ShantanuT01/DACTYL-Pretraining huggingface dataset:
The Hessian quotient equatio were studied for k-th symmetric elementary function S_k(D^2u) of eigenvalues of the Hessian matrix D^2u. Two pointwise quadratic growth conditions were found by Bao-Cheng-Guan-Ji ([1], American J. Math., 2003, 125, 301-316) ensuring Bernstein properties of Hessian quotient equation or k-Hessian equation respectively. In this paper, we will drop the point wise quadratic growth condition of [1] and prove three necessary and sufficient conditions to Bernstein property of (0.1) and (0.2), using a reverse isoperimetric type inequality, volume growth or Lp-integrable respectively.Our volume growth or Lp-integrable conditions improve largely various known point wise conditions in [1,6,7,13,18] etc.
Sketch portrait generation benefits a wide range of applications such as digital entertainment and law enforcement. Although plenty of efforts have been dedicated to this task, several issues still remain unsolved for generating vivid and detail-preserving personal sketch portraits. For example, quite a few artifacts may exist in synthesizing hairpins and glasses, and textural details may be lost in the regions of hair or mustache. Moreover, the generalization ability of current systems is somewhat limited since they usually require elaborately collecting a dictionary of examples or carefully tuning features/components. In this paper, we present a novel representation learning framework that generates an end-to-end photo-sketch mapping through structure and texture decomposition. In the training stage, we first decompose the input face photo into different components according to their representational contents (i.e., structural and textural parts) by using a pre-trained Convolutional Neural Network (CNN). Then, we utilize a Branched Fully Convolutional Neural Network (BFCN) for learning structural and textural representations, respectively. In addition, we design a Sorted Matching Mean Square Error (SM-MSE) metric to measure texture patterns in the loss function. In the stage of sketch rendering, our approach automatically generates structural and textural representations for the input photo and produces the final result via a probabilistic fusion scheme. Extensive experiments on several challenging benchmarks suggest that our approach outperforms example-based synthesis algorithms in terms of both perceptual and objective metrics. In addition, the proposed method also has better generalization ability across dataset without additional training.
Gas can be violently stripped from their galaxy disks in rich clusters, and be dispersed over 100kpc-scale tails or plumes. Young stars have been observed in these tails, suggesting they are formed in situ. This will contribute to the intracluster light, in addition to tidal stripping of old stars. We want to quantify the efficiency of intracluster star formation. We present CO(1--0) and CO(2--1) observations, made with the IRAM-30m telescope, towards the ram-pressure stripped tail northeast of NGC4388 in Virgo. HII regions found all along the tails, together with dust patches have been targeted. We detect molecular gas in 4 positions along the tail, with masses between 7x10$^5$ to 2x10$^6$ M$_\odot$. Given the large distance from the NGC 4388 galaxy, the molecular clouds must have formed in situ, from the HI gas plume. We compute the relation between surface densities of star formation and molecular gas in these regions, and find that the star formation has very low efficiency. The corresponding depletion time of the molecular gas can be up to 500 Gyr and more. Since this value exceeds a by far Hubble time, this gas will not be converted into stars, and will stay in a gaseous phase to join the intracluster medium.
This paper has two parts. First we review the description of local bulk operators in Lorentzian AdS in terms of non-local operators in the boundary CFT. We discuss how bulk locality arises in pure AdS backgrounds and how it is modified at finite N. Next we present some new results on BTZ black holes: local operators can be defined inside the horizon of a finite N BTZ black hole, in a way that suggests the BTZ geometry describes an average over black hole microstates, but with finite N effects resolving the singularity.
The general approach for the consideration of the magnetoelectric effects in ferroic nanorods is proposed in the framework of the phenomenological theory. The intrinsic surface stress, magneto- and electrostriction as well as piezoelectric and piezomagnetic effects are included into the free energy. The intrinsic surface stress under the curved nanoparticle surface is shown to play an important role in the shift of ferroelectric and ferromagnetic transition temperatures and built-in magnetic and electric fields appearance, which are inversely proportional to the nanorod radius. We consider the case of quadratic and linear magnetoelectric coupling coefficients. The linear coupling coefficient is radius independent, whereas the quadratic ones include terms inversely proportional to the nanorod radius and thus strongly increase with decrease of the radius. The predicted giant relative dielectric tunability in the vicinity of ferromagnetic and ferroelectric phase transition points induced by quadratic magnetoelectric coupling increases by 2-50 times. The quadratic magnetoelectric coupling dramatically changes the phase diagrams of ferroic nanorods when the radius decreases. In particular the second order phase transition may become a first one, the triple point state characterized by continuous set of order parameters appears at zero external electric and magnetic fields and the tricritical points appear under external fields.
We explore the evolution of the SCUBA sub-mm galaxy population using Monte Carlo simulations to generate synthetic sub-mm/radio color magnitude diagrams. To represent the local distribution of observed dust properties, we use a local far-infrared luminosity function derived from the IRAS 1.2 Jy catalog, bivariate in FIR luminosity and 60micron/100micron color. We assume a peak luminosity evolution scenario and a fixed cosmology, to fit a single parameter model to the existing sub-mm/radio data. Our best fitting model has a peak in the luminosity evolution at z=2.6.
We compute the binding energies, radii, and densities for selected medium-mass nuclei within coupled-cluster theory and employ the "bare" chiral nucleon-nucleon interaction at order N3LO. We find rather well-converged results in model spaces consisting of 15 oscillator shells, and the doubly magic nuclei 40Ca, 48Ca, and the exotic 48Ni are underbound by about 1 MeV per nucleon within the CCSD approximation. The binding-energy difference between the mirror nuclei 48Ca and 48Ni is close to theoretical mass table evaluations. Our computation of the one-body density matrices and the corresponding natural orbitals and occupation numbers provides a first step to a microscopic foundation of the nuclear shell model.
The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large times the entropy tends exponentially to a constant. For systems with no stationary density, at large times the entropy is logarithmic with a coefficient specifying the speed of the diffusion. As an example, the large time behaviors of the entropy and the variance are compared for various types of fractional-derivative diffusions.
Based on the Hugenholtz-Van Hove theorem, the symmetry energy $J$ and its density slope parameter $L$ are decomposed in terms of the nucleon self-energies within the covariant density functional (CDF) theory. It is found that two structural connections between the different ingredients of $J$ and $L$ construct the fundamental correlation between $L$ and $J$ in the relativistic covariant framework, while the additional contribution from the isovector scalar channel of nucleon-nucleon interaction and those from the second-order symmetry self-energies lead to a deviation, especially the latter limits severely its correlation coefficient and confidence level. In addition, the relationship between the Landau mass $M_L^*$ and the Dirac mass $M_D^*$ is approximated to a reliable linear correlation, which is demonstrate to be sensitive to the momentum dependence of the nucleon self-energies.
Problems connected with a choice of the spinorial basis in the $(j,0)\oplus (0,j)$ representation space are discussed. As shown it has profound significance in the relativistic quantum theory. From the methodological viewpoint this fact is related with the important dynamical role played by space-time symmetries for all kind of interactions.
In this note we provide a quick proof of the Sklar's Theorem on the existence of copulas by using the generalized inverse functions as in the one dimensional case, but a little more sophisticated.
The Rapid Temporal Survey (RATS) explores the faint, variable sky. Our observations search a parameter space which, until now, has never been exploited from the ground. Our strategy involves observing the sky close to the Galactic plane with wide-field CCD cameras. An exposure is obtained approximately every minute with the total observation of each field lasting around 2 hours. In this paper we present the first 6 epochs of observations which were taken over 5 years from 2003--2008 and cover over 31 square degrees of which 16.2 is within 10{\deg} of the Galactic plane. The number of stars contained in these data is over 3.0 x10^6. We have developed a method of combining the output of two variability tests in order to detect variability on time-scales ranging from a few minutes to a few hours. Using this technique we find 1.2 x 10^5 variables -- equal to 4.1 per cent of stars in our data. Follow-up spectroscopic observations have allowed us to identify the nature of a fraction of these sources. These include a pulsating white dwarf which appears to have a hot companion, a number of stars with A-type spectra that vary on a period in the range 20--35 min. Our primary goal is the discovery of new AM CVn systems: we find 66 sources which appear to show periodic modulation on a time-scales less than 40 min and a colour consistent with the known AM CVn systems. Of those sources for which we have spectra of, none appears to be an AM CVn system, although we have 12 candidate AM CVn systems with periods less than 25 min for which spectra are still required. Although our numbers are not strongly constraining, they are consistent with the predictions of Nelemans et al.
We consider the second order Cauchy problem   $$u''+m(|A^{1/2}u|^2)Au=0, u(0)=u_{0}, u'(0)=u_{1},$$ where $m:[0,+\infty)\to[0,+\infty)$ is a continuous function, and $A$ is a self-adjoint nonnegative operator with dense domain on a Hilbert space. It is well known that this problem admits local-in-time solutions provided that $u_{0}$ and $u_{1}$ are regular enough, depending on the continuity modulus of $m$, and on the strict/weak hyperbolicity of the equation. We prove that for such initial data $(u_{0},u_{1})$ there exist two pairs of initial data $(\overline{u}_{0},\overline{u}_{1})$, $(\widehat{u}_{0},\widehat{u}_{1})$ for which the solution is global, and such that $u_{0}=\overline{u}_{0}+\widehat{u}_{0}$, $u_{1}=\overline{u}_{1}+\widehat{u}_{1}$. This is a byproduct of a global existence result for initial data with a suitable spectral gap, which extends previous results obtained in the strictly hyperbolic case with a smooth nonlinearity $m$.
We show that applying simple dynamical rules to Baxter's eight-vertex model leads to a system which resembles a glass-forming liquid. There are analogies with liquid, supercooled liquid, glassy and crystalline states. The disordered phases exhibit strong dynamical heterogeneity at low temperatures, which may be described in terms of an emergent mobility field. Their dynamics are well-described by a simple model with trivial thermodynamics, but an emergent kinetic constraint. We show that the (second order) thermodynamic transition to the ordered phase may be interpreted in terms of confinement of the excitations in the mobility field. We also describe the aging of disordered states towards the ordered phase, in terms of simple rate equations.
We report high precision spectrophotometric observations of four planetary transits of HD 209458, in the region of the sodium resonance doublet at 589.3 nm. We find that the photometric dimming during transit in a bandpass centered on the sodium feature is deeper by (2.32 +/- 0.57) x 10^{-4} relative to simultaneous observations of the transit in adjacent bands. We interpret this additional dimming as absorption from sodium in the planetary atmosphere, as recently predicted from several theoretical modeling efforts. Our model for a cloudless planetary atmosphere with a solar abundance of sodium in atomic form predicts more sodium absorption than we observe. There are several possibilities that may account for this reduced amplitude, including reaction of atomic sodium into molecular gases and/or condensates, photoionization of sodium by the stellar flux, a low primordial abundance of sodium, or the presence of clouds high in the atmosphere.
We consider the Cauchy problem on a nonlinear conversation law with large initial data. By Green's function methods, energy methods, Fourier analysis, frequency decomposition, pseudo-differential operators, we obtain the global existence and the optimal decay estimate of $t$.
We have observed nanopattern formation with robust and controllable spatial ordering by laser-induced dewetting in nanoscopic metal films. Pattern evolution in Co film of thickness 1\leq h\leq8 nm on SiO_{2} was achieved under multiple pulse irradiation using a 9 ns pulse laser. Dewetting leads to the formation of cellular patterns which evolve into polygons that eventually break up into nanoparticles with monomodal size distribution and short range ordering in nearest-neighbour spacing R. Spatial ordering was attributed to a hydrodynamic thin film instability and resulted in a predictable variation of R and particle diameter D with h. The length scales R and D were found to be independent of the laser energy. These results suggest that spatially ordered metal nanoparticles can be robustly assembled by laser-induced dewetting.
Magneto-drag reveals the nature of compressible states and the underlying interplay of disorder and interactions. At \nu=3/2 a clear T^{4/3} dependence is observed, which signifies the metallic nature of the N=0 Landau level. In contrast, drag in higher Landau levels reveals an additional contribution, which anomalously grows with decreasing T before turning to zero following a thermal activation law. The anomalous drag is discussed in terms of electron-hole asymmetry arising from disorder and localization, and the crossover to normal drag at high fields as due to screening of disorder.
Simple supersymmetric SO(10) GUT in five dimensions is proposed, in which the fifth dimension is compactified on the $S^1/(Z_2\times Z_2^\prime)$ orbifold with two inequivalent branes at the orbifold fixed points. In this model, all matter and Higgs multiplets reside on one brane (PS brane) where the Pati-Salam (PS) symmetry is manifest, while only the SO(10) gauge multiplet resides on the bulk. The supersymmetry breaking on the other brane (SO(10) brane) is transmitted to the PS brane through the gaugino mediation with the bulk gauge multiplet. We examine sparticle mass spectrum in this setup and show that the neutralino LSP as the dark matter candidate can be realized when the compactification scale of the fifth dimension is higher than the PS symmetry breaking scale, keeping the successful gauge coupling unification after incorporating threshold corrections of Kaluza-Klein modes of the bulk gauge multiplets.
Neutron diffraction studies of antiferromagnetic CoO confined to a vycor type porous glass demonstrate a continuous magnetic phase transition with a decreased N\'eel temperature and reduced magnetic moment as compared with the bulk.
We study the fractal structure of Diffusion-Limited Aggregation (DLA) clusters on the square lattice by extensive numerical simulations (with clusters having up to $10^8$ particles). We observe that DLA clusters undergo strongly anisotropic growth, with the maximal growth rate along the axes. The naive scaling limit of a DLA cluster by its diameter is thus deterministic and one-dimensional. At the same time, on all scales from the particle size to the size of the entire cluster it has non-trivial box-counting fractal dimension which corresponds to the overall growth rate which, in turn, is smaller than the growth rate along the axes. This suggests that the fractal nature of the lattice DLA should be understood in terms of fluctuations around one-dimensional backbone of the cluster.
A Spin-polarised cylindrically symmetric exact class of solutions endowed with magnetic fields in Einstein-Cartan-Maxwell gravity is obtained. Application of matching conditions to this interior solution having an exterior as Einstein's vacuum solution shows that for this class of metrics the Riemann-Cartan (RC) rotation vanishes which makes the solution static. Therefore we end up with a magnetized static spin polarised cylinder where the pressure along the symmetry axis is negative.
We present a comparison of the characteristics of the magnetic domain walls in an atomic monolayer of Co on Pt(111) and a Ni/Fe atomic bilayer on Ir(111), based on spin-polarized scanning tunneling microscopy measurements. In both cases, the films exhibit a roughly triangular dislocation line pattern created by epitaxial strain relief, as well as out-of-plane ferromagnetic order. Domains with opposite magnetization are separated by domain walls with a unique rotational sense, demonstrating the important role of the Dzyaloshinskii-Moriya interaction induced by the Co/Pt and the Fe/Ir interfaces. The domain walls in Co/Pt(111) are straight and usually found in geometrical constrictions of the film, where they can minimize their length. In contrast, the domain walls in Ni/Fe/Ir(111) follow complicated paths, which can be correlated to the structural triangular pattern. The comparison between the two systems shows that the structural patterns, despite their similarity, have a different impact on the domain walls. In the Co/Pt(111) case, the magnetic state is not influenced by the dislocation line network, in contrast to the Ni/Fe/Ir(111) system in which the formation of the walls is favored at specific positions of the structural pattern.
The dry conversion process for making UO2 nuclear fuel pellets consists of two steps: hydrolysis of UF6 to UO2F2, followed by reducing pyrohydrolysis to UO2 in a rotary kiln. The physical characteristics (morphology, particle size distribution) of the powder obtained at the kiln end determine the final properties (sinterability, flow-ability, green strength). We developed a mathematical model describing the morphological evolution of the powder in the rotary kiln, which enables us to predict morphological characteristics of UO2 powder as functions of the processing conditions. Firstly, the powder flow in the kiln was modelled, including the exchanges between a dense phase (powder bed) and an airborne phase (particles showering down). An original feature of this model is to consider the effect of lifters for calculating the dynamic variables. Secondly, the phenomena responsible for the changes in morphology and grain size were identified and modelled. A population of fractal agglomerates was considered, whose number and size change due to Brownian and sedimentation agglomeration, sintering, breaking up, and chemical reactions. The model is based on population balances and the particle size distribution is divided into sections. Results of both dynamic and morphological calculations are compared to available measurements. Lastly, the influence of the different mechanisms of morphological evolution on the final size distribution is analysed.
We explore the distribution of position angles (PA) of galaxies in clusters. We selected for study the isolated clusters, since the distribution of the galaxy orientation in clusters with close neighbors could be altered by gravitational influence of the latter. We assume that galaxies are aligned, if their number at one $90^o$ position angle interval is more than twice higher than at the other $90^o$ interval. We study the galaxy PA distribution at the outer regions of clusters with smaller space density, where the probability of the PA variation in the result of interactions between galaxies is smaller than at the dense central regions. We found that the alignment of galaxies is more often observed in poor clusters and concluded that originally galaxies were aligned, but in the result of accretion in time of field galaxies with arbitrary orientations and also due to the mutual interactions the relative number of aligned galaxies decreases.
Some of the developments related to quantum anomalies and path integrals during the past 10 years are briefly discussed. The covered subjects include the issues related to the local counter term in the context of 2-dimensional path integral bosonization and the treatment of chiral anomaly and index theorem on the lattice. We also briefly comment on a recent analysis of the connection between the two-dimensional chiral anomalies and the four-dimensional black hole radiation.
Electron tomography (ET) allows high-resolution reconstructions of macromolecular complexes at nearnative state. Cellular structures segmentation in the reconstruction data from electron tomographic images is often required for analyzing and visualizing biological structures, making it a powerful tool for quantitative descriptions of whole cell structures and understanding biological functions. However, these cellular structures are rather difficult to automatically separate or quantify from view owing to complex molecular environment and the limitations of reconstruction data of ET. In this paper, we propose a single end-to-end deep fully-convolutional semantic segmentation network dubbed SegET with rich contextual features which fully exploitsthe multi-scale and multi-level contextual information and reduces the loss of details of cellular structures in ET images. We trained and evaluated our network on the electron tomogram of the CTL Immunological Synapse from Cell Image library. Our results demonstrate that SegET can automatically segment accurately and outperform all other baseline methods on each individual structure in our ET dataset.
Photogrammetric mesh models obtained from aerial oblique images have been widely used for urban reconstruction. However, the photogrammetric meshes also suffer from severe texture problems, especially on the road areas due to occlusion. This paper proposes a structure-aware completion approach to improve the quality of meshes by removing undesired vehicles on the road seamlessly. Specifically, the discontinuous texture atlas is first integrated to a continuous screen space through rendering by the graphics pipeline; the rendering also records necessary mapping for deintegration to the original texture atlas after editing. Vehicle regions are masked by a standard object detection approach, e.g. Faster RCNN. Then, the masked regions are completed guided by the linear structures and regularities in the road region, which is implemented based on Patch Match. Finally, the completed rendered image is deintegrated to the original texture atlas and the triangles for the vehicles are also flattened for improved meshes. Experimental evaluations and analyses are conducted against three datasets, which are captured with different sensors and ground sample distances. The results reveal that the proposed method can quite realistic meshes after removing the vehicles. The structure-aware completion approach for road regions outperforms popular image completion methods and ablation study further confirms the effectiveness of the linear guidance. It should be noted that the proposed method is also capable to handle tiled mesh models for large-scale scenes. Dataset and code are available at vrlab.org.cn/~hanhu/projects/mesh.