ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper we analyze metastability and nucleation in the context of the Kawasaki dynamics for the two-dimensional Ising lattice gas at very low temperature. Let $\Lambda\subset\mathbb{Z}^2$ be a finite box. Particles perform simple exclusion on $\Lambda$, but when they occupy neighboring sites they feel a binding energy $-U_1<0$ in the horizontal direction and $-U_2<0$ in the vertical one. Thus the Kawasaki dynamics is conservative inside the volume $\Lambda$. Along each bond touching the boundary of $\Lambda$ from the outside to the inside, particles are created with rate $\rho=e^{-\Delta\beta}$, while along each bond from the inside to the outside, particles are annihilated with rate $1$, where $\beta>0$ is the inverse temperature and $\Delta>0$ is an activity parameter. Thus, the boundary of $\Lambda$ plays the role of an infinite gas reservoir with density $\rho$. We consider the parameter regime $U_1>2U_2$ also known as the strongly anisotropic regime. We take $\Delta\in{(U_1,U_1+U_2)}$, so that the empty (respectively full) configuration is a metastable (respectively stable) configuration. We investigate how the transition from empty to full takes place with particular attention to the critical configurations that asymptotically have to be crossed with probability 1. The derivation of some geometrical properties of the saddles allows us to identify the full geometry of the minimal gates and their boundaries for the nucleation in the strongly anisotropic case. We observe very different behaviors for this case with respect to the isotropic ($U_1=U_2$) and weakly anisotropic ($U_1<2U_2$) ones. Moreover, we derive mixing time, spectral gap and sharp estimates for the asymptotic transition time for the strongly anisotropic case.
We discuss the Cherenkov process $\nu\to\nu\gamma$ in the presence of a homogeneous magnetic field. The neutrinos are taken to be massless with only standard-model couplings. The magnetic field fulfills the dual purpose of inducing an effective neutrino-photon vertex and of modifying the photon dispersion relation such that the Cherenkov condition $\omega<|{\bf k}|$ is fulfilled. For a field strength $B_{\rm crit}=m_e^2/e=4.41\times10^{13} Gauss$ and for $E=2m_e$ the Cherenkov rate is about $6\times10^{-11}s^{-1}$.
By studying the spectral aspects of the fractional part function in a well-known separable Hilbert space, we show, among other things, a rational approximation of the Riemann zeta function and its derivatives valid on every vertical line in the right half-planes $\Re s> 1/2$ and $\Re s >0.$ Moreover, we provide some discussions and explicit computations related to the fractional part function.
The diffusion of chiral active Brownian particles in three-dimensional space is studied analytically, by consideration of the corresponding Fokker-Planck equation for the probability density of finding a particle at position $\boldsymbol{x}$ and moving along the direction $\hat{\boldsymbol{v}}$ at time $t$, and numerically, by the use of Langevin dynamics simulations. The analysis is focused on the marginal probability density of finding a particle at a given location and at a given time (independently of its direction of motion), which is found from an infinite hierarchy of differential-recurrence relations for the coefficients that appear in the multipole expansion of the probability distribution which contains the whole kinematic information. This approach allows the explicit calculation of the time dependence of the mean squared displacement and the time dependence of the kurtosis of the marginal probability distribution, quantities from which the effective diffusion coefficient and the "shape" of the positions distribution are examined. Oscillations between two characteristic values were found in the time evolution of the kurtosis, namely, between the value that corresponds to a Gaussian and the one that corresponds to a distribution of spherical shell shape. In the case of an ensemble of particles, each one rotating around an uniformly-distributed random axis, it is found evidence of the so called effect "anomalous, yet Brownian, diffusion", for which particles follow a non-Gaussian distribution for the positions yet the mean squared displacement is a linear function of time.
We investigate the large time behavior of multi-dimensional aggregation equations driven by Newtonian repulsion, and balanced by radial attraction and confinement. In case of Newton repulsion with radial confinement we quantify the algebraic convergence decay rate towards the unique steady state. To this end, we identify a one-parameter family of radial steady states, and prove dimension-dependent decay rate in energy and 2-Wassertein distance, using a comparison with properly selected radial steady states. We also study Newtonian repulsion and radial attraction. When the attraction potential is quadratic it is known to coincide with quadratic confinement. Here we study the case of perturbed radial quadratic attraction, proving that it still leads to one-parameter family of unique steady states. It is expected that this family to serve for a corresponding comparison argument which yields algebraic convergence towards steady repulsive-attractive solutions.
We show that when non-unitary noise effects are taken into account the thermopower is in general asymmetric under magnetic field reversal, even for non-interacting systems. Our findings are illustrated in the example of a three-dot ring structure pierced by an Aharonov-Bohm flux.
We discuss the low-energy analysis of models involving quarks and four-fermion couplings. The relation with QCD and with other models of mesons and meson plus quarks at low energies is discussed. A short description of how the heat-kernel expansion can be used to get regularization independent information, is given. The anomaly within this class of models and a physical prescription to obtain the correct flavour anomaly while keeping as much of the VMD aspects as possible is discussed. The major part is the discussion within this framework of the order $p^4$ action and of two and some three-point functions to all orders in momenta and quark masses. Some results on hadronic matrix elements are given.
For low-redshift (z < 0.1) Type Ia supernovae (SN Ia) samples used in several cosmological analyses over the past decade, we probe for systematic bias by looking for correlations between surface brightness (SB) measurements and Hubble residuals (HR). For 292 SNe Ia, we measure SB at the location of the SN Ia from publicly available Pan-STARRS (PS1) images. The Hubble residuals are from two recent measurements with low-z SNe Ia that overlap the PS1 footprint: 1) the DES 3-year cosmology analysis, with 120 overlapping low-z SNe Ia from the Harvard-Smithsonian Center for Astrophysics surveys and Carnegie Supernova Project, and 2) the PS1 single-telescope analysis, with 172 overlapping low-z SNe Ia from the Foundation Supernova Survey. This study is motivated by previous reports of anomalous inefficiencies and flux scatter for transients on bright galaxies. We compare HR distributions of the bright and faint halves of the SB distribution: the mean HR values differ by Delta HR = 0.031 +- 0.018, consistent with no difference at the 2 sigma level. We also perform a Kolmogorov-Smirnov (KS) test for the bright and faint half HR distributions, and conclude that the two distributions are statistically consistent with a KS p-value of 0.07. However, if future studies with larger datasets find Delta HR ~ 0.03 with high significance, this difference would be a leading systematic uncertainty in measurements of the dark energy equation of state, w.
We consider the long-time behavior of solutions to the short-pulse equation. Using the method of testing by wave packets, we prove small data global existence and modified scattering.
The fractions and dimension of bars, rings and lenses are studied in the Near-IR S0 galaxy Survey (NIRS0S). We find evidence that multiple lenses in some barred S0s are related to bar resonances in a similar manner as the inner and outer rings, for which the outer/inner length ratio 2. Inner lenses in the non-barred galaxies normalized to galaxy diameter are clearly smaller than those in the barred systems. Interestingly, these small lenses in the non-barred galaxies have similar sizes as barlenses (lens-like structures embedded in a bar), and therefore might actually be barlenses in former barred galaxies, in which the outer, more elongated bar component, has been destroyed. We also find that fully developed inner lenses are on average a factor 1.3 larger than bars, whereas inner rings have similar sizes as bars. The fraction of inner lenses is found to be constant in all family classes (A, AB, B). Nuclear bars appear most frequently among the weakly barred (AB) galaxies, which is consistent with the theoretical models by Maciejewski & Athanassoula (2008). Similar sized bars as the nuclear bars were detected in seven 'non-barred' S0s. Galaxy luminosity does not uniquely define the sizes of bars or bar-related structures, neither is there any upper limit in galaxy luminosity for bar formation. Although all the family classes cover the same range of galaxy luminosity, the non-barred (A) galaxies are on average 0.6 mag brighter than the strongly barred (B) systems. Overall, our results are consistent with the idea that bars play an important role in the formation of the structure components of galaxies. The fact that multiple lenses are common in S0s, and that at least the inner lenses can have very old stellar populations, implies that the last destructive merger, or major gas accretion event, must have taken place at a fairly high redshift.
We present a comprehensive galaxy cluster study of XMMU J1230.3+1339 based on a joint analysis of X-ray data, optical imaging and spectroscopy observations, weak lensing results, and radio properties for achieving a detailed multi-component view of this newly discovered system at z=0.975. We find an optically very rich and massive system with M200$\simeq$(4.2$\pm$0.8)$\times$10^14 M$\sun$, Tx$\simeq$5.3(+0.7--0.6)keV, and Lx$\simeq$(6.5$\pm$0.7)$\times$10^44 erg/s, for which various widely used mass proxies are measured and compared. We have identified multiple cluster-related components including a central fly-through group close to core passage with associated marginally extended 1.4GHz radio emission possibly originating from the turbulent wake region of the merging event. On the cluster outskirts we see evidence for an on-axis infalling group with a second Brightest Cluster Galaxy (BCG) and indications for an additional off-axis group accretion event. We trace two galaxy filaments beyond the nominal cluster radius and provide a tentative reconstruction of the 3D-accretion geometry of the system. In terms of total mass, ICM structure, optical richness, and the presence of two dominant BCG-type galaxies, the newly confirmed cluster XMMU J1230.3+1339 is likely the progenitor of a system very similar to the local Coma cluster, differing by 7.6 Gyr of structure evolution.
Super-Eddington accretion has been suggested as a possible formation pathway of $10^9 \, M_\odot$ supermassive black holes (SMBHs) 800 Myr after the Big Bang. However, stellar feedback from BH seed progenitors and winds from BH accretion disks may decrease BH accretion rates. In this work, we study the impact of these physical processes on the formation of $z \sim 6$ quasar, including new physical prescriptions in the cosmological, data-constrained semi-analytic model GAMETE/QSOdust. We find that the feedback produced by the first stellar progenitors on the surrounding does not play a relevant role in preventing SMBHs formation. In order to grow the $z \gtrsim 6$ SMBHs, the accreted gas must efficiently lose angular momentum. Moreover disk winds, easily originated in super-Eddington accretion regime, can strongly reduce duty cycles. This produces a decrease in the active fraction among the progenitors of $z\sim6$ bright quasars, reducing the probability to observe them.
This paper presents a systematical study of stationary (rotating) cylindrical space-times of a Weyl form that are solutions to D=4 Einstein-Maxwell equations with cosmological constant. The corresponding equations of motion - with zero cosmological constant - are integrated. Then, several classes of exact solutions - obtained by restricting the range of the free constant parameters - are obtained and sub-cases corresponding to already known solutions are indicated.
We combine recently computed models of stellar evolution using a new treatment of rotation with a Bayesian statistical framework to constrain the ages and other properties of early-type stars. We find good agreement for early-type stars and clusters with known young ages, including beta Pictoris, the Pleiades, and the Ursa Majoris Moving Group. However, we derive a substantially older age for the Hyades open cluster (750+/-100 Myr compared to 625+/-50 Myr). This older age results from both the increase in main-sequence lifetime with stellar rotation and from the fact that rotating models near the main-sequence turnoff are more luminous, overlapping with slightly more massive (and shorter-lived) nonrotating ones. Our method uses a large grid of nonrotating models to interpolate between a much sparser rotating grid, and also includes a detailed calculation of synthetic magnitudes as a function of orientation. We provide a web interface at www.bayesianstellarparameters.info where the results of our analysis may be downloaded for individual early-type (B-V<~0.25) Hipparcos stars. The web interface accepts user-supplied parameters for a Gaussian metallicity prior and returns posterior probability distributions on mass, age, and orientation.
Sgr A* is considered to be a massive black hole at the Galactic center and is known to be variable in radio, millimeter, near-IR and X-rays. Recent multi-wavelength observing campaigns show a simultaneous X-ray and near-IR flare, as well as sub-millimeter and near-IR flares from Sgr A*. The flare activity is thought to be arising from the innermost region of Sgr A*. We have recently argued that the duration of flares in near-IR and submillimeter wavelengths implies that the burst of emission expands and cools on a dynamical time scale before the flares leave Sgr A*. The detection of radio flares with a time delay in the range of 20 and 40 minutes between 7 and 12mm peak emission implies adiabatic expansion of a uniform, spherical hot blob due to flare activity. We suspect that this simple outflow picture shows some of the characteristics that are known to take place in microquasars, thus we may learn much from comparative study of Sgr A* and its environment vs. microquasars.
Covariant quantization of multi-pronged open bosonic string junction is studied beyond static analysis. Its excited states are described by a set of ordinary bosons as well as some sets of twisted bosons on the world-sheet. The system is characterized by a certain large algebra of twisted type which includes a single Virasoro algebra as a subalgebra. By properly defining the physical states, one can show that there are no ghosts in the Hilbert space.
We present 2 recent results on the problems of time and observables in canonical gravity. (1) We cannot use parametrized field theory to solve the problem of time because, strictly speaking, general relativity is not a parametrized field theory. (2) We show that there are essentially no local observables for vacuum spacetimes.
Rh-terminated FeRh(001) film is known to be stable in a ferromagnetic (FM) state different from a G-type antiferromagnetic (G-AFM) bulk ground state, while an Fe-terminated FeRh(001) film has the same ground state as the bulk. In this paper, we investigate the magnetic properties of asymmetrically terminated FeRh(001) films: one surface is Fe-terminated and the other is Rh-terminated. Rh surface only ] (RhSO) FM state in asymmetrically terminated FeRh(001) film is identified to exhibit 40% increased perpendicular MCA energy as compare to that of the whole-layer (WL) FM state. This increased MCA energy is governed by Rh atom which is placed at the magnetic boundary. Since FM and G-AFM states are mixed up at the magnetic boundary, spin-orbit couplings which give positive contribution to perpendicular MCA are revealed.
In this paper we address the problem of computing asymptotic formulae for the expected values and second moments of central values of primitive Dirichlet $L$-functions $L(1/2,\chi_{8d}\otimes\psi)$ when $\psi$ is a fixed even primitive non-quadratic character of odd modulus $q$, $\chi_{8d}$ is a primitive quadratic character, $d\equiv h\pmod r$ is odd and squarefree and $r\equiv0\pmod q$ is even. Restricting to these arithmetic progressions ensures that the resulting sets of $L$-functions each form a ``family of primitive $L$-functions" in the specific sense defined by Conrey, Farmer, Keating, Rubinstein and Snaith. Soundararajan had previously computed these quantities without restricting them to arithmetic progressions. It turns out that the restriction to arithmetic progressions introduces non-diagonal terms that require significantly more detailed analysis which we carry on in this paper.
Some remarks are made on the articles by N.Milosevic, V.P.Krainov, T.Brabec and our papers are about problem of semiclassical theory of tunnel ionization.
We present an approach that combines automatic features learned by convolutional neural networks (CNN) and handcrafted features computed by the bag-of-visual-words (BOVW) model in order to achieve state-of-the-art results in facial expression recognition. To obtain automatic features, we experiment with multiple CNN architectures, pre-trained models and training procedures, e.g. Dense-Sparse-Dense. After fusing the two types of features, we employ a local learning framework to predict the class label for each test image. The local learning framework is based on three steps. First, a k-nearest neighbors model is applied in order to select the nearest training samples for an input test image. Second, a one-versus-all Support Vector Machines (SVM) classifier is trained on the selected training samples. Finally, the SVM classifier is used to predict the class label only for the test image it was trained for. Although we have used local learning in combination with handcrafted features in our previous work, to the best of our knowledge, local learning has never been employed in combination with deep features. The experiments on the 2013 Facial Expression Recognition (FER) Challenge data set, the FER+ data set and the AffectNet data set demonstrate that our approach achieves state-of-the-art results. With a top accuracy of 75.42% on FER 2013, 87.76% on the FER+, 59.58% on AffectNet 8-way classification and 63.31% on AffectNet 7-way classification, we surpass the state-of-the-art methods by more than 1% on all data sets.
The coolest known brown dwarfs are our best analogs to extrasolar gas-giant planets. The prolific detections of such cold substellar objects in the past two years has spurred intensive followup, but the lack of accurate distances is a key gap in our understanding. We present a large sample of precise distances based on homogeneous mid-infrared astrometry that robustly establish absolute fluxes, luminosities, and temperatures. The coolest brown dwarfs have temperatures of 400-450 K and masses ~5-20 times that of Jupiter, showing they bridge the gap between hotter brown dwarfs and gas-giant planets. At these extremes, spectral energy distributions no longer follow a simple correspondence with temperature, suggesting an increasing role of other physical parameters such as surface gravity, vertical mixing, clouds, and metallicity.
Percolation with edge-passage probability p and first-passage percolation are studied for the n-cube B_n ={0,1}^n with nearest neighbor edges. For oriented and unoriented percolation, p=e/n and p=1/n are the respective critical probabilities. For oriented first-passage percolation with i.i.d. edge-passage times having a density of 1 near the origin, the percolation time (time to reach the opposite corner of the cube) converges in probability to 1 as n->infty. This resolves a conjecture of David Aldous. When the edge-passage distribution is standard exponential, the (smaller) percolation time for unoriented edges is at least 0.88. These results are applied to Richardson's model on the (unoriented) n-cube. Richardson's model, otherwise known as the contact process with no recoveries, models the spread of infection as a Poisson process on each edge connecting an infected node to an uninfected one. It is shown that the time to cover the entire n-cube is bounded between 1.41 and 14.05 in probability as n->infty.
We introduce meromorphic nearby cycle functors and study their functorial properties. Moreover we apply them to monodromies of meromorphic functions in various situations. Combinatorial descriptions of their reduced Hodge spectra and Jordan normal forms will be obtained.
We present and analyze two algorithms for computing the Hilbert class polynomial $H_D$ . The first is a p-adic lifting algorithm for inert primes p in the order of discriminant D < 0. The second is an improved Chinese remainder algorithm which uses the class group action on CM-curves over finite fields. Our run time analysis gives tighter bounds for the complexity of all known algorithms for computing $H_D$, and we show that all methods have comparable run times.
LiDAR depth-only completion is a challenging task to estimate dense depth maps only from sparse measurement points obtained by LiDAR. Even though the depth-only methods have been widely developed, there is still a significant performance gap with the RGB-guided methods that utilize extra color images. We find that existing depth-only methods can obtain satisfactory results in the areas where the measurement points are almost accurate and evenly distributed (denoted as normal areas), while the performance is limited in the areas where the foreground and background points are overlapped due to occlusion (denoted as overlap areas) and the areas where there are no measurement points around (denoted as blank areas) since the methods have no reliable input information in these areas. Building upon these observations, we propose an effective Coupled U-Net (CU-Net) architecture for depth-only completion. Instead of directly using a large network for regression, we employ the local U-Net to estimate accurate values in the normal areas and provide the global U-Net with reliable initial values in the overlap and blank areas. The depth maps predicted by the two coupled U-Nets are fused by learned confidence maps to obtain final results. In addition, we propose a confidence-based outlier removal module, which removes outliers using simple judgment conditions. Our proposed method boosts the final results with fewer parameters and achieves state-of-the-art results on the KITTI benchmark. Moreover, it owns a powerful generalization ability under various depth densities, varying lighting, and weather conditions.
Spatially homogeneous but possibly anisotropic cosmologies have two main types of singularities: (1) asymptotically velocity term dominated (AVTD) - (reversing the time direction) the universe evolves to the singularity with fixed anisotropic collapse rates ; (2) Mixmaster-the anisotropic collapse rates change in a deterministicaly chaotic way. Much less is known about spatially inhomogeneous universes. It has been claimed that a generic universe would evolve toward the singularity as a different Mixmaster universe at each spatial point. I shall discuss how to predict whether a cosmology has an AVTD or Mixmaster singularity and whether or not our numerical simulations agree with these predictions.
By using the Poisson formula for resultants and the variants of chip-firing game on graphs, we provide a combinatorial method for computing a class of of resultants, i.e. the characteristic polynomials of the adjacency tensors of starlike hypergraphs including hyperpaths and hyperstars,which are given recursively and explicitly.