the base is the neutral, unprotonated form. Although most of these weak bases cause an increase in the volume of the lysosomes, increase in lysosomal volume itself causes only a minor perturbation of the intralysosomal pH. This was demonstrated in cells whose lysosomes were loaded with sucrose, and in cells vacuolated as a demonstrated in cells whose lysosomes were loaded with sucrose, and in cells vacuolated as a consequence of exposure to concanavalin A. The results of these studies are interpreted in terms of energy-dependent lysosomal acidification and leakage of protons out of the lysosomes in the form of protonated weak bases.
Stiff dynamical systems represent a central challenge in multi scale modeling across combustion, chemical kinetics, and nonlinear dynamical systems. Neural operator learning has recently emerged as a promising approach to approximate dynamical generators from data, yet stiffness imposes severe obstacles: training errors concentrate on slow manifold states, collapse of fast dynamics occurs, and the learned operator may fail to reproduce the true eigenstructure. We demonstrate three key advances enabling accurate learning of stiff operators and preserving spectral fidelity: (i) stiffness aware scaling of time derivatives, (ii) fast direction excitation via local trajectory cloud bursts, and (iii) autograd-based Jacobian diagnostics ensuring eigenstructure fidelity. Applied to the Davis-Skodje system, the approach recovers both slow and fast modes across stiffness regimes, reducing fast eigenvalue error by an order of magnitude while improving rollout fidelity. These results argue that spectral fidelity - not trajectory accuracy alone - should be a first-class target in data driven learning of stiff operators.
Density functional theory has become the world's favorite electronic structure method, and is routinely applied to both materials and molecules. Here, we review recent attempts to use modern machine-learning to improve density functional approximations. Many different researchers have tried many different approaches, but some common themes and lessons have emerged. We discuss these trends and where they might bring us in the future.
Antonio Stanziola, Simon Arridge, Ben T. Cox
et al.
A new method for solving the wave equation is presented, called the learned Born series (LBS), which is derived from a convergent Born Series but its components are found through training. The LBS is shown to be significantly more accurate than the convergent Born series for the same number of iterations, in the presence of high contrast scatterers, while maintaining a comparable computational complexity. The LBS is able to generate a reasonable prediction of the global pressure field with a small number of iterations, and the errors decrease with the number of learned iterations.
Finite-element simulations of magnetostatic fields are performed in terms of magnetic vector and total scalar potentials and compared for purpose of modeling the accelerator magnets. The potentials represent the unknown variables associated with the A and V formulations of magnetostatics to describe the magnetic fields. The simulations are carried out with a single software package, the COMSOL Multiphysics, where both formulations are implemented. The numerical performance of these methods is illustrated with the model example of a superconducting dipole magnet recently developed for operation in the isochronous cyclotron SC200. The results of calculations are analyzed and compared in terms of the relevant FEM parameters accounting for performance of computation as well as the computational cost. We show in particular that the use of scalar potential as compared to its vector counterpart substantially reduces the number of degrees of freedom, the usage of computer memory and the computational time for a similar relative error.
We propose a novel discrete method of constructing Gaussian Random Fields (GRF) based on a combination of modified spectral representations, Fourier and Blob. The method is intended for Direct Numerical Simulations of the V-Langevin equations. The latter are stereotypical descriptions of anomalous stochastic transport in various physical systems. From an Eulerian perspective, our method is designed to exhibit improved convergence rates. From a Lagrangian perspective, our method others a pertinent description of particle trajectories in turbulent velocity fields: the exact Lagrangian invariant laws are well reproduced. From a computational perspective, our method is twice as fast as standard numerical representations.
A new explicitly correlated functional form for expanding the wave function of an N-particle system with arbitrary angular momentum and parity is presented. We develop the projection-based approach, numerically exploited in our previous work [J. Chem. Phys. 149, 184105 (2018)], to explicitly correlated Gausssians with one-axis shifted centers and derive the matrix elements for the Hamiltonian and the angular momentum operators by analytically solving the integral projection operator. Variational few-body calculations without assuming the Born-Oppenheimer approximation are presented for several rotationally excited states of three- and four-particle systems. We show how the new formalism can be used as a unified framework for high-accuracy calculations of properties of small atoms and molecules.
In this paper we present a C++ implementation of the analytic derivative of a feed-forward neural network with respect to its free parameters for an arbitrary architecture, known as back-propagation. We dubbed this code NNAD (Neural Network Analytic Derivatives) and interfaced it with the widely-used ceres-solver minimiser to fit neural networks to pseudodata in two different least-squares problems. The first is a direct fit of Legendre polynomials. The second is a somewhat more involved minimisation problem where the function to be fitted takes part in an integral. Finally, using a consistent framework, we assess the efficiency of our analytic derivative formula as compared to numerical and automatic differentiation as provided by ceres-solver. We thus demonstrate the advantage of using NNAD in problems involving both deep or shallow neural networks.