ShantanuT01/DACTYL-Pretraining huggingface dataset:
We introduce the Colombeau Quaternio Algebra and study its algebraic structure. We also study the dense ideal, dense in the algebraic sense, of the algebra of Colombeau generalized numbers and use this show the existence of a maximal ting of quotions which is Von Neumann regular. Recall that it is already known that then algebra of COlombeau generalized numbers is not Von Neumann regular. We also use the study of the dense ideals to give a criteria for a generalized holomorphic function to satisfy the identity theorem.   Aragona-Fernadez-Juriaans showed that a generalized holomorphic function has a power series. This is one of the ingredients use to prove the identity theorem.
Given a place $\omega$ of a global function field $K$ over a finite field, with associated affine function ring $R_\omega$ and completion $K_\omega$, the aim of this paper is to give an effective joint equidistribution result for renormalized primitive lattice points $(a,b)\in {R_\omega}^2$ in the plane ${K_\omega}^2$, and for renormalized solutions to the gcd equation $ax+by=1$. The main tools are techniques of Goronik and Nevo for counting lattice points in well-rounded families of subsets. This gives a sharper analog in positive characteristic of a result of Nevo and the first author for the equidistribution of the primitive lattice points in $\ZZ^2$.
The strong chromatic number, $\chi_S(G)$, of an $n$-vertex graph $G$ is the smallest number $k$ such that after adding $k\lceil n/k\rceil-n$ isolated vertices to $G$ and considering {\bf any} partition of the vertices of the resulting graph into disjoint subsets $V_1, \ldots, V_{\lceil n/k\rceil}$ of size $k$ each, one can find a proper $k$-vertex-coloring of the graph such that each part $V_i$, $i=1, \ldots, \lceil n/k\rceil$, contains exactly one vertex of each color.   For any graph $G$ with maximum degree $\Delta$, it is easy to see that $\chi_S(G)\geq\Delta+1$. Recently, Haxell proved that $\chi_S(G) \leq 3\Delta -1$. In this paper, we improve this bound for graphs with large maximum degree. We show that $\chi_S(G)\leq 2\Delta$ if $\Delta \geq n/6$ and prove that this bound is sharp.
We consider the asymmetric exclusion process with a driven tagged particle on Z which has different jump rates from other particles and show that the tagged particle can have a ballistic behavior when the non-tagged particles have non-nearest-neighbor jump rates. We show the existence of some non-trivial invariant measures for the environment process viewed from the tagged particle. Our arguments are based on coupling, the martingale approach, and analyzing currents through fixed bonds.
Let $\mathcal{T}$ be a supercritical Galton-Watson tree with a bounded offspring distribution that has mean $\mu >1$, conditioned to survive. Let $\varphi_{\mathcal{T}}$ be a random embedding of $\mathcal{T}$ into $\mathbb{Z}^d$ according to a simple random walk step distribution. Let $\mathcal{T}_p$ be percolation on $\mathcal{T}$ with parameter $p$, and let $p_c = \mu^{-1}$ be the critical percolation parameter. We consider a random walk $(X_n)_{n \ge 1}$ on $\mathcal{T}_p$ and investigate the behavior of the embedded process $\varphi_{\mathcal{T}_p}(X_n)$ as $n\to \infty$ and simultaneously, $\mathcal{T}_p$ becomes critical, that is, $p=p_n\searrow p_c$. We show that when we scale time by $n/(p_n-p_c)^3$ and space by $\sqrt{(p_n-p_c)/n}$, the process $(\varphi_{\mathcal{T}_p}(X_n))_{n \ge 1}$ converges to a $d$-dimensional Brownian motion. We argue that this scaling can be seen as an interpolation between the scaling of random walk on a static random tree and the anomalous scaling of processes in critical random environments.
We use the method of gauging equations to construct the electromagnetic current operator for the two-nucleon system in a theory with a finite cutoff. The employed formulation ensures that the two-nucleon T-matrix and corresponding five-point function, in the cutoff theory, are identical to the ones formally defined by a reference theory without a cutoff. A feature of our approach is that it effectively introduces a cutoff into the reference theory in a way that maintains the long-range part of the exchange current operator; for applications to effective field theory (EFT), this property is usually sufficient to guarantee the predictive power of the resulting cutoff theory. In addition, our approach leads to Ward-Takahashi (WT) identities that are linear in the interactions.   From the point of view of EFT's where such a WT identity is satisfied in the reference theory, this ensures that gauge invariance in the cutoff theory is maintained order by order in the expansion.
We examine the influence of the quadrupole moment of a slowly rotating neutron star on the oscillations of non-slender accretion tori. We apply previously developed methods to perform analytical calculations of frequencies of the radial epicyclic mode of a torus in the specific case of the Hartle-Thorne geometry. We present here our preliminary results and provide a brief comparison between the calculated frequencies and the frequencies previously obtained assuming both standard and linearized Kerr geometry. Finally, we shortly discuss the consequences for models of high-frequency quasi-periodic oscillations observed in low-mass X-ray binaries.
The structure and kinematics of gaseous, disk-halo interfaces are imprinted with the processes that transfer mass, metals, and energy between galactic disks and their environments. We study the extraplanar diffuse ionized gas (eDIG) layer in the interacting, star-forming galaxy NGC 5775 to better understand the consequences of star-formation feedback on the dynamical state of the thick-disk interstellar medium (ISM). Combining emission-line spectroscopy from the Robert Stobie Spectrograph on the Southern African Large Telescope with radio continuum observations from Continuum Halos in Nearby Galaxies - an EVLA Survey, we ask whether thermal, turbulent, magnetic field, and cosmic-ray pressure gradients can stably support the eDIG layer in dynamical equilibrium. This model fails to reproduce the observed exponential electron scale heights of the eDIG thick disk and halo on the northeast ($h_{z,e} = 0.6, 7.5$ kpc) and southwest ($h_{z,e} = 0.8, 3.6$ kpc) sides of the galaxy at $R < 11$ kpc. We report the first definitive detection of an increasing eDIG velocity dispersion as a function of height above the disk. Blueshifted gas along the minor axis at large distances from the midplane hints at a disk-halo circulation and/or ram pressure effects caused by the ongoing interaction with NGC 5774. This work motivates further integral field unit and/or Fabry-Perot spectroscopy of galaxies with a range of star-formation rates to develop a spatially-resolved understanding of the role of star-formation feedback in shaping the kinematics of the disk-halo interface.
If the transverse jet B fields observed in BL Lac objects on parsec scales represent the toroidal component of the jet B fields, this should give rise to rotation-measure gradients across the jets, due to the systematic change in the line-of-sight component of the jet B field. We have found evidence for such rotation-measure gradients in one-third to one-half of the 1 Jy BL Lac objects we have analyzed. We present and discuss these new results, together with some of their implications for our understanding of the parsec-scale jets of AGN.
``Reports of my death are greatly exaggerated''   - Mark Twain. We consider the claim by Damour, Deser and McCarthy that nonsymmetric gravity theory has unacceptable global asymptotics. We explain why this claim is incorrect.
We show that if F is a totally real field in which p splits completely and f is a mod p Hilbert modular form with parallel weight 2<k<p, which is totally ordinary at p and has tamely ramified Galois representation at all primes dividing p, then there is a "companion form" of parallel weight k':=p+1-k. This work generalises results of Gross and Coleman-Voloch for modular forms over Q.
We analyse the dependence of the luminosity function of galaxies in groups (LF) on group dynamical state. We use the Gaussianity of the velocity distribution of galaxy members as a measurement of the dynamical equilibrium of groups identified in the SDSS Data Release 7 by Zandivarez & Martinez. We apply the Anderson-Darling goodness-of-fit test to distinguish between groups according to whether they have Gaussian or Non-Gaussian velocity distributions, i.e., whether they are relaxed or not. For these two subsamples, we compute the $^{0.1}r-$band LF as a function of group virial mass and group total luminosity. For massive groups, ${\mathcal M}>5 \times 10^{13} \ M_{\odot} \ h^{-1}$, we find statistically significant differences between the LF of the two subsamples: the LF of groups that have Gaussian velocity distributions have a brighter characteristic absolute magnitude ($\sim0.3$ mag) and a steeper faint end slope ($\sim0.25$). We detect a similar effect when comparing the LF of bright ($M^{group}_{^{0.1}r}-5\log(h)<-23.5$) Gaussian and Non-Gaussian groups. Our results indicate that, for massive/luminous groups, the dynamical state of the system is directly related with the luminosity of its galaxy members.
Leveraging the characteristics of convolutional layers, neural networks are extremely effective for pattern recognition tasks. However in some cases, their decisions are based on unintended information leading to high performance on standard benchmarks but also to a lack of generalization to challenging testing conditions and unintuitive failures. Recent work has termed this "shortcut learning" and addressed its presence in multiple domains. In text recognition, we reveal another such shortcut, whereby recognizers overly depend on local image statistics. Motivated by this, we suggest an approach to regulate the reliance on local statistics that improves text recognition performance.   Our method, termed TextAdaIN, creates local distortions in the feature map which prevent the network from overfitting to local statistics. It does so by viewing each feature map as a sequence of elements and deliberately mismatching fine-grained feature statistics between elements in a mini-batch. Despite TextAdaIN's simplicity, extensive experiments show its effectiveness compared to other, more complicated methods. TextAdaIN achieves state-of-the-art results on standard handwritten text recognition benchmarks. It generalizes to multiple architectures and to the domain of scene text recognition. Furthermore, we demonstrate that integrating TextAdaIN improves robustness towards more challenging testing conditions. The official Pytorch implementation can be found at https://github.com/amazon-research/textadain-robust-recognition.
We determine the thermal evolution of the intergalactic medium (IGM) over $3\, \mathrm{Gyr}$ of cosmic time $1.8<z<5.4$ by comparing measurements of the Ly{\alpha} forest power spectrum to a suite of $\sim70$ hydrodynamical simulations. We conduct Bayesian inference of IGM thermal parameters using an end-to-end forward modeling framework whereby mock spectra generated from our simulation grid are used to build a custom emulator which interpolates the power spectrum between thermal grid points. The temperature at mean density $T_0$ rises steadily from $T_0\sim 6000\, \mathrm{K}$ at $z=5.4$, peaks at $14000\, \mathrm{K}$ for $z\sim 3.4$, and decreases at lower redshift reaching $T_0\sim 7000\, \mathrm{K}$ by $z\sim1.8$. This evolution provides conclusive evidence for photoionization heating resulting from the reionization of He II, as well as the subsequent cooling of the IGM due to the expansion of the Universe after all reionization events are complete. Our results are broadly consistent with previous measurements of thermal evolution based on a variety of approaches, but the sensitivity of the power spectrum, the combination of high precision BOSS measurements of large-scale modes ($k\lesssim 0.02\, \mathrm{s/km}$) with our recent determination of the small-scale power, our large grid of models, and our careful statistical analysis allow us to break the well known degeneracy between the temperature at mean density $T_0$ and the slope of the temperature density relation $\gamma$ that has plagued previous analyses. At the highest redshifts $z\geq5$ we infer lower temperatures than expected from the standard picture of IGM thermal evolution leaving little room for additional smoothing of the Ly{\alpha} forest by free streaming of warm dark matter.
Added lemma provided by Michel Brion. Other (minor) changes. Submitted version.   Let k be any field, let X' be a projective and geometrically integral k-scheme and let Y' be a finite closed subscheme of X'. If f: Y'-> Y is a schematically dominant morphism between finite k-schemes and X is obtained by pinching X' along Y' via f, we describe the kernel (and, in certain cases, the cokernel) of the induced pullback map Br_{1}X -> Br_{1}X' between the corresponding algebraic (cohomological) Brauer groups of X and X'_solely_ in terms of the Brauer groups of the residue fields of Y and Y' and the Amitsur subgroups of X and X' in Br k. As an application, we compute the Brauer group of a projective and geometrically integral k-rational curve (with arbitrary singularities) over any field k. We also extend a well-known theorem of Roquette and Lichtenbaum to a class of singular curves over any local field.
Purpose: To use and test a labelling algorithm that operates on two-dimensional (2D) reformations, rather than three-dimensional (3D) data to locate and identify vertebrae.   Methods: We improved the Btrfly Net (described by Sekuboyina et al) that works on sagittal and coronal maximum intensity projections (MIP) and augmented it with two additional components: spine-localization and adversarial a priori-learning. Furthermore, we explored two variants of adversarial training schemes that incorporated the anatomical a priori knowledge into the Btrfly Net. We investigated the superiority of the proposed approach for labelling vertebrae on three datasets: a public benchmarking dataset of 302 CT scans and two in-house datasets with a total of 238 CT scans. We employed Wilcoxon signed-rank test to compute the statistical significance of the improvement in performance observed due to various architectural components in our approach.   Results: On the public dataset, our approach using the described Btrfly(pe-eb) network performed on par with current state-of-the-art methods achieving a statistically significant (p < .001) vertebrae identification rate of 88.5+/-0.2 % and localization distances of less than 7-mm. On the in-house datasets that had a higher inter-scan data variability, we obtained an identification rate of 85.1+/-1.2%.   Conclusion: An identification performance comparable to existing 3D approaches was achieved when labelling vertebrae on 2D MIPs. The performance was further improved using the proposed adversarial training regime that effectively enforced local spine a priori knowledge during training. Lastly, spine-localization increased the generalizability of our approach by homogenizing the content in the MIPs.
The spotted detached eclipsing binary (DEB) offers insights into starspots on the binary. Three spotted DEBs, KIC 8097825, KIC 6859813, and KIC 5527172, which were observed by the Kepler photometry and LAMOST spectroscopy, are studied in this work. The physical parameters of binaries are determined by binary modeling. The sizes, lifetimes, and single/double-dip ratio (SDR) of starspots are derived by starspot analysis. KIC 8097825 has large starspots. KIC 6859813 has a spot rotation period shorter than its orbital period but the system should be synchronized inferred from timescale estimation. The difference may be the result of the surface differential rotation. The KIC 5527172 has a long spot lifetime and an M dwarf component with an inflation radius. The primaries of these binaries and the secondary of KIC 8097825 have spots. Adding spotted DEBs of literature, we compare the starspots on binaries with those on the single stars. The spot sizes of starspots on 65% binaries are smaller than the median of those on single stars. The lifetimes of starspots on binaries are consistent with those on single stars when the rotation periods are larger than 3 days. SDRs for half of the binaries are consistent with those of single star systems, while another half are smaller. The relative lifetime positively correlates with the RMS and SDR but negatively correlates with the rotation period. These relations are similar to those of spots on the single star systems. Binaries with luminosity ratios close to the unit tend to have more double dips.
We present HST/WFC3 grism spectroscopy of the brightest galaxy at z>1.5 in the GOODS-South WFC3 Early Release Science grism pointing, covering the wavelength range 0.9-1.7 micron. The spectrum is of remarkable quality and shows the redshifted Balmer lines Hbeta, Hgamma, and Hdelta in absorption at z=1.902, correcting previous erroneous redshift measurements from the rest-frame UV. The average rest-frame equivalent width of the Balmer lines is 8+-1 Angstrom, which can be produced by a post-starburst stellar population with a luminosity-weighted age of ~0.5 Gyr. The M/L ratio inferred from the spectrum implies a stellar mass of ~4x10^11 Msun. We determine the morphology of the galaxy from a deep WFC3 F160W image. Similar to other massive galaxies at z~2 the galaxy is compact, with an effective radius of 2.1+-0.3 kpc. Although most of the light is in a compact core, the galaxy has two red, smooth spiral arms that appear to be tidally-induced. The spatially-resolved spectroscopy demonstrates that the center of the galaxy is quiescent and the surrounding disk is forming stars, as it shows Hbeta in emission. The galaxy is interacting with a companion at a projected distance of 18 kpc, which also shows prominent tidal features. The companion has a slightly redder spectrum than the primary galaxy but is a factor of ~10 fainter and may have a lower metallicity. It is tempting to interpret these observations as "smoking gun" evidence for the growth of compact, quiescent high redshift galaxies through minor mergers, which has been proposed by several recent observational and theoretical studies. Interestingly both objects host luminous AGNs, as indicated by their X-ray luminosities, which implies that these mergers can be accompanied by significant black hole growth. This study illustrates the power of moderate dispersion, low background near-IR spectroscopy at HST resolution, which is now available with the WFC3 grism.
Observations of accreting black holes often provoke suggestions that their jets precess. The precession is usually supposed to result from a combination of the Lense-Thirring effect and accretion disc viscosity. We show that this is unlikely for any type of black hole system, as the disc generally has too little angular momentum compared with a spinning hole to cause any significant movement of the jet direction across the sky on short timescales. Uncorrelated accretion events, as in the chaotic accretion picture of active galactic nuclei, change AGN jet directions only on timescales \gtrsim 10^7 yr. In this picture AGN jet directions are stable on shorter timescales, but uncorrelated with any structure of the host galaxy, as observed. We argue that observations of black-hole jets precessing on timescales short compared to the accretion time would be a strong indication that the accretion disc, and not the standard Blandford-Znajek mechanism, is responsible for driving the jet. This would be particularly convincing in a tidal disruption event. We suggest that additional disc physics is needed to explain any jet precession on timescales short compared with the accretion time. Possibilities include the radiation warping instability, or disc tearing.
Using a $q$-deformed Moyal algebra associated with the group of area preserving diffeomorphisms of th two-dimensional torus $T^2$, sdiff$_q (T^2)$, a $q$-deformed version for the Heavenly equations is given. Finally, the two-dimensional chiral version of Self-dual gravity in this $q$-deformed context is briefly discussed.
We resort to the methods of statistical mechanics in order to determine the effects that a deformed dispersion relation has upon the thermodynamics of a photon gas. The ensuing modifications to the density of states, partition function, pressure, internal energy, entropy, and specific heat are calculated. It will be shown that the breakdown of Lorentz invariance can be interpreted as a repulsive interaction, among the photons. Additionally, it will be proved that the presence of a deformed dispersion relation entails an increase in the entropy of the system. In other words, as a consequence of the loss of the aforementioned symmetry the number of microstates available to the corresponding equilibrium state grows.
We obtain the one-loop propagators in superstring theory for the general case when the worldsheet fields satisfy non-trivial holonomy and/or boundary conditions. Non-trivial holonomy arises in orbifold and orientifold backgrounds whereas non-trivial boundary conditions arise in backgrounds containing D-branes of different dimensionality or D-branes intersecting each other at an angle. In our derivation, we use a generalized version of the method of images. Dihedral groups play a crucial role in constructing the one-loop propagators.
Let $X$ be an $n$-element set, where $n$ is even. We refute a conjecture of J. Gordon and Y. Teplitskaya, according to which, for every maximal intersecting family $\mathcal{F}$ of $\frac{n}2$-element subsets of $X$, one can partition $X$ into $\frac{n}2$ disjoint pairs in such a way that no matter how we pick one element from each of the first $\frac{n}2 - 1$ pairs, the set formed by them can always be completed to a member of $\mathcal{F}$ by adding an element of the last pair.   The above problem is related to classical questions in extremal set theory. For any $t\ge 2$, we call a family of sets $\mathcal{F}\subset 2^X$ {\em $t$-separable} if for any ordered pair of elements $(x,y)$ of $X$, there exists $F\in\mathcal{F}$ such that $F\cap\{x,y\}=\{x\}$. For a fixed $t, 2\le t\le 5$ and $n\rightarrow\infty$, we establish asymptotically tight estimates for the smallest integer $s=s(n,t)$ such that every family $\mathcal{F}$ with $|\mathcal{F}|\ge s$ is $t$-separable.
Field redefinitions occur in string compactifications at the one loop level. We review arguments for why such redefinitions occur and study their effect on moduli stabilisation and supersymmetry breaking in the LARGE volume scenario. For small moduli, although the effect of such redefinitions can be larger than that of the $\alpha'$ corrections in both the K\"ahler and scalar potentials, they do not alter the structure of the scalar potential. For the less well motivated case of large moduli, the redefinitions can dominate all other terms in the scalar potential. We also study the effect of redefinitions on the structure of supersymmetry breaking and soft terms.
A subset $A$ of $\mathbb{Z}^n$ is called a weak antichain if it does not contain two elements $x$ and $y$ satisfying $x_i<y_i$ for all $i$. Engel, Mitsis, Pelekis and Reiher showed that for any weak antichain $A$, the sum of the sizes of its $(n-1)$-dimensional projections must be at least as large as its size $|A|$. They asked what the smallest possible value of the gap between these two quantities is in terms of $|A|$. We answer this question by giving an explicit weak antichain attaining this minimum for each possible value of $|A|$. In particular, we show that sets of the form $A_N=\{x\in\mathbb{Z}^n: 0\leq x_j\leq N-1$ for all $j$ and $x_i=0$ for some $i\}$ minimise the gap among weak antichains of size $|A_N|$.