ShantanuT01/DACTYL-Pretraining huggingface dataset:
Hamiltonian dynamics of gravitational field contained in a spacetime region with boundary $S$ being a null-like hypersurface (a wave front) is discussed. Complete Hamiltonian formula for the dynamics (with no surface integrals neglected) is derived. A quasi-local proof of the first law of black holes thermodynamics is obtained as a consequence, in case when $S$ is a non-expanding horizon. The zeroth law and Penrose inequalities are discussed from this point of view.
Dark energy stars research is an issue of great interest since recent astronomical observations with respect to measurements in distant supernovas, cosmic microwave background and weak gravitational lensing confirm that the universe is undergoing a phase of accelerated expansion and this cosmological behavior is caused by the presence of a cosmic fluid which has a strong negative pressure that allows to explain the expanding universe. In this paper, we obtained new relativistic stellar configurations within the framework of Einstein-Gauss-Bonnet (EGB) gravity considering negative anisotropic pressures and the equation of state pr={\omega}\r{ho} where pr is the radial pressure, {\omega} is the dark energy parameter, and \r{ho} is the dark energy density. We have chosen a modified version of metric potential proposed by Korkina-Orlyanskii (1991). For the new solutions we checked that the radial pressure, metric coefficients, energy density and anisotropy are well defined and are regular in the interior of the star and are dependent of the values of the Gauss-Bonnet coupling constant. The solutions found can be used in the development of dark energy stars models satisfying all physical acceptability conditions, but the causality condition and strong energy condition cannot be satisfied.
We study natural D-modules on the moduli stack of elliptic curves over a field of characteristic zero. We use this to produce an algebro-geometric version of the algebra of higher depth mock modular forms, studied from a Conformal Field Theoretic perspective by numerous authors.
We prove that the sonic surface of axisymmetric meridional stationary flows is always attached to the accretor, however small, if the adiabatic index of the gas is gamma=5/3. Using local expansions near a point-like accretor, we extend Bondi's classification of spherically symmetric flows to axisymmetric flows, introducing the possibility of angular sectors reached by no flow lines, and singular directions of infinite mass flux, in addition to the angular regions of subsonic and supersonic accretion. For gamma<5/3, we show the impossibility of subsonic accretion onto a point-like accretor when the entropy of the flow is not uniform. The special case gamma=5/3 is treated separately. We analyse the influence of the adiabatic index and Mach number of the flow at infinity on the mass accretion rate of shocked spherical flows. We propose an interpolation formula for the mass accretion rate of axisymmetric flows as a function of the Mach number and the adiabatic index, in the range 9/7<gamma<5/3.
Numerous efforts have been made to design different low level saliency cues for the RGBD saliency detection, such as color or depth contrast features, background and color compactness priors. However, how these saliency cues interact with each other and how to incorporate these low level saliency cues effectively to generate a master saliency map remain a challenging problem. In this paper, we design a new convolutional neural network (CNN) to fuse different low level saliency cues into hierarchical features for automatically detecting salient objects in RGBD images. In contrast to the existing works that directly feed raw image pixels to the CNN, the proposed method takes advantage of the knowledge in traditional saliency detection by adopting various meaningful and well-designed saliency feature vectors as input. This can guide the training of CNN towards detecting salient object more effectively due to the reduced learning ambiguity. We then integrate a Laplacian propagation framework with the learned CNN to extract a spatially consistent saliency map by exploiting the intrinsic structure of the input image. Extensive quantitative and qualitative experimental evaluations on three datasets demonstrate that the proposed method consistently outperforms state-of-the-art methods.
In this paper we develop a Fefferman-Stein theorem, a Hardy-Littlewood theorem and sharp function estimations in weighted Sobolev spaces. We also provide uniqueness and existence results for second-order elliptic and parabolic partial differential systems in weighed Sobolev spaces.
We study a generalization of the Skyrme model with the inclusion of a sixth-order term and a generalized mass term. We first analyze the model in a regime where the nonlinear sigma and Skyrme terms are switched to zero which leads to well-behaved analytical BPS-type solutions. Adding contributions from the rotational energy, we reproduce the mass of the most abundant isotopes to rather good accuracy. These BPS-type solutions are then used to compute the contributions from the nonlinear sigma and Skyrme terms when these are switched on. We then adjust the four parameters of the model using two different procedures and find that the additional terms only represent small perturbations to the system. We finally calculate the binding energy per nucleon and compare our results with the experimental values.
We analyse the mass distribution in the core of A383 (z=0.188), one of 12 X-ray luminous clusters at z~0.2 selected for a comprehensive and unbiased study of the mass distribution in massive clusters. Deep HST imaging reveals a wide variety of gravitationally lensed features in A383, including a giant arc formed from the strongly-lensed images of 2 background galaxies, 2 radial arcs, several multiply-imaged arcs and numerous arclets. Based upon the constraints from the various lensed features, we construct a detailed mass model for the central regions of the cluster, taking into account both the cluster-scale potential and perturbations from individual cluster galaxies. Keck spectroscopy of one component of the giant arc identifies it as a star-forming galaxy at z=1.01 and provides an accurate measurement of the cluster mass within the radius of the giant arc (65kpc) of (3.5+/-0.1)*10^13 Mo. Using the weak shear measured from our HST observations we extend our mass model to determine a mass of (1.8+/-0.2)*10^14 Mo within a radius of 250kpc. On smaller scales we employ the radial arcs as probes of the shape of the mass distribution in the cluster core (r<20kpc), and find that the mass profile is more peaked than a single NFW profile. The optical and X-ray properties of A383 indicate the presence of a central cooling flow, for which we derive a mass deposition rate of >200 Mo/yr. We also use the X-ray emission from A383 to obtain independent estimates of the total mass within projected radii of 65 and 250kpc: (4.0+/-1.4)*10^13 Mo and (1.2+/-0.5)*10^14 Mo, which are consistent with the lensing measurements. [Abridged]
An m-ballot path of size n is a path on the square grid consisting of north and east steps, starting at (0,0), ending at (mn,n), and never going below the line {x=my}. The set of these paths can be equipped with a lattice structure, called the m-Tamari lattice, which generalizes the usual Tamari lattice obtained when m=1. We prove that the number of intervals in this lattice is $$ \frac {m+1}{n(mn+1)} {(m+1)^2 n+m\choose n-1}. $$ This formula was recently conjectured by Bergeron in connection with the study of coinvariant spaces. The case m=1 was proved a few years ago by Chapoton. Our proof is based on a recursive description of intervals, which translates into a functional equation satisfied by the associated generating function. The solution of this equation is an algebraic series, obtained by a guess-and-check approach. Finding a bijective proof remains an open problem.
We analyze the inclusive semileptonic decays B -> X_s l^+ l^- in the framework of the supersymmetric standard model with non-universal soft-breaking terms at GUT scale. We show that the general trend of universal and non-universal models is a decreasing of branching ratio (BR) and increasing of energy asymmetry (AS). However, only non--universal models can have chances to get very large enhancements in BR and AS, corresponding to large (negative) SUSY contributions to the b -> s \gamma amplitude.
It is noticed that a certain transform of the Mittag-Leffler function Ea is completely monotone for a in [1,2]. Using the explicit expressions of its Bernstein density, an identity in law between suprema of completely asymmetric Levy a-stable processes. In the spectrally positive case, we retrieve the exact expression of a unilateral small deviation constant which had been previously obtained by a different method by Bernyk, Dalang and Peskir.
We discuss coherent QCD radiation from space-like parton branching and its effects on multi-jet final states at high-energy hadron colliders.   Coherence effects for small longitudinal momentum fractions x are not included in the branching algorithms of standard shower Monte Carlo event generators. On the other hand, they are taken into account only partially in perturbative next-to-leading-order calculations for multi-jets. Such effects are present to all orders in alpha_s and can become logarithmically enhanced with \sqrt{s} / E_T, where E_T is the hardest jet transverse energy. We present results of summing coherence effects to all orders by parton-branching Monte Carlo methods based on transverse-momentum dependent matrix elements.
In this paper, we perform Monte Carlo calculations to study the critical behavior of the spread of infectious diseases through a novel approach to the SIR epidemiological model. A stochastic lattice gas version of the model was applied on hybrid lattices which, in turn, are generated from typical square lattices when inserting a connection probability $p$ that a given lattice site has both first- and second-nearest neighbor interactions. By combining percolation theory and finite-size scaling analysis, we estimate both the critical threshold and leading critical exponent ratios of the non-absorbing SIR model in different cases of hybrid lattices. An analysis of the average size of the percolating cluster and the size distribution of non-percolating clusters of recovered individuals was carried out to determine the universality class of the model.
We analyze effective d-wave interactions in the two-dimensional extended Hubbard model at weak coupling and small to moderate doping. The interactions are computed from a renormalization group flow. Attractive d-wave interactions are generated via antiferromagnetic spin fluctuations in the pairing and charge channels. Above Van Hove filling, the d-wave charge interaction is maximal at incommensurate diagonal wave vectors, corresponding to nematic fluctuations with a diagonal modulation. Below Van Hove filling a modulation along the crystal axes can be favored. The nematic fluctuations are enhanced by the nearest-neighbor interaction in the extended Hubbard model, but they always remain smaller than the dominant antiferromagnetic, pairing, or charge density wave fluctuations.
We show that if a family of complex varieties over a base B admits a section when restricted to a very general curve in B, then the family must contain a subfamily of rationally connected varieties dominating B. As an application, we deduce the existence of one parameter families of Enriques surfaces with no section.
We investigate by Montecarlo simulation the linear response function of three dimensional structural glass models defined by short-range kinetic constraints and a trivial equilibrium Boltzmann-Gibbs measure. The breakdown of the fluctuation-dissipation theorem in the glassy phase follows the prediction of mean field low temperature mode-coupling theory.
Recent progress in computational photography has shown that we can acquire near-infrared (NIR) information in addition to the normal visible (RGB) band, with only slight modifications to standard digital cameras. Due to the proximity of the NIR band to visible radiation, NIR images share many properties with visible images. However, as a result of the material dependent reflection in the NIR part of the spectrum, such images reveal different characteristics of the scene. We investigate how to effectively exploit these differences to improve performance on the semantic image segmentation task. Based on a state-of-the-art segmentation framework and a novel manually segmented image database (both indoor and outdoor scenes) that contain 4-channel images (RGB+NIR), we study how to best incorporate the specific characteristics of the NIR response. We show that adding NIR leads to improved performance for classes that correspond to a specific type of material in both outdoor and indoor scenes. We also discuss the results with respect to the physical properties of the NIR response.
I discuss (i) hadron-hadron and photon-hadron total cross-sections, (ii) elastic scattering, (iii) the r\^{o}le of minijets in total cross-sections and the need to include them in Monte-Carlos for small-$x$ structure functions, (iv) how the two pomerons affect small-$x$ behaviour, and (v) rapidity-gap physics.
Let $n\in\mathbb{Z}^+$. Is it true that every sequence of $n$ consecutive integers greater than $n^2$ and smaller than $(n+1)^2$ contains at least one prime number? In this paper we show that this is actually the case for every $n \leq 1,193,806,023$. In addition, we prove that a positive answer to the previous question for all $n$ would imply Legendre's, Brocard's, Andrica's, and Oppermann's conjectures, as well as the assumption that for every $n$ there is always a prime number in the interval $[n,n+2\lfloor\sqrt{n}\rfloor-1]$.
The study of heat transport in low-dimensional oscillator lattices presents a formidable challenge. Theoretical efforts have been made trying to reveal the underlying mechanism of diversified heat transport behaviors. In lack of a unified rigorous treatment, approximate theories often may embody controversial predictions. It is therefore of ultimate importance that one can rely on numerical simulations in the investigation of heat transfer processes in low-dimensional lattices. The simulation of heat transport using the non-equilibrium heat bath method and the Green-Kubo method will be introduced. It is found that one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) momentum-conserving nonlinear lattices display power-law divergent, logarithmic divergent and constant thermal conductivities, respectively. Next, a novel diffusion method is also introduced. The heat diffusion theory connects the energy diffusion and heat conduction in a straightforward manner. This enables one to use the diffusion method to investigate the objective of heat transport. In addition, it contains fundamental information about the heat transport process which cannot readily be gathered otherwise.
We consider the Vlasov-HMF (Hamiltonian Mean-Field) model. We consider solutions starting in a small Sobolev neighborhood of a spatially homogeneous state satisfying a linearized stability criterion (Penrose criterion). We prove that these solutions exhibit a scattering behavior to a modified state, which implies a nonlinear Landau damping effect with polynomial rate of damping.
This paper proposes a working recipe of using Vision Transformer (ViT) in class incremental learning. Although this recipe only combines existing techniques, developing the combination is not trivial. Firstly, naive application of ViT to replace convolutional neural networks (CNNs) in incremental learning results in serious performance degradation. Secondly, we nail down three issues of naively using ViT: (a) ViT has very slow convergence when the number of classes is small, (b) more bias towards new classes is observed in ViT than CNN-based architectures, and (c) the conventional learning rate of ViT is too low to learn a good classifier layer. Finally, our solution, named ViTIL (ViT for Incremental Learning) achieves new state-of-the-art on both CIFAR and ImageNet datasets for all three class incremental learning setups by a clear margin. We believe this advances the knowledge of transformer in the incremental learning community. Code will be publicly released.
We study quenching in seven green valley galaxies on kpc scales by resolving their molecular gas content using \textsuperscript{12}CO(1-0) observations obtained with NOEMA and ALMA, and their star-formation rate using spatially resolved optical spectroscopy from the MaNGA survey. We perform radial stacking of both datasets to increase the sensitivity to molecular gas and star formation, thereby avoiding biases against strongly quenched regions. We find that both spatially resolved gas fraction ($\rm {f_{gas}}$) and star formation efficiency ($\rm {SFE}$) are responsible for quenching green valley galaxies at all radii: both quantities are suppressed with respect to typical star-forming regions. $\rm {f_{gas}}$ and $\rm {SFE}$ have roughly equal influence in quenching the outer disc. We are, however, unable to identify the dominant mechanism in the strongly quenched central regions. We find that $\rm {f_{gas}}$ is reduced by $\rm \sim 1~dex$ in the central regions, but the star formation rate is too low to be measured, leading to upper limits for the $\rm {SFE}$. Moving from the outer disc to central regions, the reduction in $\rm {f_{gas}}$ is driven by an increasing $\rm \Sigma_{\star}$ profile rather than a decreasing $\rm \Sigma_{H_{2}}$ profile. The reduced $\rm {f_{gas}}$ may therefore be caused by a decrease in the gas supply rather than molecular gas ejection mechanisms, such as winds driven by active galactic nuclei. We warn more generally that studies investigating $\rm {f_{gas}}$ may be deceiving in inferring the cause of quenching, particularly in the central (bulge-dominated) regions of galaxies.
Strain at surfaces and interfaces play an important role in the optical and electronic properties of materials. MeV ion-induced strain determination in single crystal silicon substrates and in Ag (nanoisland)/Si(111) at surface and interfaces has been carried out using transmission electron microscopy (TEM) and surface-sensitive X-ray diffraction. Ag nanoislands are grown under various surface treatments using thermal evaporation in high vacuum conditions. Irradiation has been carried out with 1.5 MeV Au^{2+} ions at various fluences and impact angles. Selected area electron diffraction (SAED) and lattice imaging (using TEM) has been used to determine the strain at surface and interfaces. Preliminary results on the use of surface-sensitive asymmetric x-ray Bragg reflection method have been discussed. The TEM results directly indicate a contraction in the silicon lattice due to ion-induced effects. The nanoislands have shadowed the ion beam resulting in lesser strain beneath the island structures in silicon substrates. High-resolution lattice imaging has also been used to determine the strain in around amorphization zones caused by the ion irradiation.
This paper presents a sample of "cold front" clusters selected from the Chandra archive. The clusters are selected based purely on the existence of surface brightness edges in their Chandra images which are modeled as density jumps. A combination of the derived density and temperature jumps across the fronts is used to select nine robust examples of cold front clusters: 1ES0657-558, Abell 1201, Abell 1758N, MS1455.0+2232, Abell 2069, Abell 2142, Abell 2163, RXJ1720.1+2638, and Abell 3667. This sample is the subject of an ongoing study aimed at relating cold fronts to cluster merger activity, and understanding how the merging environment affects the cluster constituents. Here, temperature maps are presented along with the Chandra X-ray images. A dichotomy is found in the sample in that there exists a subsample of cold front clusters which are clearly mergers based on their X-ray morphologies, and a second subsample which harbor cold fronts, but have surprisingly relaxed X-ray morphologies, and minimal evidence for merger activity at other wavelengths. For this second subsample, the existence of a cold front provides the sole evidence for merger activity at X-ray wavelengths. We discuss how cold fronts can provide additional information which may be used to constrain merger histories, and also the possibility of using cold fronts to distinguish major and minor mergers.
We investigate the atomic and electronic structure of a single layer of pentacene on the Au(111) surface using density functional theory. To find the candidate structures we strain match the pentacene crystal geometry with the Au(111) surface, in this way we find pentacene overlayer structures with a low strain. We show that the geometries obtained with this approach has lower energy than previous proposed surface geometries of pentacene on Au(111). We also show that the geometry and workfunction of the obtained structures are in excellent agreement with experimental data.
We present a new constraint for the axion monopole-dipole coupling in the range of 1 micrometer to a few millimeters, previously unavailable for experimental study. The constraint was obtained using our recent results on the observation of neutron quantum states in the Earth's gravitational field. We exploit the ultimate sensitivity of ultra-cold neutrons (UCN) in the lowest gravitational states above a material surface to any additional interaction between the UCN and the matter, if the characteristic interaction range is within the mentioned domain. In particular, we find that the upper limit for the axion monopole-dipole coupling constant is (g_p g_s)/(\hbar c)<2 x 10^{-15} for the axion mass in the ``promising'' axion mass region of ~1 meV.
Motivated by the study of dependent random variables by coupling with independent blocks of variables, we obtain first sufficient conditions for the moderate deviation principle in its functional form for triangular arrays of independent random variables. Under some regularity assumptions our conditions are also necessary in the stationary case. The results are then applied to derive moderate deviation principles for linear processes, kernel estimators of a density and some classes of dependent random variables.
We discuss physical and mathematical aspects of the over-damped motion of a Brownian particle in fluctuating potentials. It is shown that such a system can be described quantitatively by fluctuating rates if the potential fluctuations are slow compared to relaxation within the minima of the potential, and if the position of the minima does not fluctuate. Effective rates can be calculated; they describe the long-time dynamics of the system. Furthermore, we show the existence of a stationary solution of the Fokker-Planck equation that describes the motion within the fluctuating potential under some general conditions. We also show that a stationary solution of the rate equations with fluctuating rates exists.
We present new insights about accretion and ejection physics based on joint RXTE/Chandra HETGS studies of rapid X-ray variability in GRS 1915+105. For the first time, with fast phase-resolved spectroscopy of the rho state, we are able to show that changes in the broadband X-ray spectrum (RXTE) on timescales of seconds are associated with measurable changes in absorption lines (Chandra HETGS) from the accretion disk wind. Additionally, we make a direct detection of material evaporating from the radiation-pressure-dominated inner disk. Our X-ray data thus reveal the black hole as it ejects a portion of the inner accretion flow and then drives a wind from the outer disk, all in a bizarre cycle that lasts fewer than 60 seconds but can repeat for weeks. We find that the accretion disk wind may be sufficiently massive to play an active role in GRS 1915+105, not only in quenching the jet on long timescales, but also in possibly producing or facilitating transitions between classes of X-ray variability.