ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper, we study the regularity of optimal mappings in Monge's mass transfer problem. Using the approximation to Monge's cost function given by the Euclidean distance c(x,y)=dist(x,y) through the costs c_\eps(x,y)=(\eps^2+dist(x,y)^2)^{1/2}, we consider the optimal mappings T_\eps for these costs, and we prove that the eigenvalues of the Jacobian matrix DT_\eps, which are all positive, are locally uniformly bounded. By an example we prove that T_\eps is in general not uniformly Lipschitz continuous as \eps-0, even if the mass distributions are positive and smooth, and the domains are c-convex.
The omega-phi threshold peak observed by BES in J/Psi -> gamma(omega-phi) may be interpreted quantitatively in terms of a glueball component in fo(1790).
Consider the linear congruence equation $x_1+\ldots+x_k \equiv b\,(\text{mod } n)$ for $b,n\in\mathbb{Z}$. By $(a,b)_s$, we mean the largest $l^s\in\mathbb{N}$ which divides $a$ and $b$ simultaneously. For each $d_j|n$, define $\mathcal{C}_{j,s} = \{1\leq x\leq n^s | (x,n^s)_s = d^s_j\}$. Bibak et al. gave a formula using Ramanujan sums for the number of solutions of the above congruence equation with some gcd restrictions on $x_i$. We generalize their result with generalized gcd restrictions on $x_i$ by proving that for the above linear congruence, the number of solutions is $$\frac{1}{n^s}\sum\limits_{d|n}c_{d,s}(b)\prod\limits_{j=1}^{\tau(n)}\left(c_{\frac{n}{d_j},s}(\frac{n^s}{d^s})\right)^{g_j}$$ where $g_j = |\{x_1,\ldots, x_k\}\cap \mathcal{C}_{j,s}|$ for $j=1,\ldots \tau(n)$ and $c_{d,s}$ denote the generalized ramanujan sum defined by E. Cohen.
The supermassive black hole of M87 is one of the most massive black holes known and has been the subject of several stellar and gas-dynamical mass measurements; however the most recent revision to the stellar-dynamical black hole mass measurement is a factor of about two larger than the previous gas-dynamical determinations. Here, we apply comprehensive gas-dynamical models that include the propagation of emission-line profiles through the telescope and spectrograph optics to new Space Telescope Imaging Spectrograph observations from the Hubble Space Telescope. Unlike the previous gas-dynamical studies of M87, we map out the complete kinematic structure of the emission-line disk within about 40 pc from the nucleus, and find that a small amount of velocity dispersion internal to the gas disk is required to match the observed line widths. We examine a scenario in which the intrinsic velocity dispersion provides dynamical support to the disk, and determine that the inferred black hole mass increases by only 6%. Incorporating this effect into the error budget, we ultimately measure a mass of M_BH = (3.5^{+0.9}_{-0.7}) x 10^9 M_sun (68% confidence). Our gas-dynamical black hole mass continues to differ from the most recent stellar-dynamical mass by a factor of two, underscoring the need for carrying out more cross-checks between the two main black hole mass measurement methods.
Let $G$ be a $p$-divisible group over a complete discrete valuation ring $R$ of characteristic $p$. The generic fiber of $G$ determines a Galois representation $\rho$. The image of $\rho$ admits a ramification filtration and a Lie filtration. We relate these filtrations in the case $G$ is one dimensional, giving an equicharacteristic version of Sen's theorem in this setting. This result generalizes results of Gross and Chai. Additionally, we prove that the representation associated to the \'etale part of $G$ is irreducible.
How does a steady state with strong intermittency develop in time from an initial state which is statistically random? For passive sliders driven by various fluctuating surfaces, we show that the approach involves an indefinitely growing length scale which governs scaling properties. A simple model of sticky sliders suggests scaling forms for the time-dependent flatness and hyperflatness, both measures of intermittency and these are confirmed numerically for passive sliders driven by a Kardar-Parisi-Zhang surface. Aging properties are studied via a two-time flatness. We predict and verify numerically that the time-dependent flatness is, remarkably, a non-monotonic function of time, with different scaling forms at short and long times. The scaling description remains valid when clustering is more diffuse as for passive sliders evolving through Edwards-Wilkinson driving or under antiadvection, although exponents and scaling functions differ substantially.
Strongly correlated low-dimensional systems can host exotic elementary excitations carrying a fractional charge $q$ and potentially obeying anyonic statistics. In the fractional quantum Hall effect, their fractional charge has been successfully determined owing to low frequency shot noise measurements. However, a universal method for sensing them unambiguously and unraveling their intricate dynamics was still lacking. Here, we demonstrate that this can be achieved by measuring the microwave photons emitted by such excitations when they are transferred through a potential barrier biased with a dc voltage $V_{\text{dc}}$. We observe that only photons at frequencies $f$ below $qV_{\text{dc}}/h$ are emitted. This threshold provides a direct and unambiguous determination of the charge $q$, and a signature of exclusion statistics. Derived initially within the Luttinger model, this feature is also predicted by universal non-equilibrium fluctuation relations which agree fully with our measurements. Our work paves the way for further exploration of anyonic statistics using microwave measurements.
Using HST NICMOS 2 observations we have measured 1.6-micron near infrared nuclear luminosities of 100 3CR radio galaxies with z<0.3, by modeling and subtracting the extended emission from the host galaxy. We performed a multi-wavelength statistical analysis (including optical and radio data) of the properties of the nuclei following classification of the objects into FRI and FRII, and LIG (low-ionization galaxies), HIG (high-ionization galaxies) and BLO (broad-lined objects) using the radio morphology and optical spectra, respectively. The correlations among near infrared, optical, and radio nuclear luminosity support the idea that the near infrared nuclear emission of FRIs has a non-thermal origin. Despite the difference in radio morphology, the multi-wavelength properties of FRII LIG nuclei are statistically indistinguishable from those of FRIs, an indication of a common structure of the central engine. All BLOs show an unresolved near infrared nucleus and a large near infrared excess with respect to FRII LIGs and FRIs of equal radio core luminosity. This requires the presence of an additional (and dominant) component other than the non-thermal light. Considering the shape of their spectral energy distribution, we ascribe the origin of their near infrared light to hot circumnuclear dust. A near infrared excess is also found in HIGs, but their nuclei are substantially fainter than those of BLO. This result indicates that substantial obscuration along the line-of-sight to the nuclei is still present at 1.6 micron. Nonetheless, HIGs nuclei cannot simply be explained in terms of dust obscuration: a significant contribution from light reflected in a circumnuclear scattering region is needed to account for their multiwavelength properties.
We present high-fidelity, 30 milliarcsecond (200-pc) resolution ALMA rest-frame 240 $\mu$m observations of cold dust emission in three typical main-sequence star-forming galaxies (SFGs) at $z \sim 3$ in the Hubble Ultra-Deep Field (HUDF). The cold dust is distributed within the smooth disk-like central regions of star formation $1 - 3$ kpc in diameter, despite their complex and disturbed rest-frame UV and optical morphologies. No dust substructures or clumps are seen down to $\simeq 1- 3$ $M_\odot$yr$^{-1}$ (1$\sigma$) per 200-pc beam. No dust emission is observed at the locations of UV-emitting clumps, which lie $\simeq 2-10$ kpc from the bulk of star formation. Clumpy substructures can contribute no more than $1-7$% of the total star formation in these galaxies (3$\sigma$ upper limits). The lack of star-forming substructures in our HUDF galaxies is to be contrasted with the multiple substructures characteristic of submillimeter-selected galaxies (SMGs) at the same cosmic epoch, particularly the far-IR-bright SMGs with similarly high-fidelity ALMA observations of Hodge et al. (2019). Individual star-forming substructures in these SMGs contain $\sim10-30$% of their total star formation. A substructure in these SMGs is often comparably bright in the far-infrared as (or in some cases brighter than) our typical SFGs, suggesting that these SMGs originate from a class of disruptive event involving multiple objects at the scale of our HUDF galaxies. The scale of the disruptive event found in our main-sequence SFGs, characterized by the lack of star-forming substructures at our resolution and sensitivity, could be less violent, e.g., gas-rich disk instability or minor mergers.
It is well-known that reconstruction algorithms in quantitative susceptibility mapping often contain streaking artifacts. In [1], the cause of the artifacts is identified as propagation of singularities. In this work, we analyze such singularities carefully and propose some strategies to reduce the artifacts.
Edges, boundaries and contours are important subjects of study in both computer graphics and computer vision. On one hand, they are the 2D elements that convey 3D shapes, on the other hand, they are indicative of occlusion events and thus separation of objects or semantic concepts. In this paper, we aim to generate contour drawings, boundary-like drawings that capture the outline of the visual scene. Prior art often cast this problem as boundary detection. However, the set of visual cues presented in the boundary detection output are different from the ones in contour drawings, and also the artistic style is ignored. We address these issues by collecting a new dataset of contour drawings and proposing a learning-based method that resolves diversity in the annotation and, unlike boundary detectors, can work with imperfect alignment of the annotation and the actual ground truth. Our method surpasses previous methods quantitatively and qualitatively. Surprisingly, when our model fine-tunes on BSDS500, we achieve the state-of-the-art performance in salient boundary detection, suggesting contour drawing might be a scalable alternative to boundary annotation, which at the same time is easier and more interesting for annotators to draw.
Relativistic constituent quark models generally describe three-quark systems with particular interactions. The corresponding invariant mass eigenvalue spectra and pertinent eigenstates should exhibit the multiplet structure anticipated for baryon resonances. Taking into account the flavour content, spin structure, and spatial distribution of the baryon wave functions together with mass relations of the eigenvalues and decay properties of the eigenstates, we can link the theoretical mass eigenstates with the experimentally measured resonances. The resulting classification of baryon resonances differs in some respects from the one suggested by the Particle Data Group. With regard to the hadronic decay widths of light and strange baryon resonances a consistent picture emerges only, if the classification includes two-star resonances.
A theoretical study on thermonuclear fusion including deuterium-tritium (D-T) fusion and D-$^{3}$He fusion in intense laser fields has been shown in this article. With the laser fields expected to be available in the near future, some quantitative results for the laser-induced modifications to the cross-sections are given. It is reported that the cross-sections are more sensitive to the external laser fields at the lower energies. An explicit generalized form of the Gamow penetrability factor is given for the predictions of the laser-induced effects for some other similar nuclear processes.
The spectral evolution and spectral lag behavior of 92 bright pulses from 84 gamma-ray bursts (GRBs) observed by the Fermi GBM telescope are studied. These pulses can be classified into hard-to-soft pulses (H2S, 64/92), H2S-dominated-tracking pulses (21/92), and other tracking pulses (7/92). We focus on the relationship between spectral evolution and spectral lags of H2S and H2S-dominated-tracking pulses. %in hard-to-soft pulses (H2S, 64/92) and H2S-dominating-tracking (21/92) pulses. The main trend of spectral evolution (lag behavior) is estimated with $\log E_p\propto k_E\log(t+t_0)$ (${\hat{\tau}} \propto k_{\hat{\tau}}\log E$), where $E_p$ is the peak photon energy in the radiation spectrum, $t+t_0$ is the observer time relative to the beginning of pulse $-t_0$, and ${\hat{\tau}}$ is the spectral lag of photons with energy $E$ with respect to the energy band $8$-$25$ keV. For H2S and H2S-dominated-tracking pulses, a weak correlation between $k_{{\hat{\tau}}}/W$ and $k_E$ is found, where $W$ is the pulse width. We also study the spectral lag behavior with peak time $t_{\rm p_E}$ of pulses for 30 well-shaped pulses and estimate the main trend of the spectral lag behavior with $\log t_{\rm p_E}\propto k_{t_p}\log E$. It is found that $k_{t_p}$ is correlated with $k_E$. We perform simulations under a phenomenological model of spectral evolution, and find that these correlations are reproduced. We then conclude that spectral lags are closely related to spectral evolution within the pulse. The most natural explanation of these observations is that the emission is from the electrons in the same fluid unit at an emission site moving away from the central engine, as expected in the models invoking magnetic dissipation in a moderately-high-$\sigma$ outflow.
We have observed a quiet Sun region with the Swedish 1-meter Solar Telescope (SST) equipped with CRISP Imaging SpectroPolarimeter. High-resolution, high-cadence, H$\alpha$ line scanning images were taken to observe different layers of the solar atmosphere from the photosphere to upper chromosphere. We study the distribution of power in different period-bands at different heights. Power maps of the upper photosphere and the lower chromosphere show suppressed power surrounding the magnetic-network elements, known as "magnetic shadows". These also show enhanced power close to the photosphere, traditionally referred to as "power halos". The interaction between acoustic waves and inclined magnetic fields is generally believed to be responsible for these two effects. In this study we explore if small-scale transients can influence the distribution of power at different heights. We show that the presence of transients, like mottles, Rapid Blueshifted Excursions (RBEs) and Rapid Redshifted Excursions (RREs), can strongly influence the power-maps. The short and finite lifetime of these events strongly affects all powermaps, potentially influencing the observed power distribution. We show that Doppler-shifted transients like RBEs and RREs that occur ubiquitously, can have a dominant effect on the formation of the power halos in the quiet Sun. For magnetic shadows, transients like mottles do not seem to have a significant effect in the power suppression around 3 minutes and wave interaction may play a key role here. Our high cadence observations reveal that flows, waves and shocks manifest in presence of magnetic fields to form a non-linear magnetohydrodynamic system.
New observations of Sgr A have been carried out with the VLA using the broadband (2 GHz) continuum mode at 5.5 GHz, covering the central 30 pc region of the RBZ at the Galactic center. Using the MS-MFS algorithms in CASA, we have imaged Sgr A with a resolution of 1", achieving an rms 8 $\mu$Jy/beam, and a dynamic range 100,000:1.The radio image is compared with X-ray, CN emission-line and Paschen-$\alpha$ images obtained using Chandra, SMA and HST/NICMOS, respectively. We discuss several prominent radio features. The "Sgr A West Wings" extend 5 pc from the NW and SE tips of the ionized "Mini-spiral" in Sgr A West to positions located 2.9 and 2.4 arc min to the NW and SE of Sgr A*, respectively. The NW wing, along with several other prominent features, including the "NW Streamers", form an elongated radio lobe (NW lobe), oriented nearly perpendicular to the Galactic plane. This radio lobe, with a size of 14.4 pc x 7.3 pc, has a known X-ray counterpart. A row of three thermally emitting rings is observed in the NW lobe. A field containing numerous amorphous radio blobs extends for a distance of ~2 arc min beyond the tip of the SE wing; these features coincide with the SE X-ray lobe. Most of the amorphous radio blobs in the NW and SE lobes have Paschen-$\alpha$ counterparts, suggesting that a shock interaction of ambient gas concentrations with a collimated nuclear wind (outflow) that may be driven by radiation force from the central star cluster within the CND. Finally, we remark on a prominent radio feature located within the shell of the Sgr A East SNR. Because this feature -- the "Sigma Front" -- correlates well in shape and orientation with the nearby edge of the CND, we propose that it is a reflected shock wave resulting from the impact of the Sgr A East blast wave on the CND.
We show both theoretically and experimentally that the magnetization density accompanying ultrafast excitation of a semiconductor with circular polarized light varies rapidly enough to produce a detectable THz field.
Topologically stabilized polymer conformations observed in melts of nonconcatenated polymer rings and crumpled globules, are considered to be a good candidate for the description of the spatial structure of mitotic chromosomes. Despite significant efforts, the microscopic Hamiltonian capable of describing such systems, remains yet inaccessible. In this paper we consider a Gaussian network - a system with a simple Hamiltonian quadratic in all coordinates - and show that by tuning interactions, one can obtain fractal equilibrium conformations with any fractal dimension between 2 (ideal polymer chain) and 3 (crumpled globule). Monomer-to-monomer distances in topologically stabilized states, according to our analysis of available numerical data, fit very well the Gaussian distribution, giving an additional argument in support of the quadratic Hamiltonian model. Mathematically, the resulting polymer conformations can be mapped onto the trajectories of a subdiffusive fractal Brownian particle. As a by-product of our study, two novel continual integral representations of the fractal Brownian motion are proposed.
We study the consequences of nonzero neutrino masses for black holes evaporating by the emission of Hawking radiation. We find that the evolution of small, hot, black holes may be unaffected (if neutrinos are Majorana particles), or may show an increase in neutrino luminosity and a decrease in lifetime by up to a factor of 1.85 (if neutrinos are Dirac particles). However, for sufficiently large (e.g., stellar mass) black holes, neutrino emission is largely or entirely suppressed, resulting in a decrease in emitted power and an increase in lifetime by up to a factor of 7.5.
Consider a path of non-degenerate eigenstates of unitary operators or Hamiltonians with minimum eigenvalue gap G. The eigenpath traversal problem is to transform one or more copies of the initial to the final eigenstate. Solutions to this problem have applications ranging from quantum physics simulation to optimization. For Hamiltonians, the conventional way of doing this is by applying the adiabatic theorem. We give ``digital'' methods for performing the transformation that require no assumption on path continuity or differentiability other than the absence of large jumps. Given sufficient information about eigenvalues and overlaps between states on the path, the transformation can be accomplished with complexity O(L/G log(L/e)), where L is the angular length of the path and e is a specified bound on the error of the output state. We show that the required information can be obtained in a first set of transformations, whose complexity per state transformed has an additional factor that depends logarithmically on a maximum angular velocity along the path. This velocity is averaged over constant angular distances and does not require continuity. Our methods have substantially better behavior than conventional adiabatic algorithms, with fewer conditions on the path. They also improve on the previously best digital methods and demonstrate that path length and the gap are the primary parameters that determine the complexity of state transformation along a path.
We cross correlate the gravitational lensing map extracted from cosmic microwave background measurements by the Wilkinson Microwave Anisotropy Probe (WMAP) with the radio galaxy distribution from the NRAO VLA Sky Survey (NVSS) by using a quadratic estimator technique. We use the full covariance matrix to filter the data, and calculate the cross-power spectra for the lensing-galaxy correlation. We explore the impact of changing the values of cosmological parameters on the lensing reconstruction, and obtain statistical detection significances at $>3\sigma$. The results of all cross correlations pass the curl null test as well as a complementary diagnostic test using the NVSS data in equatorial coordinates. We forecast the potential for Planck and NVSS to constrain the lensing-galaxy cross correlation as well as the galaxy bias. The lensing-galaxy cross-power spectra are found to be Gaussian distributed.
For the first time, a solution to the $a_2/a_1$ sign problem in heavy meson decay based on PQCD factorization theorems. The point is to include QCD evolution effort characteristic scales involved in decay processes.
In this paper, we construct certain algebraic correspondences between genus three curves and certain type of Calabi-Yau threefolds which is double coverings of three dimensional projective space. Via this correspondences, the first cohomology groups of the curves can be embedded into the third cohomology groups of the Calabi-Yau three folds. Moreover we prove that the cokernel of this inclusion of variations ofHodge structures can not be a factor of any variations of Hodge structures comming from polarized abelian schemes.
Empirical energy density functionals (EDFs) are generally successful in describing nuclear properties across the table of nuclides. But their limitations motivate using the density-matrix expansion (DME) to embed long-range pion interactions into a Skyrme functional. Recent results on the impact of the pion were both encouraging and puzzling, necessitating a careful re-examination of the DME implementation. Here we take the first steps, focusing on two-body scalar terms in the DME. Exchange energies with long-range one-pion contributions are well approximated by all DME implementations considered, with preference for variants that do not truncate at two derivatives in every EDF term. The use of the DME for chiral pion contributions is therefore supported by this investigation. For scalar-isovector energies it is important to treat neutrons and protons separately. The results are found to apply under broad conditions, although self-consistency is not yet tested.