ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study the impact that uncertainties on assumed relations between galaxy bias parameters have on constraints of the local PNG $f_{\rm NL}$ parameter. We focus on the relation between the linear density galaxy bias $b_1$ and local PNG bias $b_\phi$ in an idealized forecast setup with multitracer galaxy power spectrum and bispectrum data. We consider two parametrizations of galaxy bias: 1) one inspired by the universality relation where $b_\phi = 2\delta_c\left(b_1 - p\right)$ and $p$ is a free parameter; and 2) another in which the product of bias parameters and $f_{\rm NL}$, like $f_{\rm NL} b_\phi$, is directly fitted for. The constraints on the $f_{\rm NL}-p$ plane are markedly bimodal, and both the central value and width of marginalized constraints on $f_{\rm NL}$ depend sensitively on the priors on $p$. Assuming fixed $p=1$ in the constraints with a fiducial value of $p=0.55$ can bias the inferred $f_{\rm NL}$ by $0.5\sigma$ to $1\sigma$; priors $\Delta p \approx 0.5$ around this fiducial value are however sufficient in our setup to return unbiased constraints. In power spectrum analyses, parametrization 2, that makes no assumptions on $b_\phi$, can distinguish $f_{\rm NL} \neq 0$ with the same significance as parametrization 1 assuming perfect knowledge of $b_\phi$ (the value of $f_{\rm NL}$ is however left unknown). A drawback of parametrization 2 is that the addition of the bispectrum information is not as beneficial as in parametrization 1. Our results motivate strongly the incorporation of mitigation strategies for bias uncertainties in PNG constraint analyses, as well as further theoretical studies on the relations between bias parameters to better inform those strategies.
We show that a tree of order $n$ has at most $O(5^{n/4})$ nonisomorphic subtrees, and that this bound is best possible. We also prove an analogous result for the number of nonisomorphic rooted subtrees of a rooted tree.
We discuss image formation in gravitational lensing systems using wave optics. Applying the Fresnel-Kirchhoff diffraction formula to waves scattered by a gravitational potential of a lens object, we demonstrate how images of source objects are obtained directly from wave functions without using a lens equation for gravitational lensing.
New CO observations at the center of cooling flow in Perseus cluster \cite{salome06} show a clear correlation of the molecular gas with the previously detected H-$\alpha$ filaments \cite{conselice01}. In this poster, we present high resolution multi-phase simulations of the Perseus Cluster, taking into account the AGN feedback in form of hot buoyant bubbles. These simulations show that significant amount of gas can cool far from the center. The AGN feedback provides some heating, but also trigger the hot gas compression, that favours cooling (positive feedback), even at high radius ($R>30 \rm{kpc}$). The cooled gas flows into the cluster core forming the observed filaments.
Mixed-based point cloud augmentation is a popular solution to the problem of limited availability of large-scale public datasets. But the mismatch between mixed points and corresponding semantic labels hinders the further application in point-wise tasks such as part segmentation. This paper proposes a point cloud augmentation approach, PointManifoldCut(PMC), which replaces the neural network embedded points, rather than the Euclidean space coordinates. This approach takes the advantage that points at the higher levels of the neural network are already trained to embed its neighbors relations and mixing these representation will not mingle the relation between itself and its label. We set up a spatial transform module after PointManifoldCut operation to align the new instances in the embedded space. The effects of different hidden layers and methods of replacing points are also discussed in this paper. The experiments show that our proposed approach can enhance the performance of point cloud classification as well as segmentation networks, and brings them additional robustness to attacks and geometric transformations. The code of this paper is available at: https://github.com/fun0515/PointManifoldCut.
In this work two different boundary conditions for first order gravity, corresponding to a null and a negative cosmological constant respectively, are studied. Both boundary conditions allows to obtain the standard black hole thermodynamics. Furthermore both boundary conditions define a canonical ensemble. Additionally the quasilocal energy definition is obtained for the null cosmological constant case.
We investigate pre-processing using the observed quenched fraction of group and cluster galaxies in the Yang et al. (2007) SDSS-DR7 group catalogue in the redshift range of 0.01 < z < 0.045. We categorize group galaxies as virialized, infall or backsplash and we apply a combination of the Dressler-Shectman statistic and group member velocities to identify subhaloes. On average the fraction of galaxies that reside in subhaloes is a function of host halo mass, where more massive systems have a higher fraction of subhalo galaxies both in the overall galaxy and infall populations. Additionally, we find that between 2 < r_200 < 3 the quiescent fraction is higher in the subhalo population with respect to both the field and non-subhalo populations. At these large radii (2 < r_200 < 3), the majority of galaxies (~ 80 %) belong to the infall population and therefore, we attribute the enhanced quenching to infalling subhalo galaxies, indicating that pre-processing has occurred in the subhalo population. We conclude that pre-processing plays a significant role in the observed quiescent fraction, but only for the most massive (M_halo > 10^14.5 M_sun) systems in our sample.
Based on one-month long MMT time-series observations of the open cluster M37, we monitored light variations of nearly 2500 red dwarfs and successfully identified 420 flare events from 312 cluster M dwarf stars. For each flare light curve, we derived observational and physical parameters, such as flare shape, peak amplitude, duration, energy, and peak luminosity. We show that cool stars produce serendipitous flares energetic enough to be observed in the $r$-band, and their temporal and peak characteristics are almost the same as those in traditional $U$-band observations. We also found many large-amplitude flares with inferred $\Delta u > 6$ mag in the cluster sample which had been rarely reported in previous ground-based observations. Following the ergodic hypothesis, we investigate in detail statistical properties of flare parameters over a range of energy ($E_{r}$ $\simeq$ $10^{31}-10^{34}$ erg). As expected, there are no statistical differences in the distributions of flare timescales, energies, and frequencies among stars of the same age and mass group. We note that our sample tend to have longer rise and decay timescales compared to those seen in field flare stars of the same spectral type and be more energetic. Flare frequency distributions follow power-law distributions with slopes $\beta \sim0.62-1.21$ for all flare stars and $\beta \sim0.52-0.97$ for stars with membership information ($P_{mem} \geq 0.2$). These are in general agreement with previous works on flare statistics of young open clusters and nearby field stars. Our results give further support to the classical age-activity relations.
We have used the Robert C. Byrd Green Bank Telescope to perform the most sensitive search to date for neutral atomic hydrogen (HI) in the circumstellar envelope (CSE) of the carbon star IRC+10216. Our observations have uncovered a low surface brightness HI shell of diameter ~1300" (~0.8 pc), centered on IRC+10216. The HI shell has an angular extent comparable to the far ultraviolet-emitting astrosphere of IRC+10216 previously detected with the GALEX satellite, and its kinematics are consistent with circumstellar matter that has been decelerated by the local interstellar medium. The shell appears to completely surround the star, but the highest HI column densities are measured along the leading edge of the shell, near the location of a previously identified bow shock. We estimate a total mass of atomic hydrogen associated with IRC+10216 CSE of M_HI~3x10e-3 M_sun. This is only a small fraction of the expected total mass of the CSE (<1%) and is consistent with the bulk of the stellar wind originating in molecular rather than atomic form, as expected for a cool star with an effective temperature T_eff<~2200 K. HI mapping of a 2 deg x 2 deg region surrounding IRC+10216 has also allowed us to characterize the line-of-sight interstellar emission in the region and has uncovered a link between diffuse FUV emission southwest of IRC+10216 and the Local Leo Cold Cloud.
We study equivariant affine embeddings of homogeneous spaces and their equivariant automorphisms. An example of a quasiaffine, but not affine, homogeneous space with finitely many equivariant automorphisms is presented. We prove the solvability of any connected group of equivariant automorphisms for an affine embedding with a fixed point and finitely many orbits. This is applied to studying the orbital decomposition for algebraic monoids and canonical embeddings of quasiaffine homogeneous spaces, i.e., those affine embeddings associated with the coordinate algebras of homogeneous spaces, provided the latter algebras are finitely generated. We pay special attention to the canonical embeddings of quotient spaces of reductive groups modulo the unipotent radicals of parabolic subgroups. For these varieties, we describe the orbital decomposition, compute the modality of the group action, and find out which of them are smooth. We also describe minimal ambient modules for these canonical embeddings provided that the acting group is simply connected.
Given a continuous, odd, semi-simple $2$-dimensional representation of $G_{\mathbb{Q},Np}$ over a finite field of odd characteristic $p$ and a prime $\ell$ not dividing $Np$, we study the relation between the universal deformation rings of the corresponding pseudo-representation for the groups $G_{\mathbb{Q},N\ell p}$ and $G_{\mathbb{Q},Np}$. As a related problem, we investigate when the universal pseudo-representation arises from an actual representation over the universal deformation ring. Under some hypotheses, we prove analogues of theorems of Boston and B\"{o}ckle for the reduced pseudo-deformation rings. We improve these results when the pseudo-representation is unobstructed and $p$ does not divide $\ell^2-1$. When the pseudo-representation is unobstructed and $p$ divides $\ell+1$, we prove that the universal deformation rings in characteristic $0$ and $p$ of the pseudo-representation for $G_{\mathbb{Q},N\ell p}$ are not local complete intersection rings. As an application of our main results, we prove a big $R=\mathbb{T}$ theorem.
We present a mapping which associates pure N-qubit states with a polynomial. The roots of the polynomial characterize the state completely. Using the properties of the polynomial we construct a way to determine the separability and the number of unentangled qubits of pure N-qubit states.
Under GRH, we establish a version of Duke's short-sum theorem for entire Artin $L$-functions. This yields corresponding bounds for residues of Dedekind zeta functions. All numerical constants in this work are explicit.
Let S be a cyclic n-ary sequence. We say that S is a {\it universal cycle} ((n,k)-Ucycle) for k-subsets of [n] if every such subset appears exactly once contiguously in S, and is a Ucycle packing if every such subset appears at most once. Few examples of Ucycles are known to exist, so the relaxation to packings merits investigation. A family {S_n} of (n,k)-Ucycle packings for fixed k is a near-Ucycle if the length of S_n is $(1-o(1))\binom{n}{k}$. In this paper we prove that near-(n,k)-Ucycles exist for all k.
MACE, a model for the propagation of mach cones in the velocity field of heavy ion collisions (as created by hydrodynamical models) is explained. It is tested on an analytical test case (static medium) and applied to velocity fields created by the Particle-in-Cell model from LHC and RHIC initial conditions.
The far-ultraviolet (FUV; 912--1700 \AA) radiation field from accreting central stars in Classical T Tauri systems influences the disk chemistry during the period of giant planet formation. Previous efforts to measure the true stellar+accretion-generated FUV luminosity (both hot gas emission lines and continua) have been complicated by a combination of low-sensitivity and/or low-spectral resolution and did not include the contribution from the bright Ly$\alpha$ emission line. In this work, we present a high-resolution spectroscopic study of the FUV radiation fields of 16 T Tauri stars whose dust disks display a range of evolutionary states. We include reconstructed Ly$\alpha$ line profiles and remove atomic and molecular disk emission (from H$_{2}$ and CO fluorescence) to provide robust measurements of both the FUV continuum and hot gas lines (e.g., Ly$\alpha$, \ion{N}{5}, \ion{C}{4}, \ion{He}{2}) for an appreciable sample of T Tauri stars for the first time. We find that the flux of the typical Classical T Tauri Star FUV radiation field at 1 AU from the central star is $\sim$ 10$^{7}$ times the average interstellar radiation field. The Ly$\alpha$ emission line contributes an average of 88% of the total FUV flux, with the FUV continuum accounting for an average of 8%. Both the FUV continuum and Ly$\alpha$ flux are strongly correlated with \ion{C}{4} flux, suggesting that accretion processes dominate the production of both of these components. On average, only $\sim$ 0.5% of the total FUV flux is emitted between the Lyman limit (912 \AA) and the H$_{2}$ (0 -- 0) absorption band at 1110 \AA. The total and component-level high-resolution radiation fields are made publicly available in machine-readable format.
We respond to S.-K. Yip's criticism of our work on the classification of spinor condensates. We explain why his criticism is unfounded, emphasizing that the phases he mentions have been addressed in our paper cond-mat/0611230. To provide a constructive aspect to this response, we use it as an opportunity to show how our classification scheme makes explicit not only spin rotations which leave spinor states invariant, but also the phase factors which need to accompany them.
The cross sections for the multiple production of the lightest neutral Higgs boson at high--energy $e^+ e^-$ colliders are presented in the framework of the Minimal Supersymmetric extension of the Standard Model (MSSM). We consider production through Higgs--strahlung, associated production of the scalar and the pseudoscalar bosons, and the fusion mechanisms for which we will use the effective longitudinal vector--boson approximation. These cross sections allow one to determine trilinear Higgs couplings $\lambda_{Hhh}$ and $\lambda_{hhh}$, which are theoretically predicted by the Higgs potential.
We explore the use of ground-based surface brightness fluctuation (SBF) measurements to constrain distances to nearby dwarf galaxies. Using archival CFHT Megacam imaging data for a sample of 27 nearby dwarfs, we demonstrate that reliable SBF measurements and distances accurate to 15\% are possible even for very low surface brightness (LSB, $\mu_{i0}>24$ mag/arcsec$^2$) galaxies with modest, $\sim$hour-long exposures with CFHT. Combining our sample with a recent sample of 7 dwarfs with SBF measured with HST from the literature, we provide the most robust empirical SBF calibration to-date for the blue colors expected for these low mass systems. Our calibration is credible over the color range $0.3\lesssim g-i\lesssim0.8$ mag. It is also the first SBF calibration tied completely to TRGB distances as each galaxy in the sample has a literature TRGB distance. We find that even though the intrinsic scatter in SBF increases for blue galaxies, the rms scatter in the calibration is still $\lesssim0.3$ mag. We verify our measurements by comparing with HST SBF measurements and detailed image simulations. We argue that ground-based SBF is a very useful tool for characterizing dwarf satellite systems and field dwarfs in the nearby, D$\lesssim$20 Mpc universe.
Electron pairing due to a repulsive Coulomb interaction in a triple quantum dot (TQD) is experimentally studied. It is found that electron pairing in two dots of a TQD is mediated by the third dot, when the third dot strongly couples with the other two via Coulomb repulsion so that the TQD is in the twofold degenerate ground states of (1, 0, 0) and (0, 1, 1) charge configurations. Using the transport spectroscopy that monitors electron transport through each individual dot of a TQD, we analyze how to achieve the degeneracy in experiments, how the degeneracy is related to electron pairing, and the resulting nontrivial behavior of electron transport. Our findings may be used to design a system with nontrivial electron correlations and functionalities.
The possibilities of global (non-perturbative) gauge anomalies for a class of gauge groups are investigated. Intimately connected to branching rules and topological aspect of gauge groups, the results are applied to the study of unification gauge groups such as SO(10), SU(5), $E_6$, $E_8$ etc. Especially, we discuss extensively about the selection rule for generation numbers $N_f+N_{mf}=even\ge 4$ in SO(10) and supersymmetric SO(10) unification theories as originally proposed by the author$^1$, where $N_f$ and $N_{mf}$ denote the generation numbers for ordinary fermions and mirror fermions respectively. This is due to the global gauge anomalies from some subgroups of SO(10) in a fundamental spinor representation such that the ill-defined 'large' gauge transformations in the subgroup cannot be unwrapped in SO(10) in the quantum theory as we noted$^1$. A similar result related to left-right symmetric models is also given.
We report here results on the analysis of correlated flux variations between the optical and GeV $\gamma$-ray bands in three bright BL Lac objects, namely AO\, 0235+164, OJ 287 and PKS 2155$-$304. This was based on the analysis of about 10 years of data from the {\it Fermi} Gamma-ray Space Telescope covering the period between 08 August 2008 to 08 August 2018 along with optical data covering the same period. For all the sources, during the flares analysed in this work, the optical and $\gamma$-ray flux variations are found to be closely correlated. From broad band spectral energy distribution modelling of different epochs in these sources using the one zone leptonic emission model, we found that the optical-UV emission is dominated by synchrotron emission from the jet. The $\gamma$-ray emission in the low synchrotron peaked sources AO\, 0235+164 and OJ 287 are found to be well fit with external Compton (EC) component, while, the $\gamma$-ray emission in the high synchrotron peaked source PKS 2155$-$304 is well fit with synchrotron self Compton component. Further we note that the $\gamma$-ray emission during the high flux state of AO 0235+164 (epochs A and B) requires seed photons from both the dusty torus and broad line region, while the $\gamma$-ray emission in OJ 287 and during epochs C and D of AO\,0235+164 can be modelled by EC scattering of infra-red photons from the torus.
Unsupervised deep learning has recently demonstrated the promise of producing high-quality samples. While it has tremendous potential to promote the image colorization task, the performance is limited owing to the high-dimension of data manifold and model capability. This study presents a novel scheme that exploits the score-based generative model in wavelet domain to address the issues. By taking advantage of the multi-scale and multi-channel representation via wavelet transform, the proposed model learns the richer priors from stacked coarse and detailed wavelet coefficient components jointly and effectively. This strategy also reduces the dimension of the original manifold and alleviates the curse of dimensionality, which is beneficial for estimation and sampling. Moreover, dual consistency terms in the wavelet domain, namely data-consistency and structure-consistency are devised to leverage colorization task better. Specifically, in the training phase, a set of multi-channel tensors consisting of wavelet coefficients is used as the input to train the network with denoising score matching. In the inference phase, samples are iteratively generated via annealed Langevin dynamics with data and structure consistencies. Experiments demonstrated remarkable improvements of the proposed method on both generation and colorization quality, particularly in colorization robustness and diversity.
The resonance arrangement $\mathcal{A}_n$ is the arrangement of hyperplanes in $\mathbb{R}^n$ given by all hyperplanes of the form $\sum_{i \in I} x_i = 0$, where $I$ is a nonempty subset of $\{1,\dots,n\}$. We consider the characteristic polynomial $\chi(\mathcal{A}_n; t)$ of the resonance arrangement, whose value $R_n$ at $-1$ is of particular interest, and corresponds to counts of generalized retarded functions in quantum field theory, among other things. No formula is known for either the characteristic polynomial or $R_n$, though $R_n$ has been computed up to $n=8$. By exploiting symmetry and using computational methods, we compute the characteristic polynomial of $\mathcal{A}_9$, and thus obtain $R_9$. The coefficients of the characteristic polynomial are also equal to the so-called Betti numbers of the complexified hyperplane arrangement; that is, the coefficient of $t^{n-i}$ is denoted by the Betti number $b_i(\mathcal{A}_n)$. Explicit formulas are known for the Betti numbers up to $b_3(\mathcal{A}_n)$. Using computational methods, we also obtain an explicit formula for $b_4(\mathcal{A}_n)$, which gives the $t^{n-4}$ coefficient of the characteristic polynomial.
We formulate a number of related generalisations of the weight part of Serre's conjecture to the case of GL(n) over an arbitrary number field, motivated by the formalism of the Breuil-M\'ezard conjecture. We give evidence for these conjectures, and discuss their relationship to previous work. We generalise one of these conjectures to the case of connected reductive groups which are unramified over Q_p, and we also generalise the second author's previous conjecture for GL(n)/Q to this setting, and show that the two conjectures are generically in agreement.
We discuss an autonomous motor based on a Brownian particle driven from thermal equilibrium by periodic in time variation of the internal potential through which the particle interacts with molecules of the surrounding thermal bath. We demonstrate for such a motor the absence of a linear response regime: The average driving force and drift velocity are shown to be quadratic in both the frequency and amplitude of the variation. The adiabatic approximation (of an infinitely slow variation) and the leading correction to it (linear in the variation's frequency) both lead to zero drift and are insufficient to describe the motor's operation.
In this paper, we prove that if $u$ is a solution to the Liouville equation \begin{align} \label{scalliouville} \Delta u+e^{2u} =0 \quad \mbox{in $\mathbb{R}^2$,} \end{align}then the diameter of $\mathbb{R}^2$ under the conformal metric $g=e^{2u}\delta$ is bounded below by $\pi$. Here $\delta$ is the Euclidean metric in $\mathbb{R}^2$. Moreover, we explicitly construct a family of solutions such that the corresponding diameters of $\mathbb{R}^2$ range over $[\pi,2\pi)$.   We also discuss supersolutions. We show that if $u$ is a supersolution and $\int_{\mathbb{R}^2} e^{2u} dx<\infty$, then the diameter of $\mathbb{R}^2$ under the metric $e^{2u}\delta$ is less than or equal to $2\pi$.   For radial supersolutions, we use both analytical and geometric approaches to prove some inequalities involving conformal lengths and areas of disks in $\mathbb{R}^2$. We also discuss the connection of the above results with the sphere covering inequality in the case of Gaussian curvature bounded below by $1$.   Higher dimensional generalizations are also discussed.