ShantanuT01/DACTYL-Pretraining huggingface dataset:
We give a variational formulation for $-\log\mathbb{E}_\nu\left[e^{-f}|\mathcal{F}_t\right]$ for a large class of measures $\nu$. We give a refined entropic characterization of the invertibility of some perturbations of the identity. We also discuss the attainability of the infimum in the variational formulation and obtain a Pr\'ekopa-Leindler theorem for conditional expectations.
Let $v$ be a product of at most three not necessarily distinct primes. We prove that there exists no strong external difference family with more than two subsets in abelian group $G$ of order $v$, except possibly when $G=C_p^3$ and $p$ is a prime greater than $3 \times 10^{12}$.
Occupancy grid mapping is an important component in road scene understanding for autonomous driving. It encapsulates information of the drivable area, road obstacles and enables safe autonomous driving. Radars are an emerging sensor in autonomous vehicle vision, becoming more widely used due to their long range sensing, low cost, and robustness to severe weather conditions. Despite recent advances in deep learning technology, occupancy grid mapping from radar data is still mostly done using classical filtering approaches.In this work, we propose learning the inverse sensor model used for occupancy grid mapping from clustered radar data. This is done in a data driven approach that leverages computer vision techniques. This task is very challenging due to data sparsity and noise characteristics of the radar sensor. The problem is formulated as a semantic segmentation task and we show how it can be learned using lidar data for generating ground truth. We show both qualitatively and quantitatively that our learned occupancy net outperforms classic methods by a large margin using the recently released NuScenes real-world driving data.
Let $E/\mathbb{Q}$ be an elliptic curve of conductor $N=p^2M$ where $p$ is an odd prime not dividing $M$. Let $\mathcal{O}_f$ be the order of conductor $f$ (relatively prime to $N$) in an imaginary quadratic field $K$ in which $p$ is inert and such that the sign of the functional equation of $E/K$ is $-1$. Associated to these data there is a Shimura curve of non-split Cartan level at $p$ and a CM point of conductor $f$ on it. We can also consider a CM point of conductor $pf$ on another Shimura curve, using a split Cartan level at $p$. These curves admit parametrizations to $E$ and taking the images of the CM points we obtain points on $E$ defined over $H_f$ and $H_{pf}$ respectively (the ring class fields of conductor $f$ and $pf$). We prove that these points arising from different Shimura curves satisfy a trace compatibility that is non-trivial if and only if the local sign of $E/\mathbb{Q}$ at $p$ is $+1$.
We present the final data release from the GALEX Arecibo SDSS Survey (GASS), a large Arecibo program that measured the HI properties for an unbiased sample of ~800 galaxies with stellar masses greater than 10^10 Msun and redshifts 0.025<z<0.05. This release includes new Arecibo observations for 250 galaxies. We use the full GASS sample to investigate environmental effects on the cold gas content of massive galaxies at fixed stellar mass. The environment is characterized in terms of dark matter halo mass, obtained by cross-matching our sample with the SDSS group catalog of Yang et al. Our analysis provides, for the first time, clear statistical evidence that massive galaxies located in halos with masses of 10^13-10^14 Msun have at least 0.4 dex less HI than objects in lower density environments. The process responsible for the suppression of gas in group galaxies most likely drives the observed quenching of the star formation in these systems. Our findings strongly support the importance of the group environment for galaxy evolution, and have profound implications for semi-analytic models of galaxy formation, which currently do not allow for stripping of the cold interstellar medium in galaxy groups.
We use the BGG-correspondence to show that there are at most three possible Hilbert functions for smooth rational surfaces of degree 11 and sectional genus 11. Surfaces with one of these Hilbert functions have been classified by Popescu. The classification for a second one is done in this paper. For the third Hilbert function the classification is still open.
Minimum error state discrimination between two mixed states \rho and \sigma can be aided by the receipt of "classical side information" specifying which states from some convex decompositions of \rho and \sigma apply in each run. We quantify this phenomena by the average trace distance, and give lower and upper bounds on this quantity as functions of \rho and \sigma. The lower bound is simply the trace distance between \rho and \sigma, trivially seen to be tight. The upper bound is \sqrt{1 - tr(\rho\sigma)}, and we conjecture that this is also tight. We reformulate this conjecture in terms of the existence of a pair of "unbiased decompositions", which may be of independent interest, and prove it for a few special cases. Finally, we point towards a link with a notion of non-classicality known as preparation contextuality.
A proof of Bell's theorem using two maximally entangled states of two qubits is presented. It exhibits a similar logical structure to Hardy's argument of ``nonlocality without inequalities''. However, it works for 100% of the runs of a certain experiment. Therefore, it can also be viewed as a Greenberger-Horne-Zeilinger-like proof involving only two spacelike separated regions.
We propose a two-color scheme of atom guide and 1D optical lattice using evanescent light fields of different transverse modes. The optical waveguide carries a red-detuned light and a blue-detuned light, with both modes far from resonance. The atom guide and 1D optical lattice potentials can be transformed to each other by using a Mach-Zehnder interferometer to accurately control mode transformation. This might provide a new approach to realize flexible transition between the guiding and trapping states of atoms.
A set of Modified Embedded Atom Method (MEAM) potentials for the interactions between Al, Si, Mg, Cu, and Fe was developed from a combination of each element's MEAM potential in order to study metal alloying. Previously published MEAM parameters of single elements have been improved for better agreement to the generalized stacking fault energy (GSFE) curves when compared with ab-initio generated GSFE curves. The MEAM parameters for element pairs were constructed based on the structural and elastic properties of element pairs in the NaCl reference structure garnered from ab-initio calculations, with adjustment to reproduce the ab-initio heat of formation of the most stable binary compounds. The new MEAM potentials were validated by comparing the formation energies of defects, equilibrium volumes, elastic moduli, and heat of formation for several binary compounds with ab-initio simulations and experiments. Single elements in their ground state crystal structure were subjected to heating to test the potentials at elevated temperatures. An Al potential was modified to avoid formation of an unphysical solid structure at high temperatures. The thermal expansion coefficient of a compound with the composition of AA 6061 alloy was evaluated and compared with experimental values. MEAM potential tests performed in this work, utilizing the universal Atomistic Simulation Environment (ASE), are distributed to facilitate reproducibility of the results.
In this paper, we prove the diffusion phenomenon for the linear wave equation with space-dependent damping. We prove that the asymptotic profile of the solution is given by a solution of the corresponding heat equation in the $L^2$-sense.
We investigate the conditions at which high-mode magnetohydrodynamic (MHD) waves propagating in a spinning solar macrospicule can become unstable with respect to the Kelvin--Helmholtz instability (KHI). We consider the macrospicule as a weakly twisted cylindrical magnetic flux tube moving along and rotating around its axis. Our study is based on the dispersion relation (in complex variables) of MHD waves obtained from the linearized MHD equations of an incompressible plasma for the macrospicule and cool ($\beta = 0$, rate of the plasma to the magnetic pressure) plasma for its environment. This dispersion equation is solved numerically at appropriate input parameters to find out an instability region or window that accommodates suitable unstable wavelengths on the order of the macro\-spicule width. It is established that an $m = 52$ MHD mode propagating in a macro\-spicule with width of $6$~Mm, axial velocity of $75$~km\,s$^{-1}$, and rotating one of $40$~km\,s$^{-1}$ can become unstable against the KHI with instability growth times of $2.2$ and $0.57$~min at $3$ and $5$~Mm unstable wavelengths, respectively. These growth times are much shorter than the macrospicule lifetime, which lasts about $15$~min. An increase or decease in the width of the jet would change the KHI growth times, which remain more or less on the same order when they are evaluated at wavelengths equal to the width or radius of the macrospicule. It is worth noting that the excited MHD modes are super-Alfv\'enic waves. A change in the background magnetic field can lead to another MHD mode number $m$ that ensures the required instability window.
The essential role of long range elastic interactions in recrystallization is demonstrated using a simple analytical model: pileup rearrangements following absorption of leading dislocations by a dislocation-free embryo provides an additional driving force that results in a drastic decrease of both the nucleation critical radius and the saddle point energy. A very sharp transition is evidenced, at which the saddle point totally disappears and nucleation becomes spontaneous. This transition occurs for a well defined critical stress corresponding to both a critical density of geometrically necessary dislocations and a critical strain, without invoking any critical nucleus size that may be reached with the help of some dislocation microstructure instability. The present model is illustrated here by the case of polycrystalline ice, but may apply to other crystalline material with significant plastic anisotropy, as Zircaloy for instance.
One-dimensional topological superconductors harbor Majorana bound states at their ends. For superconducting wires of finite length L, these Majorana states combine into fermionic excitations with an energy $\epsilon_0$ that is exponentially small in L. Weak disorder leaves the energy splitting exponentially small, but affects its typical value and causes large sample-to-sample fluctuations. We show that the probability distribution of $\epsilon_0$ is log normal in the limit of large L, whereas the distribution of the lowest-lying bulk energy level $\epsilon_1$ has an algebraic tail at small $\epsilon_1$. Our findings have implications for the speed at which a topological quantum computer can be operated.
Mn$_2$Au is an important antiferromagnetic (AF) material for spintronics applications. Due to its very high N\'eel temperature of about 1500 K, some of the basic properties are difficult to explore, such as the AF susceptibility and the exchange constants. Experimental determination of these properties is further complicated in thin films by unavoidable presence of uncompensated and quasiloose spins on antisites and at interfaces. Using x-ray magnetic circular dichroism (XMCD), we have measured the spin and orbital contribution to the susceptibility in the direction perpendicular to the in-plane magnetic moments of a Mn$_2$Au(001) film and in fields up to 8 T. By performing these measurements at a low temperature of 7 K and at room temperature, we were able to separate the loose spin contribution from the susceptibility of AF coupled spins. The value of the AF exchange constant obtained with this method for a 10 nm thick Mn$_2$Au(001) film equals to (24 $\pm$ 5) meV.
We show that the numerically exact bold-line diagrammatic theory for the $2d$ Hubbard model exhibits a non-Fermi-liquid (NFL) strange metal state, which is connected to the SYK NFL in the strong-interaction limit. The solution for the doped system features the expected phenomenology with the NFL near half-filling at strong couplings and in a wide temperature range enclosed by the atomic state at high temperatures and a Fermi liquid at low temperatures. We demonstrate, however, that this behavior in the weakly doped regime is due to the unphysical branch of the Luttinger-Ward functional. On the other hand, our analysis shows that the NFL physics is realized at larger doping.
We investigate the Barkhausen noise in ferromagnetic thin films with zigzag domain walls. We use a cellular automaton model that describes the motion of a zigzag domain wall in an impure ferromagnetic quasi-two dimensional sample with in-plane uniaxial magnetization at zero temperature, driven by an external magnetic field. The main ingredients of this model are the dipolar spin-spin interactions and the anisotropy energy. A power law behavior with a cutoff is found for the probability distributions of size, duration and correlation length of the Barkhausen avalanches, and the critical exponents are in agreement with the available experiments. The link between the size and the duration of the avalanches is analyzed too, and a power law behavior is found for the average size of an avalanche as a function of its duration.
A phase field crystal model is used to investigate the mechanisms of formation and growth of early clusters in quenched/aged dilute binary alloys, a phenomenon typically outside the scope of molecular dynamics time scales. We show that formation of early sub-critical clusters is triggered by the stress relaxation effect of quenched-in defects, such as dislocations, on the energy barrier and the critical size for nucleation. In particular, through analysis of system energetics, we demonstrate that the growth of sub-critical clusters into overcritical sizes occurs due to the fact that highly strained areas in the lattice locally reduce or even eliminate the free energy barrier for a first-order transition.
We consider rotationally invariant states in $\mathbb{C}^{N_{1}}\ot \mathbb{C}^{N_{2}}$ Hilbert space with even $N_{1}\geq 4$ and arbitrary $N_{2}\geq N_{1}$, and show that in such case there always exist states which are inseparable and remain positive after partial transposition, and thus the PPT criterion does not suffice to prove separability of such systems. We demonstrate it applying a map developed recently by Breuer [H.-P. Breuer, Phys. Rev. Lett {\bf 97}, 080501 (2006)] to states that remain invariant after partial time reversal.
A Markovian single-server queue is studied in an interactive random environment. The arrival and service rates of the queue depend on the environment, while the transition dynamics of the random environment depends on the queue length. We consider in detail two types of Markov random environments: a pure jump process and a reflected jump-diffusion. In both cases, the joint dynamics is constructed so that the stationary distribution can be explicitly found in a simple form (weighted geometric). We also derive an explicit estimate for exponential rate of convergence to the stationary distribution via coupling.
We present an investigation of the polar crown prominence that erupted on 2012 March 12. This prominence is observed at the southeast limb by SDO/AIA (end-on view) and displays a quasi vertical-thread structure. Bright U-shape/horn-like structure is observed surrounding the upper portion of the prominence at 171 angstrom before the eruption and becomes more prominent during the eruption. The disk view of STEREO-B shows that this long prominence is composed of a series of vertical threads and displays a half loop-like structure during the eruption. We focus on the magnetic support of the prominence vertical threads by studying the structure and dynamics of the prominence before and during the eruption using observations from SDO and STEREO-B. We also construct a series of magnetic field models (sheared arcade model, twisted flux rope model, and unstable model with hyperbolic flux tube (HFT)). Various observational characteristics appear to be in favor of the twisted flux rope model. We find that the flux rope supporting the prominence enters the regime of torus instability at the onset of the fast rise phase, and signatures of reconnection (post-eruption arcade, new U-shape structure, rising blobs) appear about one hour later. During the eruption, AIA observes dark ribbons seen in absorption at 171 angstrom corresponding to the bright ribbons shown at 304 angstrom, which might be caused by the erupting filament material falling back along the newly reconfigured magnetic fields. Brightenings at the inner edge of the erupting prominence arcade are also observed in all AIA EUV channels, which might be caused by the heating due to energy released from reconnection below the rising prominence.
With the help of 3D MHD simulations we investigate the collapse and fragmentation of rotating turbulent prestellar core embedded into turbulent medium. The numerical code is based on a high resolution Godunov-type finite-difference scheme. Initial turbulence is represented by the ensemble of Alfven waves with power law spectrum. Our computations show that under realistic parameters two bound fragments can appear when the density increases at $100-10^3$ times. The distance between the fragments is about $0.1$ of the initial core radius and their orbital period is comparable to the initial free fall time of the core. These results can explain the origin of binary stars with separation $0.001-0.01$ pc in the Galaxy field.
Let $q$ be a prime power of the form $q=12c^2+4c+3$ with $c$ an arbitrary integer. In this paper we construct a difference family with parameters $(2q^2;q^2,q^2,q^2,q^2-1;2q^2-2)$ in ${\mathbb Z}_2\times ({\mathbb F}_{q^2},+)$. As a consequence, by applying the Wallis-Whiteman array, we obtain Hadamard matrices of order $4(2q^2+1)$ for the aforementioned $q$'s.
We initiate and develop a framework to handle the specialization morphism as a filtered morphism for the perverse, and for the perverse Leray filtration, on the cohomology with constructible coefficients of varieties and morphisms parameterized by a curve. As an application, we use this framework to carry out a detailed study of filtered specialization for the Hitchin morphisms associated with the compactification of Dolbeault moduli spaces in [de-2018].
This paper studies time changes of Brownian motions by positive continuous additive functionals. Under a certain regularity condition on the associated Revuz measures, we prove that the resolvents of the time-changed Brownian motions are locally H\"{o}lder continuous in the spatial components. We also obtain lower bounds for the indice of the H\"{o}lder continuity.
(abridged)We present the observations of the pair of interacting galaxies NGC6285/86 carried out with the 6m SAO RAS telescope by using 1D and 2D spectroscopy. The observations of NGC6286 with a long-slit spectrograph (UAGS) near the H-alpha line revealed the rotation of the gaseous disk around an axis offset by 5''-7'' from the photometric center and a luminous gas at a distance up to 9 kpc in a direction perpendicular to the galactic plane. Using a multipupil fiber spectrograph (MPFS), we constructed the velocity fields of the stellar and gaseous components in the central region of this galaxy, which proved to be similar. The similar line-of-sight velocities of the pair and the wide (5'x 5') field of view of the scanning Fabry-Perot interferometer (IFP) allowed us to obtain images in the H-alpha and [NII]6583 emission lines and in the continuum as well as to construct the line-of-sight velocity fields and to map the distribution of the [NII]6583/H-alpha ratio for both galaxies simultaneously. Based on these data, we studied the gas kinematics in the galaxies, constructed their rotation curves, and estimated their masses. We found no evidence of gas rotation around the major axis of NGC6286, which argues against the assumption that this galaxy has a forming polar ring. The IFP observations revealed an emission nebula around this galaxy with a structure characteristic for superwind galaxies. The large [NII]6583/H-alpha ratio, which suggests the collisional excitation of its emission, and the high infrared luminosity are additional arguments for the hypothesis of a superwind in the galaxy NGC 6286. A close encounter of the two galaxies was probably responsible for the starburst and the bipolar outflow of hot gas from the central region of the disk.
We consider QCD t\bar{t}\gamma and t\bar{t}Z production at hadron colliders as a tool to measure the tt\gamma and ttZ couplings. At the Tevatron it may be possible to perform a first, albeit not very precise, test of the tt\gamma vector and axial vector couplings in t\bar{t}\gamma production, provided that more than 5 fb^{-1} of integrated luminosity are accumulated. The t\bar{t}Z cross section at the Tevatron is too small to be observable. At the CERN Large Hadron Collider (LHC) it will be possible to probe the tt\gamma couplings at the few percent level, which approaches the precision which one hopes to achieve with a next-generation e^+e^- linear collider. The LHC's capability of associated QCD t\bar{t}V (V=\gamma, Z) production has the added advantage that the tt\gamma and ttZ couplings are not entangled. For an integrated luminosity of 300 fb^{-1}, the ttZ vector (axial vector) coupling can be determined with an uncertainty of 45-85% (15-20%), whereas the dimension-five dipole form factors can be measured with a precision of 50-55%. The achievable limits improve typically by a factor of 2-3 for the luminosity-upgraded (3 ab^{-1}) LHC.
For graphs $G$ and $H$, we write $G \overset{\mathrm{rb}}{\longrightarrow} H $ if any proper edge-coloring of $G$ contains a rainbow copy of $H$, i.e., a copy where no color appears more than once. Kohayakawa, Konstadinidis and the last author proved that the threshold for $G(n,p) \overset{\mathrm{rb}}{\longrightarrow}H$ is at most $n^{-1/m_2(H)}$. Previous results have matched the lower bound for this anti-Ramsey threshold for cycles and complete graphs with at least 5 vertices. Kohayakawa, Konstadinidis and the last author also presented an infinite family of graphs $H$ for which the anti-Ramsey threshold is asymptotically smaller than $n^{-1/m_2(H)}$. In this paper, we devise a framework that provides a richer and more complex family of such graphs that includes all the previously known examples.
We consider a $(4 + 2k)$ - dimensional Einstein-Gauss-Bonnet model with the cosmological $\Lambda$-term.   Exact stable solutions with three constant Hubble-like parameters in this model are obtained. In this case, the multidimensional cosmological model deals with three factor spaces: the external 3-dimensional "our" world and internal subspaces with dimensions $k_1 = k$ and $k_2=k$.
We present a technique that combines Zeeman Doppler imaging (ZDI) principles with a potential field mapping prescription in order to gain more information about the surface field topology of rapid rotators. This technique is an improvement on standard ZDI, which can sometimes suffer from the suppression of one vector component due to the effects of stellar inclination, poor phase coverage or lack of flux from dark areas on the surface. Defining a relationship beween the different vector components allows information from one component to compensate for reduced information in another. We present simulations demonstrating the capability of this technique and discuss its prospects.