ShantanuT01/DACTYL-Pretraining huggingface dataset:
It is known that the $n$-dimensional hypercube $Q_n,$ for $n$ even, has a decomposition into $k$-cycles for $k=n, 2n,$ $2^l$ with $2 \leq l \leq n.$ In this paper, we prove that $Q_n$ has a decomposition into $2^mn$-cycles for $n \geq 2^m.$ As an immediate consequence of this result, we get path decompositions of $Q_n$ as well. This gives a partial solution to a conjecture posed by Ramras and also, it solves some special cases of a conjecture due to Erde.
We have compiled a large sample of isolated central galaxies from the Sloan Digital Sky Survey, which do not have a neighbour of comparable brightness within a projected distance of 1 Mpc. We use the colours, luminosities and surface brightnesses of satellite galaxies in the vicinity of these objects to estimate their atomic gas content and to derive the average total mass of HI gas contained in satellites as a function of projected radius from the primary. Recent calibrations of merging timescales from N-body simulations are used to estimate the rate at which this gas will accrete onto the primaries. Our estimated accretion rates fall short of those needed to maintain the observed level of star formation in these systems by nearly two orders of magnitude. Nevertheless, there are strong correlations between the total mass of gas in satellites and the colours and specific star formation rates of central galaxies of all stellar masses. The correlations are much weaker if we consider the total stellar mass in the satellites, rather than their total gas mass. We ask why star formation in the central galaxies should be correlated with gas contained in satellites at projected separations of a Mpc or more, well outside the virial radius of the dark matter halos of these systems. We suggest that gas-rich satellites trace an underlying reservoir of ionized gas that is accreted continuously, and that provides the fuel for ongoing star formation in galaxies in the local Universe.
We show that a coupling of non-colliding simple random walkers on the complete graph on $n$ vertices can include at most $n - \log n$ walkers. This improves the only previously known upper bound of $n-2$ due to Angel, Holroyd, Martin, Wilson, and Winkler ({\it Electron.~Commun.~Probab.~18}, 2013). The proof considers couplings of i.i.d.~sequences of Bernoulli random variables satisfying a similar avoidance property, for which there is separate interest. Our bound in this setting should be closer to optimal.
We present a spectroscopic catalog of the 1,564 brightest (J<9) M dwarf candidates in the northern sky, as selected from the SUPERBLINK proper motion catalog. Observations confirm 1,408 of the candidates to be late-K and M dwarfs with spectral subtypes K7-M6. From the low \mu>40 mas/yr proper motion limit and high level of completeness of the SUPERBLINK catalog in that magnitude range, we estimate that our spectroscopic census most likely includes >90% of all existing, northern-sky M dwarfs with apparent magnitude J<9. Only 682 stars in our sample are listed in the Third Catalog of Nearby Stars (CNS3); most others are relative unknowns and have spectroscopic data presented here for the first time. Spectral subtypes are assigned based on spectral index measurements of CaH and TiO molecular bands. A comparison of spectra from the same stars obtained at different observatories however reveals that spectral band index measurements are dependent on spectral resolution, spectrophotometric calibration, and other instrumental factors. After systematic corrections and a recalibration of the subtype-index relationships, we find that we can consistently and reliably classify all our stars to a half-subtype precision. The use of corrected spectral indices further requires us to recalibrate the \zeta parameter, from which we estimate metallicities +/-0.5dex accuracy in dwarfs of subtypes M2 and earlier, and +/-0.2dex accuracy for later (M3-M5) subtypes. Existing geometric parallax measurements are extracted from the literature for 624 stars, and are used to determine spectroscopic and photometric distances for all the other stars. Our catalog will be most useful to guide the selection of the best M dwarf targets for exoplanet searches, in particular those using high-precision radial velocity measurements.
The theory of affine processes on the space of positive semidefinite d x d matrices has been established in a joint work with Cuchiero, Filipovi\'c and Teichmann (2011). We confirm the conjecture stated therein that in dimension d greater than 1 this process class does not exhibit jumps of infinite total variation. This constitutes a geometric phenomenon which is in contrast to the situation on the positive real line (Kawazu and Watanabe, 1974). As an application we prove that the exponentially affine property of the Laplace transform carries over to the Fourier-Laplace transform if the diffusion coefficient is zero or invertible.
Recent low temperature heat capacity (C$_P$) measurements on polycrystalline samples of the pyrochlore antiferromagnet Tb$_{2+x}$Ti$_{2-x}$O$_{7+\delta}$ have shown a strong sensitivity to the precise Tb concentration $x$, with a large anomaly exhibited for $x \sim 0.005$ at $T_C \sim 0.5$ K and no such anomaly and corresponding phase transition for $x \le 0$. We have grown single crystal samples of Tb$_{2+x}$Ti$_{2-x}$O$_{7+\delta}$, with approximate composition $x=-0.001, +0.0042$, and $+0.0147$, where the $x=0.0042$ single crystal exhibits a large C$_P$ anomaly at $T_C$=0.45 K, but neither the $x=-0.001$ nor the $x=+0.0147$ single crystals display any such anomaly. We present new time-of-flight neutron scattering measurements on the $x=-0.001$ and the $x=+0.0147$ samples which show strong $\left(\frac{1}{2},\frac{1}{2},\frac{1}{2}\right)$ quasi-Bragg peaks at low temperatures characteristic of short range antiferromagnetic spin ice (AFSI) order at zero magnetic field but only under field-cooled conditions, as was previously observed in our $x = 0.0042$ single crystal. These results show that the strong $\left(\frac{1}{2},\frac{1}{2},\frac{1}{2}\right)$ quasi-Bragg peaks and gapped AFSI state at low temperatures under field cooled conditions are robust features of Tb$_2$Ti$_2$O$_7$, and are not correlated with the presence or absence of the C$_P$ anomaly and phase transition at low temperatures. Further, these results show that the ordered state giving rise to the C$_P$ anomaly is confined to $0 \leq x \leq 0.01$ for Tb$_{2+x}$Ti$_{2-x}$O$_{7+\delta}$, and is not obviously connected with conventional order of magnetic dipole degrees of freedom.
Many aesthetic models in computer vision suffer from two shortcomings: 1) the low descriptiveness and interpretability of those hand-crafted aesthetic criteria (i.e., nonindicative of region-level aesthetics), and 2) the difficulty of engineering aesthetic features adaptively and automatically toward different image sets. To remedy these problems, we develop a deep architecture to learn aesthetically-relevant visual attributes from Flickr1, which are localized by multiple textual attributes in a weakly-supervised setting. More specifically, using a bag-ofwords (BoW) representation of the frequent Flickr image tags, a sparsity-constrained subspace algorithm discovers a compact set of textual attributes (e.g., landscape and sunset) for each image. Then, a weakly-supervised learning algorithm projects the textual attributes at image-level to the highly-responsive image patches at pixel-level. These patches indicate where humans look at appealing regions with respect to each textual attribute, which are employed to learn the visual attributes. Psychological and anatomical studies have shown that humans perceive visual concepts hierarchically. Hence, we normalize these patches and feed them into a five-layer convolutional neural network (CNN) to mimick the hierarchy of human perceiving the visual attributes. We apply the learned deep features on image retargeting, aesthetics ranking, and retrieval. Both subjective and objective experimental results thoroughly demonstrate the competitiveness of our approach.
The generation-defining Vera C. Rubin Observatory will make state-of-the-art measurements of both the static and transient universe through its Legacy Survey for Space and Time (LSST). With such capabilities, it is immensely challenging to optimize the LSST observing strategy across the survey's wide range of science drivers. Many aspects of the LSST observing strategy relevant to the LSST Dark Energy Science Collaboration, such as survey footprint definition, single visit exposure time and the cadence of repeat visits in different filters, are yet to be finalized. Here, we present metrics used to assess the impact of observing strategy on the cosmological probes considered most sensitive to survey design; these are large-scale structure, weak lensing, type Ia supernovae, kilonovae and strong lens systems (as well as photometric redshifts, which enable many of these probes). We evaluate these metrics for over 100 different simulated potential survey designs. Our results show that multiple observing strategy decisions can profoundly impact cosmological constraints with LSST; these include adjusting the survey footprint, ensuring repeat nightly visits are taken in different filters and enforcing regular cadence. We provide public code for our metrics, which makes them readily available for evaluating further modifications to the survey design. We conclude with a set of recommendations and highlight observing strategy factors that require further research.
In this note we consider the moduli space of stable bundles of rank two on a very general quintic surface. We study the potentially obstructed points of the moduli space via the spectral covering of a twisted endomorphism. This analysis leads to generically non-reduced components of the moduli space, and components which are generically smooth of more than the expected dimension. We obtain a sharp bound asked for by O'Grady saying when the moduli space is good.
The invariant integration method for Chern-Simons theory defined on the compact hyperbolic manifold {\Gamma}\H^3 is verified in the semiclassical approximation. The semiclassical limit for the partition function is presented. We discuss briefly L^2 - analytic torsion and the eta invariant of Atiyah-Patodi-Singer for compact hyperbolic 3-manifolds.
Over the last 40 years, multi-frequency observations, coupled with advances in theoretical modelling, have led to a much fuller understanding of the nova phenomenon. Here I give a brief review of the current state of knowledge of Classical and Recurrent Novae including their central systems; the causes and consequences of their outbursts; sub-types, and possible relationships to Type Ia Supernovae. Particular attention is paid to the Recurrent Nova RS Ophiuchi as it shows a wealth of phenomena associated with its 2006 outburst. Finally, some open questions and avenues for future work are summarised.
We study the optical light curves - primarily probing the variable emission from the accretion disk - of ~ 900 extreme variability quasars (EVQs, with maximum flux variations more than 1 mag) over an observed-frame baseline of ~ 16 years using public data from the SDSS Stripe 82, PanSTARRS-1 and the Dark Energy Survey. We classify the multi-year long-term light curves of EVQs into three categories roughly in the order of decreasing smoothness: monotonic decreasing or increasing (3.7%), single broad peak and dip (56.8%), and more complex patterns (39.5%). The rareness of monotonic cases suggests that the major mechanisms driving the extreme optical variability do not operate over timescales much longer than a few years. Simulated light curves with a damped random walk model generally under-predict the first two categories with smoother long-term trends. Despite the different long-term behaviors of these EVQs, there is little dependence of the long-term trend on the physical properties of quasars, such as their luminosity, BH mass, and Eddington ratio. The large dynamic range of optical flux variability over multi-year timescales of these EVQs allows us to explore the ensemble correlation between the short-term (< 6 months) variability and the seasonal-average flux across the decade-long baseline (the rms-mean flux relation). We find that unlike the results for X-ray variability studies, the linear short-term flux variations do not scale with the seasonal-average flux, indicating different mechanisms that drive the short-term flickering and long-term extreme variability of accretion disk emission. Finally, we present a sample of 16 EVQs, where the approximately bell-shaped large amplitude variation in the light curve can be reasonably well fit by a simple microlensing model.
In this work we initiate the conformal bootstrap program for ${\mathcal N}=2$ superconformal field theories in four dimensions. We promote an abstract operator-algebraic viewpoint in order to unify the description of Lagrangian and non-Lagrangian theories, and formulate various conjectures concerning the landscape of theories. We analyze in detail the four-point functions of flavor symmetry current multiplets and of ${\mathcal N}=2$ chiral operators. For both correlation functions we review the solution of the superconformal Ward identities and describe their superconformal block decompositions. This provides the foundation for an extensive numerical analysis discussed in the second half of the paper. We find a large number of constraints for operator dimensions, OPE coefficients, and central charges that must hold for any ${\mathcal N}=2$ superconformal field theory.
We explore a nonlinear field model to describe the interplay between the ability of excitons to be Bose-condensed and their interaction with other modes of a crystal. We apply our consideration to the long-living para-excitons in Cu2O. Taking into account the exciton-phonon interaction and introducing a coherent phonon part of the moving condensate, we derive the dynamic equations for the exciton-phonon condensate. These equations can support localized solutions, and we discuss the conditions for the moving inhomogeneous condensate to appear in the crystal. We calculate the condensate wave function and energy, and a collective excitation spectrum in the semiclassical approximation; the inside-excitations were found to follow the asymptotic behavior of the macroscopic wave function exactly. The stability conditions of the moving condensate are analyzed by use of Landau arguments, and Landau critical parameters appear in the theory. Finally, we apply our model to describe the recently observed interference and strong nonlinear interaction between two coherent exciton-phonon packets in Cu2O.
We review recent studies of coherent phonons (CPs) corresponding to the radial breathing mode (RBM) and G-mode in single-wall carbon nanotubes (SWCNTs) and graphene. Because of the bandgap-diameter relationship, RBM-CPs cause bandgap oscillations in SWCNTs, modulating interband transitions at terahertz frequencies. Interband resonances enhance CP signals, allowing for chirality determination. Using pulse shaping, one can selectively excite speci!c-chirality SWCNTs within an ensemble. G-mode CPs exhibit temperature-dependent dephasing via interaction with RBM phonons. Our microscopic theory derives a driven oscillator equation with a density-dependent driving term, which correctly predicts CP trends within and between (2n+m) families. We also find that the diameter can initially increase or decrease. Finally, we theoretically study the radial breathing like mode in graphene nanoribbons. For excitation near the absorption edge, the driving term is much larger for zigzag nanoribbons. We also explain how the armchair nanoribbon width changes in response to laser excitation.
The most evident features of colour-magnitude diagrams of galaxies are the red sequence of quiescent galaxies, extending up to the brightest elliptical galaxies, and the blue cloud of star-forming galaxies, which is truncated at a luminosity L~L*. The truncation of the blue cloud indicates that in the most massive systems star formation must be quenched. For this to happen the virial-temperature galactic gas must be kept hot and any accreted cold gas must be heated. The elimination of accreted cold gas can be due to thermal evaporation by the hot interstellar medium, which in turn is prevented from cooling by feedback from active galactic nuclei.
We analyze the Blume-Emery-Griffiths (BEG) associative memory with sparse patterns and at zero temperature. We give bounds on its storage capacity provided that we want the stored patterns to be fixed points of the retrieval dynamics. We compare our results to that of other models of sparse neural networks and show that the BEG model has a superior performance compared to them.
We study the conjectured exact S-matrix for the scattering of BPS magnon boundstates in the spin-chain description of planar N=4 SUSY Yang-Mills. The conjectured S-matrix exhibits both simple and double poles at complex momenta. Some of these poles lie parametrically close to the real axis in momentum space on the branch where particle energies are positive. We show that all such poles are precisely accounted for by physical processes involving one or more on-shell intermediate particles belonging to the known BPS spectrum.
The covariant canonical formalism for four-dimensional BF theory is performed. The aim of the paper is to understand in the context of the covariant canonical formalism both the reducibility that some first class constraints have in Dirac's canonical analysis and also the role that topological terms play. The analysis includes also the cases when both a cosmological constant and the second Chern character are added to the pure BF action. In the case of the BF theory supplemented with the second Chern character, the presymplectic 3-form is different to the one of the BF theory in spite of the fact both theories have the same equations of motion while on the space of solutions they both agree to each other. Moreover, the analysis of the degenerate directions shows some differences between diffeomorphisms and internal gauge symmetries.
We study the effect of electron-electron interaction on the charge and spin structures at the edge of integer quantum Hall liquids, under three different kinds of confining potentials. Our exact diagonalization calculation for small systems indicates that the low energy excitations of \nu=1 ferromagnetic state are bosonic edge spin waves. Instabilities of the ferromagnetic state with altering confinement strength result from the softening of these edge spin waves, and formation of edge spin textures. In \nu\lesssim 2 regime, exact diagonalization on edge electron systems indicates that compact Hartree-Fock states with different total spin always become ground states in some regions of parameter space, and the ground states appear in between two compact states are their edge spin waves. The initial \nu=2 instability is toward the compact state with total spin 1. Larger systems are studied using a microscopic trial wave functions, and some quantitative predictions on the edge instabilities for a certain type of confining potential are reached in the thermodynamic limit.
We establish basic properties of a sheaf of graded algebras canonically associated to every relative affine scheme $f : X \rightarrow S$ endowed with an action of the additive group scheme $\mathbb{G}_{ a,S}$ over a base scheme or algebraic space $S$, which we call the (relative) Rees algebra of the $\mathbb{G}_{ a,S}$-action. We illustrate these properties on several examples which played important roles in the development of the algebraic theory of locally nilpotent derivations and give some applications to the construction of families of affine threefolds with Ga-actions.
We investigate the chemical bonding characteristics of the transition metal dichalcogenides based on their static and dynamical atomic charges within Density Functional Theory. The dynamical charges of the trigonal transition metal dichalcogenides are anomalously large, while in their hexagonal counterparts, their sign is even counterintuitive i.e. the transition metal takes the negative charge. This phenomenon cannot be understood simply in terms of a change in the static atomic charge as it results from a local change of polarization. We present our theoretical understanding of these phenomena based on the perturbative response of the system to a static electric field and by investigating the hybridization of the molecular orbitals near the Fermi level. Furthermore, we establish a link between the sign of the Born effective charge and the $\pi$-backbonding in organic chemistry and propose an experimental procedure to verify the calculated sign of the dynamical charge in the transition metal dichalcogenides.
We present a fourth catalog of HI sources from the Arecibo Legacy Fast ALFA (ALFALFA) Survey. We report 541 detections over 136 deg2, within the region of the sky having 22h < R.A. < 03h and 24 deg < Dec. < 26 deg . This complements a previous catalog in the region 26 deg < Dec. < 28 deg (Saintonge et al. 2008). We present here the detections falling into three classes: (a) extragalactic sources with S/N > 6.5, where the reliability of the catalog is better than 95%; (b) extragalactic sources 5.0 < S/N < 6.5 and a previously measured optical redshift that corroborates our detection; or (c) High Velocity Clouds (HVCs), or subcomponents of such clouds, in the periphery of the Milky Way. Of the 541 objects presented here, 90 are associated with High Velocity Clouds, while the remaining 451 are identified as extragalactic objects. Optical counterparts have been matched with all but one of the extragalactic objects.
The existence and uniqueness of a global positive solution is proven for the system of stochastic differential equations describing a nonautonomous stochastic density dependent predator-prey model with Holling-type II functional response disturbed by white noise, centered and non-centered Poisson noises. Sufficient conditions are obtained for stochastic ultimate boundedness, stochastic permanence, non-persistence in the mean, weak persistence in the mean and extinction of a population densities in the considered stochastic predator-prey model.
We study the semileptonic decays of the lowest-lying $bc$ baryons to the lowest-lying $cc$ baryons ($\Xi_{bc}^{(\prime*)}\to \Xi_{cc}^{(*)}$ and $\Omega_{bc}^{(\prime*)}\to \Omega_{cc}^{(*)}$), in the limit $m_b, m_c \gg \Lambda_\mathrm{QCD}$ and close to the zero recoil point. The separate heavy quark spin symmetries make it possible to describe all these decays using a single form factor. We also show how these constraints can be used to test the validity of different quark model calculations. $bb$ to $bc$ baryon decays are also discussed.