ShantanuT01/DACTYL-Pretraining huggingface dataset:
Let $\mathbb{F}_{q}$ be a finite field with $q$ elements and $\mathbb{F}_{q}[x]$ the ring of polynomials over $\mathbb{F}_{q}$. Let $l(x), k(x)$ be coprime polynomials in $\mathbb{F}_{q}[x]$ and $\Phi(k)$ the Euler function in $\mathbb{F}_{q}[x]$. Let $\pi(l, k; n)$ be the number of monic irreducible polynomials of degree $n$ in $\mathbb{F}_{q}[x]$ which are congruent to $l(x)$ module $k(x)$. For any positive integer $n$, we denote by $\Omega(n)$ the least prime divisor of $n$. In this paper, we show that $$\pi(l, k; n)=\frac{1}{\Phi(k)}\frac{q^{n}}{n}+O\left(n^{\alpha}\right)+O\left(\frac{q^{\frac{n}{\Omega{(n)}}}}{n}\right),$$ where $\alpha$ only depends on the choice of $k(x)\in\Fq$. Note that the above error term improves the one implied by Weil's conjecture. Our approach is completely elementary.
Given a smooth variety $X$ and an effective Cartier divisor $D \subset X$, we show that the cohomological Chow group of 0-cycles on the double of $X$ along $D$ has a canonical decomposition in terms of the Chow group of 0-cycles ${\rm CH}_0(X)$ and the Chow group of 0-cycles with modulus ${\rm CH}_0(X|D)$ on $X$. When $X$ is projective, we construct an Albanese variety with modulus and show that this is the universal regular quotient of ${\rm CH}_0(X|D)$.   As a consequence of the above decomposition, we prove the Roitman torsion theorem for the 0-cycles with modulus. We show that ${\rm CH}_0(X|D)$ is torsion-free and there is an injective cycle class map ${\rm CH}_0(X|D) \hookrightarrow K_0(X,D)$ if $X$ is affine. For a smooth affine surface $X$, this is strengthened to show that $K_0(X,D)$ is an extension of ${\rm CH}_1(X|D)$ by ${\rm CH}_0(X|D)$.
We discuss questions arising from the recent work of Schellekens, and also from an earlier paper by Schellekens and Yankielowicz. We summarise Schellekens' results, and proceed to discuss the uniqueness of the c=24 self-dual conformal field theory with no weight one states, i.e. the Monster module $V^\natural$. After introducing the concept of complementary representations, we examine $Z_2$-orbifold constructions in general, and then proceed to apply our considerations firstly to the specific case of the FKS constructions $H(\Lambda)$ and then to the reflection twisted theories $\widetilde H(\Lambda)$. Our techniques provide evidence for the existence of several new theories beyond those proven to exist in previous work and conjectured to exist in Schellekens and Yankielowicz.
We give new bounds and asymptotic estimates on the number of standard Young tableaux of skew shape in a variety of special cases. Our approach is based on Naruse's hook-length formula. We also compare our bounds with the existing bounds on the numbers of linear extensions of the corresponding posets.
Transport properties of highly mobile 2D electrons are studied in symmetric GaAs quantum wells placed in titled magnetic fields. Quantum positive magnetoresistance (QPMR) is observed in magnetic fields perpendicular to the 2D layer. Application of in-plane magnetic field produces a dramatic decrease of the QPMR. This decrease correlates strongly with the reduction of the amplitude of Shubnikov de Haas resistance oscillations due to modification of the electron spectrum via enhanced Zeeman splitting. Surprisingly no quantization of the spectrum is detected when the Zeeman energy exceeds the half of the cyclotron energy suggesting an abrupt transformation of the electron dynamics. Observed angular evolution of QPMR implies strong mixing between spin subbands. Theoretical estimations indicate that in the presence of spin-orbital interaction the elastic impurity scattering provides significant contribution to the spin mixing in GaAs quantum wells at high filling factors.
Combined static and molecular dynamics first-principles calculations are used to identify a direct structural link between the metastable crystalline and amorphous phases of Ge2Sb2Te5. We find that the phase transition is driven by the displacement of Ge atoms along the rocksalt [111] direction from the stable-octahedron to high-energy-unstable tetrahedron sites close to the intrinsic vacancy regions, which give rise to the formation of local 4-fold coordinated motifs. Our analyses suggest that the high figures of merit of Ge2Sb2Te5 are achieved from the optimal combination of intrinsic vacancies provided by Sb2Te3 and the instability of the tetrahedron sites provided by GeTe.
We present the results of the analysis of the very massive cluster MOO J1142$+$1527 at a redshift $z = 1.2$ based on high angular resolution NIKA2 Sunyaev-Zel'dovich (SZ) and $Chandra$ X-ray data. This multi-wavelength analysis enables us to estimate the shape of the temperature profile with unprecedented precision at this redshift and to obtain a map of the gas entropy distribution averaged along the line of sight. The comparison between the cluster morphological properties observed in the NIKA2 and $Chandra$ maps together with the analysis of the entropy map allows us to conclude that MOO J1142$+$1527 is an on-going merger hosting a cool-core at the position of the X-ray peak. This work demonstrates how the addition of spatially-resolved SZ observations to low signal-to-noise X-ray data can bring valuable insights on the intracluster medium thermodynamic properties at $z>1$.
This paper proposes a CNN cascade for semantic part segmentation guided by pose-specific information encoded in terms of a set of landmarks (or keypoints). There is large amount of prior work on each of these tasks separately, yet, to the best of our knowledge, this is the first time in literature that the interplay between pose estimation and semantic part segmentation is investigated. To address this limitation of prior work, in this paper, we propose a CNN cascade of tasks that firstly performs landmark localisation and then uses this information as input for guiding semantic part segmentation. We applied our architecture to the problem of facial part segmentation and report large performance improvement over the standard unguided network on the most challenging face datasets. Testing code and models will be published online at http://cs.nott.ac.uk/~psxasj/.
The dynamical properties of the high-density Ru(001)-(1$\times$1)-O phase has been investigated by a combined high-resolution electron energy loss spectroscopy and density functional theory study. Due to a strong static outward relaxation of the first Ru layer a soft Rayleigh phonon mode is expected. However, a Rayleigh mode stiffening together with a new high energy in-plane phonon mode above the bulk bands is found which is related to a strong adsorbate-induced intralayer force constant stiffening which counteracts an interlayer softening. This structurally rather simple system with one surface atom per (1$\times$1) unit cell demonstrates the limited applicability of previously adopted models.
The large values of the singlet and triplet two-nucleon scattering lengths locate the nuclear system close to the unitary limit. This particular position strongly constrains the low-energy observables in the three-nucleon system as depending on one parameter, the triton binding energy, and introduces correlations in the low energy sector of light nuclei. Here we analyze the propagation of these correlations to infinite nuclear matter showing that its saturation properties, the equation of state of $\beta$-stable nuclear matter and several properties of neutron stars, as their maximum mass, are well determined solely by a few number of low-energy quantities of the two- and three-nucleon systems. In this way we make a direct link between the universal behavior observed in the low-energy region of few-nucleon systems and fundamental properties of nuclear matter and neutron stars.
Detecting mass in mammogram is significant due to the high occurrence and mortality of breast cancer. In mammogram mass detection, modeling pairwise lesion correspondence explicitly is particularly important. However, most of the existing methods build relatively coarse correspondence and have not utilized correspondence supervision. In this paper, we propose a new transformer-based framework CL-Net to learn lesion detection and pairwise correspondence in an end-to-end manner. In CL-Net, View-Interactive Lesion Detector is proposed to achieve dynamic interaction across candidates of cross views, while Lesion Linker employs the correspondence supervision to guide the interaction process more accurately. The combination of these two designs accomplishes precise understanding of pairwise lesion correspondence for mammograms. Experiments show that CL-Net yields state-of-the-art performance on the public DDSM dataset and our in-house dataset. Moreover, it outperforms previous methods by a large margin in low FPI regime.
This thesis first gives a background and review of the article hep-th/0102038, where we substantiated a conjectured duality between two a priori unrelated gauge theories, N=2 quiver theory and N=2 Seiberg-Witten theory. These gauge theories have different realisations as the worldvolume theories on different D-brane configurations. We showed that there is an identity between the spaces of vacua (moduli spaces) arising in the two theories, which suggests that the corresponding string theory pictures are dual. Second, the thesis gives a background and description of the analysis performed in the three articles hep-th/0111161, hep-th/0202069 and hep-th/0304013, where we derived the most general, local, superconformal boundary conditions of the two-dimensional nonlinear sigma model. This model describes the dynamics of open strings, and the boundary conditions dictate the geometry of D-branes. In the last article we studied these boundary conditions for the special case of WZW models.
Since the early 2000s, computational visual saliency has been a very active research area. Each year, more and more new models are published in the main computer vision conferences. Nowadays, one of the big challenges is to find a way to fairly evaluate all of these models. In this paper, a new framework is proposed to assess models of visual saliency. This evaluation is divided into three experiments leading to the proposition of a new evaluation framework. Each experiment is based on a basic question: 1) there are two ground truths for saliency evaluation: what are the differences between eye fixations and manually segmented salient regions?, 2) the properties of the salient regions: for example, do large, medium and small salient regions present different difficulties for saliency models? and 3) the metrics used to assess saliency models: what advantages would there be to mix them with PCA? Statistical analysis is used here to answer each of these three questions.
We consider a linear system of differential equations describing a joint motion of elastic porous body and fluid occupying porous space. The rigorous justification, under various conditions imposed on physical parameters, is fulfilled for homogenization procedures as the dimensionless size of the pores tends to zero, while the porous body is geometrically periodic and a characteristic time of processes is small enough. Such kind of models may describe, for example, hydraulic fracturing or acoustic or seismic waves propagation. As the results, we derive different types of homogenized equations involving non-isotropic Stokes system for fluid velocity coupled with acoustic equations for the solid component or different types of acoustic equations, depending on ratios between physical parameters. The proofs are based on Nguetseng's two-scale convergence method of homogenization in periodic structures.
We present a new, close relation between column densities of OH and CH molecules based on 16 translucent sightlines (six of them new) and confirm the theoretical oscillator strengths of the OH A--X transitions at 3078 and 3082 \AA (0.00105, 0.000648) and CH B--X transitions at 3886 and 3890 \AA, (0.00320, 0.00210), respectively. We also report no difference between observed and previously modelled abundances of the OH molecule.
Consider a generalized time-dependent P\'olya urn process defined as follows. Let $d\in \mathbb{N}$ be the number of urns/colors. At each time $n$, we distribute $\sigma_n$ balls randomly to the $d$ urns, proportionally to $f$, where $f$ is a valid reinforcement function. We consider a general class of positive reinforcement functions $\mathcal{R}$ assuming some monotonicity and growth condition. The class $\mathcal{R}$ includes convex functions and the classical case $f(x)=x^{\alpha}$, $\alpha>1$. The novelty of the paper lies in extending stochastic approximation techniques to the $d$-dimensional case and proving that eventually the process will fixate at some random urn and the other urns will not receive any balls any more.
We complete the construction of the nonlift weight two cusp paramodular Hecke eigenforms for prime levels N<600, which arise in conformance with the paramodular conjecture of Brumer and Kramer.
The ground state phase diagram of the alternating spin-1/2 chains with anisotropic ferromagnetic coupling under the influence of a symmetry breaking transverse magnetic field is studied. We have used the exact diagonalization technique. In the limit where the antiferromagnetic coupling is dominant, we have identified two Ising-type quantum phase transitions. We have calculated two critical fields $h_{c_{1}}$ and   $h_{c_{2}}$, corresponding to the transition between different magnetic phases of the system. It is found that the intermediate state ($h_{c_{1}}<h<h_{c_{2}}$) is gapful, describing the stripe-antiferromagnetic phase.
We use Koll\'ar's gluing theory to prove the contraction theorem for generalized pairs. In particular, we show that we can run the MMP for any generalized log canonical pairs.
In this expository note, we give a modern proof of Hanson-Wright inequality for quadratic forms in sub-gaussian random variables. We deduce a useful concentration inequality for sub-gaussian random vectors. Two examples are given to illustrate these results: a concentration of distances between random vectors and subspaces, and a bound on the norms of products of random and deterministic matrices.
Most existing compound facial expression recognition (FER) methods rely on large-scale labeled compound expression data for training. However, collecting such data is labor-intensive and time-consuming. In this paper, we address the compound FER task in the cross-domain few-shot learning (FSL) setting, which requires only a few samples of compound expressions in the target domain. Specifically, we propose a novel cascaded decomposition network (CDNet), which cascades several learn-to-decompose modules with shared parameters based on a sequential decomposition mechanism, to obtain a transferable feature space. To alleviate the overfitting problem caused by limited base classes in our task, a partial regularization strategy is designed to effectively exploit the best of both episodic training and batch training. By training across similar tasks on multiple basic expression datasets, CDNet learns the ability of learn-to-decompose that can be easily adapted to identify unseen compound expressions. Extensive experiments on both in-the-lab and in-the-wild compound expression datasets demonstrate the superiority of our proposed CDNet against several state-of-the-art FSL methods. Code is available at: https://github.com/zouxinyi0625/CDNet.
We present analysis of commissioning $M-$band data acquired with the infrared echelle spectrograph (iSHELL) on {\it NASA's Infrared Telescope Facility}. In this paper we describe the delivered performance of the instrument for these $M-$band observations and the data reduction process. The feasibility of using iSHELL for spectro-astrometry is tested on the Herbig Ae/Be star HD~179218 and we show that sub-milliarcsecond fidelity is achievable.
M-dwarfs in extremely wide binary systems are very rare, and may thus have different formation processes from those found as single stars or close binaries in the field. In this paper we search for close companions to a new sample of 36 extremely wide M-dwarf binaries, covering a spectral type range of M1 to M5 and a separation range of 600 - 6500 AU. We discover 10 new triple systems and one new quadruple system. We carefully account for selection effects including proper motion, magnitude limits, the detection of close binaries in the SDSS, and other sample biases. The bias-corrected total high-order-multiple fraction is 45% (+18%/-16%) and the bias-corrected incidence of quadruple systems is < 5%, both statistically compatible with that found for the more common close M-dwarf multiple systems. Almost all the detected companions have similar masses to their primaries, although two very low mass companions, including a candidate brown dwarf, are found at relatively large separations. We find that the close-binary separation distribution is strongly peaked towards < 30AU separations. There is marginally significant evidence for a change in high-order M-dwarf multiplicity with binding energy and total mass. We also find 2-sigma evidence of an unexpected increased high-order-multiple fraction for the widest targets in our survey, with a high-order-multiple fraction of 21% (+17%/-7%) for systems with separations up to 2000AU, compared to 77% (+9%/-22%) for systems with separations > 4000AU. These results suggest that the very widest M-dwarf binary systems need higher masses to form or to survive.
In this paper we consider a random partition of the plane into cells, the partition being based on the nodes and links of a {\it random planar geometric graph}. The resulting structure generalises the \emph{random \tes}\ hitherto studied in the literature. The cells of our partition process, possibly with holes and not necessarily closed, have a fairly general topology summarised by a functional which is similar to the Euler characteristic. The functional can also be extended to certain cell-unions which can arise in applications. Vertices of all valencies, $0, 1, 2, ...$ are allowed. Many of the formulae from the traditional theory of random tessellations with convex cells, are made more general to suit this new structure. Some motivating examples of the structure are given.
We characterize the kinematic and chemical properties of $\sim$3,000 Sagittarius (Sgr) stream stars, including K-giants, M-giants, and BHBs, select from SEGUE-2, LAMOST, and SDSS separately in Integrals-of-Motion space. The orbit of Sgr stream is quite clear from the velocity vector in $X$-$Z$ plane. Stars traced by K-giants and M-giants present the apogalacticon of trailing steam is $\sim$ 100 kpc. The metallicity distributions of Sgr K-, M-giants, and BHBs present that the M-giants are on average the most metal-rich population, followed by K-giants and BHBs. All of the K-, M-giants, and BHBs indicate that the trailing arm is on average more metal-rich than leading arm, and the K-giants show that the Sgr debris is the most metal-poor part. The $\alpha$-abundance of Sgr stars exhibits a similar trend with the Galactic halo stars at lower metallicity ([Fe/H] $<\sim$ $-$1.0 dex), and then evolve down to lower [$\alpha$/Fe] than disk stars at higher metallicity, which is close to the evolution pattern of $\alpha$-element of Milky Way dwarf galaxies. We find $V_Y$ and metallicity of K-giants have gradients along the direction of line-of-sight from the Galactic center in $X$-$Z$ plane, and the K-giants show that $V_Y$ increases with metallicity at [Fe/H] $>\sim-$1.5 dex. After dividing the Sgr stream into bright and faint stream according to their locations in equatorial coordinate, the K-giants and BHBs show that the bright and faint stream present different $V_Y$ and metallicities, the bright stream is on average higher in $V_Y$ and metallicity than the faint stream.
We study families of scrolls containing a given rational curve and families of rational curves contained in a fixed scroll via a stratification in terms of the degree of the induced map onto P^1 and we prove that there is no rational normal scroll of minimal degree and of dimension <=n/2 containing a general binary curve inP^n.
These lectures are centered around a specific problem, the effect of weak repulsive interactions on the transition temperature $T_c$ of a Bose gas. This problem provides indeed a beautiful illustration of many of the techniques which have been discussed at this school on effective theories and renormalization group. Effective theories are used first in order to obtain a simple hamiltonian describing the atomic interactions: because the typical atomic interaction potentials are short range, and the systems that we consider are dilute, these potentials can be replaced by a contact interaction whose strength is determined by the s-wave scattering length. Effective theories are used next in order to obtain a simple formula for the shift in $T_c$: one exploits there the fact that near $T_c$ the physics is dominated by low momentum modes whose dynamics is most economically described in terms of classical fields; the ingredients needed to calculate the shift of $T_c$ can be obtained from this classical field theory. Finally the renormalization group is used both to obtain a qualitative understanding, and also as a non perturbative tool to evaluate quantitatively the shift in $T_c$.
We propose a Markovian quantum master equation that can describe the Fano effect directly, by assuming a standard cavity quantum electrodynamics system. The framework allows us to generalize the Fano formula, applicable over the weak and strong coupling regimes with pure dephasing. A formulation of its emission spectrum is also given in a consistent manner. We then find that the interference responsible for the Fano effect is robust against pure dephasing. This is counterintuitive because the impact of interference is, in general, severely reduced by decoherence processes. Our approach thus provides a basis for theoretical treatments of the Fano effect and new insights into the quantum interference in open quantum systems.
The H alpha equivalent width (EW) is the ratio of the H alpha flux to the continuum at 6565{\AA}. In normal star forming galaxies the H alpha flux is dominated by reprocessed photons from stars with masses greater than 10 M_o and the 6565{\AA} continuum is predominantly due to 0.7-3.0 M_o red giant stars. In these galaxies the H alpha EW is effectively the ratio of high mass to low mass stars and is thus sensitive to the stellar initial mass function (IMF). In Hoversten & Glazebrook 2008 we used ~131,000 galaxies from the Sloan Digital Sky Survey to show evidence for systematic variations in the IMF with galaxy luminosity. In this proceeding we use that sample, with the addition of H delta_A measurements, to investigate other parameterizations of the IMF. We find evidence for IMF variations with surface brightness, and also show that, modulo uncertainties in spectral synthesis models, that 120 M_o stars are important in accounting for the observed H alpha EW distribution.
In supersymmetric models where the gravitino is the lightest superparticle, the next-to-lightest superparticle (NLSP) is long-lived, and hence could be collected and studied in detail. We study the prospects of direct detection of lepton flavour violation in charged slepton NLSP decays. Mixing angles in the slepton sector as small as ~ 3\times 10^{-2} (9\times 10^{-3}) could be probed at the 90% confidence level if 3\times 10^3 (3\times 10^4) sleptons could be collected.
The search for extremely deformed structures in the yrast and near-yrast region of $^{28}$Si has been performed within the cranked relativistic mean field theory up to spin $I=20\hbar$. The fingerprints of clusterization are seen (well pronounced) in the superdeformed (hyperdeformed) configurations.