ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper, we prove convergence and fluctuation results for measure-valued P\'olya processes (MVPPs, also known as P\'olya urns with infinitely-many colours). Our convergence results hold almost surely and in $L^2$, under assumptions that are different from that of other convergence results in the literature. Our fluctuation results are the first second-order results in the literature on MVPPs; they generalise classical fluctuation results from the literature on finitely-many-colour P\'olya urns. As in the finitely-many-colour case, the order and shape of the fluctuations depend on whether the "spectral gap is small or large".   To prove these results, we show that MVPPs are stochastic approximations taking values in the set of measures on a measurable space $E$ (the colour space). We then use martingale methods and standard operator theory to prove convergence and fluctuation results for these stochastic approximations.
We construct solutions of an Einstein-Yang-Mills system including a cosmological constant in 4+n space-time dimensions, where the n-dimensional manifold associated with the extra dimensions is taken to be Ricci flat. Assuming the matter and metric fields to be independent of the n extra coordinates, a spherical symmetric Ansatz for the fields leads to a set of coupled ordinary differential equations. We find that for n > 1 only solutions with either one non-zero Higgs field or with all Higgs fields constant and zero gauge fields exist. We give the analytic solutions available in this model. These are ``embedded'' abelian solutions with a diverging size of the manifold associated with the extra n dimensions. Depending on the choice of parameters, these latter solutions either represent naked singularities or they possess a single horizon.   We also present solutions of the effective 4-dimensional Einstein-Yang-Mills-Higgs-dilaton model, where the higher dimensional cosmological constant induces a Liouville-type potential. The solutions are non-abelian solutions with diverging Higgs fields, which exist only up to a maximal value of the cosmological constant.
By extrapolating from observationally derived surface magnetograms of low-mass stars we construct models of their coronal magnetic fields and compare the 3D field geometry with axial multipoles. AB Dor, which has a radiative core, has a very complex field, whereas V374 Peg, which is completely convective, has a simple dipolar field. We calculate global X-ray emission measures assuming that the plasma trapped along the coronal loops is in hydrostatic equilibrium and compare the differences between assuming isothermal coronae, or by considering a loop temperature profiles. Our preliminary results suggest that the non-isothermal model works well for the complex field of AB Dor, but not for the simple field of V374 Peg.
Layered van der Waals (vdW) crystals with intrinsic magnetic properties such as high Curie temperature (TC) and large perpendicular magnetic anisotropy (PMA) are key to the development and application of spintronic devices. The ferromagnetic vdW metal Fe3-xGeTe2 (FGT) has gained prominence recently due to its high TC (220 K) and strong PMA. Here, we introduce a new metallic vdW ferromagnets, Fe5-xGe2Te2 or FG2T, which was successfully synthesized and fully characterized. FG2T is a metal that orders ferromagnetically with a very sharp transition at 250 K (bulk and single crystal thin flakes) and shows large PMA, as found by both experimental and computational studies. This work enables novel heterostructure devices with near room temperature capabilities by using FG2T as spin injector.
We derive a realistic microscopic model for doped colossal magnetoresistance manganites, which includes the dynamics of charge, spin, orbital and lattice degrees of freedom on a quantum mechanical level. The model respects the SU(2) spin symmetry and the full multiplet structure of the manganese ions within the cubic lattice. Concentrating on the hole doped domain ($0\le x\le 0.5$) we study the influence of the electron-lattice interaction on spin and orbital correlations by means of exact diagonalisation techniques. We find that the lattice can cause a considerable suppression of the coupling between spin and orbital degrees of freedom and show how changes in the magnetic correlations are reflected in dynamic phonon correlations. In addition, our calculation gives detailed insights into orbital correlations and demonstrates the possibility of complex orbital states.
We give an alternative approach to the computation of the dimension of the tangent space of the deformation space of curves with automorphisms. A homological version of the local-global principle similar to the one of J.Bertin, A. M\'ezard is proved, and a computation in the case of ordinary curves is obtained, by application of the results of S. Nakajima for the Galois module structure of the space of 2-holomorphic differentials on them.
Grain size engineering, particularly reducing grain size into the nanocrystalline regime, offers a promising pathway to further improve the strength-to-weight ratio of Al alloys. Unfortunately, the fabrication of nanocrystalline metals often requires non-equilibrium processing routes, which typically limit the specimen size and require large energy budgets. In this study, multiple dopant atoms in ternary Al alloys are deliberately selected to enable segregation to the grain boundary region and promote the formation of amorphous complexions. Three different fully dense bulk nanocrystalline Al alloys (Al-Mg-Y, Al-Fe-Y, and Al-Ni-Y) with small grain sizes were successfully fabricated using a simple powder metallurgy approach, with full densification connected directly to the onset of amorphous complexion formation. All the compositions demonstrate densities above 99% with grain sizes of <60 nm following consolidation via hot pressing at 585 oC. The very fine grain structure results in excellent mechanical properties, with nanoindentation hardness values in the range of 2.2-2.8 GPa. Detailed microstructural characterization verifies the segregation of all dopant species to grain boundaries as well as the formation of amorphous complexions, which suggests their influential role in aiding effective consolidation and endowing thermal stability in the alloys. Moreover, nanorods with a core-shell structure are also observed at the grain boundaries, which likely contribute to the stabilization of the grain structure and high strength. Finally, intermetallic particles with a sizes of hundreds of nanometers form. As a whole, the results presented here demonstrate a general alloy design strategy of segregation and boundary evolution pathway that enables the fabrication of multiple nanocrystalline Al alloys with hierarchical microstructures and improved performance.
We study the correlations between the structural parameters of dark matter haloes using Principal Component Analysis (PCA). We consider a set of eight parameters, six of which are commonly used to characterize dark matter halo properties: mass, concentration, spin, shape, overdensity, and the angle ($\Phi_L$) between the major axis and the angular momentum vector. Two additional parameters ($\x_{off}$ and $\rho_{rms}$) are used to describe the degree of `relaxedness' of the halo. We find that we can account for much of the variance of these properties with halo mass and concentration, on the one hand, and halo relaxedness on the other. Nonetheless, three principle components are usually required to account for most of the variance. We argue that halo mass is not as dominant as expected, which is a challenge for halo occupation models and semi-analytic models that assume that mass determines other halo (and galaxy) properties. In addition, we find that the angle $\Phi_L$ is not significantly correlated with other halo parameters, which may present a difficulty for models in which galaxy disks are oriented in haloes in a particular way. Finally, at fixed mass, we find that a halo's environment (quantified by the large-scale overdensity) is relatively unimportant.
SnTe is a prototypical topological crystalline insulator, in which the gapless surface state is protected by a crystal symmetry. The hallmark of the topological properties in SnTe is the Dirac cones projected to the surfaces with mirror symmetry, stemming from the band inversion near the L points of its bulk Brillouin zone, which can be measured by angle-resolved photoemission. We have obtained the (111) surface of SnTe film by molecular beam epitaxy on BaF2(111) substrate. Photon-energy-dependence of in situ angle-resolved photoemission, covering multiple Brillouin zones in the direction perpendicular tothe (111) surface, demonstrate the projected Dirac cones at the Gamma_bar and M_bar points of the surface Brillouinzone. In addition, we observe a Dirac-cone-like band structure at the Gamma point of the bulk Brillouin zone,whose Dirac energy is largely different from those at the Gamma_bar and M_bar points.
We present a method of combining cluster abundances and large-scale two-point correlations, namely galaxy clustering, galaxy--cluster cross-correlations, cluster auto-correlations, and cluster lensing. This data vector yields comparable cosmological constraints to traditional analyses that rely on small-scale cluster lensing for mass calibration. We use cosmological survey simulations designed to resemble the Dark Energy Survey Year One (DES-Y1) data to validate the analytical covariance matrix and the parameter inferences. The posterior distribution from the analysis of simulations is statistically consistent with the absence of systematic biases detectable at the precision of the DES Y1 experiment. We compare the $\chi^2$ values in simulations to their expectation and find no significant difference. The robustness of our results against a variety of systematic effects is verified using a simulated likelihood analysis of a Dark Energy Survey Year 1-like data vectors. This work presents the first-ever end-to-end validation of a cluster abundance cosmological analysis on galaxy catalog-level simulations.
Rotating black holes can power the most extreme non-thermal transient sources. They have a long-duration viscous time-scale of spin-down and produce non-thermal emissions along their spin-axis, powered by a relativistic capillary effect. We report on the discovery of exponential decay in BATSE light curves of long GRBs by matched filtering, consistent with a viscous time-scale, and identify UHECRs energies about the GZK threshold in linear acceleration of ion contaminants along the black hole spin-axis, consistent with black hole masses and lifetimes of FR II AGN. We explain the absence of UHECRs from BL Lac objects due to UHECR emissions preferably at appreciable angles away from the black hole spin-axis. Black hole spin may be key to unification of GRBs and their host environments, and to AGN and their host galaxies. Our model points to long duration bursts in radio from long GRBs without supernovae and gravitational-waves from all long GRBs.
We study the capability of future measurements of the galaxy clustering power spectrum to probe departures from a power-law spectrum for primordial fluctuations. On considering the information from the galaxy clustering power spectrum up to quasi-linear scales, i.e. $k<0.1$ h Mpc$^{-1}$, we present forecasts for DESI, Euclid and SPHEREx in combination with CMB measurements. As examples of departures in the primordial power spectrum from a simple power-law, we consider four $Planck$ 2015 best-fits motivated by inflationary models with different breaking of the slow-roll approximation. These four representative models provide an improved fit to CMB temperature anisotropies, although not at statistical significant level. As for other extensions in the matter content of the simplest $\Lambda$CDM model, the complementarity of the information in the resulting matter power spectrum expected from these galaxy surveys and in the primordial power spectrum from CMB anisotropies can be effective in constraining cosmological models. We find that the three galaxy surveys can add significant information to CMB to better constrain the extra parameters of the four models considered.
Let $S\subset\Ps^r$ ($r\geq 5$) be a nondegenerate, irreducible, smooth, complex, projective surface of degree $d$. Let $\delta_S$ be the number of double points of a general projection of $S$ to $\Ps^4$. In the present paper we prove that $ \delta_S\leq{\binom {d-2} {2}}$, with equality if and only if $S$ is a rational scroll. Extensions to higher dimensions are discussed.
We prove a result on the distribution of the general divisor functions in arithmetic progressions to smooth moduli which exceed the square root of the length.
We model a set of point-to-point transports on a network as a system of polydisperse interacting self-avoiding walks (SAWs) over a finite square lattice. The ends of each SAW may be located both at random, uniformly distributed, positions or with one end fixed at a lattice corner. The total energy of the system is computed as the sum over all SAWs, which may represent either the time needed to complete the transport over the network, or the resources needed to build the networking infrastructure. We focus especially on the second aspect by assigning a concave cost function to each site to encourage path overlap. A Simulated Annealing optimization, based on a modified BFACF Montecarlo algorithm developed for polymers, is used to probe the complex conformational substates structure. We characterize the average cost gains (and path-length variation) for increasing polymer density with respect to a Dijkstra routing and find a non-monotonic behavior as previously found in random networks. We observe the expected phase transition when switching from a convex to a concave cost function (e.g., $x^\gamma$, where $x$ represents the node overlap) and the emergence of ergodicity breaking, finally we show that the space of ground states for $\gamma<1$ is compatible with an ultrametric structure as seen in many complex systems such as some spin glasses.
An approach to modelling the universe based on the requisites of gravitational energy. This model is explained as it relates to the stages of the universal life cycle and the continued existence of the universe as it is known today. The article attempts to reconcile the most common problems with physical models of the universe and overcome doubt as to its validity through the most common questions.
Self-supervised monocular depth estimation networks are trained to predict scene depth using nearby frames as a supervision signal during training. However, for many applications, sequence information in the form of video frames is also available at test time. The vast majority of monocular networks do not make use of this extra signal, thus ignoring valuable information that could be used to improve the predicted depth. Those that do, either use computationally expensive test-time refinement techniques or off-the-shelf recurrent networks, which only indirectly make use of the geometric information that is inherently available.   We propose ManyDepth, an adaptive approach to dense depth estimation that can make use of sequence information at test time, when it is available. Taking inspiration from multi-view stereo, we propose a deep end-to-end cost volume based approach that is trained using self-supervision only. We present a novel consistency loss that encourages the network to ignore the cost volume when it is deemed unreliable, e.g. in the case of moving objects, and an augmentation scheme to cope with static cameras. Our detailed experiments on both KITTI and Cityscapes show that we outperform all published self-supervised baselines, including those that use single or multiple frames at test time.
We present a formalism to calculate finite-frequency current correlations in interacting nanoscale conductors. We work within the n-resolved density matrix approach and obtain a multi-time cumulant generating function that provides the fluctuation statistics, solely from the spectral decomposition of the Liouvillian. We apply the method to the frequency-dependent third cumulant of the current through a single resonant level and through a double quantum dot. Our results, which show that deviations from Poissonian behaviour strongly depend on frequency, demonstrate the importance of finite-frequency higher-order cumulants in fully characterizing interactions.
We present a follow-up analysis of the unique magnetic luminosity-variable carbon-atmosphere white dwarf SDSS J142625.71+575218.3. This includes the results of some 106.4 h of integrated light photometry which have revealed, among other things, the presence of a new periodicity at 319.720 s which is not harmonically related to the dominant oscillation (417.707 s) previously known in that star. Using our photometry and available spectroscopy, we consider the suggestion made by Montgomery et al. (2008) that the luminosity variations in SDSS J142625.71+575218.3 may not be caused by pulsational instabilities, but rather by photometric activity in a carbon-transferring analog of AM CVn. This includes a detailed search for possible radial velocity variations due to rapid orbital motion on the basis of MMT spectroscopy. At the end of the exercise, we unequivocally rule out the interacting binary hypothesis and conclude instead that, indeed, the luminosity variations are caused by g-mode pulsations as in other pulsating white dwarfs. This is in line with the preferred possibility put forward by Montgomery et al. (2008).
A sample of AGB/RGB stars with an excess of Li abundances is considered in order to estimate their mass loss rates. Our method is based on a correlation between the Li abundances and the stellar luminosity, using a modified version of Reimers formula. We have adopted a calibration on the basis of an empirical correlation between the mass loss rate and some stellar parameters. We conclude that most Li-rich stars have lower mass loss rates compared with the majority of AGB/RGB stars, which show no evidences of Li enhancements, so that the Li enrichment process is apparently not associated with an increased mass loss rate.
In N=4 super Yang-Mills spin chain, we compute reflection amplitudes of magnon bound-state off giant graviton. We first compute the reflection amplitude off Y=0 brane boundary and compare it with the scattering amplitude between two magnon bound-states in the bulk. We find that analytic structure of the two amplitudes are intimately related each other: the boundary reflection amplitude is a square-root of the bulk scattering amplitude. Using such relation as a guide and taking known results at weak and strong coupling limits as inputs, we find the reflection amplitude of an elementary magnon off Z=0 giant graviton boundary. The reflection phase factor is shown to solve crossing and unitarity relations. We then compute the reflection amplitude of magnon bound-state off the Z=0 brane boundary and observe that its analytic structures are again intimately related to the bulk scattering and the Y=0 boundary reflection amplitudes. We also take dyonic giant magnon limit of these reflection amplitudes and confirm that their phase-shifts agree completely with string worldsheet computations based on complex sine-Gordon soliton scattering.
A graph $G$ embedded in a surface $S$ is called an $S$-grid when every facial boundary walk has length four, that is, the topological dual graph of $G$ in $S$ is 4-regular. Aside from the case where $S$ is the torus or Klein bottle, an $S$-grid must have vertices of degrees other than four. Let the sequence of degrees other than four in $G$ be called the curvature sequence of $G$. We give a succinct characterization of $S$-grids with nonempty curvature sequence $L$ in terms of graphs that have degree sequence $L$ and are immersed in a certain way in $S$; furthermore, the immersion associated with the $S$-grid $G$ is unique and so our characterization of $S$-grids also partitions the collection of all $S$-grids.
We report a detailed theoretical study of the structural, vibrational, and optical properties of solid nitromethane using first principles density functional calculations. The ground state properties were calculated using a plane wave pseudopotential code with either the local density approximation (LDA), the generalized gradient approximation (GGA), or with a correction to include van derWaals interactions. Our calculated equilibrium lattice parameters and volume using a dispersion correction are found to be in reasonable agreement with the experimental results. Also, our calculations reproduce the experimental trends in the structural properties at high pressure. It was found to be a discontinuity in the bond length, bond angles and also a weaking of hydrogen bond strength in the pressure range from 10 to 12 GPa, picturing the structural transition from phase I to Phase II. Moreover, we predict the elastic constants of solid nitromethane and found that the corresponding bulk modulus is in good agreement with experiments. The calculated elastic constants are showing an order of C11> C22 > C33, indicating that the material is more compressible along the c-axis. We also calculated the zone center vibrational frequencies and discuss the internal and external modes of this material under pressure. From this, we found the softing of lattice modes around 8 to 12 GPa. We have also attempt the quasiparticle band structure of solid nitromethane with the G0W0 approximation and found that nitromethane is an indirect band gap insulator with a value of the band gap of about 7.8 eV with G0W0 approximation. Finally, the optical properties of this material, namely the absorptive and dispersive part of the dielectric function, and the refractive index and absorption spectra are calculated and the contribution of different transition peaks of the absorption spectra are analyzed.
We show that the set of normalized Miller-Rabin witnesses becomes equidistributed in the unit interval. This will be done by exhibiting cancellation in certain exponential sums.
Recent experiments have triggered a debate about the ability of protons to transfer through individual layers of graphene and hexagonal boron nitride (h-BN). However, calculations have shown that the barriers to proton penetration can, at more than 3 eV, be excessively high. Here, on the basis of first principles calculations, we show that the barrier for proton penetration is significantly reduced, to less than 1 eV, upon hydrogenation even in the absence of pinholes in the lattice. Analysis reveals that the barrier is reduced because hydrogenation destabilises the initial state (a deep-lying chemisorption state) and expands the honeycomb lattice through which the protons penetrate. This study offers a rationalization of the fast proton transfer observed in experiments, and highlights the ability of proton transport through single-layer materials in hydrogen rich solutions.
General criteria to check the positivity of the distribution function (phase-space consistency) of stellar systems of assigned density and anisotropy profile are useful starting points in Jeans-based modeling. Here we substantially extend previous results, and we present the inversion formula and the analytical necessary and sufficient conditions for phase-space consistency of the family of multi-component Cuddeford spherical systems: the distribution function of each density component of these systems is defined as the sum of an arbitrary number of Cuddeford distribution functions with arbitrary values of the anisotropy radius, but identical angular momentum exponent. The radial trend of anisotropy that can be realized by these models is therefore very general. As a surprising by-product of our study, we found that the ``central cusp-anisotropy theorem'' (a necessary condition for consistency relating the values of the central density slope and of the anisotropy parameter) holds not only at the center, but at all radii in consistent multi-component generalized Cuddeford systems. This last result suggests that the so--called mass--anisotropy degeneracy could be less severe than what is sometimes feared.