ShantanuT01/DACTYL-Pretraining huggingface dataset:
We establish a correspondence between toroidal compactifications of M-theory and del Pezzo surfaces. M-theory on T^k corresponds to P^2 blown up at k generic points; Type IIB corresponds to P^1\times P^1. The moduli of compactifications of M-theory on rectangular tori are mapped to Kahler moduli of del Pezzo surfaces.The U-duality group of M-theory corresponds to a group of classical symmetries of the del Pezzo represented by global diffeomorphisms. The half-BPS brane charges of M-theory correspond to spheres in the del Pezzo, and their tension to the exponentiated volume of the corresponding spheres. The electric/magnetic pairing of branes is determined by the condition that the union of the corresponding spheres represent the anticanonical class of the del Pezzo. The condition that a pair of half-BPS states form a bound state is mapped to a condition on the intersection of the corresponding spheres. We present some speculations about the meaning of this duality.
ALMA [CII] line and continuum observations of five redshift z>6 quasars are presented. This sample was selected to probe lower black hole mass quasars than most previous studies. We find a wide dispersion in properties with CFHQS J0216-0455, a low-luminosity quasar with absolute magnitude M_1450=-22.2, remaining undetected implying a limit on the star formation rate in the host galaxy of <10 solar masses per year, whereas other host galaxies have star formation rates up to hundreds of solar masses per year. Two other quasars have particularly interesting properties. VIMOS2911 is one of the least luminous z>6 quasars known with M_1450=-23.1, yet its host galaxy is experiencing a very powerful starburst. PSO J167-13 has a broad and luminous [CII] line and a neighbouring galaxy a projected distance of 5kpc away that is also detected in the [CII] line and continuum. Combining with similar observations from the literature, we study the ratio of [CII] line to far-infrared luminosity finding this ratio increases at high-redshift at a fixed far-infrared luminosity, likely due to lower dust content, lower metallicity and/or higher gas masses. We compile a sample of 21 high-redshift quasars with dynamical masses and investigate the relationship between black hole mass and dynamical mass. The new observations presented here reveal dynamical masses consistent with the relationship defined by local galaxies. However, the full sample shows a very wide scatter across the black hole mass - dynamical mass plane, whereas both the local relationship and simulations of high-redshift quasars show a much lower dispersion in dynamical mass.
The variation of total nuclear level densities (NLDs) and level density parameters with proton number $(Z)$ are studied around the $\beta$-stable isotope, $Z_{0}$, for a given mass number. We perform our analysis for a mass range $A=40$ to 180 using the NLDs from popularly used databases obtained with the single-particle energies from two different microsopic mass-models. These NLDs which include microscopic structural effects such as collective enhancement, pairing and shell corrections, do not exhibit inverted parabolic trend with a strong peak at $Z_{0}$ as predicted earlier. We also compute the NLDs using the single-particle energies from macroscopic-microscopic mass-model. Once the collective and pairing effects are ignored, the inverted parabolic trends of NLDs and the corresponding level density parameters become somewhat visible. Nevertheless, the factor that governs the $(Z-Z_{0})$ dependence of the level density parameter, leading to the inverted parabolic trend, is found to be smaller by an order of magnitude. We further find that the $(Z-Z_{0})$ dependence of NLDs is quite sensitive to the shell effects.
Supernova 1987A offers a unique opportunity to study an evolving supernova in unprecedented detail over several decades. The X-ray emission is dominated by interactions between the ejecta and the circumstellar medium, primarily the equatorial ring (ER). We analyze 3.3 Ms of NuSTAR data obtained between 2012 and 2020, and two decades of XMM-Newton data. Since ${\sim}$2013, the flux below 2 keV has declined, the 3-8 keV flux has increased, but has started to flatten, and the emission above 10 keV has remained nearly constant. The spectra are well described by a model with three thermal shock components. Two components at 0.3 and 0.9 keV are associated with dense clumps in the ER, and a 4 keV component may be a combination of emission from diffuse gas in the ER and the surrounding low-density H II region. We disfavor models that involve non-thermal X-ray emission and place constraints on non-thermal components, but cannot firmly exclude an underlying power law. Radioactive lines show a $^{44}$Ti redshift of $670^{+520}_{-380}$ km s$^{-1}$, $^{44}$Ti mass of $1.73_{-0.29}^{+0.27}\times{}10^{-4}$ solar masses, and $^{55}$Fe mass of $<4.2\times{}10^{-4}$ solar masses. The 35-65 keV luminosity limit on the compact object is $2\times{}10^{34}$ erg s$^{-1}$, and $<15$% of the 10-20 keV flux is pulsed. Considering previous limits, we conclude that there are currently no indications of a compact object, aside from a possible hint of dust heated by a neutron star in recent ALMA images.
Let $X$ be a fixed projective scheme which is flat over a base scheme $S$. The association taking a quasi-projective $S$-scheme $Y$ to the scheme parametrizing $S$-morphisms from $X$ to $Y$ is functorial. We prove that this functor preserves limits, and both open and closed immersions. As an application, we determine a partition of schemes parametrizing rational curves on the blow-ups of projective spaces at finitely many points. We compute the dimensions of its components containing rational curves outside the exceptional divisor and the ones strictly contained in it. Furthermore, we provide an upper bound for the dimension of the irreducible components intersecting the exceptional divisors properly.
We study prospects of constraining the primordial magnetic field (PMF) and its evolution during the dark ages and cosmic dawn in light of EDGES 21-cm signal. Our analysis has been carried out on a `colder IGM' background which is one of the promising avenues to interpret the EDGES signal. We consider the dark matter-baryon interactions for the excess cooling. We find that the colder IGM suppresses both the residual free electron fraction and the coupling coefficient between the ionised and neutral components. The Compton heating also gets affected in colder IGM background. Consequently, the IGM heating rate due to the PMF enhances compared to the standard scenario. Thus, a significant fraction of the magnetic energy, for $B_0 \lesssim 0.5 \, {\rm nG}$, gets transferred to the IGM and the magnetic field decays at a much faster rate compared to the simple $(1+z)^2$ scaling during the dark ages and cosmic dawn. This low PMF is an unlikely candidate for explaining the rise of the EDGES absorption signal at lower redshift. We also see that the PMF and DM-baryon interaction together introduces a plateau-like feature in the redshift evolution of the IGM temperature. We find that the upper limit on the PMF depends on the underlying DM-baryon interaction. Higher PMF can be allowed when the interaction cross-section is higher and/or the DM particle mass is lower. Our study shows that the PMF with $B_0$ up to $\sim 0.4 \, {\rm nG}$, which is ruled out in the standard model, can be allowed if DM-baryon interaction with suitable cross-section and DM mass is considered.
The fusion of two interacting heavy ions traditionally has been interpreted in terms of the penetration of the projectile into the target. Observed rates well below the Coulomb barrier are considerably lower than estimates obtained from penetration factors. One approach in the analysis of the data invokes coupling to non-elastic channels in the scattering as the source of the depletion. Another is to analyze those data in terms of tunneling in semi-classical models, with the observed depletion being taken as evidence of a ``friction'' under the barrier. A complementary approach is to consider such tunneling in terms of a fully quantal model. We investigate tunneling with both one-dimensional and three-dimensional models in a fully quantal approach to investigate possible sources for such a friction. We find that the observed phenomenon may not be explained by friction. However, we find that under certain conditions tunneling may be enhanced or diminished by up to 50%, which finds analogy with observation, without the invocation of a friction under the barrier.
The effects of a nonsimply connected spacetime with the topology of $S^{1}\times R^{3}$ in the vacua of QED and gauged-NJL theories are investigated. It is shown that the polarization effects of twisted and untwisted fermions in QED are equivalent, once the corresponding stable vacuum solution of each fermion class is taken into account. The photon propagation in QED is found to be anisotropic and characterized by several massive photon modes and a superluminal transverse mode. At small compactification radius the masses of the massive modes increase as the inverse of the radius, while the massless photon mode has a superluminal velocity that increases logarithmically with that distance. At low energies the photon masses lead to an effective confinement of the gauge fields into a $(2+1)-$dimensional manifold transverse to the compactified direction. In the gauged-NJL model, it is shown that for both twisted and untwisted fermions, the smaller the compactification radius, the larger the critical four-fermion coupling needed to generate a fermion-antifermion chiral symmetry breaking condensate.
Some low surface brightness galaxies are known to have extremely thin stellar disks with the vertical to planar axes ratio 0.1 or less, often referred to as superthin disks. Although their existence is known for over three decades, the physical origin for the thin distribution is not understood. We model the stellar thickness for a two-component (gravitationally coupled stars and gas) disk embedded in a dark matter halo, for a superthin galaxy UGC 7321 which has a dense, compact halo, and compare with a typical dwarf galaxy HoII which has a non-compact halo. We show that while the presence of gas does constrain the disk thickness, it is the compact dark matter halo which plays the decisive role in determining the superthin disk distribution in low-mass disks. Thus the compact dark matter halo significantly affects the disk structure and this could be important for the early evolution of galaxies.
Riemann conjectured that all the zeros of the Riemann $\Xi$-function are real, which is now known as the Riemann Hypothesis (RH). In this article we introduce the study of the zeros of the truncated sums $\Xi_N(z)$ in Riemann's uniformly convergent infinite series expansion of $\Xi (z)$ involving incomplete gamma functions. We conjecture that when the zeros of $\Xi_N (z)$ in the first quadrant of the complex plane are listed by increasing real part, their imaginary parts are monotone nondecreasing. We show how this conjecture implies the RH, and discuss some computational evidence for this and other related conjectures.
Stochastic averaging for a class of backward stochastic differential equations driven by both standard and fractional Brownian motions (SFrBSDEs in short), is investigated. An averaged SFrBSDEs for the original SFrBSDEs is proposed, and their solutions are quantitatively compared. Under some appropriate assumptions, the solutions to original systems can be approximated by the solutions to averaged stochastic systems in the sense of mean square and also in probability.
We studied a circular-ribbon flare, SOL2014-12-17T04:51, with emphasis on its thermal evolution as determined by the Differential Emission Measure (DEM) inversion analysis of the extreme ultraviolet (EUV) images of the Atmospheric Imaging Assembly (AIA) instrument onboard the Solar Dynamics Observatory (SDO). Both temperature and emission measure start to rise much earlier than the flare, along with an eruption and formation of a hot halo over the fan structure. In the main flare phase, another set of ribbons forms inside the circular ribbon, and expands as expected for ribbons at the footpoints of a postflare arcade. An additional heating event further extends the decay phase, which is also characteristic of some eruptive flares. The basic magnetic configuration appears to be a fan-spine topology, rooted in a minority-polarity patch surrounded by majority-polarity flux. We suggest that reconnection at the null point begins well before the impulsive phase, when the null is distorted into a breakout current sheet, and that both flare and breakout reconnection are necessary in order to explain the subsequent local thermal evolution and the eruptive activities in this confined magnetic structure. Using local DEMs, we found a postflare temperature increase inside the fan surface, indicating that the so-called EUV late phase is due to continued heating in the flare loops.
Gessel and Sagan investigated the Tutte polynomial, $T(x,y)$ using depth first search, and applied their techniques to show that the number of acyclic partial orientations of a graph is $2^gT(3,1/2)$. We provide a short deletion-contraction proof of this result and demonstrate that dually, the number of strongly connected partial orientations is $2^{n-1}T(1/2,3)$. We then prove that the number of partial orientations modulo cycle reversals is $2^gT(3,1)$ and the number of partial orientations modulo cut reversals is $2^{n-1}T(1,3)$. To prove these results, we introduce cut and cycle minimal partial orientations which provide distinguished representatives for partial orientations modulo cut and cycle reversals. These extend classes of total orientations introduced by Gioan, and Greene and Zaslavksy, and we highlight a close connection with graphic and cographic Lawrence ideals. We conclude with edge chromatic generalizations of the quantities presented, which allow for a new interpretation of the reliability polynomial for all probabilities, $p$ with $0 < p <1/2$.
An inconsistency was found in the equations used to calculate the variance of the quadrature fluctuations of a field propagating through a medium demonstrating electromagnetically induced transparency (EIT). The decoherence term used in our original paper introduces inconsistency under weak probe approximation. In this erratum we give the Bloch equations with the correct dephasing terms. The conclusions of the original paper remain the same. Both entanglement and squeezing can be delayed and preserved using EIT without adding noise when the decoherence rate is small.
We present results obtained from a Suzaku observation of the accretion powered X-ray pulsar GX 1+4. Broad-band continuum spectrum of the pulsar was found to be better described by a simple model consisting of a blackbody component and an exponential cutoff power-law than the previously used compTT continuum model. Though the pulse profile had a sharp dip in soft X-rays ($<$10 keV), phase-resolved spectroscopy confirmed that the dimming was not due to increase in photoelectric absorption. Phase-sliced spectral analysis showed the presence of a significant spectral modulation beyond 10 keV except for the dip phase. A search for the presence of cyclotron resonance scattering feature in the Suzaku spectra yielded a negative result. Iron K-shell (K$_\alpha$ and K$_\beta$) emission lines from nearly neutral iron ions ($<$Fe III) were clearly detected in the source spectrum. A significant K$_\alpha$ emission line from almost neutral Ni atoms was detected for the first time in this source. We estimated the iron abundance of $\sim$80 % of the solar value and Ni/Fe abundance ratio of about two times of the solar value. We searched for a iron Ly$_\alpha$ emission line and found a significant improvement in the spectral fitting by inclusion of this line.
In this article, the stability of a general class of spherically symmetric thin-shell wormholes is studied under perturbations preserving the symmetry. For this purpose, the equation of state at the throat is linearized around the static solutions. The formalism presented here is applied to dilaton wormholes and it is found that there is a smaller range of possible stable configurations for them than in the case of Reissner-Nordstrom wormholes with the same charge.
We compute the one-loop threshold corrections to hard supersymmetric relations involving gauge and gaugino couplings for the case of a Split-SUSY-like spectrum with moderate splitting. We show that these contributions are small, however in principle they will typically have to be taken into account if the heavy scalar sector is below 100 TeV and if one reaches, at future linear colliders, the precision that is necessary to perform this kind of measurements.
Two-dimensional (2D) intrinsic ferromagnetic semiconductors are expected to stand out in the spintronic field. Recently, the monolayer VI$_{3}$ has been experimentally synthesized but the weak ferromagnetism and low Curie temperature ($T_C$) limit its potential application. Here we report that the Janus structure can elevate the $T_C$ to 240 K. And it is discussed that the reason for high $T_C$ in Janus structure originates from the lower virtual exchange gap between $t_{2g}$ and $e_{g}$ states of nearest-neighbor V atoms. Besides, $T_C$ can be further substantially enhanced by tensile strain due to the increasing ferromagnetism driven by rapidly quenched direct exchange interaction. Our work supports a feasible approach to enhance Curie temperature of monolayer VI$_{3}$ and unveils novel stable intrinsic FM semiconductors for realistic applications in spintronics.
We report the detection of the ground state rotational emission of ammonia, ortho-NH$_3$ $(J_K=1_0\rightarrow0_0)$ in a gravitationally lensed, intrinsically hyperluminous, star-bursting galaxy at $z=2.6$. The integrated line profile is consistent with other molecular and atomic emission lines which have resolved kinematics well-modelled by a 5 kpc-diametre rotating disc. This implies that the gas responsible for NH$_3$ emission is broadly tracing the global molecular reservoir, but likely distributed in pockets of high density ($n\gtrsim5\times10^4$ cm$^{-3}$). With a luminosity of $2.8\times10^{6}$ $L_\odot$, the NH$_3$ emission represents $2.5\times10^{-7}$ of the total infrared luminosity of the galaxy, comparable to the ratio observed in the Kleinmann-Low nebula in Orion and consistent with sites of massive star formation in the Milky Way. If $L_{\rm NH_3}/L_{\rm IR}$ serves as a proxy for the 'mode' of star formation, this hints that the nature of star formation in extreme starbursts in the early Universe is similar to that of Galactic star-forming regions, with a large fraction of the cold interstellar medium in this state, plausibly driven by a storm of violent disc instabilities in the gas-dominated disc. This supports the 'full of Orions' picture of star formation in the most extreme galaxies seen close to the peak epoch of stellar mass assembly.
In this paper, we will first show that, the homogeneous polynomials which satisfy the Jacobian condition are injective on the lines that pass through the origin. Secondly, we will show that $F$ and $G'$ are paired, where $F$ is a Druzkowski map and $G'$ is a cubic homogeneous polynomial which related to $F$. Finally, we will find a more exactly bound for the degree of $F^{-1}$, where $F$ is a invertible map.
Coherence times for superconducting qubits have greatly improved over time. Moreover, small logical qubit architectures using engineered dissipation have shown great promise for further improvements in the coherence of a logical qubit manifold comprised of few physical qubits. Nevertheless, optimal working parameters for small logical qubits are generally not well understood. This work presents several approaches to finding preferential parameter configurations by looking at three different cases of increasing complexity. We begin by looking at state stabilization of a single qubit using dissipation via coupling to a lossy object. We look at the limiting factors in this approach to error correction, and how we address those by numerically optimizing the parametric coupling strength with the lossy object having an effective time-varying dissipation rate---we call this a pulse-reset cycle. We then translate this approach to more efficient state stabilization to an abstracted three-qubit flip code, and end by looking at the Very Small Logical Qubit (VSLQ). By using these techniques, we can further increase logical state lifetimes for different architectures. We show significant advantages in using a pulse-reset cycle over numerically optimized, fixed parameter spaces.
Real-time instrument tracking is a crucial requirement for various computer-assisted interventions. In order to overcome problems such as specular reflections and motion blur, we propose a novel method that takes advantage of the interdependency between localization and segmentation of the surgical tool. In particular, we reformulate the 2D instrument pose estimation as heatmap regression and thereby enable a concurrent, robust and near real-time regression of both tasks via deep learning. As demonstrated by our experimental results, this modeling leads to a significantly improved performance than directly regressing the tool position and allows our method to outperform the state of the art on a Retinal Microsurgery benchmark and the MICCAI EndoVis Challenge 2015.
In affine models, both the martingale property of stochastic exponentials and non-explosion of affine processes is characterized in terms of minimality of solutions to a system of generalized Riccati differential equations. This is the final improvement of previous results by Duffie, Filipovic and Schachermayer (2003), Mayerhofer, Muhle-Karbe and Smirnov (2011) and Keller-Ressel and Mayerhofer (2015) for processes on canonical state spaces.
We study a Dirichlet boundary value problem associated to an anisotropic differential operator on a smooth bounded of $\Bbb R^N$. Our main result establishes the existence of at least two different non-negative solutions, provided a certain parameter lies in a certain range. Our approach relies on the variable exponent theory of generalized Lebesgue-Sobolev spaces, combined with adequate variational methods and a variant of Mountain Pass lemma.
In [Curtin and Pourgholi, A group sum inequality and its application to power graphs, J. Algebraic Combinatorics, 2014], it is proved that among all directed power graphs of groups of a given order $ n $, the directed power graph of cyclic group of order $ n $ has the maximum number of undirected edges. In this paper, we continue their work and we determine a non-cyclic nilpotent group of an odd order $ n $ whose directed power graph has the maximum number of undirected edges among all non-cyclic nilpotent groups of order $n$.   We next determine non-cyclic $p$-groups whose undirected power graphs have the maximum number of edges among all groups of the same order.
The extra-dimensional model in which the bulk geometry is a slice of anti-de Sitter space is a particularly attractive extension of the Standard Model as it allows to address the gauge hierarchy problem, as well as the mass hierarchy prevailing among fermions. However, to allow for the masses of the Kaluza-Klein excitations of the known particles to be near the Terascale without conflicting with the high-precision electroweak data, one needs to promote the gauge symmetry to a left-right structure SU(2)_L x SU(2)_R x U(1) which incorporates a new quark b', the SU(2)_R doublet partner of the heavy top quark. We show that this new quark will contribute to the main production process of Higgs bosons at the LHC: the gluon-gluon fusion mechanism which proceeds through heavy quark triangular loops. In most of the parameter space in which the measured values of the heavy t,b quark masses are reproduced, the gg -> Higgs production cross section is significantly altered, even if the b' quark is too heavy to be directly accessible, m_b' > ~1TeV. Finally, we briefly discuss the new Higgs production and decay channels involving the b' quark.