Generalized Effective Reducibility

We introduce two notions of effective reducibility for set-theoretical statements, based on computability with Ordinal Turing Machines (OTMs), one of which resembles Turing reducibility while the other is modelled after Weihrauch reducibility. We give sample applications by showing that certain (algebraic) constructions are not effective in the OTM-sense and considerung the effective equivalence of various versions of the axiom of choice

Where and When: {S}pace-Time Attention for Audio-Visual Explanations

Explaining the decision of a multi-modal decision-maker requires to determine the evidence from both modalities. Recent advances in XAI provide explanations for models trained on still images. However, when it comes to modeling multiple sensory modalities in a dynamic world, it remains underexplored how to demystify the mysterious dynamics of a complex multi-modal model. In this work, we take a crucial step forward and explore learnable explanations for audio-visual recognition. Specifically, we propose a novel space-time attention network that uncovers the synergistic dynamics of audio and visual data over both space and time. Our model is capable of predicting the audio-visual video events, while justifying its decision by localizing where the relevant visual cues appear, and when the predicted sounds occur in videos. We benchmark our model on three audio-visual video event datasets, comparing extensively to multiple recent multi-modal representation learners and intrinsic explanation models. Experimental results demonstrate the clear superior performance of our model over the existing methods on audio-visual video event recognition. Moreover, we conduct an in-depth study to analyze the explainability of our model based on robustness analysis via perturbation tests and pointing games using human annotations

A Reference Section Through Fast-Spread Lower Oceanic Crust, Wadi Gideah, Samail Ophiolite (Sultanate of Oman): Petrography and Petrology

In the absence of a complete profile through fast-spreading modern oceanic crust, we established a reference profile through the whole paleo crust of the Samail ophiolite (Sultanate of Oman), which is regarded as the best analogue for fast-spreading oceanic crust on land. To establish a coherent data set, we sampled the Wadi Gideah in the Wadi-Tayin massif from the mantle section up to the sheeted dikes and performed different analytical and structural investigations on the same suite of samples. This paper reports our studies of the lower crust, a 5 km thick pile of gabbros, focusing on petrographic features and on the results of mineral analyses. Depth profiles of mineral compositions combined with petrological modeling reveal insights into the mode of magmatic formation of fast-spreading lower oceanic crust, implying a hybrid accretion mechanism. The lower two thirds of the crust, mainly consisting of layered gabbros, formed via the injection of melt sills and in situ crystallization. Here, upward moving fractionated melts mixed with more primitive melts through melt replenishments, resulting in a slight but distinct upward differentiation trend. The upper third of the gabbroic crust is significantly more differentiated, in accord with a model of downward differentiation of a primitive parental melt originated from the axial melt lens located at the top of the gabbroic crust. Our hybrid model for crustal accretion requires a system to cool the deep crust, which was established by hydrothermal fault zones, initially formed on-axis at very high temperatures

Influence of subunit structure on the oligomerization state of light harvesting complexes: a free energy calculation study

Light harvesting complexes 2 (LH2) from Rhodospirillum (Rs.) molischianum and Rhodopseudomonas (Rps.) acidophila form ring complexes out of eight or nine identical subunits, respectively. Here, we investigate computationally what factors govern the different ring sizes. Starting from the crystal structure geometries, we embed two subunits of each species into their native lipid-bilayer/water environment. Using molecular dynamics simulations with umbrella sampling and steered molecular dynamics, we probe the free energy profiles along two reaction coordinates, the angle and the distance between two subunits. We find that two subunits prefer to arrange at distinctly different angles, depending on the species, at about 42.5 deg for Rs. molischianum and at about 38.5 deg for Rps. acidophila, which is likely to be an important factor contributing to the assembly into different ring sizes. Our calculations suggest a key role of surface contacts within the transmembrane domain in constraining these angles, whereas the strongest interactions stabilizing the subunit dimers are found in the C-, and to a lesser extent, N-terminal domains. The presented computational approach provides a promising starting point to investigate the factors contributing to the assembly of protein complexes, in particular if combined with modeling of genetic variants.Comment: 28 pages, 7 figures, LaTeX2e - requires elsart.cls (included), submitted to Chemical Physic

Petrogenesis of crustal wehrlites in the Oman ophiolite: Experiments and natural rocks

In the Wadi Haymiliyah of the Oman ophiolite (Haylayn block), discordant wehrlite bodies ranging in size from tens to hundreds of meters intrude the lower crust at different levels. We combined investigations on natural wehrlites from the Wadi Haymiliyah section with an experimental study on the phase relations in a wehrlitic system in order to constrain the petrogenesis of the crustal wehrlites of the Oman ophiolite. Secondary ion mass spectrometry analyses of clinopyroxenes from different wehrlite bodies imply that the clinopyroxenes were crystallized from tholeiitic, mid-ocean ridge (MORB)–type melts. The presence of primary magmatic amphiboles in some wehrlites suggests a formation under hydrous conditions. Significantly enhanced 87Sr/86Sr isotope ratios of separates from these amphiboles imply that the source of the corresponding magmatic fluids was either seawater or subduction zone–related. The experiments revealed that under wet conditions at relatively low temperatures, a MORB magma has the potential to produce wehrlite in the ocean crust by accumulation of early olivine and clinopyroxene. These show typically high Mg# which is a consequence of the oxidizing effect of the prevailing high aH2O. First plagioclases crystallizing after clinopyroxene under wet conditions are high in An content, in contrast to the corresponding dry system. Trace element compositions of clinopyroxenes of those wehrlites from the Moho transition zone are too depleted in HREE to be in equilibrium with present-day MORB, implying a genetic relation to the V2 lavas of the Oman ophiolite, which are interpreted to be the result of fluidenhanced melting of previously depleted mantle. We present a model on the petrogenesis of the crustal wehrlites in an upper mantle wedge above an initial, shallow subduction zone at the beginning of the intraoceanic thrusting

Excitons in a Photosynthetic Light-Harvesting System: A Combined Molecular Dynamics/Quantum Chemistry and Polaron Model Study

The dynamics of pigment-pigment and pigment-protein interactions in light-harvesting complexes is studied with a novel approach which combines molecular dynamics (MD) simulations with quantum chemistry (QC) calculations. The MD simulations of an LH-II complex, solvated and embedded in a lipid bilayer at physiological conditions (with total system size of 87,055 atoms) revealed a pathway of a water molecule into the B800 binding site, as well as increased dimerization within the B850 BChl ring, as compared to the dimerization found for the crystal structure. The fluctuations of pigment (B850 BChl) excitation energies, as a function of time, were determined via ab initio QC calculations based on the geometries that emerged from the MD simulations. From the results of these calculations we constructed a time-dependent Hamiltonian of the B850 exciton system from which we determined the linear absorption spectrum. Finally, a polaron model is introduced to describe quantum mechanically both the excitonic and vibrational (phonon) degrees of freedom. The exciton-phonon coupling that enters into the polaron model, and the corresponding phonon spectral function are derived from the MD/QC simulations. It is demonstrated that, in the framework of the polaron model, the absorption spectrum of the B850 excitons can be calculated from the autocorrelation function of the excitation energies of individual BChls, which is readily available from the combined MD/QC simulations. The obtained result is in good agreement with the experimentally measured absorption spectrum.Comment: REVTeX3.1, 23 pages, 13 (EPS) figures included. A high quality PDF file of the paper is available at http://www.ks.uiuc.edu/Publications/Papers/PDF/DAMJ2001/DAMJ2001.pd