ShantanuT01/DACTYL-Pretraining huggingface dataset:
The moduli space $\cM_g$ of nonsingular projective curves of genus $g$ is compactified into the moduli $\bcM_g$ of Deligne-Mumford stable curves of genus $g$. We compactify in a similar way the moduli space of abelian varieties by adding some mildly degenerating limits of abelian varieties. A typical case is the moduli space of Hesse cubics. Any Hesse cubic is GIT-stable in the sense that its $\SL(3)$-orbit is closed in the semistable locus, and conversely any GIT-stable planar cubic is one of Hesse cubics. Similarly in arbitrary dimension, the moduli space of abelian varieties is compactified by adding only GIT-stable limits of abelian varieties. Our moduli space is a projective "fine" moduli space of possibly degenerate abelian schemes {\it with non-classical non-commutative level structure}   over $\bZ[\zeta_{N},1/N]$ for some $N\geq 3$. The objects at the boundary are singular schemes, called PSQASes, projectively stable quasi-abelian schemes.
Let $n, k$ and $a$ be positive integers. The Stirling numbers of the first kind, denoted by $s(n,k)$, count the number of permutations of $n$ elements with $k$ disjoint cycles. Let $p$ be a prime. In recent years, Lengyel, Komatsu and Young, Leonetti and Sanna, Adelberg, Hong and Qiu made some progress in the study of the $p$-adic valuations of $s(n,k)$. In this paper, by using Washington's congruence on the generalized harmonic number and the $n$-th Bernoulli number $B_n$ and the properties of $m$-th Stirling numbers of the first kind obtained recently by the authors, we arrive at an exact expression or a lower bound of $v_p(s(ap, k))$ with $a$ and $k$ being integers such that $1\le a\le p-1$ and $1\le k\le ap$. This infers that for any regular prime $p\ge 7$ and for arbitrary integers $a$ and $k$ with $5\le a\le p-1$ and $a-2\le k\le ap-1$, one has $v_p(H(ap-1,k))<-\frac{\log{(ap-1)}}{2\log p}$ with $H(ap-1, k)$ being the $k$-th elementary symmetric function of $1, \frac{1}{2}, ..., \frac{1}{ap-1}$. This gives a partial support to a conjecture of Leonetti and Sanna raised in 2017. We also present results on $v_p(s(ap^n,ap^n-k))$ from which one can derive that under certain condition, for any prime $p\ge 5$, any odd number $k\ge 3$ and any sufficiently large integer $n$, if $(a,p)=1$, then $v_p(s(ap^{n+1},ap^{n+1}-))=v_p(s(ap^n,ap^n-k))+2$. It confirms partially Lengyel's conjecture proposed in 2015.
We introduce the concept of `discrete-time persistence', which deals with zero-crossings of a continuous stochastic process, X(T), measured at discrete times, T = n \Delta T. For a Gaussian Markov process with relaxation rate \mu, we show that the persistence (no crossing) probability decays as \rho(a)^n for large n, where a = \exp(-\mu \Delta T), and we compute \rho(a) to high precision. We also define the concept of `alternating persistence', which corresponds to a<0. For a>1, corresponding to motion in an unstable potential (\mu<0), there is a nonzero probability of having no zero-crossings in infinite time, and we show how to calculate it.
We study the Cauchy problems for the Hartree-type nonlinear Dirac equations with Yukawa-type potential in two and three spatial dimensions. This paper improves our previous results \cite{chohlee,cholee}; we establish global well-posedness and scattering for large data with a certain condition. Firstly we investigate the long-time behavior of solutions to the Dirac equation satisfies good control provided that a particular dispersive norm of solutions is bounded. The key of our proof relies on modifying multilinear estimates obtained in our previous papers. Secondly, we obtain large data scattering by exploiting the Majorana condition.
Given a number $r$, we consider the dynamical system generated by repeated exponentiations modulo $r$, that is, by the map $u \mapsto f_g(u)$, where $f_g(u) \equiv g^u \pmod r$ and $0 \le f_g(u) \le r-1$. The number of cycles of the defined above dynamical system is considered for $r=p^n$.
We interpret the close link between the critical points of Mather's barrier functions and minimal homoclinic orbits with respect to the Aubry sets on $\mathbb{T}^n$. We also prove a critical point theorem for barrier functions, and the existence of such homoclinic orbits on $\mathbb{T}^2$ as an application.
Orthorhombic SrIrO3 is a typical spin-orbit-coupling correlated metal that shows diversified physical properties under the external stimuli. Here nonlinear Hall effect and weakly temperature-dependent resistance are observed in a SrIrO3 film epitaxially grown on SrTiO3 substrate. It infers that orthorhombic SrIrO3 is a semimetal oxide. However, linear Hall effect and insensitive-temperature-dependent resistance are observed in SrIrO3 films grown on (La,Sr)(Al,Ta)O3 (LSAT) substrates, suggesting a tunable semimetallic state due to band structure change in SrIrO3 films under different compressive strain. The mechanism of this evolution is explored in detail through strain-state analysis by reciprocal space mapping and electron diffraction, carrier density and mobility calculations, as well as electronic band structure evolution under compressive strain (predicted by tight-binding approximation). It might suggest that the strain-induced band shift leads to the semimetallic tuning in the SrIrO3 film grown on from SrTiO3 to LSAT substrates. Our findings illustrate the tunability of SrIrO3 properties and pave the way to induce novel physical states in SrIrO3 such as the proposed topological insulator state in heterostructures.
We revisit the phase diagram of BaTiO$_3$ under biaxial strain using a first principles-based effective Hamiltonian approach. We show that, in addition to the tetragonal ($c$), quasi-rhombohedral ($r$), and quasi-orthorhombic ($aa$) ferroelectric phases, that have been discussed previously, there are temperature and strain regions, in particular under tensile strain, where the system decomposes into multi-domain structures. In such cases, the strained system, at least on a local level, recovers the same phase sequence as the unclamped bulk material. Furthermore, we extend these results from the case of "uniform" biaxial strain to the situation where the two in-plane lattice constants are strained differently and show that similar considerations apply in this case.
We construct the action of a relativistic spinning particle from a non-linear realization of a space-time odd vector extension of the Poincar\'e group. For particular values of the parameters appearing in the lagrangian the model has a gauge world-line supersymmetry.{As a consequence of this local symmetry there are BPS solutions in the model preserving 1/5 of the supersymmetries.} A supersymmetric invariant quantization produces two decoupled 4d Dirac equations.
We present a first-principles theoretical approach for evaluating the lattice thermal conductivity based on the exact solution of the Boltzmann transport equation. We use the variational principle and the conjugate gradient scheme, which provide us with an algorithm faster than the one previously used in literature and able to always converge to the exact solution. Three-phonon normal and umklapp collision, isotope scattering and border effects are rigorously treated in the calculation. Good agreement with experimental data for diamond is found. Moreover we show that by growing more enriched diamond samples it is possible to achieve values of thermal conductivity up to three times larger than the commonly observed in isotopically enriched diamond samples with 99.93% C12 and 0.07 C13.
For an arbitrary valued field $(K,v)$ and a given extension $v(K^*)\hookrightarrow\Lambda$ of ordered groups, we analyze the structure of the tree formed by all $\Lambda$-valued extensions of $v$ to the polynomial ring $K[x]$. As an application, we find a model for the tree of all equivalence classes of valuations on $K[x]$ (without fixing their value group), whose restriction to $K$ is equivalent to $v$.   In the henselian case, we apply these results to show that there is a complete parallelism between the arithmetic properties of irreducible polynomials $F\in K[x]$, encoded by their Okutsu frames, and the valuation-theoretic properties of their induced valuations $v_F$ on $K[x]$, encoded by their MacLane-Vaqui\'e chains. This parallelism was only known for defectless irreducible polynomials.
As a prelude to what might be expected as forthcoming breakthroughs in finding new approaches toward solving three-dimensional lattice models in the twenty-first century, we review the exact solutions of two lattice models in three dimensions obtained using the conventional combinatorial and transfer matrix approaches.
We show that a particular class of variational wave functions reproduces the low-energy properties of the Hubbard model in one dimension. Our approach generalizes to finite on-site Coulomb repulsion the fully-projected wave function proposed by Hellberg and Mele [Phys. Rev. Lett. {\bf 67}, 2080 (1991)] for describing the Luttinger-liquid behavior of the doped $t{-}J$ model. Within our approach, the long-range Jastrow factor emerges from a careful minimization of the energy, without assuming any parametric form for the long-distance tail. Specifically, in the conducting phase of the Hubbard model at finite hole doping, we obtain the correct power-law behavior of the correlation functions, with the exponents predicted by the Tomonaga-Luttinger theory. By decreasing the doping, the insulating phase is reached with a continuous change of the small-$q$ part of the Jastrow factor.
It is widely recognised that the effect of doping into a Mott insulator is complicated and unpredictable, as can be seen by examining the Hall coefficient in high $T_{\rm c}$ cuprates. The doping effect, including the electron-hole doping asymmetry, may be more straightforward in doped organic Mott insulators owing to their simple electronic structures. Here we investigate the doping asymmetry of an organic Mott insulator by carrying out electric-double-layer transistor measurements and using cluster perturbation theory. The calculations predict that strongly anisotropic suppression of the spectral weight results in the Fermi arc state under hole doping, while a relatively uniform spectral weight results in the emergence of a non-interacting-like Fermi surface in the electron-doped state. In accordance with the calculations, the experimentally observed Hall coefficients and resistivity anisotropy correspond to the pocket formed by the Fermi arcs under hole doping and to the non-interacting Fermi surface under electron doping.
We present the results of Monte Carlo simulations of the magnetic properties of a model for a single nanoparticle consisting in a ferromagnetic core surrounded by an antiferromagnetic shell. The simulations of hysteresis loops after cooling in a magnetic field display exchange bias effects. In order to understand the origin of the loop shifts, we have studied the thermal dependence of the shell and interface magnetizations under field cooling. These results, together with inspection of the snapshots of the configurations attained at low temperature, show the existence of a net magnetization at the interface which is responsible for the bias of the hysteresis loops.
Galactic outflows regulate the amount of gas galaxies convert into stars. However, it is difficult to measure the mass outflows remove because they span a large range of temperatures and phases. Here, we study the rest-frame ultraviolet spectrum of a lensed galaxy at z~2.9 with prominent interstellar absorption lines from O I, tracing neutral gas, up to O VI, tracing transitional phase gas. The O VI profile mimics weak low-ionization profiles at low velocities, and strong saturated profiles at high velocities. These trends indicate that O VI gas is co-spatial with the low-ionization gas. Further, at velocities blueward of -200 km/s the column density of the low-ionization outflow rapidly drops while the O VI column density rises, suggesting that O VI is created as the low-ionization gas is destroyed. Photoionization models do not reproduce the observed O VI, but adequately match the low-ionization gas, indicating that the phases have different formation mechanisms. Photoionized outflows are more massive than O VI outflows for most of the observed velocities, although the O VI mass outflow rate exceeds the photoionized outflow at velocities above the galaxy's escape velocity. Therefore, most gas capable of escaping the galaxy is in a hot outflow phase. We suggest that the O VI absorption is a temporary by-product of conduction transferring mass from the photoionized phase to an unobserved hot wind, and discuss how this mass-loading impacts the observed circum-galactic medium.
Force-free magnetic fields are important in many astrophysical settings. Determining the properties of such force-free fields -- especially smoothness and stability properties -- is crucial to understanding many key phenomena in astrophysical plasmas, for example energy release processes that heat the plasma and lead to dynamic or explosive events. Here we report on a serious limitation on the computation of force-free fields that has the potential to invalidate the results produced by numerical force-free field solvers even for cases in which they appear to converge (at fixed grid resolution) to an equilibrium magnetic field. In the present work we discuss this problem within the context of a Lagrangian relaxation scheme that conserves magnetic flux and div(B) identically. Error estimates are introduced to assess the quality of the calculated equilibrium. We go on to present an algorithm, based on re-writing the curl operation via Stokes' theorem, for calculating the current which holds great promise for improving dramatically the accuracy of the Lagrangian relaxation procedure.
We discover that the very young very low-mass star ISO143 (M5) is driving an outflow based on spectro-astrometry of forbidden [SII] emission lines at 6716A and 6731A observed in UVES/VLT spectra. This adds another object to the handful of brown dwarfs and very low-mass stars (M5-M8) for which an outflow has been confirmed and which show that the T Tauri phase continues at very low masses. We find the outflow of ISO143 to be intrinsically asymmetric and the accretion disk to not obscure the outflow, as only the red outflow component is visible in the [SII] lines. ISO143 is only the third T Tauri object showing a stronger red outflow component in spectro-astrometry, after RW Aur (G5) and ISO217 (M6.25). We show here that including ISO143 two out of seven outflows confirmed in the very low-mass regime (M5-M8) are intrinsically asymmetric. We measure a spatial extension of the outflow in [SII] of up to 200-300 mas (about 30-50 AU) and velocities of up to 50-70 km/s. We furthermore detect line emission of ISO143 in CaII (8498), OI (8446), HeI (7065), and weakly in [FeII] (7155). Based on a line profile analysis and decomposition we demonstrate that (i) the CaII emission can be attributed to chromospheric activity, a variable wind, and the magnetospheric infall zone, (ii) the OI emission mainly to accretion-related processes but also a wind, and (iii) the HeI emission to chromospheric or coronal activity. We estimate a mass outflow rate of ISO143 of ~10^{-10} Msol/yr and a mass accretion rate in the range of ~10^{-8} to ~10^{-9} Msol/yer. These values are consistent with those of other brown dwarfs and very low-mass stars. The derived Mout/Macc ratio of 1-20% is not supporting previous findings of this number to be very large (>40%) for very low-mass objects.
Recognition of objects with subtle differences has been used in many practical applications, such as car model recognition and maritime vessel identification. For discrimination of the objects in fine-grained detail, we focus on deep embedding learning by using a multi-task learning framework, in which the hierarchical labels (coarse and fine labels) of the samples are utilized both for classification and a quadruplet-based loss function. In order to improve the recognition strength of the learned features, we present a novel feature selection method specifically designed for four training samples of a quadruplet. By experiments, it is observed that the selection of very hard negative samples with relatively easy positive ones from the same coarse and fine classes significantly increases some performance metrics in a fine-grained dataset when compared to selecting the quadruplet samples randomly. The feature embedding learned by the proposed method achieves favorable performance against its state-of-the-art counterparts.
Prevalent techniques in zero-shot learning do not generalize well to other related problem scenarios. Here, we present a unified approach for conventional zero-shot, generalized zero-shot and few-shot learning problems. Our approach is based on a novel Class Adapting Principal Directions (CAPD) concept that allows multiple embeddings of image features into a semantic space. Given an image, our method produces one principal direction for each seen class. Then, it learns how to combine these directions to obtain the principal direction for each unseen class such that the CAPD of the test image is aligned with the semantic embedding of the true class, and opposite to the other classes. This allows efficient and class-adaptive information transfer from seen to unseen classes. In addition, we propose an automatic process for selection of the most useful seen classes for each unseen class to achieve robustness in zero-shot learning. Our method can update the unseen CAPD taking the advantages of few unseen images to work in a few-shot learning scenario. Furthermore, our method can generalize the seen CAPDs by estimating seen-unseen diversity that significantly improves the performance of generalized zero-shot learning. Our extensive evaluations demonstrate that the proposed approach consistently achieves superior performance in zero-shot, generalized zero-shot and few/one-shot learning problems.
We generalize our previous model for $\gamma^* p$ scattering to $\gamma \gamma$ scattering. In the latter case the number of components naturally grows. When using the model parameters from our previous $\gamma^* p$ analysis the model cross section for $\gamma \gamma$ scattering is larger than the corresponding LEP2 experimental data by more than a factor of two. However, performing a new simultaneous fit to $\gamma^* p$ and $\gamma \gamma$ total cross section we can find an optimal set of parameters to describe both processes. We propose new measures of factorization breaking for $\gamma^* \gamma^*$ collisions and present results for our new model.
We report on a special type of solutions for the gluon propagator of pure QCD, obtained from the corresponding non-linear Schwinger-Dyson equation formulated in the Feynman gauge of the background field method. These solutions reach a finite value in the deep infrared and may be fitted using a massive propagator, with the crucial characteristic that the effective ``mass'' employed depends on the momentum transfer. Specifically, the gluon mass falls off as the inverse square of the momentum, as expected from the operator-product expansion. In addition, one may define a dimensionless quantity, which constitutes the generalization in a non-Abelian context of the universal QED effective charge. This strong effective charge displays asymptotic freedom in the ultraviolet whereas in the low-energy regime it freezes at a finite value, giving rise to an infrared fixed point for QCD.
We theoretically investigate the electronic transport properties of curved graphene waveguides by employing non-equilibrium Green's function techniques. We systematically study the dependence of the confined waveguide modes on the potential difference, the width of waveguide and side barrier. Through two-terminal electronic transport calculations, we show that the conductance of confined waveguide modes is rather robust against the bending degree of waveguide, in consistent with the band insensitivity to the side barrier. This finding of the perfectly conducting channels strongly suggests the possibility of applying the graphene waveguide in the design of low-power nanoelectronics.
We present the elements of QEDXQCD exponentiation and its interplay with shower/ME matching in precision LHC physics scenarios. Applications to single heavy gauge boson production at hadron colliders are illustrated.
We report the discovery in our HST ACS B, V, and I images of NGC 4449 of a globular cluster (GC) which appears associated with two tails of blue stars. The cluster is massive (M~1.7x10^6 M_sun) and highly flattened (\epsilon~0.24). From the color-magnitude diagrams of the resolved stars we infer active star formation in the tails over the past ~200 Myr. In a diagram of mean projected mass density inside r_e versus total mass the cluster lies at the upper end of the GC distribution, where galaxy nuclei are. The north-west tail is associated with a concentration of HI and infrared (dust/PAHs) emission which appears as part of a much longer stream wrapping around the galaxy. These properties suggest that the cluster may be the nucleus of a former gas-rich satellite galaxy undergoing tidal disruption by NGC 4449. If so, the cluster is seen in an earlier phase compared to other suggested nuclei of disrupted galaxies such as \omega Cen (Milky Way) and G1 (M31).
Human action recognition from skeletal data is a hot research topic and important in many open domain applications of computer vision, thanks to recently introduced 3D sensors. In the literature, naive methods simply transfer off-the-shelf techniques from video to the skeletal representation. However, the current state-of-the-art is contended between to different paradigms: kernel-based methods and feature learning with (recurrent) neural networks. Both approaches show strong performances, yet they exhibit heavy, but complementary, drawbacks. Motivated by this fact, our work aims at combining together the best of the two paradigms, by proposing an approach where a shallow network is fed with a covariance representation. Our intuition is that, as long as the dynamics is effectively modeled, there is no need for the classification network to be deep nor recurrent in order to score favorably. We validate this hypothesis in a broad experimental analysis over 6 publicly available datasets.
In this work we prove the real Nullstellensatz for the ring ${\mathcal O}(X)$ of analytic functions on a $C$-analytic set $X\subset{\mathbb R}^n$ in terms of the saturation of \L ojasiewicz's radical in ${\mathcal O}(X)$: The ideal ${\mathcal I}({\mathcal Z}({\mathfrak a}))$ of the zero-set ${\mathcal Z}({\mathfrak a})$ of an ideal ${\mathfrak a}$ of ${\mathcal O}(X)$ coincides with the saturation $\widetilde{\sqrt[\text{\L}]{{\mathfrak a}}}$ of \L ojasiewicz's radical $\sqrt[\text{\L}]{{\mathfrak a}}$. If ${\mathcal Z}({\mathfrak a})$ has `good properties' concerning Hilbert's 17th Problem, then ${\mathcal I}({\mathcal Z}({\mathfrak a}))=\widetilde{\sqrt[\mathsf{r}]{{\mathfrak a}}}$ where $\sqrt[\mathsf{r}]{{\mathfrak a}}$ stands for the real radical of ${\mathfrak a}$. The same holds if we replace $\sqrt[\mathsf{r}]{{\mathfrak a}}$ with the real-analytic radical $\sqrt[\mathsf{ra}]{{\mathfrak a}}$ of ${\mathfrak a}$, which is a natural generalisation of the real radical ideal in the $C$-analytic setting. We revisit the classical results concerning (Hilbert's) Nullstellensatz in the framework of (complex) Stein spaces.   Let ${\mathfrak a}$ be a saturated ideal of ${\mathcal O}({\mathbb R}^n)$ and $Y_{{\mathbb R}^n}$ the germ of the support of the coherent sheaf that extends ${\mathfrak a}{\mathcal O}_{{\mathbb R}^n}$ to a suitable complex open neighbourhood of ${\mathbb R}^n$. We study the relationship between a normal primary decomposition of ${\mathfrak a}$ and the decomposition of $Y_{{\mathbb R}^n}$ as the union of its irreducible components. If ${\mathfrak a}:={\mathfrak p}$ is prime, then ${\mathcal I}({\mathcal Z}({\mathfrak p}))={\mathfrak p}$ if and only if the (complex) dimension of $Y_{{\mathbb R}^n}$ coincides with the (real) dimension of ${\mathcal Z}({\mathfrak p})$.