ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present a general modified maximum likelihood (MML) method for inferring generative distribution functions from uncertain and biased data. The MML estimator is identical to, but easier and many orders of magnitude faster to compute than the solution of the exact Bayesian hierarchical modelling of all measurement errors. As a key application, this method can accurately recover the mass function (MF) of galaxies, while simultaneously dealing with observational uncertainties (Eddington bias), complex selection functions and unknown cosmic large-scale structure. The MML method is free of binning and natively accounts for small number statistics and non-detections. Its fast implementation in the R-package "dftools" is equally applicable to other objects, such as haloes, groups and clusters, as well as observables other than mass. The formalism readily extends to multi-dimensional distribution functions, e.g. a Choloniewski function for the galaxy mass-angular momentum distribution, also handled by dftools. The code provides uncertainties and covariances for the fitted model parameters and approximate Bayesian evidences. We use numerous mock surveys to illustrate and test the MML method, as well as to emphasise the necessity of accounting for observational uncertainties in MFs of modern galaxy surveys.
Solutions to the Einstein equations for Bianchi IX cosmologies are examined through the use of Ellis MacCallum Wainwright (expansion-normalized) variables. Using an iterative map derived from the Einstein equations one can construct an infinite number of periodic solutions. The simplest periodic solutions consist of 3-cycles. It is shown that for 3-cycles the time series of the logarithms of the expansion-normalized spatial curvature components vs normalized time (which is runs backwards towards the initial singularity), generates a set of self-similar golden rectangles. In addition the golden ratio appears in other aspects of the same time series representation.
We study meron quasiparticle excitations in the \nu = 1 quantum Hall bilayer. Considering the well known single meron state, we introduce its effective form, valid in the longdistance limit. That enables us to propose two (and more) meron states in the same limit. Further, establishing a plasma analogy of the (111) ground state, we find the impurities that play the role of merons and derive meron charge distributions. Using the introduced meron constructions in generalized (mixed) ground states and corresponding plasmas for arbitrary distance between the layers, we calculate the interaction between the construction implied impurities. We also find a correspondence between the impurity interactions and meron interactions. This suggests a possible explanation of the deconfinement of the merons recently observed in the experiments.
We derive two new analogues of a transformation formula of Ramanujan involving the Gamma and Riemann zeta functions present in the Lost Notebook. Both involve infinite series consisting of Hurwitz zeta functions and yield modular relations. As a special case of the first formula, we obtain an identity involving polygamma functions given by Andrew P. Guinand and as a limiting case of the second formula, we derive the transformation formula of Ramanujan.
We prove that for $\kappa\in(0,8)$, if $(\eta_1,\eta_2)$ is a $2$-SLE$_\kappa$ pair in a simply connected domain $D$ with an analytic boundary point $z_0$, then $\lim_{r\to 0^+}r^{-\alpha} \mathbb{P}[\mbox{dist}(z_0,\eta_j)<r,j=1,2]$ converges to a positive number for some $\alpha>0$, which is called the two-curve Green's function. The exponent $\alpha$ equals $\frac{12}{\kappa}-1$ or $2(\frac{12}{\kappa}-1)$ depending on whether $z_0$ is one of the endpoints of $\eta_1$ and $\eta_2$. We also find the convergence rate and the exact formula of the Green's function up to a multiplicative constant. To derive these results, we construct two-dimensional diffusion processes and use orthogonal polynomials to obtain their transition density.
We present an automatic procedure to perform reliable photometry of galaxies on SDSS images. We selected a sample of 5853 galaxies in the Coma and Virgo superclusters. For each galaxy, we derive Petrosian g and i magnitudes, surface brightness profiles and color profiles. Unlike the SDSS pipeline, our procedure is not affected by the well known shredding problem and efficiently extracts Petrosian magnitudes for all galaxies. Hence we derived magnitudes even from the population of galaxies missed by the SDSS that represents 25% of all Local supercluster galaxies and ~95% of galaxies with g < 11 mag. After correcting the g and i magnitudes for Galactic and internal extinction, the blue and red sequences in the color magnitude diagram are well separated, with similar slopes. In addition, we study (i) the color-magnitude diagrams in different galaxy regions, the inner (r <= 1 kpc), intermediate (0.2R{Pet} <=r<= 0.3R{Pet}) and outer, disk-dominated (r>=0.35R{Pet})) zone, and (ii), we compute template color profiles, discussing the dependences of the templates on the galaxy masses and on their morphological type. The two analyses consistently lead to a picture where elliptical galaxies show no color gradients, irrespective of their masses. Spirals, instead, display a steeper gradient in their color profiles with increasing mass, consistently with the growing relevance of a bulge and/or a bar component above 10^{10} Modot.
We show that the expansion of ejecta in Tycho's supernova remnant (SNR) is consistent with a spherically symmetric shell, based on Suzaku measurements of the Doppler broadened X-ray emission lines. All the strong K_alpha line emission show broader widths at the center than at the rim, while the centroid energies are constant across the remnant (except for Ca). This is the pattern expected for Doppler broadening due to expansion of the SNR ejecta in a spherical shell. To determine the expansion velocities of the ejecta, we applied a model for each emission line feature having two Gaussian components separately representing red- and blue-shifted gas, and inferred the Doppler velocity difference between these two components directly from the fitted centroid energy difference. Taking into account the effect of projecting a three-dimensional shell to the plane of the detector, we derived average spherical expansion velocities independently for the K_alpha emission of Si, S, Ar, and Fe, and K_beta of Si. We found that the expansion velocities of Si, S, and Ar ejecta of 4700+/-100 km/s are distinctly higher than that obtained from Fe K_alpha emission, 4000+/-300 km/s, which is consistent with segregation of the Fe in the inner ejecta. Combining the observed ejecta velocities with the ejecta proper-motion measurements by Chandra, we derived a distance to the Tycho's SNR of 4+/-1 kpc.
The wild part of Abhyankar's Inertia Conjecture for a product of certain Alternating groups is shown for any algebraically closed field of odd characteristic. For $d$ a multiple of the characteristic of the base field, a new \'etale $A_d$-cover of the affine line is obtained using an explicit equation and it is shown that it has the minimal possible upper jump.
A density based hierarchical group-finding algorithm is used to identify stellar halo structures in a catalog of M-giants from the Two Micron All Sky Survey (2MASS). The intrinsic brightness of M-giant stars means that this catalog probes deep into the halo where substructures are expected to be abundant and easy to detect. Our analysis reveals 16 structures at high Galactic latitude (greater than 15 degree), of which 10 have been previously identified. Among the six new structures two could plausibly be due to masks applied to the data, one is associated with a strong extinction region and one is probably a part of the Monoceros ring. Another one originates at low latitudes, suggesting some contamination from disk stars, but also shows protrusions extending to high latitudes, implying that it could be a real feature in the stellar halo. The last remaining structure is free from the defects discussed above and hence is very likely a satellite remnant. Although the extinction in the direction of the structure is very low, the structure does match a low temperature feature in the dust maps. While this casts some doubt on its origin, the low temperature feature could plausibly be due to real dust in the structure itself. The angular position and distance of this structure encompass the Pisces overdensity traced by RR Lyraes in Stripe 82 of the Sloan Digital Sky Survey (SDSS). However, the 2MASS M-giants indicate that the structure is much more extended than what is visible with the SDSS, with the point of peak density lying just outside Stripe 82. The morphology of the structure is more like a cloud than a stream and reminiscent of that seen in simulations of satellites disrupting along highly eccentric orbits.
A low mass star usually experiences stratification and abundance anomalies during its evolution. A 0.95 solar mass star with a metallicity Z = 0.004 is followed from the main-sequence to the Horizontal Branch (HB). On the main-sequence the larger effects of stratification may come from accretion as was suggested in relation to metallicity and planet formation. As it evolves through the giant branch, stratification appears around the hydrogen burning shell. It may create hydrodynamic instabilities and be related to abundance anomalies on the giant branch. After the He flash the star evolves to the HB. If it loses enough mass, it ends up a hot HB star (or in the field an sdB star) with effective temperatures larger than 11000 K. All sdB stars are observed to have an approximately solar iron abundance whatever their original metallicity, implying overabundances by factors of up to 100. So should the 0.95 solar mass star. How its internal hydrodynamic properties on the main sequence may influence its fate on the HB is currently uncertain.
Our aim is to compare the infrared properties of big, ``classical'' dust grains with visual extinction in the cloud L1642. In particular, we study the differences of grain emissivity between diffuse and dense regions in the cloud. The far-infrared properties of dust are based on large-scale 100um and 200um maps. Extinction through the cloud has been derived by using the star count method at B- and I-bands, and color excess method at J, H and Ks bands. Radiative transfer calculations have been used to study the effects of increasing absorption cross-section on the far-infrared emission and dust temperature. Dust emissivity, measured by the ratio of far-infrared optical depth to visual extinction, tau(far-IR)/A(V), increases with decreasing dust temperature in L1642. There is about two-fold increase of emissivity over the dust temperature range of 19K-14K. Radiative transfer calculations show that in order to explain the observed decrease of dust temperature towards the centre of L1642 an increase of absorption cross-section of dust at far-IR is necessary.This temperature decrease cannot be explained solely by the attenuation of interstellar radiation field. Increased absorption cross-section manifests itself also as an increased emissivity. We find that, due to temperature effects, the apparent value of optical depth tau(far-IR), derived from 100um and 200um intensities, is always lower than the true optical depth.
We analyze new JLAB data for inclusive electron scattering on various targets. Computed and measured total inclusive cross sections in the range $0.3\lesssim x\lesssim 0.95$ show on a logarithmic scale reasonable agreement for all targets. However, closer inspection of the Quasi-Elastic components bares serious discrepancies. EMC ratios which may contain less systematic errors fare the same. The above observations for the new data do not enable the extraction of the magnetic form factor (FF) $G_M^n$ and the Structure Function (SFs) $F_2^n$ of the neutron, although the application of exactly the same analysis to older data had been successful. We add to the above analysis older CLAS collaboration on $F_2^D$. Removing some scattered points, it appears possible to obtain the above mentioned neutron information. We compare our results with others from alternative sources. Particular attention is paid to the A=3 iso-doublet. Present data exist only for $^3$He, but the available input and charge symmetry also enable computations for $^3$H. Their average is the computed iso-scalar part and is compared with the empirical modification of $^3$He towards a fictitious A=3 iso-singlet.
We attempt to see how closely we can formally obtain the planetary and light path equations of General Relativity by employing certain operations on the familiar Newtonian equation. This article is intended neither as an alternative to nor as a tool for grasping Einstein's General Relativity. Though the exercise is understandable by readers at large, it is especially recommended to the teachers of Relativity for an appreciative understanding of its peculiarity as well as its pedagogical value in the teaching of differential equations.
We report on our results for the characterization of Si:P delta-layers grown by low temperature molecular beam epitaxy. Our data shows that the effective thickness of a delta-layer can be obtained through a weak localization analysis of electrical transport measurements performed in perpendicular and parallel magnetic fields. An estimate of the diffusivity of phosphorous in silicon is obtained by applying this method to several samples annealed at 850 Celsius for intervals of zero to 15 minutes. With further refinements, this may prove to be the most precise method of measuring delta-layer widths developed to date, including that of Secondary Ion Mass Spectrometry analysis.
Recent general relativistic simulations have shown that the coalescence of two spinning black holes (BH) can lead to recoiling speeds of the BH remnant of up to thousands of km/s as a result of the gravitational radiation emission. It is important that the accretion disc remains bound to ejected BH within the region where the gas orbital velocity is larger than the ejection speed. We considered the situation when the recoiling kick radius coincides with the radius of the broad line region (BLR). We show that in this situation the observed polarization data of accretion disk emission allow to determine the value of the recoil velocity. We present the estimates of the kick velocity for AGN with determined polarization data.
Given a set of images, whose pixel values can be considered as the components of a vector, it is interesting to estimate the modulus of such a vector in some localised areas corresponding to a compact signal. For instance, the detection/estimation of a polarized signal in compact sources immersed in a background is relevant in some fields like astrophysics. We develop two different techniques, one based on the Neyman-Pearson lemma, the Neyman-Pearson filter (NPF), and another based on prefiltering-before-fusion, the filtered fusion (FF), to deal with the problem of detection of the source and estimation of the polarization given two or three images corresponding to the different components of polarization (two for linear polarization, three including circular polarization). For the case of linear polarization, we have performed numerical simulations on two-dimensional patches to test these filters following two different approaches (a blind and a non-blind detection), considering extragalactic point sources immersed in cosmic microwave background (CMB) and non-stationary noise with the conditions of the 70 GHz \emph{Planck} channel. The FF outperforms the NPF, especially for low fluxes. We can detect with the FF extragalactic sources in a high noise zone with fluxes >= (0.42,0.36) Jy for (blind/non-blind) detection and in a low noise zone with fluxes >= (0.22,0.18) Jy for (blind/non-blind) detection with low errors in the estimated flux and position.
There is a growing interest in the study of regular black holes because they eliminate the problem of the singularity that conventional black hole models present. We analyze here the motion of different types of particles (without mass, massive and massive and charged particles) in an specific regular charged black hole solution obtained by Bronnikov in 2001. We also examine the geometry and the nature of the Bronnikov black hole, and compare it with the Reissner-Nordstrom black hole, for this we present first the features of both black holes and analyze the effective potential for each kind of particle followed by the numerical integration of the orbit equation in some cases of interest.
Motivated by a recent paper that compares the results of the analysis of the CKM angle alpha in the frequentist and in the Bayesian approaches, we have reconsidered the information on the hadronic amplitudes, which helps constraining the value of alpha in the Standard Model. We find that the Bayesian method gives consistent results irrespective of the parametrisation of the hadronic amplitudes and that the results of the frequentist and Bayesian approaches are equivalent when comparing meaningful probability ranges or confidence levels. We also find that from B to pi pi decays alone the 95% probability region for alpha is the interval [80^o,170^o], well consistent with recent analyses of the unitarity triangle where, by using all the available experimental and theoretical information, one gets alpha = (93 +- 4)^o. Last but not least, by using simple arguments on the hadronic matrix elements, we show that the unphysical region alpha ~ 0, present in several experimental analyses, can be eliminated.
The determination of the eigenenergies of a quantum anharmonic oscillator consists merely in finding the zeros of a function of the energy, namely the Wronskian of two solutions of the Schroedinger equation which are regular respectively at the origin and at infinity. We show in this paper how to evaluate that Wronskian exactly, except for numerical rounding errors. The procedure is illustrated by application to the gx2+x2N (N a positive integer) oscillator.
In these proceedings, we report on the possible signatures of a light scalar WIMP, a dark matter candidate with M_DM ~ few GeV, which is supposed to interact with the Standard Model particles through the Higgs, and which might be related to the annual modulation observed by DAMA.
In the Quantum Hall regime, near integer filling factors, electrons should only be transmitted through spatially-separated edge states. However, in mesoscopic systems, electronic transmission turns out to be more complex, giving rise to a large spectrum of magnetoresistance oscillations. To explain these observations, recent models put forward that, as edge states come close to each other, electrons can hop between counterpropagating edge channels, or tunnel through Coulomb islands. Here, we use scanning gate microscopy to demonstrate the presence of quantum Hall Coulomb islands, and reveal the spatial structure of transport inside a quantum Hall interferometer. Electron islands locations are found by modulating the tunneling between edge states and confined electron orbits. Tuning the magnetic field, we unveil a continuous evolution of active electron islands. This allows to decrypt the complexity of high magnetic field magnetoresistance oscillations, and opens the way to further local scale manipulations of quantum Hall localized states.
In this paper we focus on the relation between quasinormal modes (QNMs) and a rotating black hole shadows. As a specific example, we consider the quantum deformed Kerr black hole obtained via Newman--Janis--Azreg-A\"{\i}nou algorithm. In particular, using the geometric-optics correspondence between the parameters of a QNMs and the conserved quantities along geodesics, we show that, in the eikonal limit, the real part of QNMs is related to the Keplerian frequency for equatorial orbits. To this end, we explore the typical shadow radius for the viewing angles, $\theta_0=\pi/2$, and obtained an interesting relation in the case of viewing angle $\theta_0=0$ (or equivalently $\theta_0=\pi$). Furthermore we have computed the corresponding equatorial and polar modes and the thermodynamical stability of the quantum deformed Kerr black hole. We also investigate other astrophysical applications such as the quasiperiodic oscillations and the motion of S2 star to constrain the quantum deforming parameter.
Nonlinear electromagnetic waves with superluminal phase velocity can propagate in the winds around isolated pulsars, and around some pulsars in binary systems. Using a short-wavelength approximation, we find and analyze an integrable system of equations that govern their evolution in spherical geometry. A confined mode is identified that stagnates to finite pressure at large radius and can form a precursor to the termination shock. Using a simplified criterion, we find this mode is stable for most isolated pulsars, but may be unstable if the external pressure is high, such as in the pulsar wind nebulae in starburst galaxies and in W44. Pulsar winds in eccentric binary systems, such as PSR 1259-63, may go through phases with stable and unstable electromagnetic precursors, as well as phases in which the density is too high for these modes to propagate.
We investigate the dynamics of the kinks that emerge in a one-dimensional scalar field theory with an octic potential containing a quartic minimum and two quadratic minima. We show analytically that kink-antikink and kink-kink pairs interact with a force that scales with the fourth power of the inter-kink distance, and calculate its strength. This is done using two different techniques. The first employs a collective coordinate method to approximately solve the equation of motion for the profile of an accelerating kink. The second is based on modifying the potential to one that is able to support static solutions containing multiple kinks. We show that the two methods give consistent results. All calculations are supported by numerical work that confirms the validity of our results.
In this paper we establish a result regarding the connection between continuous maximal regularity and generation of analytic semigroups on a pair of densely embedded Banach spaces. More precisely, we show that continuous maximal regularity for a closed operator $A: E_1 \rightarrow E_0$ implies that $A$ generates a strongly continuous analytic semigroup on $E_0$ with domain equal $E_1$.
We compare predictions of large-scale cosmological hydrodynamical simulations for neutral hydrogen absorption signatures in the vicinity of 1e11 - 1e12.5 MSun haloes with observational measurements. Two different hydrodynamical techniques and a variety of prescriptions for gas removal in high density regions are examined. Star formation and wind feedback play only secondary roles in the HI absorption signatures outside the virial radius, but play important roles within. Accordingly, we identify three distinct gaseous regions around a halo: the virialized region, the mesogalactic medium outside the virial radius arising from the extended haloes of galaxies out to about two turnaround radii, and the intergalactic medium beyond. Predictions for the amount of absorption from the mesogalactic and intergalactic media are robust across different methodologies, and the predictions agree with the amount of absorption observed around star-forming galaxies and QSO host galaxies. Recovering the measured amount of absorption within the virialized region, however, requires either a higher dynamic range in the simulations, additional physics, or both.