ShantanuT01/DACTYL-Pretraining huggingface dataset:
Insulator-to-metal transition in Ca$_{2}$RuO$_{4}$ has drawn keen attention because of its sensitivity to various stimulation and its potential controllability. Here, we report a direct observation of Fermi surface, which emerges upon introducing excess oxygen into an insulating Ca$_{2}$RuO$_{4}$, by using angle-resolved photoemission spectroscopy. Comparison between energy distribution curves shows that the Mott insulating gap is closed by eV-scale spectral-weight transfer with excess oxygen. Momentum-space mapping exhibits two square-shaped sheets of the Fermi surface. One is a hole-like $\alpha$ sheet around the corner of a tetragonal Brillouin zone, and the other is an electron-like $\beta$ sheet around the $\Gamma$ point. The electron occupancies of the $\alpha$ and $\beta$ bands are determined to be $n_{\alpha}=1.6$ and $n_{\beta}=0.6$, respectively. Our result indicates that the insulator-to-metal transition occurs selectively in $d_{xz}$ and $d_{yz}$ bands and not yet in $d_{xy}$ band. This orbital selectivity is most likely explained in terms of the energy level of $d_{xy}$, which is deeper for Ca$_{2}$RuO$_{4+\delta}$ than for Ca$_{1.8}$Sr$_{0.2}$RuO$_{4}$. Consequently, we found substantial differences from the Fermi surface of other ruthenates, shedding light on a unique role of excess oxygen among the metallization methods of Ca$_{2}$RuO$_{4}$.
We show how to extend traditional intrinsic image decompositions to incorporate further layers above albedo and shading. It is hard to obtain data to learn a multi-layer decomposition. Instead, we can learn to decompose an image into layers that are "like this" by authoring generative models for each layer using proxy examples that capture the Platonic ideal (Mondrian images for albedo; rendered 3D primitives for shading; material swatches for shading detail). Our method then generates image layers, one from each model, that explain the image. Our approach rests on innovation in generative models for images. We introduce a Convolutional Variational Auto Encoder (conv-VAE), a novel VAE architecture that can reconstruct high fidelity images. The approach is general, and does not require that layers admit a physical interpretation.
We review some of the common methods for model selection: the goodness of fit, the likelihood ratio test, Bayesian model selection using Bayes factors, and the classical as well as the Bayesian information theoretic approaches. We illustrate these different approaches by comparing models for the expansion history of the Universe. In the discussion we highlight the premises and objectives entering these different approaches to model selection and finally recommend the information theoretic approach.
In this talk, I present the minimal classically scale-invariant and $CP$-symmetric extension of the standard model, containing one additional complex gauge singlet and three flavors of right-handed Majorana neutrinos, incorporated within a renormalizable framework of gravity, consistent with these symmetries; the Agravity. I particularly focus on the slow-roll inflationary paradigm within this framework, by identifying the pseudo-Nambu-Goldstone boson of the (approximate) scale symmetry with the inflaton field, constructing its one-loop effective potential, computing the slow-roll parameters and the inflationary observables, and demonstrating the compatibility of the small field inflation scenario with the latest Planck collaboration data sets.
In this paper we develop and use successive averaging methods for explaining the regularization mechanism in the the periodic Korteweg--de Vries (KdV) equation in the homogeneous Sobolev spaces $\dot{H}^s$, for $s\ge0$. Specifically, we prove the global existence, uniqueness, and Lipschitz continuous dependence on the initial data of the solutions of the periodic KdV. For the case where the initial data is in $L_2$ we also show the Lipschitz continuous dependence of these solutions with respect to the initial data as maps from $\dot{H}^s$ to $\dot{H}^s$, for $s\in(-1,0]$.
In this article, we show -- using a reasoning applicable to both the excitation spectrum in the chiral bag model and the hyperfine structure of diatomic molecules -- that the generic form of a non- abelian Berry potential appears in heavy-quark effective theory (HQET) and that the Berry potential vanishes for the soliton- heavy meson bound state in the heavy-quark limit. The vanishing of the Berry potential in HQET is shown to be related to the restoration of heavy-quark symmetry in infinite heavy-quark-mass limit in close analogy to diatomic molecules at infinite internuclear separation.
Pion exchange in S-wave between hadrons that are themselves in a relative S-wave is shown to shift energies by hundreds of MeV, leading to deeply bound quasi-molecular states. In the case of charmed mesons $D^*,D_1$ a spectroscopy arises consistent with enigmatic charmonium states observed above 4 GeV in $e^+e^-$ annihilation. A possible explanation of $Y(4260)\to \psi\pi\pi$ and $Y(4360) \to \psi'\pi\pi$ is found. We give results for all isospin and charge-conjugation combinations, and comment on flavor exotic doubly charmed states and bottomonium analogs. A search in $D\bar{D}3\pi$ is recommended to test this hypothesis. An exotic $1^{-+}$ is predicted to occur in the vicinity of the $Y$(4260).
In \cite{botero}, a top intersection product of toric b-divisors on a smooth complete toric variety is defined. It is shown that a nef toric b-divisor corresponds to a convex set and that its top intersection number equals the volume of this convex set. The goal of this article is to extend this result and define an intersection product of sufficiently positive toric b-classes of arbitrary codimension. For this, we extend the polytope algebra of McMullen (\cite{McM1}, \cite{McM2}, \cite{McM3}) to the so called \emph{convex-set algebra} and we show that it embeds in the toric b-Chow group. In this way, the convex-set algebra can be viewed as a ring for an intersection theory for sufficiently positive toric b-classes. As an application, we show that some Hodge type inequalities are satisfied for the convex-set algebra.
We are concerned with the decay of long time solutions of the initial value problem associated with the Schr\"odinger-Korteweg-de Vries system. We use recent techniques in order to show that solutions of this system decay to zero in the energy space. The result is independent of the integrability of the equations involved and it does not require any size assumptions.
For a random variable we can define a variational relationship with practical physical meaning as dI=dbar(x)-bar(dx), where I is called as uncertainty measurement. With the help of a generalized definition of expectation, bar(x)=sum_(i)g(p_i)x_i, and the expression of dI, we can find the concrete forms of the maximizable entropies for any given probability distribution function, where g(p_i) may have different forms for different statistics which includes the extensive and nonextensive statistics.
In this article we derive Talagrand's $T_2$ inequality on the path space w.r.t. the maximum norm for various stochastic processes, including solutions of one-dimensional stochastic differential equations with measurable drifts, backward stochastic differential equations, and the value process of optimal stopping problems.   The proofs do not make use of the Girsanov method, but of pathwise arguments. These are used to show that all our processes of interest are Lipschitz transformations of processes which are known to satisfy desired functional inequalities.
We consider a toy model for the supermassive compact object at the galactic center that does not require the presence of a black hole. We assume a matter distribution of weakly interacting particles with a density profile inferred from dark matter profiles in the outer regions. We show that rotation curves close to the center of the Milky Way galaxy can be explained within this model. We also show that the motion of test particles (stars) at distances of the order of 100 astronomical units can not be distinguished from the motion of corresponding particles in the Schwarzschild geometry. However, differences arise at shorter distances, suggesting that it could be possible to observationally test the validity of the model in the near future.
For integers $k\ge 2$ and $N\ge 2k+1$ there are $k!2^k$ canonical orderings of the edges of the complete $k$-uniform hypergraph with vertex set $[N] = \{1,2,\dots, N\}$. These are exactly the orderings with the property that any two subsets $A, B\subseteq [N]$ of the same size induce isomorphic suborderings. We study the associated canonisation problem to estimate, given $k$ and $n$, the least integer $N$ such that no matter how the $k$-subsets of $[N]$ are ordered there always exists an $n$-element set $X\subseteq [N]$ whose $k$-subsets are ordered canonically. For fixed $k$ we prove lower and upper bounds on these numbers that are $k$ times iterated exponential in a polynomial of $n$.
Thin astrophysical discs are very often modelled using the equations of two-dimensional hydrodynamics. We derive an extension of this model that describes more accurately the behaviour of a thin disc in the absence of self-gravity, magnetic fields and complex internal motions. The ideal fluid theory is derived directly from Hamilton's Principle for a three-dimensional fluid after making a specific approximation to the deformation gradient tensor. We express the equations in Eulerian form after projection on to a reference plane. The disc is thought of as a set of fluid columns, each of which is capable of a time-dependent affine transformation, consisting of a translation together with a linear transformation in three dimensions. Therefore, in addition to the usual two-dimensional hydrodynamics in the reference plane, the theory allows for a deformation of the midplane (as occurs in warped discs) and for the internal shearing motions that accompany such deformations. It also allows for the vertical expansions driven in non-circular discs by a variation of the vertical gravitational field around the horizontal streamlines, or by a divergence of the horizontal velocity. The equations of the affine model embody conservation laws for energy and potential vorticity, even for non-planar discs. We verify that they reproduce exactly the linear theories of three-dimensional warped and eccentric discs in a secular approximation. However, the affine model does not rely on any secular or small-amplitude assumptions and should be useful in more general circumstances.
The Adam-Gibbs (AG) relation connects the dynamics of a glass-forming liquid to its the thermodynamics via. the configurational entropy, and is of fundamental importance in descriptions of glassy behaviour. The breakdown of the Stokes-Einstein (SEB) relation between the diffusion coefficient and the viscosity (or structural relaxation times) in glass formers raises the question as to which dynamical quantity the AG relation describes. By performing molecular dynamics simulations, we show that the AG relation is valid over the widest temperature range for the diffusion coefficient and not for the viscosity or relaxation times. Studying relaxation times defined at a given wavelength, we find that SEB and the deviation from the AG relation occur below a temperature at which the correlation length of dynamical heterogeneity equals the wavelength probed.
Due to the incompatibility of the nonlinear realization of superconformal symmetry and dilatation symmetry with the dilaton as the compensator field, in the present paper it shows an alternative mechanism of spontaneous breaking the N=2 superconformal symmetry to the N=0 case. By using the approach of nonlinear transformations it is found that it leads to a space-filling brane theory with Weyl scale W(1,3) symmetry. The dynamics of the resulting Weyl scale invariant brane, along with that of other Nambu-Goldstone fields, is derived in terms of the building blocks of the vierbein and the covariant derivative from the Maurer-Cartan oneforms. A general coupling of the matter fields localized on the brane world volume to these NG fields is also constructed.
In this paper, we want to investigate some kind of Dynkin's game under ambiguity which is represented by Backward Stochastic Differential Equation (shortly BSDE) with standard generator function g(t, y, z). Under regular assumptions, a pair of saddle point can be obtained and the existence of the value function follows. The constrained case is also treated in this paper.
The study and development of software able to show the effect of aging of faces is one of the tasks of face recognition technologies. Some software solutions are used for investigations, some others to show the effects of drugs on healthy appearance, however some other applications can be proposed for the analysis of visual arts. Here we use a freely available software, which is providing interesting results, for the comparison of ancient marble busts. An analysis of Augustus busts is proposed.
Let $p \geq 3$ be a prime. Let $E/\mathbb{Q}$ and $E'/\mathbb{Q}$ be elliptic curves with isomorphic $p$-torsion modules $E[p]$ and $E'[p]$. Assume further that either (i) every $G_\mathbb{Q}$-modules isomorphism $\phi : E[p] \to E'[p]$ admits a multiple $\lambda \cdot \phi$ with $\lambda \in \mathbb{F}_p^\times$ preserving the Weil pairing; or (ii) no $G_\mathbb{Q}$-isomorphism $\phi : E[p] \to E'[p]$ preserves the Weil pairing. This paper considers the problem of deciding if we are in case (i) or (ii).   Our approach is to consider the problem locally at a prime $\ell \neq p$. Firstly, we determine the primes $\ell$ for which the local curves $E/\mathbb{Q}_\ell$ and $E'/\mathbb{Q}_\ell$ contain enough information to decide between (i) or (ii). Secondly, we establish a collection of criteria, in terms of the standard invariants associated to minimal Weierstrass models of $E/\mathbb{Q}_\ell$ and $E'/\mathbb{Q}_\ell$, to decide between (i) and (ii). We show that our results give a complete solution to the problem by local methods away from $p$.   We apply our methods to show the non-existence of rational points on certain hyperelliptic curves of the form $y^2 = x^p - \ell$ and $y^2 = x^p - 2\ell$ where $\ell$ is a prime; we also give incremental results on the Fermat equation $x^2 + y^3 = z^p$. As a different application, we discuss variants of a question raised by Mazur concerning the existence of symplectic isomorphisms between the $p$-torsion of two non-isogenous elliptic curves defined over $\mathbb{Q}$.
Vector graphic documents present visual elements in a resolution free, compact format and are often seen in creative applications. In this work, we attempt to learn a generative model of vector graphic documents. We define vector graphic documents by a multi-modal set of attributes associated to a canvas and a sequence of visual elements such as shapes, images, or texts, and train variational auto-encoders to learn the representation of the documents. We collect a new dataset of design templates from an online service that features complete document structure including occluded elements. In experiments, we show that our model, named CanvasVAE, constitutes a strong baseline for generative modeling of vector graphic documents.
Configurable and scalable continuous variable quantum networks for measurement-based quantum information protocols or multipartite quantum communication schemes can be obtained via parametric down conversion (PDC) in non-linear waveguides. In this work, we exploit symmetric group velocity matching (SGVM) to engineer the properties of the squeezed modes of the PDC. We identify type II PDC in a single waveguide as the best suited process, since multiple modes with non-negligible amount of squeezing can be obtained. We explore, for the first time, the waveguide dimensions, usually only set to ensure single-mode guiding, as an additional design parameter ensuring indistinguishability of the signal and idler fields. We investigate here potassium titanyl phosphate (KTP), which offers SGVM at telecommunications wavelengths, but our approach can be applied to any non-linear material and pump wavelength. This work paves the way towards the engineering of future large-scale quantum networks in the continuous variable regime.
Saturn's largest satellite, Titan, transited the Crab Nebula on 5 January 2003. We observed this astronomical event with the {\it Chandra} X-ray Observatory. An ``occultation shadow'' has clearly been detected and is found to be larger than the diameter of Titan's solid surface. The difference gives a thickness for Titan's atmosphere of 880 $\pm$ 60 km. This is the first measurement of Titan's atmospheric extent at X-ray wavelengths. The value measured is consistent with or slightly larger than those estimated from earlier Voyager observations at other wavelengths. We discuss the possibility of temporal variations in the thickness of Titan's atmosphere.
The eikonal model must be denoted as strongly preferable for the analysis of elastic high-energy hadron collisions. The given approach allows to derive corresponding impact parameter profiles that characterize important physical features of nucleon collisions, e.g., the range of different forces. The contemporary phenomenological analysis of experimental data is, however, not able to determine these profiles unambiguously, i.e., it cannot give the answer whether the elastic hadron collisions are more central or more peripheral than the inelastic ones. However, in the collisions of mass objects (like protons) the peripheral behavior of elastic collisions should be preferred.
We show that the valence electrons of Ba3NaRu2O9, which has a quasi-molecular structure, completely crystallize below 210 K. Using an extended Hubbard model, we show that the charge ordering instability results from long-range Coulomb interactions. However, orbital ordering, metal-metal bonding and formation of a partial spin gap enforce the magnitude of the charge separation. The striped charge order and frustrated hcp lattice of Ru2O9 dimers lead to competition with a quasi-degenerate charge-melted phase under photo-excitation at low temperature. Our results establish a broad class of simple metal oxides as models for emergent phenomena at the border between the molecular and solid states.
We present a tight binding theory to analyze the motion of electrons between carbon nanotubes bundled into a carbon nanotube rope. The theory is developed starting from a description of the propagating Bloch waves on ideal tubes, and the effects of intertube motion are treated perturbatively in this basis. Expressions for the interwall tunneling amplitudes between states on neighboring tubes are derived which show the dependence on chiral angles and intratube crystal momenta. We find that conservation of crystal momentum along the tube direction suppresses interwall coherence in a carbon nanorope containing tubes with random chiralities. Numerical calculations are presented which indicate that electronic states in a rope are localized in the transverse direction with a coherence length corresponding to a tube diameter.
We derive a model describing the evolution of a nematic liquid-crystal material under the action of thermal effects. The first and second laws of thermodynamics lead to an extension of the general Ericksen-Leslie system where the Leslie stress tensor and the Oseen-Frank energy density are considered in their general forms. The work postulate proposed by Ericksen-Leslie is traduced in terms of entropy production. We finally analyze the global-in-time well-posedness of the system for small initial data in the framework of Besov spaces.
In this paper, we extend our convexity theory for $C^2$ cost functions in optimal transportation to more general generating functions, which were originally introduced by the second author to extend the framework of optimal transportation to embrace near field geometric optics. In particular we provide an alternative geometric treatment to the previous analytic approach using differential inequalities, which also gives a different derivation of the invariance of the fundamental regularity conditions under duality. We also extend our local theory to cover the strict version of these conditions for $C^2$ cost and generating functions.
After a brief review of integrability, first in the absence and then in the presence of a boundary, I outline the construction of actions for the N=1 and N=2 boundary sine-Gordon models. The key point is to introduce Fermionic boundary degrees of freedom in the boundary actions.
The generic element of the moduli space of logarithmic connections with parabolic points on holomorphic vector bundle over the Riemann sphere can be represented by a Fuchsian equation with some singularities and some apparent singularities. We analyze the case of rank $3$ vector bundle which leads to third order Fuchsian equation. We find coordinates on an open subset of the moduli space and we construct a non-trivial part of the moduli space by blowing up along a variety in a special case.
Classification and localization are two pillars of visual object detectors. However, in CNN-based detectors, these two modules are usually optimized under a fixed set of candidate (or anchor) bounding boxes. This configuration significantly limits the possibility to jointly optimize classification and localization. In this paper, we propose a Multiple Instance Learning (MIL) approach that selects anchors and jointly optimizes the two modules of a CNN-based object detector. Our approach, referred to as Multiple Anchor Learning (MAL), constructs anchor bags and selects the most representative anchors from each bag. Such an iterative selection process is potentially NP-hard to optimize. To address this issue, we solve MAL by repetitively depressing the confidence of selected anchors by perturbing their corresponding features. In an adversarial selection-depression manner, MAL not only pursues optimal solutions but also fully leverages multiple anchors/features to learn a detection model. Experiments show that MAL improves the baseline RetinaNet with significant margins on the commonly used MS-COCO object detection benchmark and achieves new state-of-the-art detection performance compared with recent methods.
Numerical studies of the gravitational collapse of a stiff (P=rho) fluid have found the now familiar critical phenomena, namely scaling of the black hole mass with a critical exponent and continuous self-similarity at the threshold of black hole formation. Using the equivalence of an irrotational stiff fluid to a massless scalar field, we construct the critical solution as a scalar field solution by making a self-similarity ansatz. We find evidence that this solution has exactly one growing perturbation mode; both the mode and the critical exponent, gamma ~ 0.94, derived from its eigenvalue agree with those measured in perfect fluid collapse simulations. We explain why this solution is seen as a critical solution in stiff fluid collapse but not in scalar field collapse, and conversely why the scalar field critical solution is not seen in stiff fluid collapse, even though the two systems are locally equivalent.