Variational treatment of electron-polyatomic molecule scattering calculations using adaptive overset grids

The Complex Kohn variational method for electron-polyatomic molecule scattering is formulated using an overset grid representation of the scattering wave function. The overset grid consists of a central grid and multiple dense, atom-centered subgrids that allow the simultaneous spherical expansions of the wave function about multiple centers. Scattering boundary conditions are enforced by using a basis formed by the repeated application of the free particle Green's function and potential, $\hat{G}^+_0\hat{V}$ on the overset grid in a "Born-Arnoldi" solution of the working equations. The theory is shown to be equivalent to a specific Pad\'e approximant to the $T$-matrix, and has rapid convergence properties, both in the number of numerical basis functions employed and the number of partial waves employed in the spherical expansions. The method is demonstrated in calculations on methane and CF$_4$ in the static-exchange approximation, and compared in detail with calculations performed with the numerical Schwinger variational approach based on single center expansions. An efficient procedure for operating with the free-particle Green's function and exchange operators (to which no approximation is made) is also described

Polarization and ellipticity of high-order harmonics from aligned molecules generated by linearly polarized intense laser pulses

We present theoretical calculations for polarization and ellipticity of high-order harmonics from aligned N$_2$, CO$_2$, and O$_2$ molecules generated by linearly polarized lasers. Within the rescattering model, the two polarization amplitudes of the harmonics are determined by the photo-recombination amplitudes for photons emitted parallel and perpendicular to the direction of the {\em same} returning electron wave packet. Our results show clear species-dependent polarization states, in excellent agreement with experiments. We further note that the measured polarization ellipse of the harmonic furnishes the needed parameters for a "complete" experiment in molecules.Comment: 4 pages, 4 figure

Probing molecular frame photoionization via laser generated high-order harmonics from aligned molecules

Present photoionization experiments cannot measure molecular frame photoelectron angular distributions (MFPAD) from the outermost valence electrons of molecules. We show that details of the MFPAD can be retrieved with high-order harmonics generated by infrared lasers from aligned molecules. Using accurately calculated photoionization transition dipole moments for fixed-in-space molecules, we show that the dependence of the magnitude and phase of the high-order harmonics on the alignment angle of the molecules observed in recent experiments can be quantitatively reproduced. This result provides the needed theoretical basis for ultrafast dynamic chemical imaging using infrared laser pulses.Comment: 5 pages, 4 figure

Quantitative Rescattering Theory for high-order harmonic generation from molecules

The Quantitative Rescattering Theory (QRS) for high-order harmonic generation (HHG) by intense laser pulses is presented. According to the QRS, HHG spectra can be expressed as a product of a returning electron wave packet and the photo-recombination differential cross section of the {\em laser-free} continuum electron back to the initial bound state. We show that the shape of the returning electron wave packet is determined mostly by the laser only. The returning electron wave packets can be obtained from the strong-field approximation or from the solution of the time-dependent Schr\"odinger equation (TDSE) for a reference atom. The validity of the QRS is carefully examined by checking against accurate results for both harmonic magnitude and phase from the solution of the TDSE for atomic targets within the single active electron approximation. Combining with accurate transition dipoles obtained from state-of-the-art molecular photoionization calculations, we further show that available experimental measurements for HHG from partially aligned molecules can be explained by the QRS. Our results show that quantitative description of the HHG from aligned molecules has become possible. Since infrared lasers of pulse durations of a few femtoseconds are easily available in the laboratory, they may be used for dynamic imaging of a transient molecule with femtosecond temporal resolutions.Comment: 50 pages, 15 figure

SOUR: an Outliers Detection Algorithm in Learning to Rank (Abstract)

Outlier data points are known to affect negatively the learning process of regression or classification models, yet their impact in the learning-to-rank scenario has not been thoroughly investigated so far. In this talk we present our effort to solve this research problem. The full version of this work will appear at ICTIR 2022 [1]. We designed SOUR, a learning-to-rank method that detects and removes outliers before building an effective ranking model. We limit our analysis to gradient boosting decision trees, but our algorithm can be easily adapted to handle different learning strategy, such as artificial Neural Network. SOUR searches for outlier instances that are consistently incorrectly ranked in several consecutive iterations of the learning process. We performed an extensive evaluation analysis on three publicly available datasets and we empirically demonstrated that i) removing a limited number of outlier data instances before re-training a new model, provides statistically significant improvements in term of effectiveness ii) SOUR outperforms state-of-the-art de-noising and outlier detection methods such as [2]. Finally, we investigated how the removal of the outliers affects the ensemble structure and we found that the ensemble leaves were purer when trained without the presence of the outliers

Filtering out Outliers in Learning to Rank

Outlier data points are known to affect negatively the learning process of regression or classification models, yet their impact in the learning-to-rank scenario has not been thoroughly investigated so far. In this work we propose SOUR, a learning-to-rank method that detects and removes outliers before building an effective ranking model. We limit our analysis to gradient boosting decision trees, where SOUR searches for outlier instances that are incorrectly ranked in several iterations of the learning process. Extensive experiments show that removing a limited number of outlier data instances before re-training a new model provides statistically significant improvements, and that SOUR outperforms state-of-the-art de-noising and outlier detection methods

GAM Forest Explanation

Most accurate machine learning models unfortunately produce black-box predictions, for which it is impossible to grasp the internal logic that leads to a specific decision. Unfolding the logic of such black-box models is of increasing importance, especially when they are used in sensitive decision-making processes. In this work we focus on forests of decision trees, which may include hundreds to thousands of decision trees to produce accurate predictions. Such complexity raises the need of developing explanations for the predictions generated by large forests. We propose a post hoc explanation method of large forests, named GAM-based Explanation of Forests (GEF), which builds a Generalized Additive Model (GAM) able to explain, both locally and globally, the impact on the predictions of a limited set of features and feature interactions. We evaluate GEF over both synthetic and real-world datasets and show that GEF can create a GAM model with high fidelity by analyzing the given forest only and without using any further information, not even the initial training dataset

Probing autoionizing states of molecular oxygen with XUV transient absorption: Electronic symmetry dependent lineshapes and laser induced modification

The dynamics of autoionizing Rydberg states of oxygen are studied using attosecond transient absorption technique, where extreme ultraviolet (XUV) initiates molecular polarization and near infrared (NIR) pulse perturbs its evolution. Transient absorption spectra show positive optical density (OD) change in the case of $ns\sigma_g$ and $nd\pi_g$ autoionizing states of oxygen and negative OD change for $nd\sigma_g$ states. Multiconfiguration time-dependent Hartree-Fock (MCTDHF) calculation are used to simulate the transient absorption spectra and their results agree with experimental observations. The time evolution of superexcited states is probed in electronically and vibrationally resolved fashion and we observe the dependence of decay lifetimes on effective quantum number of the Rydberg series. We model the effect of near-infrared (NIR) perturbation on molecular polarization and find that the laser induced phase shift model agrees with the experimental and MCTDHF results, while the laser induced attenuation model does not. We relate the electron state symmetry dependent sign of the OD change to the Fano parameters of the static absorption lineshapes.Comment: 15 pages, 8 figure

Uncovering multiple orbitals influence in high harmonic generation from aligned N2_2

Recent measurements on high-order harmonic generation (HHG) from N$_2$ aligned perpendicular to the driving laser polarization [B. K. McFarland {\it el al}, Science {\bf 322}, 1232 (2008)] have shown a maximum at the rotational half-revival. This has been interpreted as the signature of the HHG contribution from the molecular orbital just below the highest occupied molecular orbital (HOMO). By using the recently developed quantitative rescattering theory combined with accurate photoionization transition dipoles, we show that the maximum at the rotational half-revival is indeed associated with the HOMO-1 contribution. Our results also show that the HOMO-1 contribution becomes increasingly more important near the HHG cutoff and therefore depends on the laser intensity.Comment: 9 pages, 4 figure