ShantanuT01/DACTYL-Pretraining huggingface dataset:
We analyze the $\alpha$-$^{12}$C inelastic scattering to the $0^+_2$ state of $^{12}$C, the Hoyle state, in a fully microscopic framework. With no free adjustable parameter, the inelastic cross sections at forward angles are well reproduced by the microscopic reaction calculation using the transition density of $^{12}$C obtained by the resonating group method and the nucleon-nucleon $g$ matrix interaction developed by the Melbourne group. It is thus shown that the monopole transition strength obtained by the structural calculation is consistent with that extracted from the reaction observable, suggesting no missing monopole strength of the Hoyle state.
We deal with some extensions of the space-fractional diffusion equation, which is satisfied by the density of a stable process (see Mainardi, Luchko, Pagnini (2001)): the first equation considered here is obtained by adding an exponential differential operator expressed in terms of the Riesz-Feller derivative. We prove that this produces a random additional term in the time-argument of the corresponding stable process, which is represented by the so-called Poisson process with drift. Analogously, if we add, to the space-fractional diffusion equation, a logarithmic differential operator involving the Riesz-derivative, we obtain, as a solution, the transition semigroup of a stable process subordinated by an independent gamma subordinator with drift. Finally, we show that a non-linear extension of the space-fractional diffusion equation is satisfied by the transition density of the process obtained by time-changing the stable process with an independent linear birth process with drift.
A main goal of single-molecule experiments is to evaluate equilibrium free energy differences by applying fluctuation relations to repeated work measurements along irreversible processes. We quantify the error that is made in a free energy estimate by means of the Jarzynski equality when the accumulated work expended on the whole system (including the instrument) is erroneously replaced by the work transferred to the subsystem consisting of the sole molecular construct. We find that the error may be as large as 100%, depending on the number of experiments and on the bandwidth of the data acquisition apparatus. Our theoretical estimate is validated by numerical simulations and pulling experiments on DNA hairpins using optical tweezers.
Given a graph $G$ without isolated vertices, a total Roman dominating function for $G$ is a function $f : V(G)\rightarrow \{0,1,2\}$ such that every vertex with label 0 is adjacent to a vertex with label 2, and the set of vertices with positive labels induces a graph of minimum degree at least one. The total Roman domination number $\gamma_{tR}(G)$ of $G$ is the smallest possible value of $\sum_{v\in V(G)}f(v)$ among all total Roman dominating functions $f$. The total Roman domination number of the direct product $G\times H$ of the graphs $G$ and $H$ is studied in this work. Specifically, several relationships, in the shape of upper and lower bounds, between $\gamma_{tR}(G\times H)$ and some classical domination parameters for the factors are given. Characterizations of the direct product graphs $G\times H$ achieving small values ($\le 7$) for $\gamma_{tR}(G\times H)$ are presented, and exact values for $\gamma_{tR}(G\times H)$ are deduced, while considering various specific direct product classes.
We present an algorithm to compute the Brauer group of involution surface bundles over rational surfaces.
We use previously-published moderate-resolution spectra in combination with stellar atmosphere models to derive the first measured chemical abundance ratios in the Leo II dSph galaxy. We find that for spectra with SNR > 24, we are able to measure abundances from weak Ti, Fe and Mg lines located near the calcium infrared triplet (CaT). We also quantify and discuss discrepancies between the metallicities measured from Fe I lines and those estimated from the CaT features. We find that while the most metal-poor ([Fe/H] <-2.0]) Leo II stars have Ca and Ti abundance ratios similar to those of Galactic globular clusters, the more metal-rich stars show a gradual decline of Ti, Mg and Ca abundance ratio with increasing metallicity. Finding these trends in this distant and apparently dynamically stable dSph galaxy supports the hypothesis that the slow chemical enrichment histories of the dSph galaxies is universal, independent of any interaction with the Milky Way. Combining our spectroscopic abundances with published broadband photometry and updated isochrones, we are able to approximate stellar ages for our bright RGB stars to a relative precision of 2-3 Gyr. While the derived age-metallicity relationship of Leo II hints at some amount of slow enrichment, the data are still statistically consistent with no enrichment over the history of Leo II.
Earlier attempts to extract parameters of kinetic freeze-out in Pb+Pb collisions at 158$A$GeV are critically reviewed. Many of these analyses have used approximations which have significant impact on the extracted parameters. Simple estimates are obtained which attempt to avoid the most critical approximations. It is pointed out that constraints based on pion interferometry are less reliable than those from momentum spectra. A universal set of freeze-out parameters from transverse mass spectra would require T > 135 MeV and <beta> < 0.35.
We present an X-ray diffuse scattering study of the pretransitional structural fluctuations of the magneto-elastic transition in alpha'-NaV2O5. This transition is characterized by the appearance below Tsp~35K of satellite reflections at the reduced wave vector (1/2,1/2,1/4). A large regime of structural fluctuations is measured up to 90 K. These fluctuations are three dimensional between Tsp and ~50K and quasi-one dimensional above ~60K. At 40 K the anisotropy ratio is found to be (xib :xia :xic)= (3.8 : 1.8 : 1), which reveals the importance of transverse interactions in the stabilization of the low temperature phase. We discuss our results within the framework of recent theories dealing with the simultaneous occurrence of a charge ordering, a spin gap and a lattice distortion in this intriguing compound.
Aerial images are often taken under poor lighting conditions and contain low resolution objects, many times occluded by other objects. In this domain, visual context could be of great help, but there are still very few papers that consider context in aerial image understanding and still remains an open problem in computer vision. We propose a dual-stream deep neural network that processes information along two independent pathways. Our model learns to combine local and global appearance in a complementary way, such that together form a powerful classifier. We test our dual-stream network on the task of buildings segmentation in aerial images and obtain state-of-the-art results on the Massachusetts Buildings Dataset. We study the relative importance of local appearance versus the larger scene, as well as their performance in combination on three new buildings datasets. We clearly demonstrate the effectiveness of visual context in conjunction with deep neural networks for aerial image understanding.
Two relations, the virial relation $M_{\rm ADM}=M_{\rm K}$ and the first law in the form $\delta M_{\rm ADM}=\Omega \delta J$, should be satisfied by a solution and a sequence of solutions describing binary compact objects in quasiequilibrium circular orbits. Here, $M_{\rm ADM}$, $M_{\rm K}$, $J$, and $\Omega$ are the ADM mass, Komar mass, angular momentum, and orbital angular velocity, respectively. $\delta$ denotes an Eulerian variation. These two conditions restrict the allowed formulations that we may adopt. First, we derive relations between $M_{\rm ADM}$ and $M_{\rm K}$ and between $\delta M_{\rm ADM}$ and $\Omega \delta J$ for general asymptotically flat spacetimes. Then, to obtain solutions that satisfy the virial relation and sequences of solutions that satisfy the first law at least approximately, we propose a formulation for computation of quasiequilibrium binary neutron stars in general relativity. In contrast to previous approaches in which a part of the Einstein equation is solved, in the new formulation, the full Einstein equation is solved with maximal slicing and in a transverse gauge for the conformal three-metric. Helical symmetry is imposed in the near zone, while in the distant zone, a waveless condition is assumed. We expect the solutions obtained in this formulation to be excellent quasiequilibria as well as initial data for numerical simulations of binary neutron star mergers.
We prove an old conjecture of Erd{\H o}s and Graham on sums of unit fractions: There exists a constant $b>0$ such that if we $r$-color the integers in $2,b^r]$, then there exists a monochromatic set $S$ such that $\sum_{n \in S} 1/n=1$.
We derive a set of constraints on soliton solutions using geometric deformations, and transformations by internal symmetries with space-dependent parameters. We show that Derrick's theorem and a more complete set of constraints due to Manton are special cases of these deformation constraints (DC). We demonstrate also that known soliton solutions obey the DC, and extract novel results by applying the constraints to systems of D-branes, taking into account both Dirac-Born-Infeld and Wess-Zumino actions, and examining cases with and without D-brane gauge fields. We also determine a relation with the Hamiltonian constraint for gravitational systems, and discuss configurations of finite extent, like Wilson lines.
We explore the feasibility of the discrete flavor symmetry $S_3$ to explain the pattern of neutrino masses and mixings. In the flavor basis, the neutrino mass matrix is taken to be invariant under $S_3$ symmetry at the zeroth order. The effects of breaking $S_3$ symmetry by matrices invariant under different $S_2$ subgroups of $S_3$ are studied. The resulting retrocirculant perturbation matrix leads to the perturbed $S_3$ neutrino mass matrix having a trimaximal eigenvector as suggested by the solar neutrino data. It is found that after the third order perturbation the neutrino mixings only depend on the perturbation parameter and are consistent with the current experimental data leading to very small deviations from tribimaximal mixing. These perturbations in the $S_3$ invariant neutrino mass matrix result in interesting interplay between the solar and the reactor neutrino mixing angles. We also get a strongly suppressed range of effective Majorana mass which lies well within the reach of the ongoing experiments.
Considering the stochastic Navier-Stokes system in $\mathbb{R}^d$ forced by a multiplicative white noise, we establish the local existence and uniqueness of the strong solution when the initial data take values in the critical space $\dot{B}_{p,r}^{\frac{d}{p}-1}(\mathbb{R}^d)$.   The proof is based on the contraction mapping principle, stopping time and stochastic estimates. Then we prove the global existence of strong solutions in probability if the initial data are sufficiently small, which contain a class of highly oscillating "large" data.
This paper reviews the basic features of the theory of curvature perturbations in Kerr spacetime, which is customarily written in terms of gauge invariant components of the Weyl tensor which satisfy a perturbation equation known as the Teukolsky equation. I will describe how to evolve generic perturbations about the Kerr metric and the separable form of the wave solutions that one obtains, and the relation of the Teukolsky function to the energy of gravitational waves emitted by the black hole. A discussion of a numerical scheme to evolve perturbations as a function of time and some preliminary results of our research project implementing it for matter sources falling into the black hole is included.
Visual localization, i.e., the problem of camera pose estimation, is a central component of applications such as autonomous robots and augmented reality systems. A dominant approach in the literature, shown to scale to large scenes and to handle complex illumination and seasonal changes, is based on local features extracted from images. The scene representation is a sparse Structure-from-Motion point cloud that is tied to a specific local feature. Switching to another feature type requires an expensive feature matching step between the database images used to construct the point cloud. In this work, we thus explore a more flexible alternative based on dense 3D meshes that does not require features matching between database images to build the scene representation. We show that this approach can achieve state-of-the-art results. We further show that surprisingly competitive results can be obtained when extracting features on renderings of these meshes, without any neural rendering stage, and even when rendering raw scene geometry without color or texture. Our results show that dense 3D model-based representations are a promising alternative to existing representations and point to interesting and challenging directions for future research.
We use, for the first time, the Detrend Fluctuation Analysis (DFA) to study the correlation properties of the transmitted flux fluctuations, in the Lyman-$\alpha$ (Ly$\alpha$) Forest along the lines of sight (LOS) to QSOs, at different space scales. We consider in our analysis the transmitted flux in the intergalactic medium over the redshift range 2 $\leq$ z $\leq$ 4.5 from a sample of 45 high-quality medium resolution (R $\sim$ 4300) quasar spectra obtained with Echelle Spectrograph and Imager (ESI) mounted on the Keck II 10-m telescope, and from a sample of 19 high-quality high resolution (R $\sim$ 50000) quasar spectra obtained with Ultra-Violet and Visible Echelle Spectrograh (UVES) mounted on the ESO KUEYEN 8.2 m telescope. The result of the DFA method applied to both datasets, shows that there exists a difference in the correlation properties between the short and long-range regimes: the slopes of the transmitted flux fluctuation function are different on small and large scales. The scaling exponents, $\alpha_{1}$ = 1.635$\pm$ 0.115 and $\alpha_{2}$ = 0.758$\pm$ 0.085 for the ESI/Keck sample and $\alpha_{1}$ = 1.763 $\pm 0.128$ and $\alpha_{2}$ = 0.798 $\pm 0.084$ for the UVES/VLT sample for the short and long range regime respectively. The transition between the two regims is observed at about $\sim 1.4 h^{-1} Mpc$ (comoving). The fact that $\alpha_{1}$ is always larger than $\alpha_{2}$ for each spectrum supports the common view that the Universe is smoother on large scales than on small scales. The non detection of considerable variations in the scaling exponents from LOS to LOS confirms that anisotropies cannot be ubiquitous, at least on these scales.
We present a method used to intuitively interpret the STM contrast by investigating individual wave functions originating from the substrate and tip side. We use localized basis orbital density functional theory, and propagate the wave functions into the vacuum region at a real-space grid, including averaging over the lateral reciprocal space. Optimization by means of the method of Lagrange multipliers is implemented to perform a unitary transformation of the wave functions in the middle of the vacuum region. The method enables (i) reduction of the number of contributing tip-substrate wave function combinations used in the corresponding transmission matrix, and (ii) to bundle up wave functions with similar symmetry in the lateral plane, so that (iii) an intuitive understanding of the STM contrast can be achieved. The theory is applied to a CO dimer adsorbed on a Cu(1 1 1) surface scanned by a single-atom Cu tip, whose STM image is discussed in detail by the outlined method.
This paper studies whether the generalized second law of thermodynamics is fulfilled in the transition from a generic initial Einstein static phase to the inflationary phase, with constant Hubble rate, and from the end of the latter to the conventional era of thermal radiation dominated expansion. As it turns out, the said law is satisfied provided the radiation component does not largely contribute to the total energy of the static phase.
The well-posedness for a system of partial differential equations and dynamic boundary conditions is discussed. This system is a sort of transmission problem between the dynamics in the bulk $\Omega $ and on the boundary $\Gamma$. The Poisson equation for the chemical potential, the Allen-Cahn equation for the order parameter in the bulk $\Omega$ are considered as auxiliary conditions for solving the Cahn-Hilliard equation on the boundary $\Gamma$. Recently the well-posedness for the equation and dynamic boundary condition, both of Cahn-Hilliard type, was discussed. Based on this result, the existence of the solution and its continuous dependence on the data are proved.
We theoretically investigate the effects of the excitation frequency on the plateau of high-order terahertz sideband generation (HSG) in semiconductors driven by intense terahertz (THz) fields. We find that the plateau of the sideband spectrum strongly depends on the detuning between the NIR laser field and the band gap. We use the quantum trajectory theory (three-step model) to understand the HSG. In the three-step model, an electron-hole pair is first excited by a weak laser, then driven by the strong THz field, and finally recombine to emit a photon with energy gain. When the laser is tuned below the band gap (negative detuning), the electron-hole generation is a virtual process that requires quantum tunneling to occur. When the energy gained by the electron-hole pair from the THz field is less than 3.2 times the ponderomotive energy, the electron and the hole can be driven to the same position and recombine without quantum tunneling, so the HSG will have large probability amplitude. This leads to a plateau feature of the HSG spectrum with a high-frequency cutoff at about 3.2 times the ponderomotive energy above the band gap. Such a plateau feature is similar to the case of high-order harmonics generation in atoms where electrons have to overcome the binding energy to escape the atomic core. A particularly interesting excitation condition in HSG is that the laser can be tuned above the band gap (positive detuning), corresponding to the unphysical "negative" binding energy in atoms for high-order harmonic generation. Now the electron-hole pair is generation by real excitation, but the recombination process can be real or virtual depending on the energy gained from the THz field, which determines the plateau feature in HSG.
Electron-positron pair creation near sub-Eddington accretion rate black holes is believed to be dominated by the Breit-Wheeler process (photon-photon collisions). The interacting high energy photons are produced when unscreened electric fields accelerate leptons either in coherent, macroscopic gaps or in incoherent structures embedded in the turbulent plasma flow. The latter type of acceleration results in a drizzle of pair production sourced by photons from the background radiation field whose energies are near the pair-production threshold. In this work, we use radiation GRMHD simulations to extend an earlier study of pair drizzle by Moscibrodzka et al. We focus on low-magnetization (SANE) accretion onto supermassive Kerr black holes and consider radiation due to synchrotron, bremsstrahlung, and Compton upscattering processes. We confirm that pair drizzle in M87 is sufficient to keep the magnetospheric charge density orders of magnitude above the Goldreich-Julian density. We also find that pair production peaks along the jet-disk boundary.
We present a device-independent randomness expansion protocol, involving only a constant number of non-signaling quantum devices, that achieves \emph{infinite expansion}: starting with $m$ bits of uniform private randomness, the protocol can produce an unbounded amount of certified randomness that is $\exp(-\Omega(m^{1/3}))$-close to uniform and secure against a quantum adversary. The only parameters which depend on the size of the input are the soundness of the protocol and the security of the output (both are inverse exponential in $m$). This settles a long-standing open problem in the area of randomness expansion and device-independence.   The analysis of our protocols involves overcoming fundamental challenges in the study of \emph{adaptive} device-independent protocols. Our primary technical contribution is the design and analysis of device-independent protocols which are \emph{Input Secure}; that is, their output is guaranteed to be secure against a quantum eavesdropper, \emph{even if the input randomness was generated by that same eavesdropper}!   The notion of Input Security may be of independent interest to other areas such as device-independent quantum key distribution.
In the top to random shuffle, the first a cards are removed from a deck of n cards 12 \cdots n and then inserted back into the deck. This action can be studied by treating the top to random shuffle as an element B_a, which we define formally in Section 2, of the algebra Q[S_n]. For a = 1, Adriano Garsia in "On the Powers of Top to Random Shuffling" (2002) derived an expansion formula for B_1^k for k \leq n, though his proof for the formula was non-bijective. We prove, bijectively, an expansion formula for the arbitrary finite product B_{a_1}B_{a_2} \cdots B_{a_k} where a_1, \ldots, a_k are positive integers, from which an improved version of Garsia's aforementioned formula follows. We show some applications of this formula for B_{a_1}B_{a_2} \cdots B_{a_k}, which include enumeration and calculating probabilities. Then for an arbitrary group G we define the group of G-permutations S_n^G := G \wr S_n and further generalize the aforementioned expansion formula to the algebra Q[S_n^G] for the case of finite G, and we show how other similar expansion formulae in Q[S_n] can be generalized to Q[S_n^G].
A new decomposition of the Dirac structure of nucleon self-energies in the Dirac Brueckner-Hartree-Fock (DBHF) approach is adopted to investigate the equation of state for asymmetric nuclear matter. The effective coupling constants of $\sigma $, $\omega $, $\delta $ and $\rho $ mesons with a density dependence in the relativistic mean field approach are deduced by reproducing the nucleon self-energy resulting from the DBHF at each density for symmetric and asymmetric nuclear matter. With these couplings the properties of finite nuclei are investigated. The agreement of charge radii and binding energies of finite nuclei with the experimental data are improved simultaneously in comparison with the projection method. It seems that the properties of finite nuclei are sensitive to the scheme used for the DBHF self-energy extraction. We may conclude that the properties of the asymmetric nuclear matter and finite nuclei could be well described by the new decomposition approach of the G matrix.
We report on results of astrometric observations of water vapor masers in the "water fountain" source IRAS 18286-0959 (I18286) with the VLBI Exploration of Radio Astrometry (VERA). These observations yielded an annual parallax of IRAS 18286-0959, pi=0.277+/-0.041 mas, corresponding to a heliocentric distance of D=3.61(+0.63)(-0.47) kpc. The maser feature, whose annual parallax was measured, showed the absolute proper motion of (mu_alpha, mu_delta)=(-3.2 +/- 0.3, -7.2 +/- 0.2) [mas/yr]. The intrinsic motion of the maser feature in the internal motions of the cluster of features in I18286 does not seem to trace the motion of the bipolar jet of I18286. Taking into account this intrinsic motion, the derived motion of the maser feature is roughly equal to that of the maser source I18286 itself. The proximity of I18286 to the Galactic midplane (z~10 pc) suggests that the parental star of the water fountain source in I18286 should be intermediate-mass AGB/post-AGB star, but the origin of a large deviation of the systemic source motion from that expected from the Galactic rotation curve is still unclear.