ShantanuT01/DACTYL-Pretraining huggingface dataset:
We consider the solution of Matrix Dyson Equation $-M\left(z\right)^{-1} = z + \mathcal{S}\left(M\left(z\right)\right)$, where entries of the linear operator $\mathcal{S}: \mathbb{C}^{N\times N} \rightarrow \mathbb{C}^{N\times N}$ decay exponentially. We show that $M(z)$ also has exponential off-diagonal decay and can be represented as Laurent series with coefficients determined by entries of $\mathcal{S}$. We also prove that for Hermitian random matrices with exponential correlation decay empirical density converges to the deterministic density obtained from $M(z)$. These results have already been proved in [arXiv:1604.08188] with the resolvent method, here we give an alternate proof via the conceptually much simpler moment method.
By using a classical truncated argument and introducing the local Wasserstein distance, the global existence and uniqueness are proved for the distribution dependent SDEs with local Lipschitz coefficients. Due to the measure dependence, the conditions in the sense of pointwise for classical cases can be simplified to the conditions in the sense of integral. On the basis of the well-posedness, we prove the $r$-th moment exponential stability using the measure dependent Lyapunov functions and the existence and uniqueness of invariant probability measure is studied under the integrated strong monotonicity condition. Finally, some examples are given to illustrate the results in this paper.
The narrow emission lines from the inner ring around SN 1987A during the first $\sim 2000$ days are modeled. The analysis extends that in Lundqvist & Fransson (1991) to include an improved description for the geometry, a multi-density structure of the emitting gas, results from improved calculations for the evolu- tion of the EUV radiation from the outburst, and updated atomic data. The ring has to be optically thick to the ionizing radiation, as is the case for a ring geometry, but not for a spherical shell. The density of the observed gas in the ring ranges from $(6.0\pm1.0)\EE{3} \cm3$ to $3.3\EE{4} \cm3$. The early ($t \lesssim 410$ days) UV line emission is dominated by the gas with the high- est density. Gas of lower density than $\sim 6\EE{3} \cm3$ may be present in the ring, but will not dominate the emission until after $\sim 2000$ days. The ionized mass observed up to day 1882 is $\sim 4.5\EE{-2} \Msun$. The He/H ratio is $0.25\pm0.05$, and the overall abundance of C, N and O is $0.30\pm0.05$ times solar with relative abundances ${\rm N/C} = 5.0\pm2.0$ and ${\rm N/O} = 1.1\pm0. 4$. The peak effective temperature of the burst is in the range $(5-8)\EE{5}$ K. The corresponding color temperature is $(1.0-1.5)\EE6$ K. To model the $\NV$~ $\lambda$1240 light curve, resonance scattering in a medium external to the ring is needed. It is shown that the $\NV$ line scattering can be used to discrimi- nate between models for the formation of the inner ring and the extended nebula.
The number of real roots has been a central subject in the theory of random polynomials and random functions since the fundamental papers of Littlewood-Offord and Kac in the 1940s. The main task here is to determine the limiting distribution of this random variable.   In 1974, Maslova famously proved a central limit theorem (CLT) for the number of real roots of Kac polynomials. It has remained the only limiting theorem available for the number of real roots for more than four decades.   In this paper, using a new approach, we derive a general CLT for the number of real roots of a large class of random polynomials with coefficients growing polynomially. Our result both generalizes and strengthens Maslova's theorem.
We address the time evolution of the quantum correlations ($QCs$) such as entanglement, purity, and coherence for a model of two non-interacting qubits initially prepared as a maximally entangled bipartite state. We contrast the comparative potential of the classical fields to preserve these $QCs$ in the noisy and noiseless realms. We also disclose the characteristic dynamical behavior of the $QCs$ of the two-qubit state under the static noisy effects originating from the common and different configuration models. We show that there is a direct connection between the fluctuations allowed by an environment and the $QCs$ preservation. Due to the static noisy dephasing effects, the $QCs$ are suppressed, resulting in the separability of the two-qubit entangled state after a finite duration. Here, the $QCs$ decay effects are found much smaller in the common configuration model than that of the opponent. Furthermore, this protection of the $QCs$ under static noise for large intervals is entirely attributable to the existence of the entanglement sudden death and birth phenomenon. Most importantly, we found the bipartite $QCs$ less fragile than the tripartite ones in comparison under the static noise. In the case of the measures, the concurrence is found to be sharper for showing the entanglement sudden death and birth revivals in comparison to the purity and decoherence.
In this paper, we present a novel deep learning architecture for infrared and visible images fusion problem. In contrast to conventional convolutional networks, our encoding network is combined by convolutional layers, fusion layer and dense block in which the output of each layer is connected to every other layer. We attempt to use this architecture to get more useful features from source images in encoding process. And two fusion layers(fusion strategies) are designed to fuse these features. Finally, the fused image is reconstructed by decoder. Compared with existing fusion methods, the proposed fusion method achieves state-of-the-art performance in objective and subjective assessment. Code and pre-trained models are available at https://github.com/hli1221/imagefusion_densefuse
In this paper, we investigate the existence of a "weak solutions" for a Neumann problems of $p(x)$-Laplacian-like operators, originated from a capillary phenomena, of the following form \begin{equation*}   \displaystyle\left\{\begin{array}{ll}   \displaystyle-{\rm{div}}\Big(\vert\nabla u\vert^{p(x)-2}\nabla u+\frac{\vert\nabla u\vert^{2p(x)-2}\nabla u}{\sqrt{1+\vert\nabla u\vert^{2p(x)}}}\Big)=\lambda f(x, u, \nabla u) & \mathrm{i}\mathrm{n}\ \Omega,\\   \Big(\vert\nabla u\vert^{p(x)-2}\nabla u+\frac{\vert\nabla u\vert^{2p(x)-2}\nabla u}{\sqrt{1+\vert\nabla u\vert^{2p(x)}}}\Big)\frac{\partial u}{\partial\eta}=0 & \mathrm{o}\mathrm{n}\ \partial\Omega,   \end{array}\right. \end{equation*} in the setting of the variable-exponent Sobolev spaces $W^{1,p(x)}(\Omega)$, where $\Omega$ is a smooth bounded domain in $\mathbb{R}^{N}$, $p(x)\in C_{+}(\overline{\Omega})$ and $\lambda$ is a real parameter. Based on the topological degree for a class of demicontinuous operators of generalized $(S_{+})$ type and the theory of variable-exponent Sobolev spaces, we obtain a result on the existence of weak solutions to the considered problem.
We study the complementarity of weak lensing (WL) and spectroscopic galaxy clustering (GC) surveys, by forecasting dark energy and modified gravity constraints for three upcoming survey combinations: SuMIRe (Subaru Measurement of Images and Redshifts, the combination of the Hyper Suprime-Cam lensing survey and the Prime Focus Spectrograph redshift survey), EUCLID and WFIRST. From the WL surveys, we take into account both the shear and clustering of the source galaxies and from the GC surveys, we use the three-dimensional clustering of spectroscopic galaxies, including redshift space distortions. A CMB prior is included in all cases. Focusing on the large-scale, two-point function information, we find strong synergy between the two probes. The dark energy figure of merit from WL+GC is up to a factor ~2.5 larger than from either probe alone. Considering modified gravity, if the growth factor f(z) is treated as a free function, it is very poorly constrained by WL or GC alone, but can be measured at the few percent level by the combination of the two. On the other hand, for cosmological constraints derived from (angular) power spectra and considering statistical errors only, it hardly matters whether the surveys overlap on the sky or not. For instance, the dark energy figure of merit for overlapping surveys is at most ~20 % better than in the disjoint case. This modest gain can be traced to the fundamental fact that only a small fraction of the total number of modes sampled by the GC survey (or by the WL survey) contributes to the cross-correlations between WL and GC.
While feedback is important in theoretical models, we do not really know if it works in reality. Feedback from jets appears to be sufficient to keep the cooling flows in clusters from cooling too much and it may be sufficient to regulate black hole growth in dominant cluster galaxies. Only about 10% of all quasars, however, have powerful radio jets, so jet-related feedback cannot be generic. The outflows could potentially be a more common form of AGN feedback, but measuring mass and energy outflow rates is a challenging task, the main unknown being the location and geometry of the absorbing medium. Using a novel technique, we made first such measurement in NGC 4051 using XMM data and found the mass and energy outflow rates to be 4 to 5 orders of magnitude below those required for efficient feedback. To test whether the outflow velocity in NGC 4051 is unusually low, we compared the ratio of outflow velocity to escape velocity in a sample of AGNs and found it to be generally less than one. It is thus possible that in most Seyferts the feedback is not sufficient and may not be necessary.
Supermassive black hole (BH) binaries would comprise the strongest sources of gravitational waves (GW) once they reach <<1 pc separations, for both pulsar timing arrays (PTAs) and space based (SB) detectors. While BH binaries coalescences constitute a natural outcome of the cosmological standard model and galaxy mergers, their dynamical evolution is still poorly understood and therefore their abundances at different stages. We use a dynamical model for the decay of BH binaries coupled with a cosmological simulation and semi-empirical approaches to the occupation of haloes by galaxies and BHs, in order to follow the evolution of the properties distribution of galaxies hosting BH binaries candidates to decay due to GWs emission. Our models allow us to relax simplifying hypothesis about the binaries occupation in galaxies and their mass, as well as redshift evolution. Following previously proposed electromagnetic (EM) signatures of binaries in the subpc regime, that include spectral features and variability, we model possible distributions of such signatures and also set upper limits to their lifespan. We found a bimodal distribution of hosts properties, corresponding to BH binaries suitable to be detected by PTA and the ones detectable only from space missions, as eLISA. Although it has been discussed that the peak of eLISA sources may happen at high z, we show that there must be a population of such sources in the nearby Universe that might show detectable EM signatures, representing an important laboratory for multimessenger astrophysics. We found a weak dependence of galaxy host properties on the binaries occupation, that can be traced back to the BH origin. The combination of the host correlations reported here with the expected EM signal, may be helpful to verify the presence of nearby GW candidates, and to distinguish them from 'regular' intrinsic AGN variability.
We formulate a general theory to study the time-dependent charge and energy transport of an adiabatically driven quantum dot in contact to normal and superconducting reservoirs at T=0. This setup is a generalization of a quantum RC circuit, with capacitive components due to Andreev processes and induced pairing fluctuations, in addition to the convencional normal charge fluctuations. The dynamics for the dissipation of energy is ruled by a Joule law of four channels in parallel with the universal B\"uttiker resistance R_0=e^2/2h per channel. Two transport channels are associated to the two spin components of the usual charge fluctuations, while the other two are associated to electrons and holes due to pairing fluctuations. The latter leads to an "anomalous" component of the Joule law and take place with a vanishing net current due to the opposite flows of electrons and holes.
We investigate the effect of fragmentation on the homogeneous free cooling of inelastic hard spheres, using Boltzmann kinetic theory and Direct Monte Carlo simulations. We analyze in detail a model where dissipative collisions may subsequently lead to a break-up of the grains. With a given probability, two off-springs are then created from one of the two colliding partners, with conservation of mass, momentum and kinetic energy. We observe a scaling regime characterized by a single collisional average, that quantifies the deviations from Gaussian behaviour for the joint size and velocity distribution function. We also discuss the possibility of a catastrophe whereby the number of particles diverges in a finite time. This phenomenon appears correlated to a ``shattering'' transition marked by a delta singularity at vanishingly small grains for the rescaled size distribution.
Reasoning about complex visual scenes involves perception of entities and their relations. Scene graphs provide a natural representation for reasoning tasks, by assigning labels to both entities (nodes) and relations (edges). Unfortunately, reasoning systems based on SGs are typically trained in a two-step procedure: First, training a model to predict SGs from images; Then, a separate model is created to reason based on predicted SGs. In many domains, it is preferable to train systems jointly in an end-to-end manner, but SGs are not commonly used as intermediate components in visual reasoning systems because being discrete and sparse, scene-graph representations are non-differentiable and difficult to optimize. Here we propose Differentiable Scene Graphs (DSGs), an image representation that is amenable to differentiable end-to-end optimization, and requires supervision only from the downstream tasks. DSGs provide a dense representation for all regions and pairs of regions, and do not spend modelling capacity on areas of the images that do not contain objects or relations of interest. We evaluate our model on the challenging task of identifying referring relationships (RR) in three benchmark datasets, Visual Genome, VRD and CLEVR. We describe a multi-task objective, and train in an end-to-end manner supervised by the downstream RR task. Using DSGs as an intermediate representation leads to new state-of-the-art performance.
We collect some classical results about holomorphic 1-forms of a reduced complex curve singularity, in particular of a complete intersection, and use them to compare the Milnor number, the Tjurina number and the dimension of the torsion part of the 1-forms.
We present a study of the nuclear morphology of a sample of narrow- and broad-line Seyfert 1 galaxies (NLS1's and BLS1's) based on broad-band images in the Hubble Space Telescope archives. In our previous study, we found that large-scale stellar bars at > 1 kpc from the nucleus are more common in NLS1's than BLS1's. In this paper we find that NLS1's preferentially have grand-design dust spirals within approx. 1 kpc of their centers. We also find that NLS1's have a higher fraction of nuclear star-forming rings than BLS1's. We find that many of the morphological differences are due to the presence or absence of a large-scale stellar bar within the spiral host galaxy. In general, barred Seyfert 1s tend to have grand-design dust spirals at their centers, confirming the results of other researchers. The high fraction of grand-design nuclear dust spirals and stellar nuclear rings observed in NLS1's host galaxies suggests a means for efficient fueling of their nuclei to support their high Eddington ratios.
Starting from isentropic compressible Navier-Stokes equations with growth term in the continuity equation, we rigorously justify that performing an incompressible limit one arrives to the two-phase free boundary fluid system.
A short introduction to structure formation is given, followed by a discussion of the possible characteristics of the initial perturbations assuming a generic inflationary origin. Observational data related to large-scale structure and the cosmic microwave background radiation is then used in an attempt to constrain the characteristics of such perturbations. Future directions are also explored.   The possibility of direct detection of a stochastic gravitational wave background produced during an inflationary phase in the early Universe is briefly discussed, as well as the available evidence regarding the present value of the total energy density in the Universe.
We present a quantization scheme of an arbitrary measure space based on overcomplete families of states and generalizing the Klauder and the Berezin-Toeplitz approaches. This scheme could reveal itself as an efficient tool for quantizing physical systems for which more traditional methods like geometric quantization are uneasy to implement. The procedure is illustrated by (mostly two-dimensional) elementary examples in which the measure space is a $N$-element set and the unit interval. Spaces of states for the $N$-element set and the unit interval are the 2-dimensional euclidean $\R^2$ and hermitian $\C^2$ planes.
This work, together with its companion paper, Secco and Samuroff et al. (2021), presents the Dark Energy Survey Year 3 cosmic shear measurements and cosmological constraints based on an analysis of over 100 million source galaxies. With the data spanning 4143 deg$^2$ on the sky, divided into four redshift bins, we produce the highest significance measurement of cosmic shear to date, with a signal-to-noise of 40. We conduct a blind analysis in the context of the $\Lambda$CDM model and find a 3% constraint of the clustering amplitude, $S_8\equiv \sigma_8 (\Omega_{\rm m}/0.3)^{0.5} = 0.759^{+0.025}_{-0.023}$. A $\Lambda$CDM-Optimized analysis, which safely includes smaller scale information, yields a 2% precision measurement of $S_8= 0.772^{+0.018}_{-0.017}$ that is consistent with the fiducial case. The two low-redshift measurements are statistically consistent with the Planck Cosmic Microwave Background result, however, both recovered $S_8$ values are lower than the high-redshift prediction by $2.3\sigma$ and $2.1\sigma$ ($p$-values of 0.02 and 0.05), respectively. The measurements are shown to be internally consistent across redshift bins, angular scales and correlation functions. The analysis is demonstrated to be robust to calibration systematics, with the $S_8$ posterior consistent when varying the choice of redshift calibration sample, the modeling of redshift uncertainty and methodology. Similarly, we find that the corrections included to account for the blending of galaxies shifts our best-fit $S_8$ by $0.5\sigma$ without incurring a substantial increase in uncertainty. We examine the limiting factors for the precision of the cosmological constraints and find observational systematics to be subdominant to the modeling of astrophysics. Specifically, we identify the uncertainties in modeling baryonic effects and intrinsic alignments as the limiting systematics.
We point out that the transition probabilities used in a recent perturbative calculation of pair creation in an external magnetic field in the expanding de Sitter space with the $in$ and $out$ fermion states defined by the Bunch-Davies modes [C. Crucean et al., Phys. Rev. D 73 044019 (20016)] are gauge dependent quantities. We examine the gauge variations of these amplitudes assuming a decoupling of the interaction at infinite times, which allows to conclude that the source of the problem lies in the nonoscillatory behavior of the fermion current in the infinite future.
Variations of the sunspot number are important indicators of the solar activity cycles. The sunspot formation is a result of a dynamo process inside the Sun, which is far from being understood. We use simple dynamical models of the dynamo process to simulate the magnetic field evolution and investigate general properties of the sunspot number variations during the solar cycles. We have found that the classical Parker's model with a standard kinetic helicity quenching cannot represent the typical profiles of the solar-cycle variations of the sunspot number, and also does not give chaotic solutions. For modeling of the solar cycle properties we use a nonlinear dynamo model of Kleeorin and Ruzmaikin (1982), which takes into account dynamics of the turbulent magnetic helicity. We have obtained a series of periodic and chaotic solutions for different layers of the convective zone. The solutions qualitatively reproduce some basic observational features of the solar cycle properties, in particular, the relationship between the growth time and the cycle amplitude. Also, on the longer time scale the dynamo model with the magnetic helicity has intermittent solutions, which may be important for modeling long-term variations of the solar cycles.
We consider a two-point spatial lattice approximation to an open string moving in a flat background with B field. It gives a constrained dipole system under the influence of a vector potential. Solving and quantizing this system recover all the essential features of a noncommutative space. In particular, open string interactions induce a canonical product structure on the Hilbert space of the dipole system. It coincides with the usual star product, even though the position operators can be thought of as mutually commuting. Modification of gauge transformations in this noncommutative space also naturally emerges.
The structure of $3/2^{-}$ and $1/2^{+}$ states in $^{11}$B is investigated with an $\alpha+\alpha+t$ orthogonality condition model (OCM) based on the Gaussian expansion method. Full levels up to the $3/2^{-}_{3}$ and $1/2^{+}_2$ states around the $\alpha+\alpha+t$ threshold ($E_x$=11.1 MeV) are reproduced consistently with the experimental energy levels. It is shown that the $3/2_{3}^{-}$ state located around the $^{7}$Li+$\alpha$ threshold has an $\alpha+\alpha+t$ cluster structure, whereas the $3/2_{1}^{-}$ and $3/2_{2}^{-}$ states have a shell-model-like compact structure. We found that the $3/2_{3}^{-}$ state does not possess an $\alpha$-condensate-like nature similar to the $0^{+}_{2}$ state of $^{12}$C (Hoyle state) which has a dilute $3\alpha$-condensate structure described by a $(0S_{\alpha})^3$ configuration with about $70$\% probability, although the monopole transition strength of the former is as large as that of the latter. We discuss the reasons why the $3/2_{3}^{-}$ state does not have the condensate character. On the other hand, the $1/2^{+}_{1}$ state just below the $^{7}$Li+$\alpha$ threshold has a cluster structure which can be interpreted as a parity-doublet partner of the $3/2^{-}_3$ state. We indicate that the $12.56$-MeV state ($J^{\pi}=1/2^{+}_{2}$) just above the $\alpha+\alpha+t$ threshold observed in the $^7$Li($^{7}$Li,$^{11}$B$^*$)$t$ reaction etc. is of the dilute-cluster-gas-like, and is a strong candidate for the Hoyle-analogue state which has a configuration of $(0S_{\alpha})^{2}(0S_{t})$ with about $65$\% probability from the analyses of the single-cluster motions in $^{11}$B. The structure property of the $1/2^{+}$ resonant state is analyzed with the complex scaling method.
Various possibilities of polar self-organisation in low molar mass nematic, smectic and columnar liquid crystals are discussed with particular focus on the underlying molecular symmetries and interactions. Distinction is made between vector and pseudovector polarities, their quantification in terms of molecular order parameters and their relation to spontaneous electric polarisation and to molecular chirality. The understanding of the molecular mechanisms that give rise to polar ordering in existing lamellar and columnar phases may be useful for the design of new polar variants of common a-polar liquid crystals. Keywords:Polar Nematics; Ferroelectric Liquid Crystals; Polar Ordering.