ShantanuT01/DACTYL-Pretraining huggingface dataset:
We have studied properties of a classical $N_S$-body double-well system coupled to an $N_B$-body bath, performing simulations of $2(N_S+N_B)$ first-order differential equations with $N_S \simeq 1 - 10$ and $N_B \simeq 1 - 1000$. A motion of Brownian particles in the absence of external forces becomes chaotic for appropriate model parameters such as $N_B$, $c_o$ (coupling strength), and $\{\omega_n\}$ (oscillator frequency of bath): For example, it is chaotic for a small $N_B$ ($\lesssim 100$) but regular for a large $N_B$ ($\gtrsim 500$). Detailed calculations of the stationary energy distribution of the system $f_S(u)$ ($u$: an energy per particle in the system) have shown that its properties are mainly determined by $N_S$, $c_o$ and $T$ (temperature) but weakly depend on $N_B$ and $\{\omega_n \}$. The calculated $f_S(u)$ is analyzed with the use of the $\Gamma$ distribution. Difference and similarity between properties of double-well and harmonic-oscillator systems coupled to finite bath are discussed.
We use global magnetohydrodynamic simulations to study the influence of net vertical magnetic fields on the structure of geometrically thin ($H/r \approx 0.05$) accretion disks in the Newtonian limit. We consider initial mid-plane gas to magnetic pressure ratios $\beta_0 = 1000,\, 300$ and $100$, spanning the transition between weakly and strongly magnetized accretion regimes. We find that magnetic pressure is important for the disks' vertical structure in all three cases, with accretion occurring at $z/R\approx 0.2$ in the two most strongly magnetized models. The disk midplane shows outflow rather than accretion. Accretion through the surface layers is driven mainly by stress due to coherent large scale magnetic field rather than by turbulent stress. Equivalent viscosity parameters measured from our simulations show similar dependencies on initial $\beta_0$ to those seen in shearing box simulations, though the disk midplane is not magnetic pressure dominated even for the strongest magnetic field case. Winds are present but are not the dominant driver of disk evolution. Over the (limited) duration of our simulations, we find evidence that the net flux attains a quasi-steady state at levels that can stably maintain a strongly magnetized disk. We suggest that geometrically thin accretion disks in observed systems may commonly exist in a magnetically "elevated" state, characterized by non-zero but modest vertical magnetic fluxes, with potentially important implications for disk phenomenology in X-ray binaries (XRBs) and active galactic nuclei (AGN).
The semiclassical method for description of the radiative strength function is used for asymmetric nuclei with $N \ne Z$. The theory is based on the linearized Vlasov-Landau equations in two-component finite Fermi liquid. The dependence of the shape $E1$ strength on the coupling constant between proton and neutron subsystems was studied.
As an important and challenging problem in computer vision, video saliency detection is typically cast as a spatiotemporal context modeling problem over consecutive frames. As a result, a key issue in video saliency detection is how to effectively capture the intrinsical properties of atomic video structures as well as their associated contextual interactions along the spatial and temporal dimensions. Motivated by this observation, we propose a graph-theoretic video saliency detection approach based on adaptive video structure discovery, which is carried out within a spatiotemporal atomic graph. Through graph-based manifold propagation, the proposed approach is capable of effectively modeling the semantically contextual interactions among atomic video structures for saliency detection while preserving spatial smoothness and temporal consistency. Experiments demonstrate the effectiveness of the proposed approach over several benchmark datasets.
We investigate the dynamics of a lattice soliton on a monatomic chain in the presence of damping and external forces. We consider Stokes and hydrodynamical damping. In the quasi-continuum limit the discrete system leads to a damped and forced Boussinesq equation. By using a multiple-scale perturbation expansion up to second order in the framework of the quasi-continuum approach we derive a general expression for the first-order velocity correction which improves previous results. We compare the soliton position and shape predicted by the theory with simulations carried out on the level of the monatomic chain system as well as on the level of the quasi-continuum limit system. For this purpose we restrict ourselves to specific examples, namely potentials with cubic and quartic anharmonicities as well as the truncated Morse potential, without taking into account external forces. For both types of damping we find a good agreement with the numerical simulations both for the soliton position and for the tail which appears at the rear of the soliton. Moreover we clarify why the quasi-continuum approximation is better in the hydrodynamical damping case than in the Stokes damping case.
Traffic forecasting is an important element of mobility management, an important key that drives the logistics industry. Over the years, lots of work have been done in Traffic forecasting using time series as well as spatiotemporal dynamic forecasting. In this paper, we explore the use of vision transformer in a UNet setting. We completely remove all convolution-based building blocks in UNet, while using 3D shifted window transformer in both encoder and decoder branches. In addition, we experiment with the use of feature mixing just before patch encoding to control the inter-relationship of the feature while avoiding contraction of the depth dimension of our spatiotemporal input. The proposed network is tested on the data provided by Traffic Map Movie Forecasting Challenge 2021(Traffic4cast2021), held in the competition track of Neural Information Processing Systems (NeurIPS). Traffic4cast2021 task is to predict an hour (6 frames) of traffic conditions (volume and average speed)from one hour of given traffic state (12 frames averaged in 5 minutes time span). Source code is available online at https://github.com/bojesomo/Traffic4Cast2021-SwinUNet3D.
Harris and Morrison constructed semistable families f:F \to Y of k-gonal curves of genus g such that for every k the corresponding modular curves give a sweeping family in the k-gonal locus in the moduli space. Their construction depends on the choice of a smooth curve X. We show that if the genus g(X) is sufficiently high with respect to g, then the ratio K_F^2 / \chi(O_F) is 8 asymptotically with respect to g(X). We show also that if the gonality is maximal and some conjectured estimates of Harris and Morrison hold, the slope of the fibration f: F\to Y is 12 asymptotically with respect to g and that F is a surface of positive index.
In 1994 Lazard proposed an improved method for cylindrical algebraic decomposition (CAD). The method comprised a simplified projection operation together with a generalized cell lifting (that is, stack construction) technique. For the proof of the method's validity Lazard introduced a new notion of valuation of a multivariate polynomial at a point. However a gap in one of the key supporting results for his proof was subsequently noticed. In the present paper we provide a complete validity proof of Lazard's method. Our proof is based on the classical parametrized version of Puiseux's theorem and basic properties of Lazard's valuation. This result is significant because Lazard's method can be applied to any finite family of polynomials, without any assumption on the system of coordinates. It therefore has wider applicability and may be more efficient than other projection and lifting schemes for CAD.
Andromeda is our nearest neighbouring disk galaxy and a prime target for detailed modelling of the evolutionary processes that shape galaxies. We analyse the nature of M31's triaxial bulge with an extensive set of N-body models, which include Box/Peanut (B/P) bulges as well as initial classical bulges (ICBs). Comparing with IRAC 3.6$\mu m$ data, only one model matches simultaneously all the morphological properties of M31's bulge, and requires an ICB and a B/P bulge with 1/3 and 2/3 of the total bulge mass respectively. We find that our pure B/P bulge models do not show concentrations high enough to match the S\'ersic index ($n$) and the effective radius of M31's bulge. Instead, the best model requires an ICB component with mass $M^{\rm ICB}=1.1\times10^{10}{\rm M_{\odot}}$ and three-dimensional half-mass radius $r_{\rm half}^{\rm ICB}$=0.53 kpc (140 arcsec). The B/P bulge component has a mass of $M^{\rm B/P}=2.2\times10^{10}{\rm M_{\odot}}$ and a half-mass radius of $r_{\rm half}^{\rm B/P}$=1.3 kpc (340 arcsec). The model's B/P bulge extends to $r^{\rm B/P}$=3.2 kpc (840 arcsec) in the plane of the disk, as does M31's bulge. In this composite bulge model, the ICB component explains the velocity dispersion drop observed in the centre within $R<$190 pc (50 arcsec), while the B/P bulge component reproduces the observed rapid rotation and the kinematic twist of the observed zero velocity line. This model's pattern speed is $\Omega_p$=38 km/s/kpc, placing corotation at $r_{\rm cor}$=5.8 kpc (1500 arcsec). The outer Lindblad resonance (OLR) is then at $r_{\rm OLR}$=10.4kpc, near the 10kpc-ring of M31, suggesting that this structure may be related to the bar's OLR. By comparison with an earlier snapshot, we estimate that M31's thin bar extends to $r_{\rm bar}^{\rm thin}\sim$4.0 kpc (1000 arcsec) in the disk plane, and in projection extends to $R_{\rm bar}^{\rm thin}\sim$2.3 kpc (600 arcsec).
We consider the measure on multiple chordal Schramm-Loewner evolution ($SLE_\kappa$) curves. We establish a derivative estimate and use it to give a direct proof that the partition function is $C^2$ if $\kappa<4$.
Let $\alpha\in(0,2)$ and $X_t$ be a symmetric $\alpha$-stable process. We define the scattering length $\Gamma(v)$ of the positive potential $v$ and prove several of its basic properties. We use the scattering length to findestimates for the first eigenvalue of the Schr\"odinger operator of the ``Neumann'' fractional Laplacian in a cube with potential $v$.
We study the effect of isospin degree of freedom on balance energy throughout the mass range between 50 and 350 for two sets of isobaric systems with N/A = 0.5 and 0.58. Our fndings indicate that different values of balance energy for two isobaric systems may be mainly due to the Coulomb repulsion. We also demonstrate clearly the dominance of Coulomb repulsion over symmetry energy.
The space of H1 martingales is interesting because of its duality with the space of BMO martingales. It is straightforward to show that every H1 martingale is a uniformly integrable martingale. However, the converse is not true. That is to say, some uniformly integrable martingales are not H1 martingales. This brief note provides a template for systematically constructing such processes.
The multicritical points of the $O(N)$ invariant $N$ vector model in the large $N$ limit are reexamined. Of particular interest are the subtleties involved in the stability of the phase structure at critical dimensions. In the limit $N \to \infty$ while the coupling $g \to g_c$ in a correlated manner (the double scaling limit) a massless bound state $O(N)$ singlet is formed and powers of $1/N$ are compensated by IR singularities. The persistence of the $N \to \infty$ results beyond the leading order is then studied with particular interest in the possible existence of a phase with propagating small mass vector fields and a massless singlet bound state. We point out that under certain conditions the double scaled theory of the singlet field is non-interacting in critical dimensions.
We establish large deviation estimates for Poisson driven models of infectious disease, and apply those estimates to the time of exit from the basin of attraction of an endemic equilibrium. We apply our results to the classical SIRS model.
This is a review of recent advances in our understanding of how Andreev reflection at a superconductor modifies the excitation spectrum of a quantum dot. The emphasis is on two-dimensional impurity-free structures in which the classical dynamics is chaotic. Such Andreev billiards differ in a fundamental way from their non-superconducting counterparts. Most notably, the difference between chaotic and integrable classical dynamics shows up already in the level density, instead of only in the level--level correlations. A chaotic billiard has a gap in the spectrum around the Fermi energy, while integrable billiards have a linearly vanishing density of states. The excitation gap E_gap corresponds to a time scale h/E_gap which is classical (h-independent, equal to the mean time t_dwell between Andreev reflections) if t_dwell is sufficiently large. There is a competing quantum time scale, the Ehrenfest time t_E, which depends logarithmically on h. Two phenomenological theories provide a consistent description of the t_E-dependence of the gap, given qualitatively by E_gap min(h/t_dwell,h/t_E). The analytical predictions have been tested by computer simulations but not yet experimentally.
The observation of the coherent elastic neutrino-nucleus scattering (CE$\nu$NS) provides us opportunities to explore a wide class of new physics. In the Standard Model (SM), the CE$\nu$NS process arises from the vector and axial-vector neutral currents through the exchange of $Z$ boson and the axial-vector current contribution turns out to be subdominant. It is thus natural to consider the extra contributions to CE$\nu$NS from more generic new physics beyond the SM with (axial-)vector interactions associated with a new vector mediator $Z'$. Besides the ordinary CE$\nu$NS, the active neutrinos can convert into a new exotic fermion $\chi$ through the process $\nu N\to \chi N$ mediated by $Z'$ without violating the coherence. It would be interesting to consider the implication of this conversion for the new fermion sector beyond the SM. We consider the framework of a simplified neutrino model in which a new Dirac fermion $\chi$ interacts with active neutrinos and a leptophobic vector mediator $Z'$. We evaluate both the tree-level and loop-level contributions to the CE$\nu$NS and in particular the loop diagrams produce active neutrino elastic scattering process $\nu N\to \nu N$ with the fermion $\chi$ inside the loops. When the interaction between $Z'$ and the SM quarks is vector type and axial-vector type, the CE$\nu$NS processes are respectively dominated by the tree-level and loop-level contributions. We investigate the constraints on the model parameters by fitting to the COHERENT data, assuming a wide range of $m_\chi$. The parameter space with $m_\chi$ larger than the maximal energy of incoming neutrinos can be constrained by including the loop-level contribution. More importantly, the inclusion of loop diagrams can place constraint on axial-vector interaction whose tree-level process is absent in the coherent neutrino-nucleus scattering.
Chemical functionalization has proven to be a promising means of tailoring the unique properties of graphene. For example, hydrogenation can yield a variety of interesting effects, including a metal-insulator transition or the formation of localized magnetic moments. Meanwhile, graphene grown by chemical vapor deposition is the most suitable for large-scale production, but the resulting material tends to be polycrystalline. Up to now there has been relatively little focus on how chemical functionalization, and hydrogenation in particular, impacts the properties of polycrystalline graphene. In this work, we use numerical simulations to study the electrical properties of hydrogenated polycrystalline graphene. We find a strong correlation between the spatial distribution of the hydrogen adsorbates and the charge transport properties. Charge transport is weakly sensitive to hydrogenation when adsorbates are confined to the grain boundaries, while a uniform distribution of hydrogen degrades the electronic mobility. This difference stems from the formation of the hydrogen-induced resonant impurity states, which are inhibited when the honeycomb symmetry is locally broken by the grain boundaries. These findings suggest a tunability of electrical transport of polycrystalline graphene through selective hydrogen functionalization, and also have implications for hydrogen-induced magnetization and spin lifetime of this material.
Given a finite, flat morphism between embeddable noetherian schemes of pure dimension 1, we define the notion of direct and inverse image for generalized divisors and generalized line bundles. In the case when we deal with (possibly reducible, non-reduced) projective curves over a field and the codomain curve is smooth, we introduce the compactified Jacobians parametrizing torsion-free rank-1 sheaves and we study the Norm and inverse image maps between compactified Jacobians. Finally, we introduce and study the Prym stack defined as the kernel of the Norm map.
The classical Metropolis-Hastings (MH) algorithm can be extended to generate non-reversible Markov chains. This is achieved by means of a modification of the acceptance probability, using the notion of vorticity matrix. The resulting Markov chain is non-reversible. Results from the literature on asymptotic variance, large deviations theory and mixing time are mentioned, and in the case of a large deviations result, adapted, to explain how non-reversible Markov chains have favorable properties in these respects.   We provide an application of NRMH in a continuous setting by developing the necessary theory and applying, as first examples, the theory to Gaussian distributions in three and nine dimensions. The empirical autocorrelation and estimated asymptotic variance for NRMH applied to these examples show significant improvement compared to MH with identical stepsize.
For an ample line bundle $\mathcal{L}$ on a complete toric surface $X$, we consider the subset $V_{\mathcal{L}} \subset \vert \mathcal{L} \vert$ of irreducible, nodal, rational curves contained in the smooth locus of $X$. We study the monodromy map from the fundamental group of $V_{\mathcal{L}}$ to the permutation group on the set of nodes of a reference curve $C \in V_{\mathcal{L}}$. We identify a certain obstruction map $\varPsi_{X}$ defined on the set of nodes of $C$ and show that the image of the monodromy is exactly the group of deck transformations of $\varPsi_{X}$, provided that $\mathcal{L}$ is sufficiently big (in a sense we precise below). Along the way, we provide a handy tool to compute the image of the monodromy for any pair $(X, \mathcal{L})$. Eventually, we present a family of pairs $(X, \mathcal{L})$ with small $\mathcal{L}$ and for which the image of the monodromy is strictly smaller than expected.
Define $\theta(x)=(x-1)/3$ if $x\geq 1$, and $\theta(x)=2x/(1-x)$ if $x<1$. We conjecture that the orbit of every positive rational number ends in 0. In particular, there does not exist any positive rational fixed point for a map in the semigroup $\Omega$ generated by the maps $3x+1$ and $x/(x+2)$. In this paper, we prove that the asymptotic density of the set of elements in $\Omega$ that have rational fixed points is zero.
Significant transition strength in light $\alpha$-conjugate nuclei at low energy, typically below 10 MeV, has been observed in many experiments. In this work the isoscalar low-energy response of N=Z nuclei is explored using the Finite Amplitude Method (FAM) based on the microscopic framework of nuclear energy density functionals. Depending on the multipolarity of the excitation and the equilibrium deformation of a particular isotope, the low-energy strength functions display prominent peaks that can be attributed to vibration of cluster structures: $\alpha$+$^{12}$C+$\alpha$ and $\alpha$+$^{16}$O in $^{20}$Ne, $^{12}$C+$^{12}$C in $^{24}$Mg, 4$\alpha$+$^{12}$C in $^{28}$Si, etc. Such cluster excitations are favored in light nuclei with large deformation.
We analyze the GeV gamma-ray emission data from the vicinity of the supernova remnant (SNR) HB9 (G160.9+2.6) from the \textit{Fermi}-LAT 12-year observations to quantify the evolution of diffusive shock acceleration (DSA) in the SNR. In the vicinity of HB9, there are molecular clouds whose locations do not coincide with the SNR shell in the line of sight. We detect significant gamma-ray emissions above 1~GeV spatially coinciding with the two prominent cloud regions, as well as a emission from the SNR shell, the latter of which is consistent with the results of previous studies. The energy spectrum above 1~GeV in each region is fitted with a simple power-law function of $dN/dE \propto E^{-\Gamma}$. The fitting result indicates harder spectra with power-law indices of $\Gamma$ = $1.84 \pm 0.18$ and $1.84 \pm 0.14$ than that at the SNR shell with $\Gamma$= $2.55 \pm 0.10$. The observed spectra from the cloud regions are found to be consistent with the theoretically expected gamma-ray emissions originating in the protons that escaped from SNR HB9, where particles can be accelerated up to higher energies than those at the shell at present. The resultant diffusion coefficient in the vicinity of the SNR is comparable to that of the Galactic mean.
Dust modeling is crucial to infer dust properties and budget for galaxy studies. However, there are systematic disparities between dust grain models that result in corresponding systematic differences in the inferred dust properties of galaxies. Quantifying these systematics requires a consistent fitting analysis. We compare the output dust parameters and assess the differences between two dust grain models, Compiegne et al (2011), and THEMIS (Jones et al 2013, Kohler et al 2015). In this study, we use a single fitting method applied to all the models to extract a coherent and unique statistical analysis. We fit the models to the dust emission seen by Spitzer and Herschel in the Small and Large Magellanic Clouds (SMC and LMC). The observations cover the infrared (IR) spectrum from a few microns to the sub-millimeter range. For each fitted pixel, we calculate the full n-D likelihood, based on the method described in Gordon et al (2014). The free parameters are both environmental ($U$, the interstellar radiation field strength; $\alpha_\mathrm{ISRF}$, power-law coefficient for a multi-U environment; $\Omega^*$, the starlight strength) and intrinsic to the model ($Y_\mathrm{i}$: abundances of the grain species $i$; $\alpha_\mathrm{sCM20}$, coefficient in the small carbon grain size distribution). Fractional residuals of 5 different sets of parameters show that fitting THEMIS brings a more accurate reproduction of the observations than the Compiegne model. However, independent variations of the dust species show strong model-dependencies. We find that the abundance of silicates can only be constrained to an upper-limit and the silicate/carbon ratio is different than that seen in our Galaxy. In the LMC, our fits result in dust masses slightly lower than those found in literature , by a factor lower than 2. In the SMC, we find dust masses in agreement with previous studies.
Zdenek Svestka's research work influenced many fields of solar physics, especially in the area of flare research. In this article I take five of the areas that particularly interested him and assess them in a "then and now" style. His insights in each case were quite sound, although of course in the modern era we have learned things that he could not readily have envisioned. His own views about his research life have been published recently in this journal, to which he contributed so much, and his memoir contains much additional scientific and personal information (Svestka, 2010).