Duncan Little

The size of a website’s active user base directly affects its value. Thus, it is important to monitor and influence a user’s likelihood to return to a site. Essential to this is predicting when a user will return. Current state of the art approaches to solve this problem come in two flavors: (1) Recurrent Neural Network (RNN) based solutions and (2) survival analysis methods. We observe that both techniques are severely limited when applied to this problem. Survival models can only incorpo-… Show more

The size of a website’s active user base directly affects its value. Thus, it is important to monitor and influence a user’s likelihood to return to a site. Essential to this is predicting when a user will return. Current state of the art approaches to solve this problem come in two flavors: (1) Recurrent Neural Network (RNN) based solutions and (2) survival analysis methods. We observe that both techniques are severely limited when applied to this problem. Survival models can only incorpo- rate aggregate representations of users instead of automatically learning a representation directly from a raw time series of user actions. RNNs can automatically learn features, but can not be directly trained with ex- amples of non-returning users who have no target value for their return time. We develop a novel RNN survival model that removes the limita- tions of the state of the art methods. We demonstrate that this model can successfully be applied to return time prediction on a large e-commerce dataset with a superior ability to discriminate between returning and non-returning users than either method applied in isolation. Show less

Cross sections are presented for dissociative recombination and electron-impact vibrational excitation of the ArH+ molecular ion at electron energies appropriate for the interstellar environment. The R-matrix method is employed to determine the molecular structure data, i.e. the position and width of the resonance states. The cross sections and the corresponding Maxwellian rate coefficients are computed using a method based on the Multichannel Quantum Defect Theory. The main result of the paper… Show more

Cross sections are presented for dissociative recombination and electron-impact vibrational excitation of the ArH+ molecular ion at electron energies appropriate for the interstellar environment. The R-matrix method is employed to determine the molecular structure data, i.e. the position and width of the resonance states. The cross sections and the corresponding Maxwellian rate coefficients are computed using a method based on the Multichannel Quantum Defect Theory. The main result of the paper is the very low dissociative recombination rate found at temperatures below 1000K. This is in agreement with the previous upper limit measurement in merged beams and offers a realistic explanation to the presence of ArH+ in exotic interstellar conditions. Show less

We investigate the formation of multiple-core-hole states of molecular nitrogen interacting with a free-electron laser pulse. In previous work, we obtained bound and continuum molecular orbitals in the single-center expansion scheme and used these orbitals to calculate photo-ionization and Auger decay rates. We extend our formulation to track the proportion of the population that accesses single-site versus two-site double-core-hole states, before the formation of the final atomic ions. We… Show more

We investigate the formation of multiple-core-hole states of molecular nitrogen interacting with a free-electron laser pulse. In previous work, we obtained bound and continuum molecular orbitals in the single-center expansion scheme and used these orbitals to calculate photo-ionization and Auger decay rates. We extend our formulation to track the proportion of the population that accesses single-site versus two-site double-core-hole states, before the formation of the final atomic ions. We investigate the pulse parameters that favor the formation of the single-site and two-site double-core-hole states as well as triple-core-hole states for 525 eV and 1100 eV photons. Show less

Random forests are among the most popular classification and regression methods used in industrial applications. To be effective, the parameters of random forests must be carefully tuned. This is usually done by choosing values that minimize the prediction error on a held out dataset. We argue that error reduction is only one of several metrics that must be considered when optimizing random forest parameters for commercial applications. We propose a novel metric that captures the stability of… Show more

Random forests are among the most popular classification and regression methods used in industrial applications. To be effective, the parameters of random forests must be carefully tuned. This is usually done by choosing values that minimize the prediction error on a held out dataset. We argue that error reduction is only one of several metrics that must be considered when optimizing random forest parameters for commercial applications. We propose a novel metric that captures the stability of random forest predictions, which we argue is key for scenarios that require successive predictions. We motivate the need for multi-criteria optimization by showing that in practical applications, simply choosing the parameters that lead to the lowest error can introduce unnecessary costs and produce predictions that are not stable across independent runs. To optimize this multi-criteria trade-off, we present a new framework that efficiently finds a principled balance between these three considerations using Bayesian optimisation. The pitfalls of optimising forest parameters purely for error reduction are demonstrated using two publicly available real world datasets. We show that our framework leads to parameter settings that are markedly different from the values discovered by error reduction metrics alone. Show less

We compute molecular continuum orbitals in the single center expansion scheme. We then employ these orbitals to obtain molecular Auger rates and single-photon ionization cross sections to study the interaction of N2 with Free-Electron-Laser (FEL) pulses. The nuclei are kept fixed. We formulate rate equations for the energetically allowed molecular and atomic transitions and we account for dissociation through additional terms in the rate equations. Solving these equations for different… Show more

We compute molecular continuum orbitals in the single center expansion scheme. We then employ these orbitals to obtain molecular Auger rates and single-photon ionization cross sections to study the interaction of N2 with Free-Electron-Laser (FEL) pulses. The nuclei are kept fixed. We formulate rate equations for the energetically allowed molecular and atomic transitions and we account for dissociation through additional terms in the rate equations. Solving these equations for different parameters of the FEL pulse, allows us to identify the most efficient parameters of the FEL pulse for obtaining the highest contribution of double core hole states (DCH) in the final atomic ion fragments. Finally we identify the contribution of DCH states in the electron spectra and show that the DCH state contribution is more easily identified in the photo-ionization rather than the Auger transitions. Show less

TIMEDELn implements the time-delay method of determining resonance parameters from the characteristic Lorentzian form displayed by the largest eigenvalues of the time-delay matrix. TIMEDELn constructs the time-delay matrix from input K-matrices and analyses its eigenvalues. This new version implements multi-resonance fitting and may be run serially or as a high performance parallel code with three levels of parallelism. TIMEDELn takes K-matrices from a scattering calculation, either read from a… Show more

TIMEDELn implements the time-delay method of determining resonance parameters from the characteristic Lorentzian form displayed by the largest eigenvalues of the time-delay matrix. TIMEDELn constructs the time-delay matrix from input K-matrices and analyses its eigenvalues. This new version implements multi-resonance fitting and may be run serially or as a high performance parallel code with three levels of parallelism. TIMEDELn takes K-matrices from a scattering calculation, either read from a file or calculated on a dynamically adjusted grid, and calculates the time-delay matrix. This is then diagonalized, with the largest eigenvalue representing the longest time-delay experienced by the scattering particle. A resonance shows up as a characteristic Lorentzian form in the time-delay: the program searches the time-delay eigenvalues for maxima and traces resonances when they pass through different eigenvalues, separating overlapping resonances. It also performs the fitting of the calculated data to the Lorentzian form and outputs resonance positions and widths. Any remaining overlapping resonances can be fitted jointly. The branching ratios of decay into the open channels can also be found. The program may be run serially or in parallel with three levels of parallelism. The parallel code modules are abstracted from the main physics code and can be used independently. Show less

Cross sections for the dissociative recombination of N+2 for v+i=0–3 are computed using multichannel quantum defect theory with molecular data generated using the R-matrix method. The calculation is completely ab initio and includes three electronic cores of the ion. Extensive comparisons are made with previous experimental and theoretical studies. Our cross section is in excellent agreement with experimental results and other theoretical results. Cross sections and isotropic rate coefficients… Show more

Cross sections for the dissociative recombination of N+2 for v+i=0–3 are computed using multichannel quantum defect theory with molecular data generated using the R-matrix method. The calculation is completely ab initio and includes three electronic cores of the ion. Extensive comparisons are made with previous experimental and theoretical studies. Our cross section is in excellent agreement with experimental results and other theoretical results. Cross sections and isotropic rate coefficients are provided for all computed vibrational levels. Show less

Resonant vibrational excitation cross sections and the corresponding rate coefficients for electron–N2 collisions occurring through the N2- (X 2\Pi g)$ resonant state are reviewed. New calculations are performed using accurate potential energy curves for the N2 electronic ground state, taken from the literature, and for the N2- resonant state, obtained from R-matrix calculations. The calculations are extended to resonant excitation processes involving the N2 ground state vibrational… Show more

Resonant vibrational excitation cross sections and the corresponding rate coefficients for electron–N2 collisions occurring through the N2- (X 2\Pi g)$ resonant state are reviewed. New calculations are performed using accurate potential energy curves for the N2 electronic ground state, taken from the literature, and for the N2- resonant state, obtained from R-matrix calculations. The calculations are extended to resonant excitation processes involving the N2 ground state vibrational continuum, leading to dissociation. Electron-impact dissociation is found to be significant from higher vibrational levels. Accurate analytical fits for the complete set of the rate coefficients are provided. The behavior of the dissociative cross sections is investigated for rotationally excited N2 molecules, with J = 50, 100 and 150, and for different vibrational levels. Show less

A systematic calculation of the positions and widths of the resonances converging on the first two excited states of N2+ (A2Pi u and B 2Sigma u+) is presented. A closely-spaced grid of geometries is used to give continuous resonance curves without the need for curve fitting. Three methods, fitting the eigenphase sum, the time-delay method and the R-matrix specific QB method, are tested. Fits to the longest three time-delays are found to give the most reliable and complete determination of the… Show more

A systematic calculation of the positions and widths of the resonances converging on the first two excited states of N2+ (A2Pi u and B 2Sigma u+) is presented. A closely-spaced grid of geometries is used to give continuous resonance curves without the need for curve fitting. Three methods, fitting the eigenphase sum, the time-delay method and the R-matrix specific QB method, are tested. Fits to the longest three time-delays are found to give the most reliable and complete determination of the resonance parameters. The low excitation energies of the A and B ion states results in complex resonance features with many avoided crossings leading to pronounced structures in both the resonance curves and the associated widths. The resonance curves likely to be important for dissociative recombination are identified. Their positions generally agree well with the calculations of Guberman, although in some cases their widths are narrower. Full data on all curves is provided. Show less

Potential energy curves for electronically excited states of molecular nitrogen are calculated using three different ab initio procedures. The most comprehensive of these involves the use of scattering calculations, performed at negative energy using the UK molecular R-matrix method. Such calculations are used to characterize all the Rydberg states of N2 with n ≤ 6 and ℓ ≤ 4 as well as many higher states including some Rydberg states associated with the first excited A 2Πu state of N2+. Many of… Show more

Potential energy curves for electronically excited states of molecular nitrogen are calculated using three different ab initio procedures. The most comprehensive of these involves the use of scattering calculations, performed at negative energy using the UK molecular R-matrix method. Such calculations are used to characterize all the Rydberg states of N2 with n ≤ 6 and ℓ ≤ 4 as well as many higher states including some Rydberg states associated with the first excited A 2Πu state of N2+. Many of these states are previously unknown. The calculations are performed at a dense grid of internuclear separations allowing the many avoided crossings present in the system to be mapped out in detail. Extensive comparisons are made with the previously available data for excited states of N2. Show less