ShantanuT01/DACTYL-Pretraining huggingface dataset:
We perform an asymptotic analysis of models of population dynamics with a fractional Laplacian and local or nonlocal reaction terms. The first part of the paper is devoted to the long time/long range rescaling of the fractional Fisher-KPP equation. This rescaling is based on the exponential speed of propagation of the population. In particular we show that the only role of the fractional Laplacian in determining this speed is at the initial layer where it determines the thickness of the tails of the solutions. Next, we show that such rescaling is also possible for models with non-local reaction terms, as selection-mutation models. However, to obtain a more relevant qualitative behavior for this second case, we introduce, in the second part of the paper, a second rescaling where we assume that the diffusion steps are small. In this way, using a WKB ansatz, we obtain a Hamilton-Jacobi equation in the limit which describes the asymptotic dynamics of the solutions, similarly to the case of selection-mutation models with a classical Laplace term or an integral kernel with thin tails. However, the rescaling introduced here is very different from the latter cases. We extend these results to the multidimensional case.
Motivated by applications in Markov chain Monte Carlo, we discuss what it means for one Markov chain to be an approximation to another. Specifically included in that discussion are situations in which a Markov chain with continuous state space is approximated by one with finite state space. A simple sufficient condition for close approximation is derived, which indicates the existence of three distinct approximation regimes. Counterexamples are presented to show that these regimes are real and not artifacts of the proof technique. An application to the ``ball walk'' of Lov\'asz and Simonovits is provided as an illustrative example.
From both theory and experiment, scattering of minority electrons is expected to be weaker than scattering of majority electrons in both dilute Fe(Cr) alloys and at Fe(Cr)/Cr interfaces. We show that Fe(Cr)/Cr/Fe(Cr) trilayer nanopillars display a normal magnetoresistance--i.e., largest resistance at low magnetic fields and smallest at high fields, but an inverted current-driven switching--i.e., positive current flowing from the fixed to the reversing layer switches the trilayer from higher to lower resistance, and negative current switches it from lower to higher.
Ab initio calculations show that the coupling between antiferrodistortive(AFD) distortions and magnetization in perovskite Bi2FeMnO6 is prohibited to make magnetization rotate as on-site Coulomb interaction($U$) is larger than 2.7 eV, where anomalies in antiferromagnetic(AFM) vectors and band gap varying with on-site Coulomb interaction can be observed. This coupling is attributed to the antisymmetric Dzyaloshinskii-Moriya interaction(DMI) driven by the eg-eg states AFM interaction and charge redistribution with respect to different AFD distortions.
Classifying the strengthes of three-body forces 3BFs with the condition that observables must be cut-off independent, i.e. renormalised at each order, leads to surprising results with relevance for example for thermal neutron capture on the deuteron. Details and a better bibliography in Ref. [1].
We consider the detailed dynamics of an array of quantised superfluid vortices in the framework of general relativity, as required for quantitative modelling of realistic neutron star cores. Our model builds on the variational approach to relativistic (multi-) fluid dynamics, where the vorticity plays a central role. The description provides a natural extension of, and as it happens a better insight into, existing Newtonian models. In particular, we account for the mutual friction associated with scattering of a second "normal" component in the mixture off of the superfluid vortices.
We construct configuration spaces for cyclic covers of the projective line that admit extra automorphisms and we describe the locus of curves with given automorphism group. As an application we provide examples of arbitrary high genus that are defined over their field of moduli and are not hyperelliptic.
For an algebraic K3 surface with complex multiplication (CM), algebraic fibres of the associated twistor space away from the equator are again of CM type. In this paper, we show that algebraic fibres corresponding to points at the same altitude of the twistor base $S^2\simeq \mathbb{P}^1_\mathbb{C}$ share the same CM endomorphism field. Moreover, we determine all the admissible Picard numbers of the twistor fibres.
We give a sufficient condition under which an applied rotation on medium particles stabilizes a slow probe in the rotation center. The symmetric part of the stiffness matrix thus gets a positive Lamb shift with respect to equilibrium. For illustration we take diffusive medium particles with a self-potential in the shape of a Mexican hat, high around the origin. There is a short-range attraction between the medium particles and the heavier probe, all immersed in an equilibrium thermal bath. For no or small rotation force on the medium particles, the origin is an unstable fixed point for the probe and the precise shape of the self-potential at large distances from the origin is irrelevant for the statistical force there. Above a certain rotation threshold, while the medium particles are still repelled from the origin, the probe stabilizes there and more details of the medium-density at large distance start to matter. The effect is robust around the quasi-static limit with rotation threshold only weakly depending on the temperature but the stabilization gets stronger at lower temperatures.
Exact static, spherically symmetric solutions to the Einstein-Maxwell-scalar equations, with a dilatonic-type scalar-vector coupling, in $D$-dimensional gravity with a chain of $n$ Ricci-flat internal spaces are considered. Their properties and special cases are discussed. A family of multidimensional dilatonic black-hole solutions is singled out, depending on two integration constants (related to black hole mass and charge) and three free parameters of the theory (the coordinate sphere, internal space dimensions, and the coupling constant). The behaviour of the solutions under small perturbations preserving spherical symmetry, is studied. It is shown that the black-hole solutions without a dilaton field are stable, while other solutions, possessing naked singularities, are catastrophically unstable.
We present a new method for inferring the gravitational potential of the Galactic disk, using the time-varying structure of a phase-space spiral in the $(z,w)$-plane (where $z$ and $w$ represent vertical position and vertical velocity). Our method of inference extracts information from the shape of the spiral and disregards the bulk density distribution that is usually used to perform dynamical mass measurements. In this manner, it is complementary to traditional methods that are based on the assumption of a steady state. Our method consists of fitting an analytical model for the phase-space spiral to data, where the spiral is seen as a perturbation of the stellar number density in the $(z,w)$-plane. We tested our method on one-dimensional simulations, which were initiated in a steady state and then perturbed by an external force similar to that of a passing satellite. We were able to retrieve the true gravitational potentials of the simulations with high accuracy. The gravitational potential at 400-500 parsec distances from the disk mid-plane was inferred with an error of only a few percent. This is the first paper of a series in which we plan to test and refine our method on more complex simulations, as well as apply our method to Gaia data.
High brightness temperature radio transients such as pulsars and fast radio bursts require the coherent radiation of particles. The antenna class of coherent radiation models require a large number of charged particles radiating in phase, therefore the particles must be spatially confined and have well-aligned velocities. Given these necessary conditions, we look at the magnetic field induced by the currents associated with coherently emitting accelerated particles and consider the interaction between the radiating particles and the induced magnetic field. We find a maximum luminosity of coherent curvature radiation that depends on source parameters such as surface magnetic field and neutron star spin period. We find that coherent radio emission across all luminosities can be explained by coherent curvature radiation and suggest it could be universally responsible for both FRBs and extreme galactic sources. Using the Crab Pulsar as an example, we constrain the emission parameters and origin of the most extreme nanoshots to within 60km of the pulsar surface assuming coherent curvature radiation. In agreement with recent observations, we also predict simultaneous X-ray emission from small-scale particle gyration due to the induced field.
We describe powder and single-crystal inelastic neutron scattering experiments on a spinel-type antiferromagnet GeCo$_2$O$_4$, represented by an effective total angular momentum J_eff = 1/2. Several types of non-dispersive short-range magnetic excitations were discovered. The scattering intensity maps in $\vec{Q}$ space are well reproduced by dynamical structure factor analyses using molecular model Hamiltonians. The results of analyses strongly suggest that the molecular excitations below T_N arise from a hidden molecular-singlet ground state, in which ferromagnetic subunits are antiferromagnetically coupled. The quasielastic excitations above T_N are interpreted as its precursor. A combination of frustration and J_eff = 1/2 might induce these quantum phenomena.
The Hubble Frontier Fields represent the opportunity to probe the high-redshift evolution of the main sequence of star-forming galaxies to lower masses than possible in blank fields thanks to foreground lensing of massive galaxy clusters. We use the BEAGLE SED-fitting code to derive stellar masses, $\mathrm{M_{\star}}=\log(M/\mathrm{M_{\odot}})$, SFRs, $\Psi=\log(\psi/\mathrm{M_{\odot}}\,\mathrm{yr}^{-1})$ and redshifts from galaxies within the ASTRODEEP catalogue. We fit a fully Bayesian hierarchical model of the main sequence over $1.25<z<6$ of the form $\Psi = \alpha_\mathrm{9.7}(z) + \beta(\mathrm{M_{\star}}-9.7) + \mathcal{N}(0,\sigma^2)$ while explicitly modelling the outlier distribution. The redshift-dependent intercept at $\mathrm{M_{\star}}=9.7$ is parametrized as $\alpha_\mathrm{9.7}(z) = \log[N (1+z)^{\gamma}] + 0.7$. Our results agree with an increase in normalization of the main sequence to high redshifts that follows the redshift-dependent rate of accretion of gas onto dark matter halos with $\gamma=2.40^{+0.18}_{-0.18}$. We measure a slope and intrinsic scatter of $\beta=0.79^{+0.03}_{-0.04}$ and $\sigma=0.26^{+0.02}_{-0.02}$. We find that the sampling of the SED provided by the combination of filters (Hubble + ground-based Ks-band + Spitzer 3.6 and 4.5 $\mathrm{\mu m}$) is insufficient to constrain $\mathrm{M_{\star}}$ and $\Psi$ over the full dynamic range of the observed main sequence, even at the lowest redshifts studied. While this filter set represents the best current sampling of high-redshift galaxy SEDs out to $z>3$, measurements of the main sequence to low masses and high redshifts still strongly depend on priors employed in SED fitting (as well as other fitting assumptions). Future data-sets with JWST should improve this.
The modern time-delay cosmography aims to infer the cosmological parameters with a competitive precision from observing a multiply imaged quasar. The success of this technique relies upon a robust modeling of the lens mass distribution. Unfortunately strong degeneracies between density profiles that lead to almost the same lensing observables may bias precise estimate for the Hubble constant. The source position transformation (SPT), which covers the well-known mass sheet transformation (MST) as a special case, defines a new framework to investigate these degeneracies. In this paper, we present pySPT, a Python package dedicated to the SPT. We describe how it can be used to evaluate the impact of the SPT on lensing observables. We review most of its capabilities and elaborate on key features that we used in a companion paper regarding SPT and time delays. pySPT also comes with a sub-package dedicated to simple lens modeling. It can be used to generate lensing related quantities for a wide variety of lens models, independently from any SPT analysis. As a first practical application, we present a correction to the first estimate of the impact on time delays of the SPT, which has been experimentally found in Schneider and Sluse (2013) between a softened power-law and a composite (baryons + dark matter) lenses. We find that the large deviations predicted in Schneider and Sluse (2014) have been overestimated due to a minor bug (now fixed) in the public lens modeling code lensmodel (v1.99). We conclude that the predictions for the Hubble constant deviate by $\sim 7$\%, first and foremost caused by an MST. The latest version of pySPT is available at https://github.com/owertz/pySPT. We also provide tutorials to describe in detail how making the best use of pySPT at https://github.com/owertz/pySPT_tutorials.
A simple, novice-friendly scheme for classifying the image configurations of quadruply lensed quasars is proposed. With only six classes, it is intentionally coarse-grained. It focuses on the kitelikeness and circularity of these configurations, or the absence thereof. Other features are deliberately ignored, their importance to professional astronomers notwithstanding. Readers are invited to test drive the scheme on a sample of 12 quadruply lensed quasar systems. The theoretical underpinnings of the scheme are described in a technical appendix.
The joint distribution of maximum increase and decrease for Brownian motion up to an independent exponential time is computed. This is achieved by decomposing the Brownian path at the hitting times of the infimum and the supremum before the exponential time. It is seen that an important element in our formula is the distribution of the maximum decrease for the three dimensional Bessel process with drift started from 0 and stopped at the first hitting of a given level. From the joint distribution of the maximum increase and decrease it is possible to calculate the correlation coefficient between these at a fixed time and this is seen to be -0.47936... .
We define homology groups for flat irregular singular connections on surfaces and a pairing between these and the de Rham cohomology of the connection, generalizing work of S. Bloch and H. Enault in dimension one. Assuming a conjecture of C. Sabbah (known to be true if the rank of the vector bundle is at most 5), we prove perfectness of the pairing. We comment on certain new phenomena appearing in dimension two.
$\texttt{PyCosmo}$ is a Python-based framework for the fast computation of cosmological model predictions. One of its core features is the symbolic representation of the Einstein-Boltzmann system of equations. Efficient $\texttt{C/C++}$ code is generated from the $\texttt{SymPy}$ symbolic expressions making use of the $\texttt{sympy2c}$ package. This enables easy extensions of the equation system for the implementation of new cosmological models. We illustrate this with three extensions of the $\texttt{PyCosmo}$ Boltzmann solver to include a dark energy component with a constant equation of state, massive neutrinos and a radiation streaming approximation. We describe the $\texttt{PyCosmo}$ framework, highlighting new features, and the symbolic implementation of the new models. We compare the $\texttt{PyCosmo}$ predictions for the $\Lambda$CDM model extensions with $\texttt{CLASS}$, both in terms of accuracy and computational speed. We find a good agreement, to better than 0.1% when using high-precision settings and a comparable computational speed. Links to the Python Package Index (PyPI) page of the code release and to the PyCosmo Hub, an online platform where the package is installed, are available at: https://cosmology.ethz.ch/research/software-lab/PyCosmo.html.
We review the theory and observations of star cluster disruption. The three main phases and corresponding typical timescales of cluster disruption are: I) Infant Mortality (~10^7 yr), II) Stellar Evolution (~10^8 yr) and III) Tidal relaxation (~10^9 yr). During all three phases there are additional tidal external perturbations from the host galaxy. In this review we focus on the physics and observations of Phase I and on population studies of Phases II & III and external perturbations concentrating on cluster-GMC interactions. Particular attention is given to the successes and short-comings of the Lamers cluster disruption law, which has recently been shown to stand on a firm physical footing.
In this paper we consider some aspects of the relativistic dynamics of a cylindrical shell of counter rotating particles. In some sense these are the simplest systems with a physically acceptable matter content that display in a well defined sense an interaction with the radiative modes of the gravitational field. These systems have been analyzed previously, but in most cases resorting to approximations, or considering a particular form for the initial value data. Here we show that there exists a family of solutions where the space time inside the shell is flat and the equation of motion of the shell decouples completely from the gravitational modes. The motion of the shell is governed by an equation of the same form as that of a particle in a time independent one dimensional potential. We find that under appropriate initial conditions one can have collapsing, bounded periodic, and unbounded motions. We analyze and solve also the linearized equations that describe the dynamics of the system near a stable static solutions, keeping a regular interior. The surprising result here is that the motion of the shell is completely determined by the configuration of the radiative modes of the gravitational field. In particular, there are oscillating solutions for any chosen period, in contrast with the "approximately Newtonian plus small radiative corrections" motion expectation. We comment on the physical meaning of these results and provide some explicit examples. We also discuss the relation of our results to the initial value problem for the linearized dynamics of the shell.
We report the results of our experimental studies on the magnetic, transport and thermoelectric properties of the ferromagnetic metal CoMnSb. Sizable anomalous Hall conductivity $\sigma_{yx}$ and transverse thermoelectric conductivity $\alpha_{yx}$ are found experimentally and comparable in size to the values estimated from density-functional theory. Our experiment further reveals that CoMnSb exhibits $-T\ln T$ critical behavior in $\alpha_{yx}(T)$, deviating from Fermi liquid behavior $\alpha_{yx}\sim T$ over a decade of temperature between 10 K to 400 K, similar to ferromagnetic Weyl and nodal-line semimetals. Our theoretical calculation for CoMnSb also predicts the $-T\ln T$ behavior when the Fermi energy locates near the Weyl nodes in momentum space.
We study separating systems of the edges of a graph where each member of the separating system is a path. We conjecture that every $n$-vertex graph admits a separating path system of size $O(n)$ and prove this in certain interesting special cases. In particular, we establish this conjecture for random graphs and graphs with linear minimum degree. We also obtain tight bounds on the size of a minimal separating path system in the case of trees.
We discuss a phenomenological method which allows to determine the singular asymptotic behaviours for a pure fluid at equilibrium, when the liquid-gas critical point and the tangent plane to the characteristic surface of this point are localized experimentally, in the pressure, density and temperature coordinates.
Consider a large uniformly mixing dynamic population, which has constant birth rate and exponentially distributed lifetimes, with mean population size $n$. A Markovian SIR (susceptible $\to$ infective $\to$ recovered) infectious disease, having importation of infectives, taking place in this population is analysed. The main situation treated is where $n\to\infty$, keeping the basic reproduction number $R_0$ as well as the importation rate of infectives fixed, but assuming that the quotient of the average infectious period and the average lifetime tends to 0 faster than $1/\log n$. It is shown that, as $ n \to \infty$, the behaviour of the 3-dimensional process describing the evolution of the fraction of the population that are susceptible, infective and recovered, is encapsulated in a 1-dimensional regenerative process $S=\{ S(t);t\ge 0\}$ describing the limiting fraction of the population that are susceptible. The process $S$ grows deterministically, except at one random time point per regenerative cycle, where it jumps down by a size that is completely determined by the waiting time since the previous jump. Properties of the process $S$, including the jump size and stationary distributions, are determined.
Camera captured human pose is an outcome of several sources of variation. Performance of supervised 3D pose estimation approaches comes at the cost of dispensing with variations, such as shape and appearance, that may be useful for solving other related tasks. As a result, the learned model not only inculcates task-bias but also dataset-bias because of its strong reliance on the annotated samples, which also holds true for weakly-supervised models. Acknowledging this, we propose a self-supervised learning framework to disentangle such variations from unlabeled video frames. We leverage the prior knowledge on human skeleton and poses in the form of a single part-based 2D puppet model, human pose articulation constraints, and a set of unpaired 3D poses. Our differentiable formalization, bridging the representation gap between the 3D pose and spatial part maps, not only facilitates discovery of interpretable pose disentanglement but also allows us to operate on videos with diverse camera movements. Qualitative results on unseen in-the-wild datasets establish our superior generalization across multiple tasks beyond the primary tasks of 3D pose estimation and part segmentation. Furthermore, we demonstrate state-of-the-art weakly-supervised 3D pose estimation performance on both Human3.6M and MPI-INF-3DHP datasets.
We consider coverings of real algebraic curves to real rational algebraic curves. We show the existence of such coverings having prescribed topological degree on the real locus. From those existence results we prove some results on Brill-Noether Theory for pencils on real curves. For coverings having topological degree 0 we introduce the covering number k and we prove the existence of coverings of degree 4 with prescribed covering number.
It is shown that Bohmian mechanics is internally consistent in the sense that the equations of motion typically have global solutions despite the fact that the velocity field is singular at the nodes of the wave function and at other points. This result is fundamental for the derivation of the quantum formalism. The role of the quantum flux is emphasized.