ShantanuT01/DACTYL-Pretraining huggingface dataset:
We show that every gammoid has special digraph representations, such that a representation of the dual of the gammoid may be easily obtained by reversing all arcs. In an informal sense, the duality notion of a poset applied to the digraph of a special representation of a gammoid commutes with the operation of forming the dual of that gammoid. We use these special representations in order to define a complexity measure for gammoids, such that the classes of gammoids with bounded complexity are closed under duality, minors, and direct sums.
The radius and surface composition of an exploding massive star, as well as the explosion energy per unit mass, can be measured using early ultraviolet (UV) observations of core-collapse supernovae (CC SNe). We present the results from a simultaneous \GALEX and Palomar Transient Factory (PTF) search for early UV emission from SNe. We analyze five CC SNe for which we obtained $NUV$ measurements before the first ground-based $R$-band detection. We introduce SOPRANOS, a new maximum likelihood fitting tool for models with variable temporal validity windows, and use it to fit the \citet{SapirWaxman2017} shock cooling model to the data. We report four Type II SNe with progenitor radii in the range of $R_*\approx600-1100R_\odot$ and a shock velocity parameter in the range of $v_{s*}\approx 2700-6000 \,\rm km\,s^{-1}$ ($E/M\approx2-8\times10^{50}\,\rm erg/M_\odot$) and one type IIb SN with $R_*\approx210R_\odot$ and $v_{s*}\approx11000 \rm\, km\,s^{-1}$ ($E/M\approx1.8\times10^{51}\,\rm erg/M_\odot$). Our pilot GALEX/PTF project thus suggests that a dedicated, systematic SN survey in the $NUV$ band, such as the wide-field UV explorer \textit{ULTRASAT} mission, is a compelling method to study the properties of SN progenitors and SN energetics.
The BSSN and standard gauge equations are written in covariant form with respect to spatial coordinate transformations. The BSSN variables are defined as tensors with no density weights. This allows us to evolve a given set of initial data using two different coordinate systems and to relate the results using the familiar tensor transformation rules. Two variants of the covariant equations are considered. These differ from one another in the way that the determinant of the conformal metric is evolved.
Efficient and faithful implementation of quantum information tasks, e.g., quantum computing, quantum communication and quantum metrology, requires robust and state-independent decoherence-suppressing measures to protect quantum information carriers. Here we present an experimental demonstration of a robust distribution scheme in which one photon of an entangled photon pair is successfully encoded into and decoded from a decoherence-free subspace (DFS) by a state-independent scheme. We achieved a high-fidelity distribution of the entangled state over fibre communication channel, and also demonstrated that the scheme is robust against fragility of the reference frame. The scheme, thanks to its state-independence, is also applicable to multipartite case where the photon to be distributed is entangled with many other photons. Such a universal scheme opens the possibility of robust distribution of quantum information among quantum communication and computing networks.
Let A be an indecomposable principally polarized abelian variety of dimension g . Third order theta functions embed A in a projective space P(V_3), while second order theta functions embed the Kummer variety K=A/<-1> in a projective space P(V_2). Coble observed that for g = 2 there is a unique cubic hypersurface in P(V_3) that is singular along A, and for g = 3 a unique quartic hypersurface in P(V_2) singular along K . We explain these facts by a simple analysis of the representations of the corresponding Heisenberg group.
Context. Recent observations have shown that magnetic flux cancellation occurs at the photosphere more frequently than previously thought.   Aims. In order to understand the energy release by reconnection driven by flux cancellation, we previously studied a simple model of two cancelling polarities of equal flux. Here, we further develop our analysis to achieve a more general setup where the two cancelling polarities have unequal magnetic fluxes and where many new features are revealed.   Methods. We carried out an analytical study of the cancellation of two magnetic fragments of unequal and opposite flux that approach one another and are located in an overlying horizontal magnetic field.   Results. The energy release as microflares and nanoflares occurs in two main phases. During phase 1a, a separator is formed and reconnection is driven at it as it rises to a maximum height and then moves back down to the photosphere, heating the plasma and accelerating plasma jets in the process. During phase 1b, once the separator moves back to the photosphere, it bifurcates into two null points. Reconnection is no longer driven at the separator and an isolated magnetic domain connecting the two polarities is formed. During phase 2, the polarities cancel out at the photosphere as magnetic flux submerges below the photosphere and as reconnection occurs at and above the photosphere and plasma jets and a mini-filament eruption can be produced.
We consider the problem: $$\inf_{{u}\in {H}^{1}_{g}(\Omega),\|u\|_{q}=1} \int_{\Omega}{p(x)}|\nabla{u(x)}|^{2}dx-\lambda\int_{\Omega}| u(x)|^{2}dx$$ where $\Omega$ is a bounded domain in $\R^{n}$, ${n}\geq{4}$, $ p : \bar{\Omega}\longrightarrow \R$ is a given positive weight such that $p\in H^{1}(\Omega)\cap C(\bar{\Omega})$, $0< c_1 \leq p(x) \leq c_2$, $\lambda$ is a real constant and $q=\frac{2n}{n-2}$ and $g$ a given positive boundary data. The goal of this present paper is to show that minimizers do exist. We distinguish two cases, the first is solved by a convex argument while the second is not so straightforward and will be treated using the behavior of the weight near its minimum and the fact that the boundary datum is not zero.
Detailed studies of stellar populations in the halos of the Milky Way and the Andromeda (M 31) galaxies have shown increasing numbers of tidal streams and dwarf galaxies, attesting to a complicated and on-going process of hierarchical structure formation. The most prominent feature in the halo of M 31 is the Giant Stellar Stream, a structure ~4.5 degrees in extent along the sky, which is close to, but not coincident with the galaxy's minor axis. The stars that make up this stream are kinematically and chemically distinct from the other stars in the halo. Here, we present HST/COS high-resolution ultraviolet absorption spectra of three Active Galactic Nuclei sight lines which probe the M 31 halo, including one that samples gas in the main southwestern portion of the Giant Stream. We see two clear absorption components in many metal species at velocities typical of the M 31 halo and a third, blue-shifted component which arises in the stream. Photoionization modeling of the column density ratios in the different components shows gas in an ionization state typical of that seen in other galaxy halo environments and suggests solar to slightly super-solar metallicity, consistent with previous findings from stellar spectroscopy.
Traffic grooming is a major issue in optical networks. It refers to grouping low rate signals into higher speed streams, in order to reduce the equipment cost. In SONET WDM networks, this cost is mostly given by the number of electronic terminations, namely ADMs. We consider the case when the topology is a unidirectional ring. In graph-theoretical terms, the traffic grooming problem in this case consists in partitioning the edges of a request graph into subgraphs with a maximum number of edges, while minimizing the total number of vertices of the decomposition. We consider the case when the request graph has bounded maximum degree $\Delta$, and our aim is to design a network being able to support any request graph satisfying the degree constraints. The existing theoretical models in the literature are much more rigid, and do not allow such adaptability. We formalize the problem, and solve the cases $\Delta=2$ (for all values of $C$) and $\Delta = 3$ (except the case C=4). We also provide lower and upper bounds for the general case.
We have conducted a pilot survey for z>3.5 quasars by combining the FIRST radio survey with the SDSS. While SDSS already targets FIRST sources for spectroscopy as quasar candidates, our survey includes fainter quasars and greatly improves the discovery rate by using strict astrometric criteria for matching the radio and optical positions. Our method allows for selection of high-redshift quasars with less color bias than with optical selection, as using radio selection essentially eliminates stellar contamination. We report the results of spectroscopy for 45 candidates, including 29 quasars in the range 0.37 < z < 5.2, with 7 having redshifts z>3.5. We compare quasars selected using radio and optical criteria, and find that radio-selected quasars have a much higher fraction of moderately-reddened objects. We derive a radio-loud quasar luminosity function at 3.5<z<4.0, and find that it is in good agreement with expectations from prior SDSS results.
We consider the nonlinear heat equation $u_t-\Delta u =|u|^p+b |\nabla u|^q$ in $(0,\infty)\times \R^n$, where $n\geq 1$, $p>1$, $q\geq 1$ and $b>0$. First, we focus our attention on positive solutions and obtain an optimal Fujita-type result: any positive solution blows up in finite time if $p\leq 1+\frac{2}{n}$ or $q\leq 1+\frac{1}{n+1}$, while global classical positive solutions exist for suitably small initial data when $p>1+\frac{2}{n}$ and $q> 1+\frac{1}{n+1}$. Although finite time blow-up cannot be produced by the gradient term alone and should be considered as an effect of the source term $|u|^p$, this result shows that the gradient term induces an interesting phenomenon of discontinuity of the critical Fujita exponent, jumping from $p=1+\frac{2}{n}$ to $p=\infty$ as $q$ reaches the value $1+\frac{1}{n+1}$ from above. Next, we investigate the case of sign-changing solutions and show that if $p\le 1+\frac{2}{n}$ or $0<(q-1)(np-1)\le 1$, then the solution blows up in finite time for any nontrivial initial data with nonnegative mean. Finally, a Fujita-type result, with a different critical exponent, is % also obtained for sign-changing solutions to the inhomogeneous version of this problem.
I report the analysis of an ultraluminous X-ray source (ULX) located in the galaxy NGC 1291. This X-ray point source is denominated IXO6 in the Catalog of Candidate IXO (Colbert & Ptak). An Intermediate-luminosity X-ray Object (IXO) is defined as an off-nuclear, compact object with luminosity Lx [2-10keV] >= 1039 erg s-1. The cutoff Lx is defined as a value greater than the Eddington luminosity of a 1.4 Mo black hole (10 38.3 erg s-1). IXO is an early denomination of what is call now a ULX point source. The Catalog was derived from a ROSAT survey and represents 87 IXOS in 54 galaxies. IXO6 was selected because of being positioned in the outer disk of the galaxy, with no near X-ray source neighbors. The study of this ULX pretends to confirm certain assumptions related to this class of objects (Roberts et al.)
We prove the existence of maximizers of Sobolev-Strichartz estimates for a general class of propagators, involving relevant examples, as for instance the wave, Dirac and the hyperbolic Schrodinger flows.
We study the connection between the generation of a fat point scheme supported at general points in the plane and the behaviour of the cotangent bundle with respect to some rational curves particularly relevant for the scheme. We put forward two conjectures, giving examples and partial results in support of them.
Why does controlling quantum phenomena appear easy to achieve? Why do effective quantum controls appear easy to find? Why is chemical synthesis and property optimization easier than expected? How to explain the commonalities across the optimal control applications in quantum mechanics, chemistry, material science, biological evolution and engineering? The theory of quantum control landscapes (QCL) is developed by Prof. Rabitz and his colleagues to address these puzzling questions. Unfortunately, the obtained conclusions are subject of gross misinterpretations which are spread in hundreds of published papers. We investigate, summarize and report several previously unknown subtleties of the QCL theory which have far-reaching implications for nearly all practical applications.
Interactions of ultra-high-energy cosmic rays with background photons set a limit to the distance cosmic rays reaching us above a certain energy can originate from, making measurements of their fluxes insensitive to properties of sources at high redshifts. On the other hand, the secondary PeV--EeV neutrinos produced in UHECR propagation can reach the Earth even from very high redshifts, and electromagnetic cascades initiated by secondary photons and electrons/positrons contribute to the diffuse gamma-ray background. Therefore, a multi-messenger analysis combining UHECR, neutrino, and gamma-ray data can still provide information about the cosmological evolution of UHECR sources. In this work, we compare predicted particle fluxes from Monte Carlo simulations in various scenarios with recent experimental data, and discuss the conclusions that can be drawn about UHECR sources and their cosmological evolution.
This paper studies a special class of states for the dual conformal field theories associated with supersymmetric $AdS_5\times X$ compactifications, where $X$ is a Sasaki-Einstein manifold with additional $U(1)$ symmetries. Under appropriate circumstances, it is found that elements of the chiral ring that maximize the additional $U(1)$ charge at fixed R-charge are in one to one correspondence with multitraces of a single composite field. This is also equivalent to Schur functions of the composite field. It is argued that in the formal zero coupling limit that these dual field theories have, the different Schur functions are orthogonal. Together with large $N$ counting arguments, one predicts that various extremal three point functions are identical to those of ${\cal N}=4 $ SYM, except for a single normalization factor, which can be argued to be related to the R-charge of the composite word. The leading and subleading terms in $1/N$ are consistent with a system of free fermions for a generalized oscillator algebra. One can further test this conjecture by constructing coherent states for the generalized oscillator algebra that can be interpreted as branes exploring a subset of the moduli space of the field theory and use these to compute the effective K\"ahler potential on this subset of the moduli space.
Few-shot object detection (FSOD) aims at learning a detector that can fast adapt to previously unseen objects with scarce annotated examples, which is challenging and demanding. Existing methods solve this problem by performing subtasks of classification and localization utilizing a shared component (e.g., RoI head) in the detector, yet few of them take the distinct preferences of two subtasks towards feature embedding into consideration. In this paper, we carefully analyze the characteristics of FSOD, and present that a general few-shot detector should consider the explicit decomposition of two subtasks, as well as leveraging information from both of them to enhance feature representations. To the end, we propose a simple yet effective Adaptive Fully-Dual Network (AFD-Net). Specifically, we extend Faster R-CNN by introducing Dual Query Encoder and Dual Attention Generator for separate feature extraction, and Dual Aggregator for separate model reweighting. Spontaneously, separate state estimation is achieved by the R-CNN detector. Besides, for the acquisition of enhanced feature representations, we further introduce Adaptive Fusion Mechanism to adaptively perform feature fusion in different subtasks. Extensive experiments on PASCAL VOC and MS COCO in various settings show that, our method achieves new state-of-the-art performance by a large margin, demonstrating its effectiveness and generalization ability.
In this paper we construct the Poincare line bundle for the stack of Higgs bundles on smooth projective curves and show that it induces a fully-faithful Fourier-Mukai transform on the category of quasi-coherent sheaves.
We study the effect of long-range disorder created by charge impurities on the carrier density distribution of graphene-based heterostructures. We consider heterostructures formed by two graphenic sheets (either single layer graphene, SLG, or bilayer graphene, BLG) separated by a dielectric film. We present results for symmetric heterostructures, SLG-SLG and BLG-BLG, and hybrid ones, BLG-SLG. As for isolated layers, we find that the presence of charged impurities induces strong carrier density inhomogeneities, especially at low dopings where the density landscape breaks up in electron-hole puddles. We provide quantitative results for the strength of the carrier density inhomogeneities and for the screened disorder potential for a large range of experimentally relevant conditions. For heterostructures in which BLG is present we also present results for the band-gap induced by the perpendicular electric field generated self-consistently by the disorder potential and by the distribution of charges in the heterostructure. For SLG-SLG heterostructures we discuss the relevance of our results for the understanding of the recently observed metal-insulator transition in each of the graphene layers forming the heterostructure. Moreover, we calculate the correlation between the density profiles in the two graphenic layers and show that for standard experimental conditions the two profiles are well correlated.
We present a new method to determine the age spread of resolved stellar populations in a starburst cluster. The method relies on a two-step process. In the first step, kinematic members of the cluster are identified based on multi-epoch astrometric monitoring. In the second step, a Bayesian analysis is carried out, comparing the observed photometric sequence of cluster members with sets of theoretical isochrones. When applying this methodology to optical and near-infrared high angular resolution Hubble Space Telescope (HST) and adaptive optics observations of the ~5 Myr old starburst cluster Westerlund 1 and ~2 Myr old starburst cluster NGC 3603 YC, we derive upper limits for the age spreads of 0.4 and 0.1 Myr, respectively. The results strongly suggest that star formation in these starburst clusters happened almost instantaneously.
We present a new measurement of structure growth at $z \simeq 0.08$ obtained by correlating the cosmic microwave background (CMB) lensing potential map from the \textit{Planck} satellite with the angular distribution of the 2MASS Photometric Redshift galaxies. After testing for, and finding no evidence for systematic effects, we calculate the angular auto- and cross-power spectra. We combine these spectra to estimate the amplitude of structure growth using the bias-independent $D_G$ estimator introduced by Giannantonio et al. 2016. We find that the relative amplitude of $D_G$ with respect to the predictions based on \textit{Planck} cosmology is $A_D(z=0.08) = 1.00 \pm 0.21$, fully consistent with the expectations for the standard cosmological model. Considering statistical errors only, we forecast that a joint analysis between an LSST-like photometric galaxy sample and lensing maps from upcoming ground-based CMB surveys like the Simons Observatory and CMB-S4 can yield sub-percent constraints on the growth history and differentiate between different models of cosmic acceleration.
We prove a quenched invariance principle for a class of random walks in random environment on $\mathbb{Z}^d$, where the walker alters its own environment. The environment consists of an outgoing edge from each vertex. The walker updates the edge $e$ at its current location to a new random edge $e'$ (whose law depends on $e$) and then steps to the other endpoint of $e'$. We show that a native environment for these walks (i.e., an environment that is stationary in time from the perspective of the walker) consists of the wired uniform spanning forest oriented toward the walker, plus an independent outgoing edge from the walker.
The X-ray emission from the supernova remnant DEM L 71 is measured and analysed using the high-resolution cameras and spectrometers on board XMM-Newton. The spectrum from the outer shell is reproduced very well by two plasma components of kT = 0.3 and 0.8 keV. The abundance value from this shell is consistent with the average LMC values. More extreme temperature variations are possibly indicated by spatial variations in the O VII forbidden/resonance line ratio, which could imply that in some regions the plasma is cooling dramatically and recombining. However, an alternative and equally interesting possibility is that the variation in forbidden/resonance ratios is due to resonant scattering, which would reduce resonance line emission along lines of sight with a high O VII column density. The inner region is hotter (kT = 1.1 keV) and shows enhanced Fe and Si abundances. We estimate the Fe and Si ejecta mass to be 0.7-1.1 M_sun and 0.1--0.15 M_sun, respectively. The morphology, mass estimates and abundances strongly suggest that DEM L 71 is the result of a type Ia explosion, as indicated by previous measurements.
Normal-mode coupling is a helioseismic technique that uses measurements of mode eigenfunctions to infer the interior structure of the Sun. This technique has led to insights into the evolution and structure of toroidal flows in the solar interior. Here, we validate an inversion algorithm for normal-mode coupling by generating synthetic seismic measurements associated with input flows and comparing the input and inverted velocities. We study four different cases of input toroidal flows and compute synthetics that take into account the partial visibility of the Sun. We invert the synthetics using Subtractive Optimally Localized Averages (SOLA) and also try to mitigate the systematics of mode leakage. We demonstrate that, ultimately, inversions are only as good as the model we assume for the correlation between flow velocities.
Dan Romik recently considered the Taylor coefficients of the Jacobi theta function around the complex multiplication point $i$. He then conjectured that the Taylor coefficients $d(n)$ either vanish or are periodic modulo any prime ${p}$; this was proved by the combined efforts of Scherer and Guerzhoy-Mertens-Rolen, who considered arbitrary half integral weight modular forms. We refine previous work for $p \equiv 1 \pmod{4}$ by displaying a concise algebraic relation between $d\left( n+ \frac{p-1}{2} \right)$ and $d(n)$ related to the $p$-adic factorial, from which we can deduce periodicity with an effective period.
We report imaging photometry of the radio-jet black hole candidate source GRS 1915+105 in the infrared K band. The observations reveal rapid infrared flare events on timescales of less than an hour. These events are strikingly similar to those regularly observed in radio monitoring at 15 GHz. Furthermore, when dereddened, the infrared events have comparable amplitudes to the radio oscillations, and observations at 15 GHz made approx. 8 hr after our infrared observations reveal that the source was indeed displaying radio oscillations at this time. We suggest that we have observed infrared synchrotron emission from this source. We estimate the equipartition magnetic field and power required to accelerate the particles for the repeated radio events, and find both to be orders of magnitude greater than those estimated for any other X-ray binary.
In this note it is shown that associating to a principally polarized abelian variety its de Rham cohomology defines a faithfully flat morphism of the moduli space of principally polarized abelian varieties in positive characteristics to the moduli space of symplectic $F$-Zips as defined in \cite{MW}.