ShantanuT01/DACTYL-Pretraining huggingface dataset:
Given any $\gamma>0$ and for $\eta=\{\eta_v\}_{v\in \mathbb Z^2}$ denoting a sample of the two-dimensional discrete Gaussian free field on $\mathbb Z^2$ pinned at the origin, we consider the random walk on~$\mathbb Z^2$ among random conductances where the conductance of edge $(u, v)$ is given by $\mathrm{e}^{\gamma(\eta_u + \eta_v)}$. We show that, for almost every~$\eta$, this random walk is recurrent and that, with probability tending to~1 as $T\to \infty$, the return probability at time~$2T$ decays as $T^{-1+o(1)}$. In addition, we prove a version of subdiffusive behavior by showing that the expected exit time from a ball of radius~$N$ scales as $N^{\psi(\gamma)+o(1)}$ with $\psi(\gamma)>2$ for all~$\gamma>0$. Our results rely on delicate control of the effective resistance for this random network. In particular, we show that the effective resistance between two vertices at Euclidean distance~$N$ behaves as~$N^{o(1)}$.
In this note, we classify smooth equivariant compactifications of $\mathbb{G}_a^n$ which are Fano manifolds with index $\geq n-2$.
Based on the current measurement of the neutron distribution radius ($R_n$) of $^{208}$Pb through the PREX-2 data, we re-visited the recently developed G3 and IOPB-I force parameter by fine-tuning some of the specific couplings within the relativistic mean-field model. The $\omega-\rho-$mesons coupling $\Lambda_{\omega}$ and the $\rho-$meson coupling $g_{\rho}$ are refitted to reproduce the experimental neutron radius of $^{208}$Pb without compromising the bulk properties of finite nuclei and infinite nuclear matter observables. The modified parameter sets are applied to calculate the gross properties of finite nuclei for a few double closed-shell nuclei and further used to obtain the various infinite nuclear matter observables at saturation. In addition to these, the force parameters are adopted to calculate the properties of high isospin asymmetry dense system such as neutron star matter and tested for the validation for the constraint from GW170817 binary neutron star merger events. The tuned forces are predicting relatively good results for finite and infinite nuclear matter systems and the current limitation on neutron radius from PREX-2. A systematic analysis using these two refitted parameter sets over the nuclear chat will be communicated shortly.
This work aims at investigating the characteristics of the molecular gas associated with the nebula G18.8+1.8, linked to the Wolf-Rayet star HD168206 (WR 113), and its relation to other components of its local interstellar medium.   We carried out molecular observations of the 12CO(J=1-0) and (J=2-1) lines with angular resolution of 44 arcsec and 22 arcsec using the SEST telescope. Complementary NANTEN data of the 12CO(1-0) line were also used. The dust emission was analyzed using Spitzer-IRAC images at 8.0 microns, and WISE data at 3.4, 4.6, and 12.0 microns.   The SEST data allowed us to identify a molecular component (Cloud 3) having velocities in the interval from ~ +30 to +36 km/s which is most probably linked to the nebula. Morphological and kinematical properties suggest that Cloud 3 constitute a wind-blown molecular half-shell, which expands around WR113. The ratio R_(2-1/1-0) and excitation temperatures indicate that the molecular gas is being irradiated by strong UV radiation. The location of the inner optical ring in the outer edge of Cloud 3 suggests that the stars SerOB2-1, -2, -3, -63, and -64 are responsables for the ionization of Cloud 3 and the inner ring nebula. A comparison between the spatial distribution of the molecular gas and the PAH emission at 8 $\mu$m indicates the existence of a PDR between the ionized and the molecular gas.   A search for candidate young stellar objects (YSOs) in the region around G18.8+1.8 based on available 2MASS, MSX, IRAS, and Spitzer-IRAC catalogs resulted in the detection of about sixty sources, some of them projected onto Cloud 3. Two small spots of clustered candidates YSOs are projected near the outer border of Cloud 3, although a triggered stellar formation scenario is doubtful.
We demonstrate a measure theoretical approach to the local regularity of weak supersolutions to elliptic and parabolic equations in divergence form. In the first part, we show that weak supersolutions become lower semicontinuous after redefinition on a set of measure zero. The proof relies on a general principle, i.e. the De Giorgi type lemma, which offers a unified approach for a wide class of elliptic and parabolic equations, including an anisotropic elliptic equation, the parabolic $p$-Laplace equation, and the porous medium equation. In the second part, we shall show that for parabolic problems the lower semicontinuous representative at an instant can be recovered pointwise from the "essliminf" of past times. We also show that it can be recovered by the limit of certain integral average of past times. The proof hinges on the expansion of positivity for weak supersolutions. Our results are structural properties of partial differential equations, independent of any kind of comparison principle.
Radio signals are delayed when propagating through plasma. This type of delay is frequency-dependent and is usually used for estimating the projected number density of electrons along the line of sight, called the dispersion measure. The dense and clumpy distribution of plasma can cause refractive deflections of radio signals, analogous to lensing effects. Similar to gravitational lensing, there are two contributions to the time delay effect in plasma lensing: a geometric delay, due to increased path length of the signal, and a dispersive delay due to the change of speed of light in a plasma medium. We show the delay time for two models of the plasma distribution, and point out that the estimated dispersion measure can be biased. Since the contribution of the geometric effect can be comparable to that of the dispersive delay, the bias in the measured dispersion measure can be dramatically large if plasma lensing effects are not taken into account when signals propagate through a high-density gradient clump of plasma.
We consider the gravitational recoil due to non-reflection-symmetric gravitational wave emission in the context of axisymmetric Robinson-Trautman spacetimes. We show that regular initial data evolve generically into a final configuration corresponding to a Schwarzschild black-hole moving with constant speed. For the case of (reflection-)symmetric initial configurations, the mass of the remnant black-hole and the total energy radiated away are completely determined by the initial data, allowing us to obtain analytical expressions for some recent numerical results that have been appeared in the literature. Moreover, by using the Galerkin spectral method to analyze the non-linear regime of the Robinson-Trautman equations, we show that the recoil velocity can be estimated with good accuracy from some asymmetry measures (namely the first odd moments) of the initial data. The extension for the non-axisymmetric case and the implications of our results for realistic situations involving head-on collision of two black holes are also discussed.
For smooth open toric varieties, we establish strong approximation off infinity with Brauer-Manin obstruction.
We use mergers of microstates to obtain the first smooth horizonless microstate solutions corresponding to a BPS three-charge black hole with a classically large horizon area. These microstates have very long throats, that become infinite in the classical limit; nevertheless, their curvature is everywhere small. Having a classically-infinite throat makes these microstates very similar to the typical microstates of this black hole. A rough CFT analysis confirms this intuition, and indicates a possible class of dual CFT microstates.   We also analyze the properties and the merging of microstates corresponding to zero-entropy BPS black holes and black rings. We find that these solutions have the same size as the horizon size of their classical counterparts, and we examine the changes of internal structure of these microstates during mergers.
The majority of cataclysmic variable (CV) stars contain a stochastic noise component in their light curves, commonly referred to as flickering. This can significantly affect the morphology of CV eclipses and increases the difficulty in obtaining accurate system parameters with reliable errors through eclipse modelling. Here we introduce a new approach to eclipse modelling, which models CV flickering with the help of Gaussian processes (GPs). A parameterised eclipse model - with an additional GP component - is simultaneously fit to 8 eclipses of the dwarf nova ASASSN-14ag and system parameters determined. We obtain a mass ratio $q$ = 0.149 $\pm$ 0.016 and inclination $i$ = 83.4 $^{+0.9}_{-0.6}$ $^{\circ}$. The white dwarf and donor masses were found to be $M_{w}$ = 0.63 $\pm$ 0.04 $M_{\odot}$ and $M_{d}$ = 0.093 $^{+0.015}_{-0.012}$ $M_{\odot}$, respectively. A white dwarf temperature $T_{w}$ = 14000 $^{+2200}_{-2000}$ K and distance $d$ = 146 $^{+24}_{-20}$ pc were determined through multicolour photometry. We find GPs to be an effective way of modelling flickering in CV light curves and plan to use this new eclipse modelling approach going forward.
Transmission and reflectivity of La_x Ca_14-x Cu_24 O_41 two-leg spin-1/2 ladders were measured in the mid-infrared regime between 500 and 12000 1/cm. This allows us to determine the optical conductivity sigma_1 directly and with high sensitivity. Here we show data for x=4 and 5 with the electrical field polarized parallel to the rungs (E||a) and to the legs (E||c). Three characteristic peaks are identified as magnetic excitations by comparison with two different theoretical calculations.
This paper is the continuation of our earlier considerations on cellular automata with Toom local rule (TCA) as the alternative to kinetic Ising systems. The arguments for TCA stationary states not being the equilibrium states are found in simulations.
We conducted a deep survey of resolved sub-systems among wide binaries with solar-type components within 67 pc from the Sun. Images of 61 stars in the K and H bands were obtained with the NICI adaptive-optics instrument on the 8-m Gemini-South telescope. Our maximum detectable magnitude difference is about 5mag and 7.8mag at 0.15" and 0.9" separations, respectively. This enables a complete census of sub-systems with stellar companions in the projected separation range from 5 to 100 AU. Out of 7 such companions found in our sample, only one was known previously. We determine that the fraction of sub-systems with projected separations above 5 AU is 0.12 +- 0.04 and that the distribution of their mass ratio is flat, with a power-law index 0.2 +- 0.5. Comparing this with the properties of closer spectroscopic sub-systems (separations below 1 AU), it appears that the mass-ratio distribution does not depend on the separation. The frequency of sub-systems in the separation ranges below 1 AU and between 5 and 100 AU is similar, about 0.15. Unbiased statistics of multiplicity higher than two, advanced by this work, provide constraints on star-formation theory.
Given a fixed product of non-isogenous abelian varieties at least one of which is general, we show how to construct complete families of indecomposable abelian varieties whose very general fiber is isogenous to the given product and whose connected monodromy group is a product of symplectic groups or is a unitary group. As a consequence, we show how to realize any product of symplectic groups of total rank $g$ as the connected monodromy group of a complete family of $g'$-dimensional abelian varieties for any $g'\ge g$. These methods also yield a construction of a new Kodaira fibration with fiber genus $4$.
We compare the observed spatial offsets of short gamma-ray bursts from their host galaxies with their predicted distributions, assuming that they originate in double neutron star binaries that form from field stars. We find that, for the majority of bursts, this model is sufficient to explain the observed offsets, although there is a trend towards larger offsets than predicted. One burst, GRB 060502B, has an offset that is clearly anomalous. We discuss possible reasons for the large offsets, including host galaxy misidentification, and suggest that some of the largest-offset bursts may originate in the merger of double neutron star binaries that form dynamically in the cores of globular clusters.
The evaluation, systematic analysis and numerical study of the semileptonic $\tau$-lepton decays with two mesons in the final state has been made in the frame of the standard model extended by right handed neutrinos. In the analysis, heavy-neutrino nondecoupling effects, finite quark masses, quark and meson mixings, finite widths of vector mesons, chiral symmetry breakings in vector-meson--pseudoscalar-meson vertices and effective Higgs-boson--pseudoscalar-meson couplings have been included. Numerical estimates reveal that the decays $\tau^-\to e^-\pi^-\pi^+$, $\tau^-\to e^-K^-K^+$ and $\tau^-\to e^-K^0\bar{K}^0$ have branching ratios of the order of $10^{-6}$, close to present-day experimental sensitivities.
We propose a twisted D=N=2 superspace formalism. The relation between the twisted super charges including the BRST charge, vector and pseudo scalar super charges and the N=2 spinor super charges is established. We claim that this relation is essentially related with the Dirac-K\"ahler fermion mechanism. We show that a fermionic bilinear form of twisted N=2 chiral and anti-chiral superfields is equivalent to the quantized version of BF theory with the Landau type gauge fixing while a bosonic bilinear form leads to the N=2 Wess-Zumino action. We then construct a Yang-Mills action described by the twisted N=2 chiral and vector superfields, and show that the action is equivalent to the twisted version of the D=N=2 super Yang-Mills action, previously obtained from the quantized generalized topological Yang-Mills action with instanton gauge fixing.
Materials with strong spin-orbit coupling (SOC) have in recent years become a subject of intense research due to their potential applications in spintronics and quantum information technology. In particular, in systems which break inversion symmetry, SOC facilitates the Rashba-Dresselhaus effect, leading to a lifting of spin degeneracy in the bulk and intricate spin textures of the Bloch wave functions. Here, by combining angular resolved photoemission (ARPES) and low temperature scanning tunneling microscopy (STM) measurements with relativistic first-principles band structure calculations, we examine the role of SOC in single crystals of noncentrosymmetric BiPd. We report the detection of several Dirac surface states, one of which exhibits an extremely large spin splitting. Unlike the surface states in inversion-symmetric systems, the Dirac surface states of BiPd have completely different properties at opposite faces of the crystal and are not trivially linked by symmetry. The spin-splitting of the surface states exhibits a strong anisotropy by itself, which can be linked to the low in-plane symmetry of the surface termination.
Searching for black hole echo signals with gravitational waves provides a means of probing the near-horizon regime of these objects. We demonstrate a pipeline to efficiently search for these signals in gravitational wave data and calculate model selection probabilities between signal and no-signal hypotheses. As an example of its use we calculate Bayes factors for the Abedi-Dykaar-Afshordi (ADA) model on events in LIGO's first observing run and compare to existing results in the literature. We discuss the benefits of using a full likelihood exploration over existing search methods that used template banks and calculated p-values. We use the waveforms of ADA, although the method is easily extendable to other waveforms. With these waveforms we are able to demonstrate a range of echo amplitudes that is already is ruled out by the data.
I give a brief overview of fault-tolerant quantum computation, with an emphasis on recent work and open questions.
Oftentimes, patterns can be represented through different modalities. For example, leaf data can be in the form of images or contours. Handwritten characters can also be either online or offline. To exploit this fact, we propose the use of self-augmentation and combine it with multi-modal feature embedding. In order to take advantage of the complementary information from the different modalities, the self-augmented multi-modal feature embedding employs a shared feature space. Through experimental results on classification with online handwriting and leaf images, we demonstrate that the proposed method can create effective embeddings.
The long charge carrier lifetime of the hybrid organic-inorganic perovskites (HOIPs) is the key for their remarkable performance as a solar cell material. The microscopic mechanism for the long lifetime is still in debate. Here, by using muon spin relaxation technique that probes the fluctuation of local magnetic fields, we show that the muon depolarization rate ($\Delta$) of a prototype HOIP methylammonium lead iodide (MAPbI$_3$) shows a sharp decrease with increasing temperature in two steps above 120 K and 190 K across the structural transition from orthorhombic to tetragonal structure at 162 K. Our analysis shows that the reduction of $\Delta$ is quantitatively in agreement with the expected behavior due to the rapid development of MA jumping rotation around the $C_3$ and $C_4$ symmetry axes. Our results provide direct evidence for the intimate relation between the rotation of the electric dipoles of MA molecules and the charge carrier lifetime in HOIPs.
A relativistic collisionless shock propagating into an unmagnetized medium leaves behind a strong large-scale magnetic field. This seems to follow from two assumptions: (i) GRB afterglows are explained by synchrotron emission of a relativistic shock, (ii) magnetic field can't exist on microscopic scales only, it would decay by phase space mixing. Assumption (i) is generally accepted because of an apparent success of the shock synchrotron phenomenological model of GRB afterglow. Assumption (ii) is confirmed in this work by a low-dimensional numerical simulation. One may hypothesize that relativistic shock velocities are not essential for the magnetic field generation, and that all collisionless shocks propagating into an unmagnetized medium generate strong large-scale magnetic fields. If this hypothesis is true, the first cosmical magnetic fields could have been generated in shocks of the first virialized objects.
On a metric graph we introduce the notion of a free divisor as a replacement for the notion of a base point free complete linear system on a curve. By means of an example we show that the Clifford inequality is the only obstruction for the existence of very special free divisors on a graph. This is different from the situation of base point free linear systems on curves. It gives rise to the existence of many types of divisors on graphs that cannot be lifted to curves maintaining the rank and it also shows that classifications made for linear systems of some fixed small positive Clifford index do not hold (exactly the same) on graphs.
In the paper, high temperature induced phase transformation in chemically grown CdO thin films has been demonstrated whereas their corresponding electronic origin is further investigated by density functional theory. In particular, cubic rocksalt to hexagonal wurtzite PT in 900 degree centigrade annealed CdO thin films is confirmed by Xray diffraction , consistent with High Resolution Transmission Electron Microscopy. Such high temperature treatment also leads to significant enhancement in optical band gap from 2.2 to 3.2 eV as manifested by UV-Visible spectroscopy. Moreover, atomic force microscopy and scanning electron microscopy clearly evidence the structural evolution via formation of nano-sheet network in wurtzite phased CdO films. Furthermore, Xray Absorption spectra at oxygen k edge revealed a notable shift in inflection point of absorption edge while X-ray Photoelectron spectroscopy of Cd 3d and O 1s suggested the gradual reduction in CdO2 phase with increasing annealing temperature. In addition, different complementary techniques including Rutherford Backscattering, Raman Spectroscopy have also been exploited to understand the aforementioned PT and their structural correlation. Finally, molecular dynamics simulation along with density functional theory calculations suggest that symmetry modification at Brillouin zone boundary provides a succinct signature for such PT in CdO thin film.
A population of unidentified gamma-ray sources is forming a structure resembling a halo around the Galactic center. These sources are highly variable, and hence they should be associated with compact objects. Microquasars are objects undergoing accretion with relativistic jets; if such an object has a low-mass, evolved, donor star, it might be found in the Galactic halo. If these low-mass microquasars can generate detectable gamma-ray emission, then they are natural candidates to account for the halo high-energy sources. We aim to construct models for high-energy emission of low-mass microquasars, which could produce a significant luminosity in the gamma-ray domain. We consider that a significant fraction of the relativistic particles in the jets of low-mass microquasars are protons and then we study the production of high-energy emission through proton synchrotron radiation and photopion production. Photopair production and leptonic processes are considered as well. We compute a number of specific models with different parameters to explore the possibilities of this scenario.} We find that important luminosities, in the range of $10^{34}-10^{37}$ erg s$^{-1}$, can be achieved by proton synchrotron radiation in the Gamma-Ray Large Area Space Telescope (GLAST) energy range, and lower, but still significant luminosities at higher energies for some models. We conclude that the "proton microquasar" model offers a very interesting alternative to account for the halo gamma-ray sources and presents a variety of predictions that might be tested in the near future by instruments like GLAST, the High-Energy Stereoscopic System II (HESS II), the Major Atmospheric Gamma-ray Imaging Cherenkov telescope II (MAGIC II), and neutrino telescopes like IceCube.
We study the Higgs sector of supersymmetric models containing two Higgs doublets with a light MSSM-like CP odd Higgs, $m_A \lesssim 10$ GeV, and $\tan \beta \lesssim 2.5$. In this scenario all Higgses resulting from two Higgs doublets: light and heavy CP even Higgses, $h$ and $H$, the CP odd Higgs, $A$, and the charged Higgs, $H^\pm$, could have been produced at LEP or the Tevatron, but would have escaped detection because they decay in modes that have not been searched for or the experiments are not sensitive to. Especially $H \to ZA$ and $H^\pm \to W^{\pm \star} A$ with $A \to c \bar c, \tau^+ \tau^-$ present an opportunity to discover some of the Higgses at LEP, the Tevatron and also at B factories. In addition, the $2.8 \sigma$ excess of the branching ratio $W \to \tau \nu$ with respect to the other leptons measured at LEP correlates well with the existence of the charged Higgs with properties typical for this scenario. Dominant $\tau$- and $c$-rich decay products of all Higgses require modified strategies for their discovery at the LHC.