ShantanuT01/DACTYL-Pretraining huggingface dataset:
The recent explosion of research interest in Weyl semimetals has led to many proposed Weyl semimetal candidates and a few experimental observations of a Weyl semimetal in real materials. Through this experience, we have come to appreciate that typical Weyl semimetals host many Weyl points. For instance, the first Weyl semimetal observed in experiment, TaAs, hosts 24 Weyl points. Similarly, the Mo$_x$W$_{1-x}$Te$_2$ series, recently under study as the first Type II Weyl semimetal, has eight Weyl points. However, it is well-understood that for a Weyl semimetal without inversion symmetry but with time-reversal symmetry, the minimum number of Weyl points is four. Realizing such a minimal Weyl semimetal is fundamentally relevant because it would offer the simplest "hydrogen atom" example of an inversion-breaking Weyl semimetal. At the same time, transport experiments and device applications may be simpler in a system with as few Weyl points as possible. Recently, TaIrTe$_4$ has been predicted to be a minimal, inversion-breaking Weyl semimetal. However, crucially, the Weyl points and Fermi arcs live entirely above the Fermi level, making them inaccessible to conventional angle-resolved photoemission spectroscopy (ARPES). Here we use pump-probe ARPES to directly access the band structure above the Fermi level in TaIrTe$_4$. We directly observe Weyl points and topological Fermi arcs, showing that TaIrTe$_4$ is a Weyl semimetal. We find that, in total, TaIrTe$_4$ has four Weyl points, providing the first example of a minimal inversion-breaking Weyl semimetal. Our results hold promise for accessing exotic transport phenomena arising in Weyl semimetals in a real material.
We classify Fano fivefolds of index two which are blow-ups of smooth manifolds along a smooth center.
We provide a unified approach to the three main non-compact models of random geometry, namely the Brownian plane, the infinite-volume Brownian disk, and the Brownian half-plane. This approach allows us to investigate relations between these models, and in particular to prove that complements of hulls in the Brownian plane are infinite-volume Brownian disks.
Some deviations from special relativity--especially isotropic effects--are most efficiently constrained using particles with velocities very close to 1. While there are extremely tight bounds on some of the relevant parameters coming from astrophysical observations, many of these rely on our having an accurate understanding of the dynamics of high-energy sources. It is desirable to have reliable laboratory constraints on these same parameters. The fastest-moving particles in a laboratory were electrons and positrons at LEP. The energetics of the LEP beams were extremely well understood, and measurements of the synchrotron emission rate indicate that that any isotropic deviation of the speed of light from 1 must be smaller than 5 x 10^(-15).
We propose a weakly-supervised approach that takes image-sentence pairs as input and learns to visually ground (i.e., localize) arbitrary linguistic phrases, in the form of spatial attention masks. Specifically, the model is trained with images and their associated image-level captions, without any explicit region-to-phrase correspondence annotations. To this end, we introduce an end-to-end model which learns visual groundings of phrases with two types of carefully designed loss functions. In addition to the standard discriminative loss, which enforces that attended image regions and phrases are consistently encoded, we propose a novel structural loss which makes use of the parse tree structures induced by the sentences. In particular, we ensure complementarity among the attention masks that correspond to sibling noun phrases, and compositionality of attention masks among the children and parent phrases, as defined by the sentence parse tree. We validate the effectiveness of our approach on the Microsoft COCO and Visual Genome datasets.
One of the interesting problems in arithmetic dynamics is to study the stability of polynomials over a field. In this paper, we study the stability of $f(z)=z^d+\frac{1}{c}$ for $d\geq 2$, $c\in{\mathbb{Z}\setminus\{0\}}$. We show that for infinite families of $d\geq 3$, whenever $f(z)$ is irreducible, all its iterates are irreducible, that is, $f(z)$ is stable. For $c\equiv 1\pmod{4}$, we show that all the iterates of $z^2+\frac{1}{c}$ are irreducible. Also we show that for $d=3$, if $f(z)$ is reducible, then the number of irreducible factors of each iterate of $f(z)$ is exactly $2$ for $|c|\leq{10^{12}}$.
The ferroelectric phase of the multiferroic hexagonal manganites (h-ReMnO3) has been reported to undergo a series of magnetic transitions involving long-range ordering/reorientation of 4fRe3+ and/or 3dMn3+ spins below room temperature. These transitions have attracted a lot of attention in recent years due to the geometrically frustrated nature of magnetic interactions. We have revisited these transitions in high quality single crystals of h-DyMnO3 using dc and ac susceptibility measurements as a function of temperature (T), magnetic field (H) and frequency (w) supplemented by specific heat measurements. Taking h-DyMnO3 as an example, we show that the Dy3+ spins below TN~68K are in a superferrimagnetic (SFIM) state whereas they undergo spin-glass (SG) transition below TDy3+~7K. Our observations demonstrate that neither the N\'eel transition at TN~68K nor the transition at TDy3+~7K is associated with long-range ordered states of Dy3+ spins as believed so far in the literature. The SG state of h-DyMnO3 is quite exotic as it occurs in an ordered compound purely due to geometrical frustration without any random disorder. Further, it shows an interesting crossover from de Almeida-Thouless type exponent (m=2/3) to Gabay-Toulouse type (m=2) with increasing field which cannot be explained in terms of the existing mean field theories of SG transition in Ising or Heisenberg systems but is expected for a vector X-Y SG system. Our observations call for a systematic reinvestigation of the nature of magnetic transitions involving Re3+ ions in other h-ReMnO3 also.
Aims. We aim to characterise the magnetism of a large fraction of the north polar region close to a maximum of activity, when the polar regions are reversing their dominant polarity.   Methods. We make use of full spectropolarimetric data from the CRisp Imaging Spectro-Polarimeter installed at the Swedish Solar Telescope. The data consist of a photospheric spectral line, which is used to infer the various physical parameters of different quiet Sun regions by means of the solution of the radiative transfer equation. We focus our analysis on the properties found for the north polar region and their comparison to the same analysis applied to data taken at disc centre and low-latitude quiet Sun regions for reference. We also analyse the spatial distribution of magnetic structures throughout the north polar region.   Results. We find that the physical properties of the polar region (line-of-sight velocity, magnetic flux, magnetic inclination and magnetic azimuth) are compatible with those found for the quiet Sun at disc centre and are similar to the ones found at low latitudes close to the limb. Specifically, the polar region magnetism presents no specific features. The structures for which the transformation from a line-of-sight to a local reference frame was possible harbour large magnetic fluxes ($>10^{17}$ Mx) and are in polarity imbalance with a dominant positive polarity, the largest ones ($>10^{19}$ Mx) being located below $73^{\circ}$ latitude.
Cosmological solutions of the Brans-Dicke theory with an added cosmological constant are investigated with an emphasis to select a conformal frame in order to implement the scenario of a decaying cosmological constant, featuring an ever growing scalar field. We focus particularly on Jordan frame, the original frame with the nonminimal coupling, and conformally transformed Einstein frame without it. For the asymptotoic attractor solutions as well as the "hesitation behavior," we find that none of these conformal frames can be accepted as the basis of analyzing primordial nucleosynthesis. As a remedy, we propose to modify the prototype BD theory, by introducing a scale-invariant scalar-matter coupling, thus making Einstein frame acceptable. The invariacne is broken as a quantum anomaly effect due to the non-gravitational interactions, entailing naturally the fifth force, characterized by a finite force-range and WEP violation. A tentative estimate shows that the theoretical prediction is roughly consistent with the observational upper bounds. Further efforts to improve the experimental accuracy is strongly encouraged.
Comptonization is a very important phenomenon in astrophysics. Kompaneets equation describes up-Comptonization process in nonrelativistic astrophysics, while it fails for down-Comptonization Scattering which is the most important radiative transfer process in hard X-rays and $\gamma$-rays astronomy. In this study, we explore both up-Comptonization and down-Comptonization processes. A new relativistic corrections is introduced to the Kompaneets equation which is valid in both nonrelativistic energy regime with the photon energy $h\nu << m_ec^2$ and the electron temperature $KT_e << m_ec^2$. Numerical comparisons are presented which show excellent agreement between the Kompaneets equation and the new equation.
The three-body energy-dependent effective interaction given by the Bloch-Horowitz (BH) equation is evaluated for various shell-model oscillator spaces. The results are applied to the test case of the three-body problem (triton and He3), where it is shown that the interaction reproduces the exact binding energy, regardless of the parameterization (number of oscillator quanta or value of the oscillator parameter b) of the low-energy included space. We demonstrate a non-perturbative technique for summing the excluded-space three-body ladder diagrams, but also show that accurate results can be obtained perturbatively by iterating the two-body ladders. We examine the evolution of the effective two-body and induced three-body terms as b and the size of the included space Lambda are varied, including the case of a single included shell, Lambda hw=0 hw. For typical ranges of b, the induced effective three-body interaction, essential for giving the exact three-body binding, is found to contribute ~10% to the binding energy.
The universal adjacency matrix $U$ of a graph $\Gamma$, with adjacency matrix $A$, is a linear combination of $A$, the diagonal matrix $D$ of vertex degrees, the identity matrix $I$, and the all-1 matrix $J$ with real coefficients, that is, $U=c_1 A+c_2 D+c_3 I+ c_4 J$, with $c_i\in {\mathbb R}$ and $c_1\neq 0$. Thus, as particular cases, $U$ may be the adjacency matrix, the Laplacian, the signless Laplacian, and the Seidel matrix. In this note, we show that basically the same method introduced before by the authors can be applied for determining the spectra and bases of all the corresponding eigenspaces of arbitrary lifts of graphs (regular or not).
Previous studies have shown that the large, diffuse galaxies NGC1052-DF2 and NGC1052-DF4 both have populations of unusually luminous globular clusters as well as a very low dark matter content. Here we present newly-obtained deep Hubble Space Telescope (HST) Advanced Camera for Surveys (ACS) imaging of one of these galaxies, NGC1052-DF4. We use these data to measure the distance of the galaxy from the location of the tip of the red giant branch (TRGB). We find a rapid increase in the number of detected stars fainter than $m_{F814W} \sim 27.3$, which we identify as the onset of the red giant branch. Using a forward modeling approach that takes the photometric uncertainties into account, we find a TRGB magnitude of $m_{F814W,\rm TRGB}=27.47 \pm 0.16$. The inferred distance, including the uncertainty in the absolute calibration, is $D_{\rm TRGB}=20.0 \pm 1.6$ Mpc. The TRGB distance of NGC1052-DF4 is consistent with the previously-determined surface brightness fluctuation distance of $D_{\rm SBF}=18.7\pm 1.7$ Mpc to NGC1052-DF2 and is consistent with the distance of the bright elliptical galaxy NGC1052. We conclude that the unusual properties of these galaxies cannot be explained by distance errors.
In this article we prove local well-posedness of the system of equations $\partial_t h_{i}= \sum_{j=1}^{i}\partial_x^2 h_{i}+ (\partial_x h_{i})^2 + \xi $ on the circle where $1\leq i\leq N$ and $\xi$ is a space-time white noise. We attempt to generalize the renormalization procedure which gives the Hopf-Cole solution for the single layer equation and our $h_1$ (solution to the first layer) coincides with this solution. However, we observe that cancellation of logarithmic divergences that occurs at the first layer does not hold at higher layers and develop explicit combinatorial formulae for them.
This note is inspired by the work of Deligne on the local behavior of Hodge structures at infinity. We study limit mixed Hodge structures of degenerating families of compact hyperk\"ahler manifolds. We show that when the monodromy action on $H^2$ has maximal index of unipotency, the limit mixed Hodge structures on all cohomology groups are of Hodge-Tate type.
We show that, if $\alpha > 0$ is a real number, $n \ge 2$ and $\ell \ge 2$ are integers, and $q$ is a prime power, then every simple matroid $M$ of sufficiently large rank, with no $U_{2,\ell}$-minor, no rank-$n$ projective geometry minor over a larger field than $\GF(q)$, and satisfying $|M| \ge \alpha q^{r(M)}$, has a rank-$n$ affine geometry restriction over $\GF(q)$. This result can be viewed as an analogue of the Multidimensional Density Hales-Jewett Theorem for matroids.
We explore the sensitivity of limb darkening coefficients computed from stellar atmosphere models to different least-squares fitting methods. We demonstrate that conventional methods are strongly biased to fitting the stellar limb. Our suggested method of fitting by minimizing the radially integrated squared residual yields improved fits with better flux conservation. The differences of the obtained coefficients from commonly used values are observationally significant. We show that the new values are in better agreement with solar limb darkening measurements as well as with coefficients reported from analyses of eclipsing binary light curves.
There are numerous combinatorial objects associated to a Grassmannian permutation $w_\lambda$ that index cells of the totally nonnegative Grassmannian. We study several of these objects and their $q$-analogues in the case of permutations $w$ that are not necessarily Grassmannian. We give two main results: first, we show that certain acyclic orientations, rook placements avoiding a diagram of $w$, and fillings of a diagram of $w$ are equinumerous for all permutations $w$. Second, we give a $q$-analogue of a result of Hultman-Linusson-Shareshian-Sj\"ostrand by showing that under a certain pattern condition the Poincar\'e polynomial for the Bruhat interval of $w$ essentially counts invertible matrices avoiding a diagram of $w$ over a finite field. In addition to our main results, we include at the end a number of open questions.
We prove all the maximizers of the sharp Hardy-Littlewood-Sobolev inequality are smooth. More generally, we show all the nonnegative critical functions are smooth, radial with respect to some points and strictly decreasing in the radial direction. In particular, this resolves all the cases left open by previous works of Chen, Li and Ou on the corresponding integral systems.
In the minimal supersymmetric standard model (MSSM) with complex parameters, supersymmetric loop effects can lead to \emph{CP} violation. We calculate the rate asymmetries of decays of charginos into the lightest neutralino and a $W$ boson on the basis of the most important loop contributions in the third generation squark sectors. It turns out that the \emph{CP} violating asymmetries can be a few per cent in typical regions of the parameter space of the MSSM. These processes would provide very promising channels for probing \emph{CP} violation in the MSSM at future high-energy colliders.
We numerically investigate the dynamics of multiply charged hydrogenic ions in near-optical linearly polarized laser fields with intensities of order 10^16 to 10^17 W/cm^2. Depending on the charge state Z of the ion the relation of strength between laser field and ionic core changes. We find around Z=12 typical multiphoton dynamics and for Z=3 tunneling behaviour, however with clear relativistic signatures. In first order in v/c the magnetic field component of the laser field induces a Z-dependent drift in the laser propagation direction and a substantial Z-dependent angular momentum with repect to the ionic core. While spin oscillations occur already in first order in v/c as described by the Pauli equation, spin induced forces via spin orbit coupling only appear in the parameter regime where (v/c)^2 corrections are significant. In this regime for Z=12 ions we show strong splittings of resonant spectral lines due to spin-orbit coupling and substantial corrections to the conventional Stark shift due to the relativistic mass shift while those to the Darwin term are shown to be small. For smaller charges or higher laser intensities, parts of the electronic wavepacket may tunnel through the potential barrier of the ionic core, and when recombining are shown to give rise to keV harmonics in the radiation spectrum. Some parts of the wavepacket do not recombine after ionisation and we find very energetic electrons in the weakly relativistic regime of above threshold ionization.
The crossing properties of the matrix elements of non-local operators, parameterized by Generalized Parton Distribution, are considered. They are especially simple in terms of the Double Distributions which are common for the various kinematical regions. As a result, Double Distributions may be in principle extracted from the combined data in these regions by making use of the inverse Radon transform, known as a standard method in tomography. The ambiguities analogous to the ones for the vetor potential in the two-dimensional magneto-statics are outlined. The possible generalizations are discussed.
We prove here the Melin H\"ormander inequality for operators with multiple characteristics.
We review recent observational and theoretical results concerning the presence of actinide nuclei on the surfaces of old halo stars and their use as an age determinant. We present model calculations which show that the observed universality of abundances for 56 < Z < 75 elements in these stars does not imply a unique astrophysical site for the r-process. Neither does it imply a universality of abundances of nuclei outside of this range. In particular, we show that a variety of astrophysical $r$-process models can be constructed which reproduce the same observed universal r-process curve for 56 < Z < 75 nuclei, yet have vastly different abundances for Z >= 75 and possibly Z <= 56 as well. This introduces an uncertainty into the use of the Th/Eu chronometer as a means to estimate the ages of the metal deficient stars. We do find, however, that the U/Th ratio is a robust chronometer. This is because the initial production ratio of U to Th is almost independent of the astrophysical nucleosynthesis environment. The largest remaining uncertainties in the U/Th initial production ratio are due to the input nuclear physics models.
With the data from the Atmospheric Imaging Assembly (AIA) and the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO), we present a magnetic interaction between an isolated coronal hole (CH) and an emerging active region (AR). The AR emerged nearby the CH and interacted with it. Bright loops constantly formed between them, which led to a continuous retreat of the CH boundaries (CHBs). Meanwhile, two coronal dimmings respectively appeared at the negative polarity of the AR and the east boundary of the bright loops, and the AR was partly disturbed. Loop eruptions followed by a flare occurred in the AR. The interaction was also accompanied by many jets and an arc-shaped brightening that appeared to be observational signatures of magnetic reconnection at the CHBs. By comparing the observations with the derived coronal magnetic configuration, it is suggested that the interaction between the CH and the AR excellently fitted in with the model of interchange reconnection. It appears that our observations provide obvious evidences for interchange reconnection.
We introduce screw functions for Dirichlet series in the extended Selberg class. Then we prove that the Grand Riemann Hypothesis for a member of the extended Selberg class is equivalent to the nonpositivity of the corresponding screw function.
Using a broadband, high spectral resolution survey toward Orion KL acquired with Herschel/HIFI as part of the HEXOS key program, we derive the abundances of H$_2$O and HDO in the different spatial/velocity components associated with this massive star-forming region: the Hot Core, Compact Ridge, and Plateau. A total of 20 transitions of H$_2$$^{18}$O, 14 of H$_2$$^{17}$O, 37 of HD$^{16}$O, 6 of HD$^{18}$O, and 6 of D$_2$O are used in the analysis, spanning from ground state transitions to over 1200 K in upper-state energy. Low-excitation lines are detected in multiple components, but the highest-excitation lines ($E_u >$ 500 K) are well modeled as emitting from a small ($\sim 2"$) clump with a high abundance of H$_2$O ($\chi = 6.5 \times 10^{-4}$ relative to H$_2$) and a HDO/H$_2$O ratio of 0.003. Using high spatial resolution ($1.5" \times 1.1"$) images of two transitions of HDO measured by ALMA as part of its science verification phase, we identify this component as located near, but not directly coincident with, known continuum sources in the Hot Core region. Significant HDO/H$_2$O fractionation is also seen in the Compact Ridge and Plateau components. The outflowing gas, observed with both emission and absorption components, has a lower HDO/H$_2$O ratio than the compact components in Orion KL, which we propose could be due to modification by gas-phase shock chemistry.
We present our calculation of the correlator $<T\{V_sV_s^\dag\} >$ between two external vector-currents with the quantum-numbers of a charged kaon. The renormalized expression to $O(p^6)$ in $SU(3) \times SU(3)$ standard chiral perturbation theory is finite and scale-independent. The result is used to determine, via an IMFESR, the phenomenologically relevant finite $O(p^6)$-counterterm combination $Q_V$ in a way which is not sensitive to isospin breaking.
This is a survey primarily about determining the border rank of tensors, especially those relevant for the study of the complexity of matrix multiplication. This is a subject that on the one hand is of great significance in theoretical computer science, and on the other hand touches on many beautiful topics in algebraic geometry such as classical and recent results on equations for secant varieties (e.g., via vector bundle and representation-theoretic methods) and the geometry and deformation theory of zero dimensional schemes.
In this note we set up the elliptic and the parabolic Dirichlet problem for linear nonlocal operators. As opposed to the classical case of second order differential operators, here the "boundary data" are prescribed on the complement of a given bounded set. We formulate the problem in the classical framework of Hilbert spaces and prove unique solvability using standard techniques like the Fredholm alternative.