ShantanuT01/DACTYL-Pretraining huggingface dataset:
The initial value problem for the $L^{2}$ critical semilinear Schr\"odinger equation with periodic boundary data is considered. We show that the problem is globally well posed in $H^{s}({\Bbb T^{d}})$, for $s>4/9$ and $s>2/3$ in 1D and 2D respectively, confirming in 2D a statement of Bourgain in \cite{bo2}. We use the ``$I$-method''. This method allows one to introduce a modification of the energy functional that is well defined for initial data below the $H^{1}({\Bbb T^{d}})$ threshold. The main ingredient in the proof is a "refinement" of the Strichartz's estimates that hold true for solutions defined on the rescaled space, $\Bbb T^{d}_{\lambda} = \Bbb R^{d}/{\lambda \Bbb Z^{d}}$, $d=1,2$.
Fuzzy dark matter (FDM) is a well motivated candidate for dark matter (DM) as its tiny mass and large de-Broglie wavelength suppress small-scale matter fluctuations, thereby solving some of the small-scale discrepancies in $\Lambda$CDM. Although it has been ruled out as the single component of DM by several observables, there is still a region in the FDM parameter space (the "FDM window", $10^{-25}\,\mathrm{eV}\lesssim m_\mathrm{FDM}\lesssim10^{-23}\,\mathrm{eV}$) where FDM is allowed to comprise a large portion of the total DM. In this work, for the first time, we study the signature of FDM (comprised of ultra-light axions) in fractions less than unity on the 21cm signal and its detectability by 21cm interferometers such as HERA, taking into account the degeneracy with both astrophysical and cosmological parameters, using a new pipeline that combines modified versions of the CAMB and 21cmFAST codes. Our forecasts imply that HERA in its design performance will be sensitive to FDM fractions as small as 1% in the FDM window, and improve over existing bounds for other masses by up to an order of magnitude.
Optical Character Recognition (OCR) on historical printings is a challenging task mainly due to the complexity of the layout and the highly variant typography. Nevertheless, in the last few years great progress has been made in the area of historical OCR, resulting in several powerful open-source tools for preprocessing, layout recognition and segmentation, character recognition and post-processing. The drawback of these tools often is their limited applicability by non-technical users like humanist scholars and in particular the combined use of several tools in a workflow. In this paper we present an open-source OCR software called OCR4all, which combines state-of-the-art OCR components and continuous model training into a comprehensive workflow. A comfortable GUI allows error corrections not only in the final output, but already in early stages to minimize error propagations. Further on, extensive configuration capabilities are provided to set the degree of automation of the workflow and to make adaptations to the carefully selected default parameters for specific printings, if necessary. Experiments showed that users with minimal or no experience were able to capture the text of even the earliest printed books with manageable effort and great quality, achieving excellent character error rates (CERs) below 0.5%. The fully automated application on 19th century novels showed that OCR4all can considerably outperform the commercial state-of-the-art tool ABBYY Finereader on moderate layouts if suitably pretrained mixed OCR models are available. The architecture of OCR4all allows the easy integration (or substitution) of newly developed tools for its main components by standardized interfaces like PageXML, thus aiming at continual higher automation for historical printings.
The paper investigates existence and uniqueness for a stochastic differential equation (SDE) with distributional drift depending on the law density of the solution. Those equations are known as McKean SDEs. The McKean SDE is interpreted in the sense of a suitable singular martingale problem. A key tool used in the investigation is the study of the corresponding Fokker-Planck equation.
We explore quantum nonlocality in one of the simplest bipartite scenarios. Several new facet-defining Bell inequalities for the {[3 3 3] [3 3 3]} scenario are obtained with their quantum violations analyzed in details. Surprisingly, all these inequalities involving only genuine ternary-outcome measurements can be violated maximally by some two-qubit entangled states, such as the maximally entangled two-qubit state. This gives further evidence that in analyzing the quantum violation of Bell inequalities, or in the application of the latter to device-independent quantum information processing tasks, the commonly-held wisdom of equating the local Hilbert space dimension of the optimal state with the number of measurement outcomes is not necessarily justifiable. In addition, when restricted to the minimal qubit subspace, it can be shown that one of these Bell inequalities requires non-projective measurements to attain maximal quantum violation, thereby giving the first example of a facet-defining Bell inequality where a genuine positive-operator-valued measure is relevant. We experimentally demonstrate the quantum violation of this and two other Bell inequalities for this scenario using energy-time entangled photon pairs. Using the obtained measurement statistics, we demonstrate how characterization of the underlying resource in the spirit of device-independence, but supplemented with auxiliary assumptions, can be achieved. In particular, we discuss how one may get around the fact that, due to finite-size effects, raw measurement statistics typically violate the non-signaling condition.
We develop a novel deep contour detection algorithm with a top-down fully convolutional encoder-decoder network. Our proposed method, named TD-CEDN, solves two important issues in this low-level vision problem: (1) learning multi-scale and multi-level features; and (2) applying an effective top-down refined approach in the networks. TD-CEDN performs the pixel-wise prediction by means of leveraging features at all layers of the net. Unlike skip connections and previous encoder-decoder methods, we first learn a coarse feature map after the encoder stage in a feedforward pass, and then refine this feature map in a top-down strategy during the decoder stage utilizing features at successively lower layers. Therefore, the deconvolutional process is conducted stepwise, which is guided by Deeply-Supervision Net providing the integrated direct supervision. The above proposed technologies lead to a more precise and clearer prediction. Our proposed algorithm achieved the state-of-the-art on the BSDS500 dataset (ODS F-score of 0.788), the PASCAL VOC2012 dataset (ODS F-score of 0.588), and and the NYU Depth dataset (ODS F-score of 0.735).
In recent years, the availability of large, complete cluster samples has enabled numerous cosmological parameter inference analyses using cluster number counts. These have provided constraints on the cosmic matter density $\Omega_m$ and the amplitude of matter density fluctuations $\sigma_8$ alternative to those obtained from other standard probes. However, systematics uncertainties, such as the mass calibration bias and selection effects, may still significantly affect these data analyses. Hence, it is timely to explore other proxies of galaxy cluster cosmology that can provide cosmological constraints complementary to those obtained from cluster number counts. Here, we use measurements of the cluster sparsity from weak lensing mass estimates of the LC$^2$-{\it single} and HSC-XXL cluster catalogs to infer constraints on a flat $\Lambda$CDM model. The cluster sparsity has the advantage of being insensitive to selection and mass calibration bias. On the other hand, it primarily constrains a degenerate combination of $\Omega_m$ and $\sigma_8$ (along approximately constant curves of $S_8=\sigma_8\sqrt{\Omega_m/0.3}$), and to less extent the reduced Hubble parameter $h$. Hence, in order to break the internal parameter degeneracies we perform a combined likelihood analysis of cluster sparsities with cluster gas mass fraction measurements and BAO data. We find marginal constraints that are competitive with those from other standard cosmic probes: $\Omega_m=0.316\pm 0.013$, $\sigma_8=0.757\pm 0.067$ (corresponding to $S_8=0.776\pm 0.064$) and $h=0.696\pm 0.017$ at $1\sigma$. Moreover, assuming a conservative Gaussian prior on the mass bias of gas mass fraction data, we find a lower limit on the gas depletion factor $Y_{b,500c}\gtrsim 0.89$.
Standard model is reconstructed using the generalized differential calculus extended on the discrete space $M_4\times Z_3$. $Z_3$ is necessary for the inclusion of strong interaction. Our starting point is the generalized gauge field expressed as $A(x,y)=\!\sum_{i}a^\dagger_{i}(x,y){\bf d}a_i(x,y), (y=0,\pm)$, where $a_i(x,y)$ is the square matrix valued function defined on $M_4\times Z_3$ and ${\bf d}=d+{\chi}$ is generalized exterior derivative. We can construct the consistent algebra of $d_{\chi}$ with the introduction of the symmetry breaking function $M(y)$ and the spontaneous breakdown of gauge symmetry is coded in ${d_{\chi}}$.   The gauge field $A_\mu(x,y)$ and Higgs field $\Phi(x,y)$ are written in terms of $a_i(x,y)$ and $M(y)$, which might suggest $a_i(x,y)$ to be more fundamental object. The unified picture of the gauge field and Higgs field as the generalized connection in non-commutative geometry is realized. Not only Yang-Mills-Higgs lagrangian but also Dirac lagrangian, invariant against the gauge transformation, are reproduced through the inner product between the differential forms. Two model constructions are presented, which are distinguished in the particle assignment of Higgs field $\Phi(x,y)$.
We describe the generalization of Analytic Perturbation Theory (APT) for QCD observables, initiated by Radyushkin, Krasnikov, Pivovarov, Shirkov and Solovtsov, to fractional powers of coupling -- Fractional APT (FAPT). The basic aspects of FAPT is shortly summarized. We describe how to treat heavy-quark thresholds in FAPT and then show how to resum perturbative series in both the one-loop APT and FAPT. As an application we consider FAPT description of the Higgs boson decay $H^0\to b\bar{b}$. The main conclusion is: To achieve an accuracy of the order of 1% it is enough to take into account up to the third correction.
We investigate a critical scaling law for the cluster heterogeneity $H$ in site and bond percolations in $d$-dimensional lattices with $d=2,...,6$. The cluster heterogeneity is defined as the number of distinct cluster sizes. As an occupation probability $p$ increases, the cluster size distribution evolves from a monodisperse distribution to a polydisperse one in the subcritical phase, and back to a monodisperse one in the supercritical phase. We show analytically that $H$ diverges algebraically approaching the percolation critical point $p_c$ as $H\sim |p-p_c|^{-1/\sigma}$ with the critical exponent $\sigma$ associated with the characteristic cluster size. Interestingly, its finite-size-scaling behavior is governed by a new exponent $\nu_H = (1+d_f/d)\nu$ where $d_f$ is the fractal dimension of the critical percolating cluster and $\nu$ is the correlation length exponent. The corresponding scaling variable defines a singular path to the critical point. All results are confirmed by numerical simulations.
Nanoscale single-crystals possess modified phonon dispersions due to the truncation of the crystal. The introduction of surfaces alters the population of phonons relative to the bulk and introduces anisotropy arising from the breaking of translational symmetry. Such modifications exist throughout the Brillouin zone, even in structures with dimensions of several nanometers, posing a challenge to the characterization of vibrational properties and leading to uncertainty in predicting the thermal, optical, and electronic properties of nanomaterials. Synchrotron x-ray thermal diffuse scattering studies find that freestanding Si nanomembranes with thicknesses as large as 21 nm exhibit a higher scattering intensity per unit thickness than bulk silicon. In addition, the anisotropy arising from the finite thickness of these membranes produces particularly intense scattering along reciprocal-space directions normal to the membrane surface compared to corresponding in-plane directions. These results reveal the dimensions at which calculations of materials properties and device characteristics based on bulk phonon dispersions require consideration of the nanoscale size of the crystal.
Lepton Flavor Universality Violation (LFUV) in $B$ decays in both neutral $b\rightarrow s l^+ l^-$ and charged $b\rightarrow cl\bar{\nu}_{l}$ processes observed in the ratios $R_{K^{(*)}}$ and $R_{D^{(*)}}$ is investigated in the framework of a model based on the extended symmetry gauge $SU(3)_{C}\otimes SU(3)_{L}\otimes U(1)_{X}$ whose leptonic sector consists of five triplets. It is shown that in order to explain the experimentally observed deviations from the Standard Model in these flavor changing transitions, a non-minimal version of the model has to be considered. We investigate the ability of this model in accommodating the model-independent scenarios currently favored by global fits.
We present the results of determination of the age, helium mass fraction (Y), metallicity ([Fe/H]), and abundances of the elements C, N, O, Na, Mg, Ca, Ti, C and Mn for the Galactic globular cluster NGC 6652. We use its medium-resolution integrated-light spectrum from the library of Schiavon and our population synthesis method to fulfill this task. We select the evolutionary isochrone and stellar mass function for our analysis, which provide the best approximation to the shapes and intensities of the observed Balmer line profiles. The determined elemental abundances, age and metallicity are characteristic of stellar populations in the Galactic Bulge.
In the cores of young dense star clusters repeated stellar collisions involving the same object can occur, which has been suggested to lead to the formation of an intermediate-mass black hole. In order to verify this scenario we compute the detailed evolution of the merger remnant of three sequences. We follow the evolution until the onset of carbon burning and estimate the final remnant mass to determine the ultimate fate of a runaway merger sequence.   We use a detailed stellar evolution code to follow the evolution of the collision product. At each collision, we mix the two colliding stars, taking account of mass loss during the collision. During the stellar evolution we apply mass loss rates from the literature, as appropriate for the evolutionary stage of the merger remnant. We compute models for high ($Z=0.02$) and low ($Z=0.001$) metallicity to quantify metallicity effects.   We find that the merger remnant becomes a Wolf-Rayet star before the end of core hydrogen burning. Mass loss from stellar winds dominates over the mass increase due to repeated mergers for all three merger sequences that we consider. In none of our high metallicity models an intermediate-mass black hole is formed, instead our models have a mass of 10--14 \Msun{} at the onset of carbon burning. For low metallicity we expect the final remnant of the merger sequence to explode as a pair creation supernova. We find that our metal-rich models become inflated as a result of developing an extended low-density envelope. This may increase the probability of further collisions, but self-consistent $N$-body calculations with detailed evolution of runaway mergers are required to verify this.
In this paper we study fundamental directional properties of sets under the assumption of condition (SSP) (introduced in a previous paper). We show several transversality theorems in the singular case and an (SSP)-structure preserving theorem. As an illustration, our transversality results are used to prove several facts concerning complex analytic varieties. The (SSP)-property is most suitable for understanding transversality in the Lipschitz category. This property is shared by a large class of sets, in particular by subanalytic sets or by definable sets in an o-minimal structure.
We conjecture the exact shock statistics in the inviscid decaying Burgers equation in D>1 dimensions, with a special class of correlated initial velocities, which reduce to Brownian for D=1. The prediction is based on a field-theory argument, and receives support from our numerical calculations. We find that, along any given direction, shocks sizes and locations are uncorrelated.
A grid comb model is a generalization of the well known comb model, and it consists of $N$ backbones. For $N=1$ the system reduces to the comb model where subdiffusion takes place with the transport exponent $1/2$. We present an exact analytical evaluation of the transport exponent of anomalous diffusion for finite and infinite number of backbones. We show that for an arbitrarily large but finite number of backbones the transport exponent does not change. Contrary to that, for an infinite number of backbones, the transport exponent depends on the fractal dimension of the backbone structure.
Three-dimensional numerical magnetohydrodynamic (MHD) simulations are performed to investigate how a magnetically confined mountain on an accreting neutron star relaxes resistively. No evidence is found for non-ideal MHD instabilities on a short time-scale, such as the resistive ballooning mode or the tearing mode. Instead, the mountain relaxes gradually as matter is transported across magnetic surfaces on the diffusion time-scale, which evaluates to $\tau_\mathrm{I} \sim 10^5 - 10^8$ yr (depending on the conductivity of the neutron star crust) for an accreted mass of $M_a = 1.2 \times 10^{-4} M_\odot$. The magnetic dipole moment simultaneously reemerges as the screening currents dissipate over $\tau_\mathrm{I}$. For nonaxisymmetric mountains, ohmic dissipation tends to restore axisymmetry by magnetic reconnection at a filamentary neutral sheet in the equatorial plane. Ideal-MHD oscillations on the Alfv\'{e}n time-scale, which can be excited by external influences, such as variations in the accretion torque, compress the magnetic field and hence decrease $\tau_\mathrm{I}$ by \change{one order of magnitude} relative to its standard value (as computed for the static configuration). The implications of long-lived mountains for gravitational wave emission from low-mass X-ray binaries are briefly explored.
Stars in galaxies form in giant molecular clouds that coalesce when the atomic hydrogen is converted into molecules. There are currently two dominant models for what property of the galactic disk determines its molecular fraction: either hydrostatic pressure driven by the gravity of gas and stars, or a combination of gas column density and metallicity. To assess the validity of these models, we compare theoretical predictions to the observed atomic gas content of low-metallicity dwarf galaxies with high stellar densities. The extreme conditions found in these systems are optimal to distinguish the two models, otherwise degenerate in nearby spirals. Locally, on scales <100 pc, we find that the state of the interstellar medium is mostly sensitive to the gas column density and metallicity rather than hydrostatic pressure. On larger scales where the average stellar density is considerably lower, both pressure and shielding models reproduce the observations, even at low metallicity. We conclude that models based on gas and dust shielding more closely describe the process of molecular formation, especially at the high resolution that can be achieved in modern galaxy simulations or with future radio/millimeter arrays.
Based on $16,283$ early-type galaxies (ETGs) in $0.025\le z_\mathrm{spec}<0.055$ from Sloan Digital Sky Survey data, we show that the fundamental plane (FP) of ETGs is not a plane in the strict sense but is a curved surface with a twisted shape whose orthogonal direction to the surface is shifted as the central velocity dispersion ($\sigma_0$) or mean surface brightness within the half-light radius ($\mu_e$) changes. When ETGs are divided into subsamples according to $\sigma_0$, the coefficient of $\mu_e$ of the FP increases, whereas the zero-point of the FP decreases at higher $\sigma_0$. Taking the $z$ band as an example, the coefficient of $\mu_e$ rises from $0.28$ to $0.36$ as $\sigma_0$ increases from $\sim100$ to $\sim300$ km s$^{-1}$. At the same time, the zero-point of the FP falls from $-7.5$ to $-9.0$ in the same $\sigma_0$ range. The consistent picture on the curved nature of the FP is also reached by inspecting changes in the FP coefficients for ETG subsamples with different $\mu_e$. By examining scaling relations that are projections of the FP, we suggest that the warped nature of the FP may originate from dry merger effects that are imprinted more prominently in ETGs with higher masses.
A one-dimensional fermionic system, such as a superconducting wire, may host Majorana zero-energy edge modes (MZMs) at its edges when it is in the topological phase. MZMs provide a path to realising fault-tolerant quantum computation, and so are the focus of intense experimental and theoretical studies. However, given a Hamiltonian, determining whether MZMs exist is a daunting task as it relies on knowing the spectral properties of the Hamiltonian in the thermodynamic limit. The Kitaev chain is a paradigmatic non-interacting model that supports MZMs and the Hamiltonian can be fully diagonalised. However, for interacting models, the situation is far more complex. Here we consider a different classification of models, namely, ones with frustration-free Hamiltonians. Within this class of models, interacting and non-interacting systems are treated on an equal footing, and we identify exactly which Hamiltonians can realise MZMs.
Spin-orbit (SO) coupling is the crucial parameter to drive topological insulating phases in electronic band models. In particular, the generic emergence of SO coupling involves the Rashba term which fully breaks the SU(2) spin symmetry. As soon as interactions are taken into account, however, many theoretical studies have to content themselves with the analysis of a simplified U(1) conserving SO term without Rashba coupling. We intend to fill this gap by studying the Kane-Mele-Hubbard (KMH) model in the presence of Rashba SO coupling and present the first systematic analysis of the effect of Rashba SO coupling in a correlated two-dimensional topological insulator. We apply the variational cluster approach (VCA) to determine the interacting phase diagram by computing local density of states, magnetization, single particle spectral function, and edge states. Preceded by a detailed VCA analysis of the KMH model in the presence of U(1) conserving SO coupling, we find that the additional Rashba SO coupling drives new electronic phases such as a metallic regime and a direct-gap only topological insulating phase which persist in the presence of interactions.
If the background universe is observed through a significant amount of diffusely distributed foreground dust, then studies at optical wavelengths may be severely biased. Previous studies investigating effects of foreground dust on background sources assumed the dust to be ``compactly'' distributed, ie. on scales comparable to the visible extent of normal galaxies. We show however that diffuse dust is more effective at obscuring background sources. Galaxy clusters are a likely location for ``large-scale'' diffusely distributed dust, and its effect on the counts of background sources is explored. We also explore the implications of a hypothesised diffuse intergalactic dust component uniformly distributed to high redshift with comoving mass density equal to that associated with local galaxies. In this case, we predict a deficit in background sources about three times greater than that found in previous studies.