Miracle-dz/UniFAR-FTUs huggingface dataset:
Solution of Linear Systems and Matrix Inversion in the TT-Format

Tensors arise naturally in high-dimensional problems in chemistry, financial mathematics, and many other areas. The numerical treatment of such problems is difficult due to the curse of dimensionality: the number of unknowns and the computational complexity grow exponentially with the dimension of the problem. To break the curse of dimensionality, low-parametric representations, or formats, have to be used. In this paper we make use of the TT-format (tensor-train format) which is one of the most effective stable representations of high-dimensional tensors. Basic linear algebra operations in the TT-format are now well developed. Our goal is to provide a “black-box” type of solver for linear systems where both the matrix and the right-hand side are in the TT-format. An efficient DMRG (density matrix renormalization group) method is proposed, and several tricks are employed to make it work. The numerical experiments confirm the effectiveness of our approach.
ngram-OAXE: Phrase-Based Order-Agnostic Cross Entropy for Non-Autoregressive Machine Translation

Recently, a new training oaxe loss has proven effective to ameliorate the effect of multimodality for non-autoregressive translation (NAT), which removes the penalty of word order errors in the standard cross-entropy loss. Starting from the intuition that reordering generally occurs between phrases, we extend oaxe by only allowing reordering between ngram phrases and still requiring a strict match of word order within the phrases. Extensive experiments on NAT benchmarks across language pairs and data scales demonstrate the effectiveness and universality of our approach. Further analyses show that ngram noaxe indeed improves the translation of ngram phrases, and produces more fluent translation with a better modeling of sentence structure.
Multi-level quasi-Monte Carlo finite element methods for a class of elliptic partial differential equations with random coefficients

Quasi-Monte Carlo (QMC) methods are applied to multi-level Finite Element (FE) discretizations of elliptic partial differential equations (PDEs) with a random coefficient, to estimate expected values of linear functionals of the solution. The expected value is considered as an infinite-dimensional integral in the parameter space corresponding to the randomness induced by the random coefficient. We use a multi-level algorithm, with the number of QMC points depending on the discretization level, and with a level-dependent dimension truncation strategy. In some scenarios, we show that the overall error is $\mathcal{O}(h^2)$, where $h$ is the finest FE mesh width, or $\mathcal{O}(N^{-1+\delta})$ for arbitrary $\delta>0$, where $N$ is the maximal number of QMC sampling points. For these scenarios, the total work is essentially of the order of one single PDE solve at the finest FE discretization level. The analysis exploits regularity of the parametric solution with respect to both the physical variables (the variables in the physical domain) and the parametric variables (the parameters corresponding to randomness). Families of QMC rules with "POD weights" ("product and order dependent weights") which quantify the relative importance of subsets of the variables are found to be natural for proving convergence rates of QMC errors that are independent of the number of parametric variables.
Carbon cycling and burial in New Zealand's fjords

Understanding carbon cycling in continental margin settings is critical for constraining the global carbon cycle. Here we apply a multiproxy geochemical approach to evaluate regional carbon cycle dynamics in six New Zealand fjords. Using carbon and nitrogen concentrations and isotopes, lipid biomarkers, and redox‐sensitive element concentrations, we show that the New Zealand fjords have carbon‐rich surface sediments in basins that promote long‐term storage (i.e., semirestricted basins with sediment accumulation rates of up to 4 mm yr−1). Using δ13C distributions to develop a mixing model, we find that organic carbon in fjord sediments is well‐mixed from marine and terrestrial sources in down‐fjord gradients. This is driven by high regional precipitation rates of >6 m yr−1, which promote carbon accumulation in fjord basins through terrestrial runoff. In addition, we have identified at least two euxinic subbasins, based on uranium, molybdenum, iron, and cadmium enrichment, that contain >7% organic carbon. Because the strength and position of the Southern Hemisphere westerly winds control precipitation and fjord circulation, carbon delivery and storage in the region are intimately linked to westerly wind variability. We estimate that the fjord region (759 km2) may be exporting up to 1.4 × 107 kgC yr−1, outpacing other types of continental margins in rates of carbon burial by up to 3 orders of magnitude.
Griffith Taylor, Ernest Andrews et al.: early ideas on the development of the river systems of the Sydney region, eastern Australia, and subsequent ideas on the associated geomorphological problems

Abstract Thomas Griffith Taylor was one of Australia's leading geoscientists in the early twentieth century. He also developed ideas on race and environment at Sydney University, supposing that brachycephalic people had greater intellectual capacity than dolichocephalics, so that Chinese settlement in Australia was desirable. In consequence, Taylor's promotion at Sydney University was blocked. He therefore moved to a chair at Chicago, and thence to Toronto. He retired to Sydney in 1951 and in his old age published a classic study of the landforms of the region: Sydneyside Scenery (1958, published by Angus & Robertson, Sydney). This little book, although scientifically somewhat dated even at the time of its publication, summarized Taylor's earlier geomorphological ideas about Sydney and its hinterland. It applied Davisian ideas to the Sydney region, harking back to the work that Taylor and others had done in the early twentieth century. Taylor's ideas about the Sydney region's river patterns are described and their relationship to supposed Earth movements. In particular, Davisian ideas about river capture and antecedent drainage, and the topography of the Blue Mountains, are discussed in relation to the empirical information and theoretical ideas available in the early twentieth century. Taylor's ideas, as described in 1958, seem(ed) plausible, but they were subsequently thrown in doubt or invalidated by consideration of the form of diatremes in the Blue Mountains, by new geological theory, new data about the ages of rocks and minerals and estimates of the timing of Earth movements, closer mapping of structures, etc. The case exemplifies both the explanatory power, and the weaknesses, of Davisian geomorphology. E.C. Andrews preceded Taylor in introducing American geomorphological ideas into Australia and propounded the idea of Late Tertiary–Pleistocene uplift in eastern Australia, which was held responsible for many of the features that Taylor described. Other important contributors were W. G. Woolnough (1876–1958) and T. W. E. David (1858–1934), who taught Woolnough, Andrews and Taylor. A consensual view of the geomorphological and tectonic history of the Sydney region has still not been achieved.
Exterior mass estimates and $L^2$ restriction bounds for Neumann data along hypersurfaces

We study the problem of estimating the $L^2$ norm of Laplace eigenfunctions on a compact Riemannian manifold $M$ when restricted to a hypersurface $H$. We prove mass estimates for the restrictions of eigenfunctions $\phi_h$, $(h^2 \Delta - 1)\phi_h = 0$, to $H$ in the region exterior to the coball bundle of $H$, on $h^{\delta}$-scales ($0\leq \delta < 2/3$). We use this estimate to obtain an $O(1)$ $L^2$-restriction bound for the Neumann data along $H. $ The estimate also applies to eigenfunctions of semiclassical Schr\"odinger operators.
Calculating the optimal time when albedo approximates its daily average: an example using soil surfaces with various roughnesses at different latitudes

This paper describes how the blue-sky albedo of soil varies during the whole year from midday to sunset under clear-sky conditions. A hemispherical-directional reflectance model was used to calculate albedo variations associated with smooth, moderate and rough soil surfaces, located between the latitude angles of 75° in the Northern and Southern Hemispheres. We calculate the time when the albedo, acquired by an instantaneous observation, best represents its daily averaged value. This optimal time range is assessed in the context of remote-sensing satellite technology.
New oxygen isotope evidence for long-term Cretaceous climatic change in the Southern Hemisphere

A new composite δ 18 O record, generated from calcareous fine-fraction and bulk sediments from the Exmouth Plateau, details long-term Cretaceous climatic change at mid-latitudes in the Southern Hemisphere. Assessment of new and previously published δ 18 O data indicates that a mid-Cretaceous global climatic optimum was achieved sometime between the time of the Cenomanian-Turonian boundary and the middle Turonian, when surface-ocean paleotemperatures were the highest of the past 115 m.y. Periods of cooling and warming that reversed the general patterns were superimposed on long-term Aptian-Turonian warming and Turonian-Maastrichtian cooling trends, respectively. Extrapolation of Southern Hemisphere paleotemperature trends to Maastrichtian paleotemperature data from a low-latitude Pacific guyot implies that maximum mid-Cretaceous low-latitude paleotemperatures could have been in excess of 33 °C.
An investigation of the magnetic carriers and demagnetization characteristics of the Gulang loess section, northwestern Chinese Loess Plateau

We report the results of a rock magnetic and paleomagnetic investigation of unit L9 of the Gulang (GL) loess section, in the northwestern Chinese Loess Plateau (CLP). We demonstrate that the dominant magnetic remanence carriers are coarse‐grained pseudo single‐domain/multidomain magnetite particles, and hematite. The application of either thermal (THD) or alternating‐field demagnetization (AFD) yielded several normal polarity intervals interbedded with intervals of reversed polarity, but which cannot be correlated with standard geomagnetic polarity time scales. A greater number of normal polarity intervals, however, were evident after THD than after AFD. We propose that the normal polarities are either the result of overprinting of a viscous remanent magnetization (VRM) carried by coarse magnetite particles on the original depositional remanent magnetization (DRM); or that they represent genuine geomagnetic excursions (such as the Kamikatsura and Santa Rosa excursions) which are difficult to identify. In addition, we propose that in the case of the GL loess section, the effect of thermal demagnetization tails of a VRM is a possible reason why THD treatment yielded a greater number of normal polarity intervals than does AFD. However, reversed polarities obtained by either THD or AFD may be credible for sedimentary intervals with a relatively high content of hematite particles which preserve the primary DRM. Although numerous studies have proposed that THD provides more reliable paleomagnetic directions for loess sediments from the CLP, our results suggest that careful attention needs to be paid to the type of demagnetization method chosen, especially in the case of coarse‐grained loess deposits.
Carboniferous continental margin deposits in southern Tuscany, Italy: results from geological mapping of the geotopes Farma Valley and San Antonio Mine Area

Relics of the Carboniferous shelf, slope and basin margin section occur as intensely tectonized slices within the middle Tertiary Monticiano‐Roccastrada metamorphic core complex in southern Tuscany. These sedimentary successions are interpreted as predominantly siliciclastic second‐order sequence stratigraphic cycles, deposited in a successor basin (Farma Basin) established near the Southern Convergence Front of the westmediterranean Hercynides. The units developed as highstand systems tracts above a downlap surface and buried pelagites of a starved, moderately deep‐water basin (Risanguigno Basin). The Risanguigno Basin was characterized by dys‐ and anoxic conditions and underwent partial tectonic inversion during the early Carboniferous. Detailed mapping has revealed that Carboniferous turbidites deposited on the slope, base of slope and Farma Basin margin are present in the eastern part of the Farma Valley and in the San Antonio Mine Area. Coeval lithologies—storm influenced deposits of the inner shelf and lower shoreface—crop out in the western part of the Farma Valley. Both units, considered to be related to storm‐triggered offshore bottom currents bypassing the outer shelf, are covered by offlapping shallow marine and littoral clastics probably of Permian age. Subsequent tectonic uplift and partial inversion of the Farma Basin resulted in subaerial exposure, erosion of the upper part of the basin fill and deposition of the terrestrial Verrucano Group (middle Triassic), which sealed these early Carboniferous to late Permian sequences considered to represent a late Palaeozoic preligurian failed rift. Copyright © 2008 John Wiley & Sons, Ltd.
(Just) A Spoonful of Refinements Helps the Registration Error Go Down

We tackle data-driven 3D point cloud registration. Given point correspondences, the standard Kabsch algorithm provides an optimal rotation estimate. This allows to train registration models in an end-to-end manner by differentiating the SVD operation. However, given the initial rotation estimate supplied by Kabsch, we show we can improve point correspondence learning during model training by extending the original optimization problem. In particular, we linearize the governing constraints of the rotation matrix and solve the resulting linear system of equations. We then iteratively produce new solutions by updating the initial estimate. Our experiments show that, by plugging our differentiable layer to existing learning-based registration methods, we improve the correspondence matching quality. This yields up to a 7% decrease in rotation error for correspondence-based data-driven registration methods.
Streamlined bedrock terrain and fast ice flow, Jakobshavns Isbrae, West Greenland: implications for ice stream and ice sheet dynamics

This study investigates the marginal subglacial bedrock bedforms of Jakobshavns Isbrae, West Greenland, in order to examine the processes governing bedform evolution in ice stream and ice sheet areas, and to reconstruct the interplay between ice stream and ice sheet dynamics. Differences in bedform morphology (roche moutonnee or whaleback) are used to explore contrasts in basal conditions between fast and slow ice flow. Bedform density is higher in ice stream areas and whalebacks are common. We interpret that this is related to higher ice velocities and thicker ice which suppress bed separation. However, modification of whalebacks by plucking occurs during deglaciation due to ice thinning, flow deceleration, crevassing and fluctuations in basal water pressure. The bedform evidence points to widespread basal sliding during past advances of Jakobshavns Isbrae. This was encouraged by increased basal temperatures and melting at depth, as well as the steep marginal gradients of Jakobshavns Isfjord which allowed rapid downslope evacuation of meltwater leading to strong ice/bedrock coupling and scouring. In contrast to soft‐bedded ice stream bedforms, the occurrence of fixed basal perturbations and higher bed roughness in rigid bed settings prevents the basal ice subsole from maintaining a stable form which, coupled with secondary plucking, counteracts the development of bedforms with high elongation ratios. Cross‐cutting striae and double‐plucked, rectilinear bedforms suggest that Jakobshavns Isbrae became partially unconfined during growth phases, causing localised diffluent flow and changes in ice sheet dynamics around Disko Bugt. It is likely that Disko Bugt harboured a convergent ice flow system during repeated glacial cycles, resulting in the formation of a large coalesced ice stream which reached the continental shelf edge.
Multiple codings for self-similar sets with overlaps

In this paper we consider a class $\mathcal{E}$ of self-similar sets with overlaps. In particular, for a self-similar set $E\in \mathcal{E}$ and $k=1,2,\cdots, \aleph_0$ or $2^{\aleph_0}$ we investigate the Hausdorff dimension of the subset $U_k(E)$ which contains all points $x\in E$ having exactly $k$ different codings. This generalizes many results obtained in \cite{Dajani_Jiang_Kong_Li-2015} and \cite{Dajani_Jiang_2015}.
Multi-variable verification of hydrological processes in the upper North Saskatchewan River basin, Alberta, Canada

Abstract The ACRU agro-hydrological modelling system was set up to simulate the impacts of climate change on the hydrological responses of the 3856-km2 Cline River watershed, the major headwater of the upper North Saskatchewan River basin in central Alberta, Canada. The physical–conceptual ACRU model was set up to simulate all elements of the hydrological cycle on a daily time step for the 1961–1990 baseline period, to serve as the basis for later climate change impact simulations. After parameterization, the output from the ACRU model was verified against temperature, snow water equivalent, glacier mass balance, potential evapotranspiration, and two sets of long-term daily streamflow records. The multi-variable verification analyses were implemented to instil confidence that the simulated streamflow time series is based on a realistic combination of bio-physical parameters and represents the watershed behaviour in terms of annual water yields, seasonality, shape and magnitude of the hydrographs, and streamflow variability. Editor Z.W. Kundzewicz Citation Nemeth, M.W. , Kienzle, S.W. and Byrne, J.M. , 2012. Multi-variable verification of hydrological processes in the upper North Saskatchewan River basin, Alberta, Canada. Hydrological Sciences Journal, 57 (1), 84–102.
Effects of Reinforcement on Liquefaction Resistance of Solani Sand

AbstractA study on liquefaction resistance of Solani sand reinforced with geogrid sheet, geosynthetic fiber, and natural coir fiber is reported. Tests were carried out on shake table (vibration table) with sand samples prepared at a relative density of 25%, with and without reinforcements. Synthetic geogrid sheets were used in three different combinations of three, four, and five layers. In case of fibers, the percentage of fibers by weight of dry sand were taken as 0.25, 0.50, and 0.75% and mixed randomly with the sand sample. The liquefaction parameters, such as the maximum pore water pressure (Umax⁡), maximum pore water pressure built-up time, stay time for Umax⁡, and pore water pressure dissipation time were measured corresponding to various levels of accelerations varying from 0.1–0.4 g. The frequency of the dynamic load was kept constant at 5 Hz. The liquefaction resistance of sand was evaluated in terms of maximum pore water pressure ratio (rumax⁡). Test results indicated that on inclusion of fiber.
Constraints on the Timing of Pan‐African Granulite‐Facies Metamorphism in the Kerala Khondalite Belt of Southern India: SHRIMP Mineral Ages and Nd Isotopic Systematics

The supracrustal Kerala Khondalite Belt (KKB; southern India) constitutes an important but little understood terrain in the evolution of East Gondwana. Here we report SHRIMP U‐Pb zircon and titanite ages for a suite of metasedimentary rocks from the KKB. Metamorphic ages at \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage[OT2,OT1]{fontenc} \newcommand\cyr{ \renewcommand\rmdefault{wncyr} \renewcommand\sfdefault{wncyss} \renewcommand\encodingdefault{OT2} \normalfont \selectfont} \DeclareTextFontCommand{\textcyr}{\cyr} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \landscape $$530.2\pm 4.4$$ \end{document} and \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage[OT2,OT1]{fontenc} \newcommand\cyr{ \renewcommand\rmdefault{wncyr} \renewcommand\sfdefault{wncyss} \renewcommand\encodingdefault{OT2} \normalfont \selectfont} \DeclareTextFontCommand{\textcyr}{\cyr} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \landscape $$525\pm 4.5$$ \end{document} Ma were obtained from metapelitic and metapsammitic migmatites, respectively. These ages are interpreted to date peak metamorphism because both rock types have extensively melted under granulite‐facies conditions. A similar age ( \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage[OT2,OT1]{fontenc} \newcommand\cyr{ \renewcommand\rmdefault{wncyr} \renewcommand\sfdefault{wncyss} \renewcommand\encodingdefault{OT2} \normalfont \selectfont} \DeclareTextFontCommand{\textcyr}{\cyr} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \landscape $$520\pm 4.7$$ \end{document} Ma) was obtained from titanite from a granulite‐facies calc‐silicate rock. These ages are within error of SHRIMP ages for granulite‐facies assemblages in Lützow‐Holm Bay, East Antarctica, the Highland and Wanni Complexes of Sri Lanka, and Southern Madagascar. We propose that this timing reflects a short span (∼10 m.yr.) of high‐temperature granulite‐facies metamorphism and concomitant widespread migmatization that marks the final stage of collision between East and West Gondwana.