ShantanuT01/DACTYL-Pretraining huggingface dataset:
Given a bounded autonomous vector field $b \colon \mathbb R^d \to \mathbb R^d$, we study the uniqueness of bounded solutions to the initial value problem for the related transport equation \begin{equation*} \partial_t u + b \cdot \nabla u= 0. \end{equation*} We are interested in the case where $b$ is of class BV and it is nearly incompressible. Assuming that the ambient space has dimension $d=2$, we prove uniqueness of weak solutions to the transport equation. The starting point of the present work is the result which has been obtained in \cite{BG} (where the \emph{steady} case is treated). Our proof is based on splitting the equation onto a suitable partition of the plane: this technique was introduced in \cite{ABC1}, using the results on the structure of level sets of Lipschitz maps obtained in \cite{ABC2}. Furthermore, in order to construct the partition, we use Ambrosio's superposition principle \cite{ambrosiobv}.
In this paper we investigate the asymptotic behaviour of the componentwise maxima for two bivariate skew elliptical triangular arrays with components given in terms of skew transformations of bivariate spherical random vectors. We find the weak limit of the normalized maxima for both cases that the random radius pertaining to the elliptical random vectors is either in the Gumbel or in the Weibull max-domain of attractions.
The relation between GPD's and color transparency is explored. The discovery of color transparency in pionic diffractive dissociation reactions allows us to make specific predictions for the behavior of the pion generalized parton distribution, and provide a further test of any model of the pion form factor.
Apparent variability of the longitudinal magnetic fields in most stars is caused by rotation, which quantitavely changes projection of the magnetic field configuration on the line of sight. This is a purely geometrical effect and is not related to possible intrinsic changes of the field. In some stars we observe changes of the magnetic phase curve with time, which means that parameters of the magnetic field change. Such changes occur in some objects in time scale of several years, which is few orders of magnitude faster than predicted by theory. Those changes imply need for improvement of the theory of magnetic field evolution. We demonstrate changes of the rotational phase curves in few stars.
In this work, we investigate the Cauchy problem for the spatially inhomogeneous non-cutoff Kac equation. If the initial datum belongs to the spatially critical Besov space, we can prove the well-posedness of weak solution under a perturbation framework. Furthermore, it is shown that the solution enjoys Gelfand-Shilov regularizing properties with respect to the velocity variable and Gevrey regularizing properties with respect to the position variable. In comparison with the recent result in [18], the Gelfand-Shilov regularity index is improved to be optimal. To the best of our knowledge, our work is the first one that exhibits smoothing effect for the kinetic equation in Besov spaces.
We study a model of particle acceleration coupled with an MHD model of magnetic reconnection in unstable twisted coronal loops. The kink instability leads to the formation of helical currents with strong parallel electric fields resulting in electron acceleration. The motion of electrons in the electric and magnetic fields of the reconnecting loop is investigated using a test-particle approach taking into account collisional scattering. We discuss the effects of Coulomb collisions and magnetic convergence near loop footpoints on the spatial distribution and energy spectra of high-energy electron populations and possible implications on the hard X-ray emission in solar flares.
V$_{2}$O$_{5}$ in its $\omega$ phase (Li$_{3}$V$_{2}$O$_{5}$) with excess lithium is a potential alternative to the graphite anode for lithium-ion batteries at low temperature and fast charging conditions due to its safer voltage (0.6 V vs Li$^{+}$/Li(s)) and high lithium transport rate. In-operando cationic disorder, as observed in most ordered materials, can produce significant changes in charge compensation mechanisms, anionic activity, lithium diffusion and operational voltages. In this work, we report the variation in structural distortion, electronic structure and migration barrier accompanied by disorder using first-principles calculations. Due to segregation of lithium atoms in the disordered state, we observe greater distortion, emergence of metallic behaviour and potential anionic activity from non-bonding oxygen states near the Fermi level. Redox capacity can be tuned by doping with 3d metals which can adjust the participating cationic states, and by fluorine substitution which can stabilize or suppress anionic states. Moreover, suppression of anionic activity is found to decrease structural distortion, crucial for mitigating voltage fade and hysteresis. Diffusion barrier calculations in the presence of disorder indicate the activation of the remaining 3D-paths for lithium hopping which are unavailable in the ordered configuration, explaining its fast-charging ability observed in experiments.
High-throughput ab-initio calculations, cluster expansion techniques and thermodynamic modeling have been synergistically combined to characterize the binodal and the spinodal decompositions features in the pseudo-binary lead chalcogenides PbSe-PbTe, PbS-PbTe, and PbS-PbSe. While our results agree with the available experimental data, our consolute temperatures substantially improve with respect to previous computational modeling. The computed phase diagrams corroborate that the formation of spinodal nanostructures causes low thermal conductivities in these alloys. The presented approach, making a rational use of online quantum repositories, can be extended to study thermodynamical and kinetic properties of materials of technological interest.
Modern nuclear theory presents a fascinating study in contrasting approaches to the structure of hadrons and nuclei. Nowhere is this more apparent than in the treatment of the pion cloud. As this discussion really begins with Yukawa, it is entirely appropriate that this invited lecture at the Yukawa Institute in Kyoto should deal with the issue.
Point of care diagnostics using microscopy and computer vision methods have been applied to a number of practical problems, and are particularly relevant to low-income, high disease burden areas. However, this is subject to the limitations in sensitivity and specificity of the computer vision methods used. In general, deep learning has recently revolutionised the field of computer vision, in some cases surpassing human performance for other object recognition tasks. In this paper, we evaluate the performance of deep convolutional neural networks on three different microscopy tasks: diagnosis of malaria in thick blood smears, tuberculosis in sputum samples, and intestinal parasite eggs in stool samples. In all cases accuracy is very high and substantially better than an alternative approach more representative of traditional medical imaging techniques.
We propose an alternative scenario for the dark matter generation from an evolving cosmological constant which interacts with the dominant background in certain intermediate phase of the universe, and relaxes to the observed small value at present. In this way, it is shown that the interaction of the cosmological constant with the radiation or matter might generate the dark matter densities with a varied mass spectrum in the universe with their characteristic arc-like frozen signatures on the Cosmic Microwave Background Radiation (CMBR). This approach also suggests a possible solution to the long standing cosmological constant problem.
Indications of disequilibrium throughout the Milky Way (MW) highlight the need for compact,flexible, non-parametric descriptions of phase--space distributions of galaxies. We present a new representation of the current Dark Matter (DM) distribution and potential derived from N-body simulations of the Milky Way and Large Magellanic Cloud (LMC) system using Basis Function Expansions (BFEs). We incorporate methods to maximize the physical signal in the representation. As a result, the simulations of $10^8$ DM particles representing the MW--LMC system can be described by 354 coefficients. We find that the LMC induces asymmetric perturbations (odd l, m) to the MW's halo, which are not well-described by oblate, prolate, or triaxial halos. Furthermore, the energy in high-order even modes (l,m $\geq$ 2) is similar to average triaxial halos found in cosmological simulations. As such, the response of the MW's halo to the LMC must be accounted for in order to recover the imprints of its assembly history. The LMC causes the outer halo ($\geq$ 30 kpc) to shift from the disk center of mass (COM) by $\sim$15-25 kpc at present day, manifesting as a dipole in the BFE and in the radial velocities of halo stars. The shift depends on the LMC's infall mass, the distortion of the LMC's halo and the MW halo response. Within 30 kpc, halo tracers are expected to orbit the COM of the MW's disk, regardless of LMC infall mass. The LMC's halo is also distorted by MW tides, we discuss the implications for its mass loss and the subsequent effects on current Magellanic satellites.
This paper is concerned with the switching game of a one-dimensional backward stochastic differential equation (BSDE). The associated Bellman-Isaacs equation is a system of matrix-valued BSDEs living in a special unbounded convex domain with reflection on the boundary along an oblique direction. In this paper, we show the existence of an adapted solution to this system of BSDEs with oblique reflection by the penalization method, the monotone convergence, and the a priori estimates.
From a Principal Component Analysis (PCA) of 78 z~3 high quality quasar spectra in the SDSS-DR7, we derive the principal components characterizing the QSO continuum over the full wavelength range available. The shape of the mean continuum, is similar to that measured at low-z (z~1), but the equivalent width of the emission lines are larger at low redshift. We calculate the correlation between fluxes at different wavelengths and find that the emission line fluxes in the red part of the spectrum are correlated with that in the blue part. We construct a projection matrix to predict the continuum in the Lyman-$\alpha$ forest from the red part of the spectrum. We apply this matrix to quasars in the SDSS-DR7 to derive the evolution with redshift of the mean flux in the Lyman-$\alpha$ forest due to the absorption by the intergalactic neutral hydrogen. A change in the evolution of the mean flux is apparent around z~3 in the sense of a steeper decrease of the mean flux at higher redshifts. The same evolution is found when the continuum is estimated from the extrapolation of a power-law continuum fitted in the red part of the quasar spectrum if a correction, derived from simple simulations, is applied. Our findings are consistent with previous determinations using high spectral resolution data. We provide the PCA eigenvectors over the wavelength range 1020-2000 \AA\ and the distribution of their weights that can be used to simulate QSO mock spectra.
The monotone secant conjecture posits a rich class of polynomial systems, all of whose solutions are real. These systems come from the Schubert calculus on flag manifolds, and the monotone secant conjecture is a compelling generalization of the Shapiro conjecture for Grassmannians (Theorem of Mukhin, Tarasov, and Varchenko). We present some theoretical evidence for this conjecture, as well as computational evidence obtained by 1.9 teraHertz-years of computing, and we discuss some of the phenomena we observed in our data.
We study the low-temperature behavior of a magnetic impurity which is weakly coupled to correlated conduction electrons. To account for conduction electron interactions a diagrammatic approach in the frame of the 1/N expansion is developed. The method allows us to study various consequences of the conduction electron correlations for the ground state and the low-energy excitations. We analyse the characteristic energy scale in the limit of weak conduction electron interactions. Results are reported for static properties (impurity valence, charge susceptibility, magnetic susceptibility, and specific heat) in the low-temperature limit.
We report high signal-to-noise Spitzer IRS spectra of a sample of eleven classical T Tauri stars. Molecular emission from rotational transitions of H2O and OH and ro-vibrational bands of simple organic molecules (CO2, HCN, C2H2) is common among the sources in the sample. The gas temperatures (200-800 K) and emitting areas we derive are consistent with the emission originating in a warm disk atmosphere in the inner planet formation region at radii < 2 AU. The H2O emission appears to form under a limited range of excitation conditions, as shown by the similarity in relative strengths of H2O features from star to star and the narrow range in derived temperature and column density. Emission from highly excited rotational levels of OH is present in all stars; the OH emission flux increases with the stellar accretion rate, and the OH/H2O flux ratio shows a relatively small scatter. We interpret these results as evidence for OH production via FUV photo-dissociation of H2O in the disk surface layers. No obvious explanation is found for the observed range in the relative emission strengths of different organic molecules or in their strength with respect to water. We put forward the possibility that these variations reflect a diversity in organic abundances due to star-to-star differences in the C/O ratio of the inner disk gas. Stars with the largest HCN/H2O flux ratios in our sample have the largest disk masses. We speculate that such a trend could result if higher mass disks are more efficient at planetesimal formation and sequestration of water in the outer disk, leading to enhanced C/O ratios and abundances of organic molecules in the inner disk. A comparison of our derived HCN to H2O column density ratio to comets, hot cores, and outer T Tauri star disks suggests that the inner disks are chemically active.
In the framework of the Landau-Ginzburg-Devonshire (LGD) approach we studied finite size effects of the phase diagram and domain structure evolution in spherical nanoparticles of uniaxial ferroelectric. The particle surface is covered by a layer of screening charge characterized by finite screening length. The phase diagram, calculated in coordinates "particle radius vs. screening length" has a wide region of versatile poly-domain structures separating single-domain ferroelectric and nonpolar paraelectric phases. Unexpectedly, we revealed a region of stable irregular labyrinthine domains in the nanoparticles of uniaxial ferroelectric CuInP2S6 with the first order paraelectric-ferroelectric phase transition. We established that the origin of labyrinthine domains is the mutual balance of LGD, polarization gradient and electrostatic energies. The branching of the domain walls appears and increases rapidly when the polarization gradient energy decreases below the critical value. Allowing for the generality of LGD approach, we expect that the gradient-induced morphological transition can be the source of labyrinthine domains appearance in many spatially-confined ferroics with long-range order parameter, including relaxors, ferromagnetics, antiferrodistortive materials and materials with incommensurate ferroic phases.
The dynamical discrete web (DyDW),introduced in recent work of Howitt and Warren, is a system of coalescing simple symmetric one-dimensional random walks which evolve in an extra continuous dynamical time parameter \tau. The evolution is by independent updating of the underlying Bernoulli variables indexed by discrete space-time that define the discrete web at any fixed \tau. In this paper, we study the existence of exceptional (random) values of \tau where the paths of the web do not behave like usual random walks and the Hausdorff dimension of the set of exceptional such \tau. Our results are motivated by those about exceptional times for dynamical percolation in high dimension by H\"{a}ggstrom, Peres and Steif, and in dimension two by Schramm and Steif. The exceptional behavior of the walks in the DyDW is rather different from the situation for the dynamical random walks of Benjamini, H\"{a}ggstrom, Peres and Steif. For example, we prove that the walk from the origin S^\tau_0 violates the law of the iterated logarithm (LIL) on a set of \tau of Hausdorff dimension one. We also discuss how these and other results extend to the dynamical Brownian web, the natural scaling limit of the DyDW.
With large spin-orbit coupling, the $t_{2g}^5$ electron configuration in $d$-metal oxides is prone to highly anisotropic exchange interactions and exotic magnetic properties. In $5d^5$ iridates, given the existing variety of crystal structures, the magnetic anisotropy can be tuned from antisymmetric to symmetric Kitaev-type, with interaction strengths that outsize the isotropic terms. By many-body electronic-structure calculations we here address the nature of the magnetic exchange and the intriguing spin-glass behavior of Li$_2$RhO$_3$, a $4d^5$ honeycomb oxide. For pristine crystals without Rh-Li site inversion, we predict a dimerized ground state as in the isostructural $5d^5$ iridate Li$_2$IrO$_3$, with triplet spin dimers effectively placed on a frustrated triangular lattice. With Rh-Li anti-site disorder, we explain the observed spin-glass phase as a superposition of different, nearly degenerate symmetry-broken configurations.
In addition to the Kitaev ($K$) interaction, candidate Kitaev materials also possess Heisenberg ($J$) and off-diagonal symmetric ($\Gamma$) couplings. We investigate the quantum ($S = 1/2$) $K$-$J$-$\Gamma$ model on the honeycomb lattice by a variational Monte Carlo (VMC) method. In addition to the "generic" Kitaev spin liquid (KSL), we find that there is just one proximate KSL (PKSL) phase, while the rest of the phase diagram contains different magnetically ordered states. The PKSL is a gapless Z$_2$ state with 14 Majorana cones, which in contrast to the KSL has a gapless spin response. In a magnetic field applied normal to the honeycomb plane, it realizes two of Kitaev's gapped chiral spin-liquid phases, of which one is non-Abelian with Chern number $\nu = 5$ and the other is Abelian with $\nu = 4$. These two phases could be distinguished by their thermal Hall conductance.
The Euclid space mission, designed to probe evolution of the Dark Energy, will map a large area of the sky at three adjacent near-IR filters, Y, J and H. This coverage will also enable mapping source-subtracted cosmic infrared background (CIB) fluctuations with unprecedented accuracy on sub-degree angular scales. Here we propose methodology, using the Lyman-break tomography applied to the Euclid-based CIB maps, to accurately isolate the history of CIB emissions as a function of redshift from 10 < z < 20, and to identify the baryonic acoustic oscillations (BAOs) at those epochs. To identify the BAO signature, we would assemble individual CIB maps over conservatively large contiguous areas of >~ 400 sq deg. The method can isolate the CIB spatial spectrum by z to sub-percent statistical accuracy. We illustrate this with a specific model of CIB production at high z normalized to reproduce the measured Spitzer-based CIB fluctuation. We show that even if the latter contain only a small component from high-z sources, the amplitude of that component can be accurately isolated with the methodology proposed here and the BAO signatures at z>~ 10 are recovered well from the CIB fluctuation spatial spectrum. Probing the BAO at those redshifts will be an important test of the underlying cosmological paradigm, and would narrow the overall uncertainties on the evolution of cosmological parameters, including the Dark Energy. Similar methodology is applicable to the planned WFIRST mission, where we show that a possible fourth near-IR channel at > 2 micron would be beneficial.
The role of symmetry in computer vision has waxed and waned in importance during the evolution of the field from its earliest days. At first figuring prominently in support of bottom-up indexing, it fell out of favor as shape gave way to appearance and recognition gave way to detection. With a strong prior in the form of a target object, the role of the weaker priors offered by perceptual grouping was greatly diminished. However, as the field returns to the problem of recognition from a large database, the bottom-up recovery of the parts that make up the objects in a cluttered scene is critical for their recognition. The medial axis community has long exploited the ubiquitous regularity of symmetry as a basis for the decomposition of a closed contour into medial parts. However, today's recognition systems are faced with cluttered scenes, and the assumption that a closed contour exists, i.e. that figure-ground segmentation has been solved, renders much of the medial axis community's work inapplicable. In this article, we review a computational framework, previously reported in Lee et al. (2013), Levinshtein et al. (2009, 2013), that bridges the representation power of the medial axis and the need to recover and group an object's parts in a cluttered scene. Our framework is rooted in the idea that a maximally inscribed disc, the building block of a medial axis, can be modeled as a compact superpixel in the image. We evaluate the method on images of cluttered scenes.
We study the dynamics of quantum systems interacting with a stream of entangled qubits. Under fairly general conditions, we present a detailed framework describing the conditional dynamical maps for the system, called quantum trajectories, when the qubits are measured. Depending on the measurement basis, these quantum trajectories can be jump-type or diffusive-type, and they can exhibit features not present with quantum optical and single-qubit trajectories. As an example, we consider the case of two remote atoms, where jump-type quantum trajectories herald the birth and death of entanglement.
We observed with the VLA, PdBI, and SMA the centimeter and millimeter continuum, N2H+(1-0), and CO(2-1) emission associated with a dusty cloud harboring a nascent cluster with intermediate-mass protostars. At centimeter wavelengths we found a strong source, tracing a UCHII region, at the eastern edge of the dusty cloud, with a shell-like structure, and with the near-infrared counterpart falling in the center of the shell. This is presumably the most massive source of the forming cluster. About 15'' to the west of the UCHII region and well embedded in the dusty cloud, we detected a strong millimeter source, MM1, associated with centimeter and near-infrared emission. MM1 seems to be driving a prominent high-velocity CO bipolar outflow, and is embedded in a ridge of dense gas traced by N2H+. We estimated that MM1 is an intermediate-mass source in the Class 0/I phase. About 15'' to the south of MM1, and still more deeply embedded in the dusty cloud, we detected a compact millimeter source, MM2, with neither centimeter nor near-infrared emission, but with water maser emission. MM2 is associated with a clump of N2H+, whose kinematics reveal a clear velocity gradient and additionally we found signposts of infall motions. MM2, being deeply embedded within the dusty cloud, with an associated water maser but no hints of CO outflow emission, is an intriguing object, presumably of intermediate mass. In conclusion, the UCHII region is found at the border of a dusty cloud which is currently undergoing active star formation. Two intermediate-mass protostars in the dusty cloud seem to have formed after the UCHII region and have different properties related to the outflow phenomenon.