ShantanuT01/DACTYL-Pretraining huggingface dataset:
We revisit the longstanding question of whether first brightest cluster galaxies are statistically drawn from the same distribution as other cluster galaxies or are "special", using the new non-parametric, empirically based model presented in Vale&Ostriker (2006) for associating galaxy luminosity with halo/subhalo masses. We introduce scatter in galaxy luminosity at fixed halo mass into this model, building a conditional luminosity function (CLF) by considering two possible models: a simple lognormal and a model based on the distribution of concentration in haloes of a given mass. We show that this model naturally allows an identification of halo/subhalo systems with groups and clusters of galaxies, giving rise to a clear central/satellite galaxy distinction.   We then use these results to build up the dependence of brightest cluster galaxy (BCG) magnitudes on cluster luminosity, focusing on two statistical indicators, the dispersion in BCG magnitude and the magnitude difference between first and second brightest galaxies. We compare our results with two simple models for BCGs: a statistical hypothesis that the BCGs are drawn from a universal distribution, and a cannibalism scenario merging two galaxies from this distribution. The statistical model is known to fail from work as far back as Tremaine&Richstone (1977). We show that neither the statistical model nor the simplest possibility of cannibalism provide a good match for observations. Our CLF models both give similar results, in good agreement with observations. Specifically, we find <m_1> between -25 and -25.5 in the K-band, sigma(m_1)~0.25 and <Delta_12> between 0.6 and 0.8, for cluster luminosities in the range of 10^12 to 10^13 h^-2 L_sun.
Flares, energetic eruptions on the surfaces of stars, are an unmistakable manifestation of magnetically driven emission. Their occurrence rates and energy distributions trace stellar characteristics such as mass and age. But before flares can be used to constrain stellar properties, the flaring-age-mass relation requires proper calibration. This work sets out to quantify flaring activity of independently age-dated main sequence stars for a broad range of spectral types using optical light curves obtained by the Kepler satellite. Drawing from the complete K2 archive, we searched 3435 $\sim 80$ day long light curves of 2111 open cluster members for flares using the open-source software packages K2SC to remove instrumental and astrophysical variability from K2 light curves, and AltaiPony to search and characterize the flare candidates. We confirmed a total of 3844 flares on high probability open cluster members with ages from zero age main sequence (Pleiades) to 3.6 Gyr (M67). We extended the mass range probed in the first study of this series to span from Sun-like stars to mid-M dwarfs. We added the Hyades (690 Myr) to the sample as a comparison cluster to Praesepe (750 Myr), the 2.6 Gyr old Ruprecht 147, and several hundred light curves from the late K2 Campaigns in the remaining clusters. The flare energy distribution was similar in the entire parameter space, following a power law relation with exponent $\alpha\approx 1.84-2.39$. The flaring rates declined with age, and declined faster for higher mass stars. We found evidence that a rapid decline in flaring activity occurred in M1-M2 dwarfs around Hyades/Praesepe age, when these stars spun down to rotation periods of about 10 days, while higher mass stars had already transitioned to lower flaring rates, and lower mass stars still resided in the saturated activity regime. (abridged)
We have studied the magnetic field dependence of the ground state energies in a small Si quantum dot. At low fields the first five electrons are added in a spin-up -- spin-down sequence minimizing the total spin. This sequence does not hold for larger number of electrons in the dot. At high fields the dot undergoes transitions between states with different spins driven entirely by Zeeman energy. We identify some features that can be attributed to transitions between different spin configurations preserving the total spin of the dot. For a few peaks we observed large linear shifts that correspond to the change of the spin of the dot by 3/2. Such a change requires that an electron in the dot flips its spin during every tunneling event.
ACO2163 is one of the hottest (mean $kT=12-15.5$ keV) and extremely X-ray overluminous merging galaxy clusters which is located at $z=0.203$. The cluster hosts one of the largest giant radio halos which are observed in most of the merging clusters, and a candidate radio relic. Recently, three merger shock fronts were detected in this cluster, explaining its extreme temperature and complex structure. Furthermore, previous XMM-Newton and Chandra observations hinted at the presence of a shock front that is associated with the gas `bullet' crossing the main cluster in the west-ward direction, and which heated the intra-cluster medium, leading to adiabatic compression of the gas behind the 'bullet'. The goal of this paper is to report on the detection of this shock front as revealed by the temperature discontinuity in the X-ray XMM-Newton image, and the edge in the Very Large Array (VLA) radio image. We also report on the detection of a relic source in the north-eastern region of the radio halo in the KAT-7 data, confirming the presence of an extended relic in this cluster. The brightness edge in the X-rays corresponds to a shock front with a Mach number $M= 2.2\pm0.3$, at a distance of 0.2 Mpc from the cluster centre. An estimate from the luminosity jump gives $M=1.9\pm0.4$. We consider a simple explanation for the electrons at the shock front, and for the observed discrepancy between the average spectral index of the radio halo emission and that predicted by the $M=2.2$ shock which precedes the 'bullet'.
Autonomous driving technology is developing rapidly and nowadays first autonomous rides are being provided in city areas. This requires the highest standards for the safety and reliability of the technology. Motion prediction part of the general self-driving pipeline plays a crucial role in providing these qualities. In this work we present one of the solutions for Waymo Motion Prediction Challenge 2022 based on MultiPath++ ranked the 3rd as of May, 26 2022. Our source code is publicly available on GitHub.
We have studied experimentally the low temperature conductivity of mesoscopic size InAs/GaSb quantum well Hall bar devices in the inverted regime. Using a pair of electrostatic gates we were able to move the Fermi level into the electron-hole hybridization state, and observe a mini gap. Temperature dependence of the conductivity in the gap shows residual conductivity, which can be consistently explained by the contributions from the free as well as the hybridized carriers in the presence of impurity scattering, as proposed by Naveh and Laikhtman [Euro. Phys. Lett., 55, 545-551 (2001)]. Experimental implications for the stability of proposed helical edge states will be discussed.
Low surface brightness galaxies (LSBGs) represent a significant percentage of local galaxies but their formation and evolution remain elusive. They may hold crucial information for our understanding of many key issues (i.e., census of baryonic and dark matter, star formation in the low density regime, mass function). The most massive examples - the so called giant LSBGs - can be as massive as the Milky Way, but with this mass being distributed in a much larger disk. Malin 1 is an iconic giant LSBG, perhaps the largest disk galaxy known. We attempt to bring new insights on its structure and evolution on the basis of new images covering a wide range in wavelength. We have computed surface brightness profiles (and average surface brightnesses in 16 regions of interest), in six photometric bands (FUV, NUV, u, g, i, z). We compared these data to various models, testing a variety of assumptions concerning the formation and evolution of Malin 1. We find that the surface brightness and color profiles can be reproduced by a long and quiet star-formation history due to the low surface density; no significant event, such as a collision, is necessary. Such quiet star formation across the giant disk is obtained in a disk model calibrated for the Milky Way, but with an angular momentum approximately 20 times larger. Signs of small variations of the star-formation history are indicated by the diversity of ages found when different regions within the galaxy are intercompared.For the first time, panchromatic images of Malin 1 are used to constrain the stellar populations and the history of this iconic example among giant LSBGs. Based on our model, the extreme disk of Malin 1 is found to have a long history of relatively low star formation (about 2 Msun/yr). Our model allows us to make predictions on its stellar mass and metallicity.
In a three-level atomic system coupled by two equal-amplitude laser fields with a frequency separation 2$\delta$, a weak probe field exhibits a multiple-peaked absorption spectrum with a constant peak separation $\delta$. The corresponding probe dispersion exhibits steep normal dispersion near the minimum absorption between the multiple absorption peaks, which leads to simultaneous slow group velocities for probe photons at multiple frequencies separated by $\delta$. We report an experimental study in such a bichromatically coupled three-level $\Lambda$ system in cold $^{87}$Rb atoms. The multiple-peaked probe absorption spectra under various experimental conditions have been observed and compared with the theoretical calculations.
The symmetry algebra of the two-dimensional anisotropic quantum harmonic oscillator with rational ratio of frequencies, which is characterizing ``pancake'' nuclei, is identified as a non-linear extension of the u(2) algebra. The finite dimensional representation modules of this algebra are studied and the energy eigenvalues are determined using algebraic methods of general applicability to quantum superintegrable systems. For labelling the degenerate states an ``angular momentum'' operator is introduced, the eigenvalues of which are roots of appropriate generalized Hermite polynomials. In the special case with frequency ratio 2:1 the resulting algebra is identified as the finite W algebra W$_3^{(2)}$.
Most research on nanocrystalline alloys has been focused on planned doping of metals with other metallic elements, but nonmetallic impurities are also prevalent in the real world. In this work, we report on the combined effects of metallic dopants and nonmetallic impurities on grain boundary energy and strength using first-principles calculations, with a $\Sigma$5 (310) grain boundary in Cu chosen as a model system. We find a clear correlation between the grain boundary energy and the change in excess free volume of doped grain boundaries. A combination of a larger substitutional dopant and an interstitial impurity can fill the excess free volume more efficiently and further reduce the grain boundary energy. We also find that the strengthening effects of dopants and impurities are dominated by the electronic interactions between the host Cu atoms and the two types of dopant elements. For example, the significant competing effects of metal dopants such as Zr, Nb, and Mo with impurities on the grain boundary strength are uncovered from the density of states of the d electrons. As a whole, this work deepens the field's understanding of the interaction between metallic dopants and nonmetallic impurities on grain boundary properties, providing a guide for improving the thermal stability of materials while avoiding embrittling effects.
A uniform gradient for functions u which satisfy a system of N second-order partial differential inequalities is given in this paper. Some structure conditions are given for the coefficients of the matrices of second-order terms and of first-order terms. This result can be applied to study the gradient estimate of a class of second-order degenerate elliptic partial differential equations.
A robust nanoelectromechanical switch is proposed based upon an asymmetric pendant moiety anchored to an organic backbone between two C60 fullerenes, which in turn are connected to gold electrodes. Ab initio density functional calculations are used to demonstrate that an electric field induces rotation of the pendant group, leading to a non-linear current-voltage relation. The non-linearity is strong enough to lead to negative differential resistance at modest source-drain voltages.
The optical spectrum of the cubic helimagnetic metal FeGe has been investigated in the frequency range from 0.01 - 3.1 eV for different temperatures from 30 K to 296 K. The optical conductivity shows the evolution of a low energy (0.22 eV) interband transition and the development of a narrow free carrier response with a strong energy and temperature dependence. The frequency dependent effective mass and scattering rate derived from the optical data indicate the formation of dressed quasi-particles with a mass renormalization factor of 12. Similar to FeSi the spectral weight in FeGe is not recovered over a broad frequency range, an effect usually attributed to the influence of the on-site Coulomb interaction.
While the objective of conventional quantum key distribution (QKD) is to secretly generate and share the classical bits concealed in the form of maximally mixed quantum states, that of private quantum channel (PQC) is to secretly transmit individual quantum states concealed in the form of maximally mixed states using shared one-time pad and it is called Gaussian private quantum channel (GPQC) when the scheme is in the regime of continuous variables. We propose a GPQC enhanced with squeezed coherent states (GPQCwSC), which is a generalization of GPQC with coherent states only (GPQCo) [Phys. Rev. A 72, 042313 (2005)]. We show that GPQCwSC beats the GPQCo for the upper bound on accessible information. As a subsidiary example, it is shown that the squeezed states take an advantage over the coherent states against a beam splitting attack in a continuous variable QKD. It is also shown that a squeezing operation can be approximated as a superposition of two different displacement operations in the small squeezing regime.
In this paper we prove that the branch curve of a general projection of a surface to the plane is irreducible, with only nodes and cusps.
In this paper we study canonical $\gamma$-structures, a class of RNA pseudoknot structures that plays a key role in the context of polynomial time folding of RNA pseudoknot structures. A $\gamma$-structure is composed by specific building blocks, that have topological genus less than or equal to $\gamma$, where composition means concatenation and nesting of such blocks. Our main result is the derivation of the generating function of $\gamma$-structures via symbolic enumeration using so called irreducible shadows. We furthermore recursively compute the generating polynomials of irreducible shadows of genus $\le \gamma$. $\gamma$-structures are constructed via $\gamma$-matchings. For $1\le \gamma \le 10$, we compute Puiseux-expansions at the unique, dominant singularities, allowing us to derive simple asymptotic formulas for the number of $\gamma$-structures.
The tight upper bound $\operatorname{pt}_+(G) \leq \left\lceil \frac{\left\vert \operatorname{V}(G) \right\vert - \operatorname{Z}_+(G)}{2} \right\rceil$ is established for the positive semidefinite propagation time of a graph in terms of its positive semidefinite zero forcing number. To prove this bound, two methods of transforming one positive semidefinite zero forcing set into another and algorithms implementing these methods are presented. Consequences of the bound, including a tight Nordhaus-Gaddum sum upper bound on positive semidefinite propagation time, are established.
The paper concerns the image, level and sojourn time sets associated with sample paths of the Rosenblatt process. We obtain results regarding the Hausdorff (both classical and macroscopic), packing and intermediate dimensions, and the logarithmic and pixel densities. As a preliminary step we also establish the time inversion property of the Rosenblatt process, as well as some technical points regarding the distribution of $Z$.
We performed ultrasonic measurements on (Ta$_{0.952}$V$_{0.048}$)$_2$NiSe$_5$ to investigate the contribution of acoustic phonons at the zone center to structural and possible excitonic transitions. The transverse elastic constant $C_{55}$ with irreducible representation $B_\mathrm{2g}$ exhibits softening over 90\% above a transition temperature of $T_\mathrm{s} = 280$ K, indicating the soft mode of corresponding TA phonons. Our analysis based on the quadrupole response indicates that the electron-phonon interaction contributes to the excitonic transition in addition to the hybridization between the conduction and valence bands if the excitonic transition is realized.
Structured light illumination is an active 3-D scanning technique based on projecting/capturing a set of striped patterns and measuring the warping of the patterns as they reflect off a target object's surface. In the case of phase measuring profilometry (PMP), the projected patterns are composed of a rolling sinusoidal wave, but as a set of time-multiplexed patterns, PMP requires the target surface to remain motionless or for scanning to be performed at such high rates that any movement is small. But high speed scanning places a significant burden on the projector electronics to produce contone patterns inside of short exposure intervals. Binary patterns are, therefore, of great value, but converting contone patterns into binary comes with significant risk. As such, this paper introduces a contone-to-binary conversion algorithm for deriving binary patterns that best mimic their contone counterparts. Experimental results will show a greater than 3 times reduction in pattern noise over traditional halftoning procedures.
We present a fluctuation theorem for quantum bipartite systems in which the subsystems exchange information with each other. Our information fluctuation theorem includes correlations by introducing a quantum mechanical mutual information content and a statistical probability distribution which allows one to consider statistical averages when computing the thermodynamic and informational quantities. The fundamental limit of heat transferred from a heat reservoir for quantum bipartite systems involving the quantum mutual information is then derived. We illustrate the use of our thermodynamic inequality in quantum computing and discuss our results in terms of Landauer's principle.
We use a variant of Wan's method to prove two Ramanujan-Orr type formulas for $1/\pi$. This variant needs to know in advance the formulas for $1/\pi$ that we want to prove, but avoids the need of solving a system of equations.
The structure of all triangle free graphs G = (V,E) with |E| - 6|V| + 13\alpha(G) = 0 is determined, yielding an affirmative answer to a question of Stanis{\l}aw Radziszowski and Donald Kreher.
The low-temperature magnetic structure of \HG has been studied by high-resolution powder neutron diffraction. Long-range incommensurate magnetic order sets in at T$_N\sim$22K with propagation vector \textbf{k}=(0,0,$\sim$0.18). On cooling below T$_N$, the propagation vector increases and saturates at the commensurate value \textbf{k}=(0,0,0.25). The magnetic structure below T$_N$ consists of ferromagnetic layers in the \textit{ab}-plane stacked in a spiral arrangement along the \textit{c}-axis. Symmetry analysis using corepresentations theory reveals a point group symmetry in the ordered magnetic phase of 422 (D$_4$), which is incompatible with macroscopic ferroelectricity. This finding indicates that the spontaneous electric polarization observed experimentally cannot be coupled to the magnetic order parameter.
We present several recent developments on ELSV-type formulae and topological recursion concerning Chiodo classes and several kind of Hurwitz numbers. The main results appeared in D. Lewanski, A. Popolitov, S. Shadrin, D. Zvonkine, "Chiodo formulas for the r-th roots and topological recursion", Lett. Math. Phys. (2016).
We quantify the variability of faint unresolved optical sources using a catalog based on multiple SDSS imaging observations. The catalog covers SDSS Stripe 82, and contains 58 million photometric observations in the SDSS ugriz system for 1.4 million unresolved sources. In each photometric bandpass we compute various low-order lightcurve statistics and use them to select and study variable sources. We find that 2% of unresolved optical sources brighter than g=20.5 appear variable at the 0.05 mag level (rms) simultaneously in the g and r bands. The majority (2/3) of these variable sources are low-redshift (<2) quasars, although they represent only 2% of all sources in the adopted flux-limited sample. We find that at least 90% of quasars are variable at the 0.03 mag level (rms) and confirm that variability is as good a method for finding low-redshift quasars as is the UV excess color selection (at high Galactic latitudes). We analyze the distribution of lightcurve skewness for quasars and find that is centered on zero. We find that about 1/4 of the variable stars are RR Lyrae stars, and that only 0.5% of stars from the main stellar locus are variable at the 0.05 mag level. The distribution of lightcurve skewness in the g-r vs. u-g color-color diagram on the main stellar locus is found to be bimodal (with one mode consistent with Algol-like behavior). Using over six hundred RR Lyrae stars, we demonstrate rich halo substructure out to distances of 100 kpc. We extrapolate these results to expected performance by the Large Synoptic Survey Telescope and estimate that it will obtain well-sampled 2% accurate, multi-color lightcurves for ~2 million low-redshift quasars, and will discover at least 50 million variable stars.
We construct the Green function for second-order elliptic equations in non-divergence form when the mean oscillations of the coefficients satisfy the Dini condition. We show that the Green's function is BMO in the domain and establish logarithmic pointwise bounds. We also obtain pointwise bounds for first and second derivatives of the Green's function.
We prove existence of small amplitude, $2\pi \slash \om$-periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions, for any frequency $ \om $ belonging to a Cantor-like set of positive measure and for a new set of nonlinearities. The proof relies on a suitable Lyapunov-Schmidt decomposition and a variant of the Nash-Moser Implicit Function Theorem. In spite of the complete resonance of the equation we show that we can still reduce the problem to a {\it finite} dimensional bifurcation equation. Moreover, a new simple approach for the inversion of the linearized operators required by the Nash-Moser scheme is developed. It allows to deal also with nonlinearities which are not odd and with finite spatial regularity.
Based on the colour measurements from a multi-band, multi-component 2D decomposition's of S0 and spiral galaxies using SDSS images, we found that bars are bluer in S0 galaxies compared to the spiral galaxies. Most of the S0s in our sample have stellar masses $\sim L_{*}$ galaxies. The environment might have played an important role as most of the S0s with bluer bars are in the intermediate-density environment. The possibility of minor mergers and tidal interactions which occurs frequently in the intermediate-density environment might have caused either a bar to form and/or induce star formation in the barred region of S0 galaxies. The underlying discs show the usual behaviour being redder in S0s compared to spiral galaxies while the bulges are red and old for both S0 and spiral galaxies. The finding of bluer bars in S0 galaxies is a puzzling issue and poses an interesting question at numerical and theoretical studies most of which shows that the bars are long-lived structures with old stellar populations.