ShantanuT01/DACTYL-Pretraining huggingface dataset:
Deep convolutional neural networks have achieved remarkable progress on a variety of medical image computing tasks. A common problem when applying supervised deep learning methods to medical images is the lack of labeled data, which is very expensive and time-consuming to be collected. In this paper, we present a novel semi-supervised method for medical image segmentation, where the network is optimized by the weighted combination of a common supervised loss for labeled inputs only and a regularization loss for both labeled and unlabeled data. To utilize the unlabeled data, our method encourages the consistent predictions of the network-in-training for the same input under different regularizations. Aiming for the semi-supervised segmentation problem, we enhance the effect of regularization for pixel-level predictions by introducing a transformation, including rotation and flipping, consistent scheme in our self-ensembling model. With the aim of semi-supervised segmentation tasks, we introduce a transformation consistent strategy in our self-ensembling model to enhance the regularization effect for pixel-level predictions. We have extensively validated the proposed semi-supervised method on three typical yet challenging medical image segmentation tasks: (i) skin lesion segmentation from dermoscopy images on International Skin Imaging Collaboration (ISIC) 2017 dataset, (ii) optic disc segmentation from fundus images on Retinal Fundus Glaucoma Challenge (REFUGE) dataset, and (iii) liver segmentation from volumetric CT scans on Liver Tumor Segmentation Challenge (LiTS) dataset. Compared to the state-of-the-arts, our proposed method shows superior segmentation performance on challenging 2D/3D medical images, demonstrating the effectiveness of our semi-supervised method for medical image segmentation.
We show that there exists pairs of consecutive primes less than $x$ whose difference is larger than $t(1+o(1))(\log{x})(\log\log{x})(\log\log\log\log{x})(\log\log\log{x})^{-2}$ for any fixed $t$. Our proof works by incorporating recent progress in sieve methods related to small gaps between primes into the Erdos-Rankin construction. This answers a well-known question of Erdos.
We performed geometric pulsar light curve modeling using static, retarded vacuum, and offset polar cap (PC) dipole $B$-fields (the latter is characterized by a parameter $\epsilon$), in conjunction with standard two-pole caustic (TPC) and outer gap (OG) emission geometries. The offset-PC dipole $B$-field mimics deviations from the static dipole (which corresponds to $\epsilon=0$). In addition to constant-emissivity geometric models, we also considered a slot gap (SG) $E$-field associated with the offset-PC dipole $B$-field and found that its inclusion leads to qualitatively different light curves. Solving the particle transport equation shows that the particle energy only becomes large enough to yield significant curvature radiation at large altitudes above the stellar surface, given this relatively low $E$-field. Therefore, particles do not always attain the radiation-reaction limit. Our overall optimal light curve fit is for the retarded vacuum dipole field and OG model, at an inclination angle $\alpha=78{_{-1}^{+1}}^{\circ}$ and observer angle $\zeta=69{_{-1}^{+2}}^{\circ}$. For this $B$-field, the TPC model is statistically disfavored compared to the OG model. For the static dipole field, neither model is significantly preferred. We found that smaller values of $\epsilon$ are favored for the offset-PC dipole field when assuming constant emissivity, and larger $\epsilon$ values favored for variable emissivity, but not significantly so. When multiplying the SG $E$-field by a factor of 100, we found improved light curve fits, with $\alpha$ and $\zeta$ being closer to best fits from independent studies, as well as curvature radiation reaction at lower altitudes.
Using a combination of general-relativistic magnetohydrodynamics simulations and ray tracing of synchrotron emission, we study the effect of modest (24 degrees) misalignment between the black hole spin and plasma angular momentum, focusing on the variability of total flux, image centroids, and image sizes. We consider both millimeter and infrared (IR) observables motivated by Sagittarius A* (Sgr A*), though our results apply more generally to optically thin flows. For most quantities, tilted accretion is more variable, primarily due to a significantly hotter and denser "coronal" region well off the disk midplane. We find (1) a 150% increase in millimeter light curve variability when adding tilt to the flow; (2) the tilted image centroid in the millimeter shifts on a scale of 3.7 microarcseconds over 28 hours (5000 gravitational times) for some electron temperature models; (3) tilted disk image diameters in the millimeter can be 10% larger (52 versus 47 microarcseconds) than those of aligned disks at certain viewing angles; (4) the tilted models produce significant IR flux, similar to that seen in Sgr A*, with comparable or even greater variability than observed; (5) for some electron models, the tilted IR centroid moves by more than 50 microarcseconds over several hours, in a similar fashion to the centroid motion detected by the GRAVITY interferometer.
In this paper, we generalize the partial fraction decomposition which is fundamental in the theory of multiple zeta values, and prove a relation between Tornheim's double zeta functions of three complex variables. As applications, we give new integral representations of several zeta functions, an extension of the parity result to the whole domain of convergence, concrete expressions of Tornheim's double zeta function at non-positive integers and some results for the behavior of a certain Witten's zeta function at each integer. As an appendix, we show a functional equation for Euler's double zeta function.
We point out a correspondence between classical and quantum states, by showing that for every classical distribution over phase--space, one can construct a corresponding quantum state, such that in the classical limit of $\hbar\to 0$ the latter converges to the former with respect to all measurable quantities.
In this paper we study the free boundary regularity for almost-minimizers of the functional \begin{equation*} J(u)=\int_{\mathcal O} |\nabla u(x)|^2 +q^2_+(x)\chi_{\{u>0\}}(x) +q^2_-(x)\chi_{\{u<0\}}(x)\ dx \end{equation*} where $q_\pm \in L^\infty(\mathcal O)$. Almost-minimizers satisfy a variational inequality but not a PDE or a monotonicity formula the way minimizers do (see [AC], [ACF], [CJK], [W]). Nevertheless we succeed in proving that, under a non-degeneracy assumption on $q_\pm$, the free boundary is uniformly rectifiable. Furthermore, when $q_-\equiv 0$, and $q_+$ is H\"older continuous we show that the free boundary is almost-everywhere given as the graph of a $C^{1,\alpha}$ function (thus extending the results of [AC] to almost-minimizers).
The mathematical constant pi has recently been computed up to 22,459,157,718,361 decimal and 18,651,926,753,033 hexadecimal digits. As a simple check for the normality of pi, the frequencies of all sequences with length one, two and three in the base 10 and base 16 representations are extracted. All evaluated frequencies are found to be consistent with the hypothesis of pi being a normal number in these bases.
Spectral super-resolution (SSR) aims at generating a hyperspectral image (HSI) from a given RGB image. Recently, a promising direction for SSR is to learn a complicated mapping function from the RGB image to the HSI counterpart using a deep convolutional neural network. This essentially involves mapping the RGB context within a size-specific receptive field centered at each pixel to its spectrum in the HSI. The focus thereon is to appropriately determine the receptive field size and establish the mapping function from RGB context to the corresponding spectrum. Due to their differences in category or spatial position, pixels in HSIs often require different-sized receptive fields and distinct mapping functions. However, few efforts have been invested to explicitly exploit this prior.   To address this problem, we propose a pixel-aware deep function-mixture network for SSR, which is composed of a new class of modules, termed function-mixture (FM) blocks. Each FM block is equipped with some basis functions, i.e., parallel subnets of different-sized receptive fields. Besides, it incorporates an extra subnet as a mixing function to generate pixel-wise weights, and then linearly mixes the outputs of all basis functions with those generated weights. This enables us to pixel-wisely determine the receptive field size and the mapping function. Moreover, we stack several such FM blocks to further increase the flexibility of the network in learning the pixel-wise mapping. To encourage feature reuse, intermediate features generated by the FM blocks are fused in late stage, which proves to be effective for boosting the SSR performance. Experimental results on three benchmark HSI datasets demonstrate the superiority of the proposed method.
Recent observational studies of the Galactic bulge by APOGEE have revealed that about 1% of the bulge stars have rather high nitrogen abundances ([N/Fe]>0.5). We here numerically investigate in what physical conditions these N-rich stars (NRS) can be formed in spherical and disky stellar systems with stellar masses of 10^7-10^9 M_sun that are the bulge's building blocks. The principal results are as follows. A large fraction (>0.5) of new stars formed from interstellar medium polluted (ISM) by ejecta of asymptotic giant branch stars can have [N/Fe]>0.5 within stellar systems, if the gas mass fraction of ISM (f_g) is low (< 0.03). The mass fraction of NRS among all stars (f_nrs) can be higher than 1% within 0.5 Gyr timescale of star formation, if the mean stellar densities (rho_s) of the systems are higher than 0.1 M_sun/ pc^3. The [N/Fe] distributions depend on rho_s, f_g, and age distributions of their host stellar systems. NRS have compact and disky spatial distributions within their host systems and have rotational kinematics. Based on these results, we propose that the vast majority of the bulge's NRS originate not from globular clusters (GCs) but from its high-density building blocks. We suggest that NRS in the Galactic stellar halo have the same origin as those in the bulge. We also suggest that low-density dwarf spheroidal and gas-rich dwarfs are unlikely to form NRS. GCs are not only the formation sites of NRS.
After growing successfully TaP single crystal, we measured its longitudinal resistivity (rhoxx) and Hall resistivity (rhoyx) at magnetic fields up to 9T in the temperature range of 2-300K. It was found that at 2K its magnetoresistivity (MR) reaches to 328000 percent, at 300K to 176 percent at 8T, and both do not appear saturation. We confirmed that TaP is indeed a low carrier concentration, hole-electron compensated semimetal, with a high mobility of hole muh=371000 cm2V-1s-1, and found that a magnetic-field-induced metal-insulator transition occurs at room temperature. Remarkably, as a magnetic field (H) is applied in parallel to the electric field (E), the negative MR due to chiral anomaly is observed, and reaches to -3000 percent at 9T without any signature of saturation, too, which distinguishes with other Weyl semimetals (WSMs). The analysis on the Shubnikov-de Haas (SdH) oscillations superimposing on the MR reveals that a nontrivial Berry phase with strong offset of 0.3958 realizes in TaP, which is the characteristic feature of the charge carriers enclosing a Weyl nodes. These results indicate that TaP is a promising candidate not only for revealing fundamental physics of the WSM state but also for some novel applications.
Electrical energy storage systems (EESSs) with high energy density and power density are essential for the effective miniaturization of future electronic devices. Among different EESSs available in the market, dielectric capacitors relying on swift electronic and ionic polarization-based mechanisms to store and deliver energy already demonstrate high power densities. However, different intrinsic and extrinsic contributions to energy dissipations prevent ceramic-based dielectric capacitors from reaching high recoverable energy density levels. Interestingly, relaxor ferroelectric-based dielectric capacitors, because of their low remnant polarization, show relatively high energy density and thus display great potential for applications requiring high energy density properties. Here, some of the main strategies to improve the energy density properties of perovskite lead-free relaxor systems are reviewed. This includes (i) chemical modification at different crystallographic sites, (ii) chemical additives that do not target lattice sites and (iii) novel processing approaches dedicated to bulk ceramics, thick and thin films, respectively. Recent advancements are summarized concerning the search for relaxor materials with superior energy density properties and the appropriate choice of both composition and processing route to match various needs in the application. Finally, future trends in computationally-aided materials design are presented.
Coupled transitions between distinct ordered phases are important aspects behind the rich phase complexity of correlated oxides that hinders our understanding of the underlying phenomena. For this reason, fundamental control over complex transitions has become a leading motivation of the designer approach to materials. We have devised a series of new superlattices by combining a Mott insulator and a correlated metal to form ultra-short period superlattices, which allow one to disentangle the simultaneous orderings in $RE$NiO$_3$. Tailoring an incommensurate heterostructure period relative to the bulk charge ordering pattern suppresses the charge order transition while preserving metal-insulator and antiferromagnetic transitions. Such selective decoupling of the entangled phases resolves the long-standing puzzle about the driving force behind the metal-insulator transition and points to the site selective Mott transition as the operative mechanism. This designer approach emphasizes the potential of heterointerfaces for selective control of simultaneous transitions in complex materials with entwined broken symmetries.
We propose a series of new subalgebras of the $W_{1+\infty}$ algebra parametrized by polynomials $p(w)$, and study their quasifinite representations. We also investigate the relation between such subalgebras and the $\hat{\mbox{gl}}(\infty)$ algebra. As an example, we investigate the $\Win$ algebra which corresponds to the case $p(w)=w$, presenting its free field realizations and Kac determinants at lower levels.
We consider the Dirichlet problem for the biharmonic equation on an arbitrary convex domain and prove that the second derivatives of the variational solution are bounded in all dimensions.
The collapsar model for gamma-ray bursts requires three essential ingredients: a massive core, removal of the hydrogen envelope, and enough angular momentum in the core. We study current massive star evolution models of solar metallicity to determine which massive star physics is capable of producing these ingredients. In particular, we investigate the role of hydrodynamic and magnetic internal angular momentum transport and binary mass and angular momentum transfer. We follow the evolution of rotating single stars and of binary systems that include rotational processes for both stars. Neglecting magnetic fields, we show that the cores of massive single stars can maintain a high specific angular momentum when evolved with the assumption that mean molecular weight gradients suppress rotational mixing processes. In binary systems that undergo mass transfer during core hydrogen burning the mass receiving star accretes large amounts of high angular momentum material, leading to a spin-up of the core. We find, however, that this merely compensates for the tidal angular momentum loss due to spin-orbit coupling, which leads to synchronous rotation before the mass transfer event. Therefore the resulting cores do not rotate faster than in single stars. We also present models that include magnetic fields generated by differential rotation and we consider the internal angular momentum transport by magnetic torques. We investigate the capability of magnetic torques to efficiently pump angular momentum into the cores of accreting stars. Despite our finding that this mechanism works, the magnetic coupling of core and envelope after the accreting star ends core hydrogen burning leads to slower rotation than in the non-magnetic case.
QCD sum rules on the light-cone are derived for the sum $f^+ + f^-$ of the $B\to \pi$ and $D\to \pi$ form factors taking into account contributions up to twist four. Combining the results with the corresponding $f^+$ form factors calculated previously by the same method, we obtain the scalar form factors $f^0$. Our sum rule predictions are compared with lattice results, current-algebra constraints, and quark-model calculations. Furthermore, we calculate decay distributions and the integrated width for the semileptonic decay $B \to \pi \bar{\tau}\nu_\tau$ which is sensitive to $f^0$. Finally, the dependence of the sum rules on the heavy quark mass and the asymptotic scaling laws are discussed.
The high spin ultracold atom models with a special form of contact interactions, i.e., the scattering lengthes in the total spin-$2,4 \cdots$ channels are equal but may be different from that in the spin-0 channel, is studied. It is found that those models have either $Sp(2s+1)$-symmetry for the fermions or $SO(2s+1)$-symmetry for the bosons in the spin sector. Based on the symmetry analysis, a new class of exactly solvable models is proposed and solved via the Bethe ansatz. The ground states for repulsive fermions are also discussed.
The uncharted territory of the high-redshift ($z\gtrsim3$) Universe holds the key to understand the evolution of quasars. In an attempt to identify the most extreme members of the quasar population, i.e., blazars, we have carried out a multi-wavelength study of a large sample of radio-loud quasars beyond $z=3$. Our sample consists of 9 $\gamma$-ray detected blazars and 133 candidate blazars selected based on the flatness of their soft X-ray spectra (0.3$-$10 keV photon index $\leq1.75$), including 15 with NuSTAR observations. The application of the likelihood profile stacking technique reveals that the high-redshift blazars are faint $\gamma$-ray emitters with steep spectra. The high-redshift blazars host massive black holes ($\langle \log~M_{\rm BH,~M{\odot}} \rangle>9$) and luminous accretion disks ($\langle L_{\rm disk} \rangle>10^{46}$ erg s$^{-1}$). Their broadband spectral energy distributions are found to be dominated by high-energy radiation indicating their jets to be among the most luminous ones. Focusing on the sources exhibiting resolved X-ray jets (as observed with the Chandra satellite), we find the bulk Lorentz factor to be larger with respect to other $z>3$ blazars, indicating faster moving jets. We conclude that the presented list of the high-redshift blazars may act as a reservoir for follow-up observations, e.g., with NuSTAR, to understand the evolution of relativistic jets at the dawn of the Universe.
We have identified eighty-four small, high density groups of galaxies out to z ~ 0.2 in a region of ~ 2000 square degrees around the north galactic pole using DPOSS (the Digitized Second Palomar Observatory Sky Survey). The groups have at least four galaxies satisfying more stringent criteria than those used by Hickson in his pioneering work in 1982: the adopted limiting surface brightness for each group is brighter (24 mag/arcsec^2 instead of 26 mag/arcsec^2), and the spread in magnitude among the member galaxies is narrower (two magnitudes instead of three). We also adopt a slightly modified version of the isolation criterion used by Hickson, in order to avoid rejecting groups with projected nearby faint background galaxies. A 10% contamination rate due to projection effects is expected for this sample based on extensive simulations.
We report and analyse FIR observations of two Herbig Be stars, R Mon and PDS 27, obtained with Herschel's instruments PACS and SPIRE. We construct SEDs and derive the infrared excess. We extract line fluxes from the PACS and SPIRE spectra and construct rotational diagrams in order to estimate the excitation temperature of the gas. We derive CO, [OI] and [CI] luminosities to determine physical conditions of the gas, as well as the dominant cooling mechanism. We confirm that the Herbig Be stars are surrounded by remnants from their parental clouds, with an IR excess that mainly originates in a disc. In R Mon we detect [OI], [CI], [CII], CO (26 transitions), water and OH, while in PDS 27 we only detect [CI] and CO (8 transitions). We attribute the absence of OH and water in PDS 27 to UV photo-dissociation and photo-evaporation. From the rotational diagrams, we find several components for CO: we derive $T_{rot}$ 949$\pm$90 K, 358$\pm$20 K & 77$\pm$12 K for R Mon, 96$\pm$12 K & 31$\pm$4 K for PDS 27 and 25$\pm$8 K & 27$\pm$6 K for their respective compact neighbours. The forsterite feature at 69$\mu$m was not detected in either of the sources, probably due to the lack of (warm) crystalline dust in a flat disc. We find that cooling by molecules is dominant in the Herbig Be stars, while this is not the case in Herbig Ae stars where cooling by [OI] dominates. Moreover, we show that in the Herbig Be star R Mon, outflow shocks are the dominant gas heating mechanism, while in Herbig Ae stars this is stellar. The outflow of R Mon contributes to the observed line emission by heating the gas, both in the central spaxel/beam covering the disc and the immediate surroundings, as well as in those spaxels/beams covering the parabolic shell around it. PDS 27, a B2 star, has dispersed a large part of its gas content and/or destroyed molecules; this is likely given its intense UV field.
We study discrete solitons (kinks) accessible in state-of-the-art trapped ion experiments, considering zigzag crystals and quasi-3D configurations, both theoretically and experimentally. We first extend the theoretical understanding of different phenomena predicted and recently experimentally observed in the structure and dynamics of these topological excitations. Employing tools from topological degree theory, we analyze bifurcations of crystal configurations in dependence on the trapping parameters, and investigate the formation of kink configurations and the transformations of kinks between different structures. This allows us to accurately define and calculate the effective potential experienced by solitons within the Wigner crystal, and study how this (so-called Peierls-Nabarro) potential gets modified to a nonperiodic globally trapping potential in certain parameter regimes. The kinks' rest mass (energy) and spectrum of modes are computed and the dynamics of linear and nonlinear kink oscillations are analyzed. We also present novel, experimentally observed, configurations of kinks incorporating a large-mass defect realized by an embedded molecular ion, and of pairs of interacting kinks stable for long times, offering the perspective for exploring and exploiting complex collective nonlinear excitations, controllable on the quantum level.
We explore a number of explicit response formulae around the boundary driven zero range process to changes in the exit and entrance rates. In such a nonequilibrium regime kinetic (and not only thermodynamic) aspects make a difference in the response. Apart from a number of formal approaches, we illustrate a general decomposition of the linear response into entropic and frenetic contributions, the latter being realized from changes in the dynamical activity at the boundaries. In particular, in this way one obtains nonlinear modifications to the Green-Kubo relation. We end by bringing some general remarks about the situation where that nonequilibrium response remains given by the (equilibrium) Kubo formula such as for the density profile in the boundary driven Lorentz gas.