CERTIFYING CONFLUENCE PROOFS VIA RELATIVE TERMINATION AND RULE LABELING

The rule labeling heuristic aims to establish confluence of (left-)linear term rewrite systems via decreasing diagrams. We present a formalization of a confluence criterion based on the interplay of relative termination and the rule labeling in the theorem prover Isabelle. Moreover, we report on the integration of this result into the certifier CeTA, facilitating the checking of confluence certificates based on decreasing diagrams. The power of the method is illustrated by an experimental evaluation on a (standard) collection of confluence problems

Attosecond two-photon interferometry for doubly excited states of helium

We show that the correlation dynamics in coherently excited doubly excited resonances of helium can be followed in real time by two-photon interferometry. This approach promises to map the evolution of the two-electron wave packet onto experimentally easily accessible non-coincident single electron spectra. We analyze the interferometric signal in terms of a semi-analytical model which is validated by a numerical solution of the time-dependent two-electron Schr\"odinger equation in its full dimensionality.Comment: 5 pages, 4 figure

Probing Electron Correlation via Attosecond XUV Pulses in the Two-Photon Double Ionization of Helium

Recent experimental developments of high-intensity, short-pulse XUV light sources are enhancing our ability to study electron-electron correlations. We perform time-dependent calculations to investigate the so-called "sequential" regime (photon energy above 54.4 eV) in the two-photon double ionization of helium. We show that attosecond pulses allow to induce and probe angular and energy correlations of the emitted electrons. The final momentum distribution reveals regions dominated by the Wannier ridge break-up scenario and by post-collision interaction.Comment: 4 pages, 5 figure

Universal features in sequential and nonsequential two-photon double ionization of helium

We analyze two-photon double ionization of helium in both the nonsequential and sequential regime. We show that the energy spacing between the two emitted electrons provides the key parameter that controls both the energy and the angular distribution and reveals the universal features present in both the nonsequential and sequential regime. This universality, i.e., independence of photon energy, is a manifestation of the continuity across the threshold for sequential double ionization. For all photon energies, the energy distribution can be described by a universal shape function that contains only the spectral and temporal information entering second-order time-dependent perturbation theory. Angular correlations and distributions are found to be more sensitive to the photon energy. In particular, shake-up interferences have a large effect on the angular distribution. Energy spectra, angular distributions parameterized by the anisotropy parameters, and total cross sections presented in this paper are obtained by fully correlated time-dependent ab initio calculations.Comment: 12 pages, 8 figure

Improving automatic confluence analysis of rewrite systems by redundant rules

We describe how to utilize redundant rewrite rules, i.e., rules that can be simulated by other rules, when (dis)proving confluence of term rewrite systems. We demonstrate how automatic confluence provers benefit from the addition as well as the removal of redundant rules. Due to their simplicity, our transformations were easy to formalize in a proof assistant and are thus amenable to certification. Experimental results show the surprising gain in power

Spike Afterpotentials Shape the In Vivo Burst Activity of Principal Cells in Medial Entorhinal Cortex

Principal neurons in rodent medial entorhinal cortex (MEC) generate high-frequency bursts during natural behavior. While in vitro studies point to potential mechanisms that could support such burst sequences, it remains unclear whether these mechanisms are effective under in vivo conditions. In this study, we focused on the membrane-potential dynamics immediately following action potentials (APs), as measured in whole-cell recordings from male mice running in virtual corridors (Domnisoru et al., 2013). These afterpotentials consisted either of a hyperpolarization, an extended ramp-like shoulder, or a depolarization reminiscent of depolarizing afterpotentials (DAPs) recorded in vitro in MEC principal neurons. Next, we correlated the afterpotentials with the cells' propensity to fire bursts. All DAP cells with known location resided in Layer II, generated bursts, and their interspike intervals (ISIs) were typically between 5 and 15 ms. The ISI distributions of Layer-II cells without DAPs peaked sharply at around 4 ms and varied only minimally across that group. This dichotomy in burst behavior is explained by cell-group-specific DAP dynamics. The same two groups of bursting neurons also emerged when we clustered extracellular spike-train autocorrelations measured in real 2D arenas (Latuske et al., 2015). Apart from slight variations in grid spacing, no difference in the spatial coding properties of the grid cells across all three groups was discernible. Layer III neurons were only sparsely bursting (SB) and had no DAPs. As various mechanisms for modulating ion-channels underlying DAPs exist, our results suggest that temporal features of MEC activity can be altered while maintaining the cells' overall spatial tuning characteristics. SIGNIFICANCE STATEMENT Depolarizing afterpotentials (DAPs) are frequently observed in principal neurons from slice preparations of rodent medial entorhinal cortex (MEC), but their functional role in vivo is unknown. Analyzing whole-cell data from mice running on virtual tracks, we show that DAPs do occur during behavior. Cells with prominent DAPs are found in Layer II; their interspike intervals (ISIs) reflect DAP time-scales. In contrast, neither the rarely bursting cells in Layer III, nor the high-frequency bursters in Layer II, have a DAP. Extracellular recordings from mice exploring real 2D arenas demonstrate that grid cells within these three groups have similar spatial coding properties. We conclude that DAPs shape the temporal response characteristics of principal neurons in MEC with little effect on spatial properties

Attosecond streaking of correlated two-electron transitions in helium

We present fully ab initio simulations of attosecond streaking for ionization of helium accompanied by shake-up of the second electron. This process represents a prototypical case for strongly correlated electron dynamics on the attosecond timescale. We show that streaking spectroscopy can provide detailed information on the Eisenbud-Wigner-Smith time delay as well as on the infrared field dressing of both bound and continuum states. We find a novel contribution to the streaking delay that stems from the interplay of electron-electron and infrared-field interactions in the exit channel. We quantify all the contributions with attosecond precision and provide a benchmark for future experiments.Comment: 5 pages, 4 figure

Nonsequential two-photon double ionization of helium

We present accurate time-dependent ab initio calculations on fully differential and total integrated (generalized) cross sections for the nonsequential two-photon double ionization of helium at photon energies from 40 to 54 eV. Our computational method is based on the solution of the time-dependent Schroedinger equation and subsequent projection of the wave function onto Coulomb waves. We compare our results with other recent calculations and discuss the emerging similarities and differences. We investigate the role of electronic correlation in the representation of the two-electron continuum states, which are used to extract the ionization yields from the fully correlated final wave function. In addition, we study the influence of the pulse length and shape on the cross sections in time-dependent calculations and address convergence issues.Comment: 14 pages, 10 figures; final version (acknowledgements and reference added, typos fixed