ShantanuT01/DACTYL-Pretraining huggingface dataset:
Let P^n denote the n-dimensional projective space defined over the algebraic closure of a finite field F_q, let V contained P^n be a complete intersection defined over F_q of dimension r and singular locus of dimension at most s, and let \pi:V-->P^{s+1} be a "generic" linear mapping. We obtain an effective version of the Bertini smoothness theorem concerning \pi, namely an explicit upper bound of the degree of a proper Zariski closed subset of P^{s+1} which contains all the points defining singular fibers of \pi. For this purpose we make essential use of the concept of polar variety associated to the set of exceptional points of \pi. As a consequence of our effective Bertini theorem we obtain results of existence of smooth rational points of V, namely conditions on q which imply that V has a smooth q-rational point. Finally, for s=r-2 and s=r-3 we obtain estimates on the number of q-rational points of V, and we discuss how these estimates can be used in order to determine the average value set of "small" families of univariate polynomials with coefficients in F_q.
Cold dark matter (CDM) has shown to be an excellent candidate for the dark matter (DM) of the Universe at large scales, however it presents some challenges at the galactic level. The scalar field dark matter (SFDM), also called fuzzy, wave, Bose-Einstein condensate or ultra-light axion DM, is identical to CDM at cosmological scales but different at the galactic ones. SFDM forms core halos, it has a natural cut-off in its matter power spectrum and it predicts well-formed galaxies at high redshifts. In this work we reproduce the rotation curves of high-resolution low surface brightness (LSB) and SPARC galaxies with two SFDM profiles: (1)~The soliton+NFW profile in the fuzzy DM (FDM) model, arising empirically from cosmological simulations of real, non-interacting scalar field (SF) at zero temperature, and (2)~the multistate SFDM (mSFDM) profile, an exact solution to the Einstein-Klein-Gordon equations for a real, self-interacting SF, with finite temperature into the SF potential, introducing several quantum states as a realistic model for a SFDM halo. From the fits with the soliton+NFW profile, we obtained for the boson mass $0.212< m_\psi/(10^{-23} \mathrm{eV}/c^2)<27.0$ and for the core radius $0.326< r_c/\mathrm{kpc}<8.96$. From the combined analysis with the LSB galaxies, we obtained $m_\psi = 0.554 \times10^{-23}\mathrm{eV}$, a result in tension with the severe cosmological constraints. Also, we show the analytical mSFDM model fits the observations as well as or better than the empirical soliton+NFW profile, and it reproduces naturally the wiggles present in some galaxies, being a theoretically motivated framework additional or alternative to the FDM profile.
We investigate the sedimentation of a cloud of rigid, spherical particles of identical radii under gravity in a Stokes fluid. Both inertia and rotation of particles are neglected. We consider the homogenization limit of many small particles in the case of a dilute system in which interactions between particles are still important. In the relevant time scale, we rigorously prove convergence of the dynamics to the solution of a macroscopic equation. This macroscopic equation resembles the Stokes equations for a fluid of variable density subject to gravitation.
We present powder inelastic neutron scattering measurements of the S=1 dimerized antiferromagnet Ba$_3$Mn$_2$O$_8$. The $T=1.4$ K magnetic spectrum exhibits a spin-gap of $\Delta \approx 1.0$ meV and a dispersive spectrum with a bandwidth of approximately 1.5 meV. Comparison to coupled dimer models describe the dispersion and scattering intensity accurately and determine the exchange constants in Ba$_3$Mn$_2$O$_8$. The wave vector dependent scattering intensity confirms the proposed S=1 dimer bond. Temperature dependent measurements of the magnetic excitations indicate the presence of both singlet-triplet and thermally activated triplet-quintet excitations.
We are interested in automatic scene understanding from geometric cues. To this end, we aim to bring semantic segmentation in the loop of real-time reconstruction. Our semantic segmentation is built on a deep autoencoder stack trained exclusively on synthetic depth data generated from our novel 3D scene library, SynthCam3D. Importantly, our network is able to segment real world scenes without any noise modelling. We present encouraging preliminary results.
Let $\mathbb{G}_{n,\alpha}$ be the set of connected graphs with order $n$ and independence number $\alpha$. Given $k=n-\alpha$, the graph with minimum spectral radius among $\mathbb{G}_{n,\alpha}$ is called the minimizer graph. Stevanovi\'{c} in the classical book [D. Stevanovi\'{c}, Spectral Radius of Graphs, Academic Press, Amsterdam, 2015.] pointed that determining minimizer graph in $\mathbb{G}_{n,\alpha}$ appears to be a tough problem on page $96$. Very recently, Lou and Guo in \cite{Lou} proved that the minimizer graph of $\mathbb{G}_{n,\alpha}$ must be a tree if $\alpha\ge\lceil\frac{n}{2}\rceil$. In this paper, we further give the structural features for the minimizer graph in detail, and then provide of a constructing theorem for it. Thus, theoretically we completely determine the minimizer graphs in $\mathbb{G}_{n,\alpha}$ along with their spectral radius for any given $k=n-\alpha\le \frac{n}{2}$. As an application, we determine all the minimizer graphs in $\mathbb{G}_{n,\alpha}$ for $\alpha=n-1,n-2,n-3,n-4,n-5,n-6$ along with their spectral radii, the first four results are known in \cite{Xu,Lou} and the last two are new.
We study the dimension properties of the spectral measure of the Circular $\beta$-Ensembles. For $\beta \geq 2$ it it was previously shown by Simon that the spectral measure is almost surely singular continuous with respect to Lebesgue measure on $\partial \mathbb{D}$ and the dimension of its support is $1 - 2/\beta$. We reprove this result with a combination of probabilistic techniques and the so-called Jitomirskaya-Last inequalities. Our method is simpler in nature and mostly self-contained, with an emphasis on the probabilistic aspects rather than the analytic. We also extend the method to prove a large deviations principle for norms involved in the Jitomirskaya-Last analysis.
With the general aim to classify BPS solutions in N=2, D=5 supergravity with hypermultiplets and vector multiplets, here we consider a family of static spacetime metrics containing black hole-like solutions, with generic hypermultiplets coupled to radially symmetric electrostatic vector multiplets. We derive the general conditions which the fields must satisfy and determine the form of the fixed point solutions.
We develop a General Fluctuation Formula for phase variables that are odd under time reversal. Simulations are used to verify the new formula.
We define the rank-metric zeta function of a code as a generating function of its normalized $q$-binomial moments. We show that, as in the Hamming case, the zeta function gives a generating function for the weight enumerators of rank-metric codes. We further prove a functional equation and derive an upper bound for the minimum distance in terms of the reciprocal roots of the zeta function. Finally, we show invariance under suitable puncturing and shortening operators and study the distribution of zeroes of the zeta function for a family of codes.
Twin-peak quasi-periodic oscillations (QPOs) are observed in the X-ray power-density spectra of several accreting low-mass neutron star (NS) binaries. In our previous work we have considered several QPO models. We have identified and explored mass-angular-momentum relations implied by individual QPO models for the atoll source 4U 1636-53. In this paper we extend our study and confront QPO models with various NS equations of state (EoS). We start with simplified calculations assuming Kerr background geometry and then present results of detailed calculations considering the influence of NS quadrupole moment (related to rotationally induced NS oblateness) assuming Hartle-Thorne spacetimes. We show that the application of concrete EoS together with a particular QPO model yields a specific mass-angular-momentum relation. However, we demonstrate that the degeneracy in mass and angular momentum can be removed when the NS spin frequency inferred from the X-ray burst observations is considered. We inspect a large set of EoS and discuss their compatibility with the considered QPO models. We conclude that when the NS spin frequency in 4U 1636-53 is close to 580Hz we can exclude 51 from 90 of the considered combinations of EoS and QPO models. We also discuss additional restrictions that may exclude even more combinations. Namely, there are 13 EOS compatible with the observed twin peak QPOs and the relativistic precession model. However, when considering the low frequency QPOs and Lense-Thirring precession, only 5 EOS are compatible with the model.
String backgrounds associated with gauged $G/H$ WZNW models generically depend on $\alpha'$ or $1/k$. The exact expressions for the corresponding metric $G_{\m\n}$, antisymmetric tensor $B_{\m\n}$, and dilaton $\phi$ can be obtained by eliminating the $2d$ gauge field from the local part of the effective action of the gauged WZNW model. We show that there exists a manifestly gauge-invariant prescription for the derivation of the antisymmetric tensor coupling. When the subgroup $H$ is one-dimensional and $G$ is simple the antisymmetric tensor is given by the semiclassical ($\alpha'$-independent) expression. We consider in detail the simplest non-trivial example with non-trivial $B_{\m\n}$ -- the D=3 sigma model corresponding to the $[SL(2,R) x R]/R$ gauged WZNW theory (`charged black string') and show that the exact expressions for $G_{\m\n}$, $B_{\m\n}$ and $\phi$ solve the Weyl invariance conditions in the two-loop approximation. Similar conclusion is reached for the closely related $SL(2,R)/R$ chiral gauged WZNW model. We find that there exists a scheme in which the semiclassical background is also a solution of the two-loop conformal invariance equations (but the tachyon equation takes a non-canonical form). We discuss in detail the role of field redefinitions (scheme dependence) in establishing a correspondence between the sigma model and conformal field theory results.
Popular scientific summary -- The atmosphere of the Sun is envisioned as composed of inherently complex, non-homogeneous, and dynamic layers. A detailed understanding of the physical processes involved in these layers is still lacking. For example, it is largely unknown why the outermost layer of the Sun's atmosphere (the solar corona) is so much hotter than the photosphere by millions of degrees. Astrophysicists think that the layer sandwiched between the photosphere and the corona, known as the interface region, may hold the key to a better understanding of the nature of this enigma. With the help of coordinated high-resolution, ground- and space-based observations from the Swedish 1-m Solar Telescope (SST) on La Palma, Spain, and NASA's Interface Region Imaging Spectrograph (IRIS) and Solar Dynamics Observatory (SDO), along with the support from an advanced numerical simulation, I aim to unlock some of the mysteries surrounding the dynamics of the interface region with a focus on small-scale jets, known as "spicules". Spicules are found almost everywhere on the Sun's surface and at any given moment there can be as many as 10 million of them rapidly shooting outwards. They are often found to be heated beyond chromospheric temperatures and appear in the transition region and (even) coronal passbands. Because of their "omnipresence", it is suggested that they play a major role in energizing the outer atmospheric layers of the Sun. This thesis focuses on the physical characteristics and dynamics of spicules, along with their role in mass-balance and heating of the solar atmosphere.
High-precision space-based photometry obtained by the \emph{Kepler} and \emph{TESS} missions has revealed evidence of rotational modulation associated with main sequence (MS) A and late-B type stars. Generally, such variability in these objects is attributed to inhomogeneous surface structures (e.g. chemical spots), which are typically linked to strong magnetic fields ($B\gtrsim100\,{\rm G}$) visible at the surface. It has been reported that $\approx44$~per~cent of all A-type stars observed during the \emph{Kepler} mission exhibit rotationally modulated light curves. This is surprising considering that $\lesssim10$~per~cent of all MS A-type stars are known to be strongly magnetic (i.e. they are Ap/Bp stars). We present a spectroscopic monitoring survey of 44 A and late-B type stars reported to exhibit rotational modulation in their \emph{Kepler} light curves. The primary goal of this survey is to test the hypothesis that the variability is rotational modulation by comparing each star's rotational broadening ($v\sin{i}$) with the equatorial velocities ($v_{\rm eq}$) inferred from the photometric periods. We searched for chemical peculiarities and binary companions in order to provide insight into the origin of the apparent rotational modulation. We find that 14 stars in our sample have $v\sin{i}>v_{\rm eq}$ and/or have low-mass companions that may contribute to or be responsible for the observed variability. Our results suggest that more than $10$~per~cent of all MS A and late-B type stars may exhibit inhomogeneous surface structures; however, the incidence rate is likely $\lesssim30$~per~cent.
We present results of analysis of the dark matter (DM) pairwise velocity statistics in different Cosmic Web environments. We use the DM velocity and density field from the Millennium 2 simulation together with the NEXUS+ algorithm to segment the simulation volume into voxels uniquely identifying one of the four possible environments: nodes, filaments, walls or cosmic voids. We show that the PDFs of the mean infall velocities $v_{12}$ as well as its spatial dependence together with the perpendicular and parallel velocity dispersions bear a significant signal of the large-scale structure environment in which DM particle pairs are embedded. The pairwise flows are notably colder and have smaller mean magnitude in wall and voids, when compared to much denser environments of filaments and nodes. We discuss on our results, indicating that they are consistent with a simple theoretical predictions for pairwise motions as induced by gravitational instability mechanism. Our results indicate that the Cosmic Web elements are coherent dynamical entities rather than just temporal geometrical associations. In addition it should be possible to observationally test various Cosmic Web finding algorithms by segmenting available peculiar velocity data and studying resulting pairwise velocity statistics
Stereo dense image matching can be categorized to low-level feature based matching and deep feature based matching according to their matching cost metrics. Census has been proofed to be one of the most efficient low-level feature based matching methods, while fast Convolutional Neural Network (fst-CNN), as a deep feature based method, has small computing time and is robust for satellite images. Thus, a comparison between fst-CNN and census is critical for further studies in stereo dense image matching. This paper used cost function of fst-CNN and census to do stereo matching, then utilized semi-global matching method to obtain optimized disparity images. Those images are used to produce digital surface model to compare with ground truth points. It addresses that fstCNN performs better than census in the aspect of absolute matching accuracy, histogram of error distribution and matching completeness, but these two algorithms still performs in the same order of magnitude.
In this article, we present a configurable field-effect transistor (FET), where not only polarity (n- and p-type), but the conduction mechanism of a FET can also be configured dynamically. As a result, we can have both types of devices, high-performance MOSFET and low-power TFET, for computational and power efficient system on chip (SoC) products. The calibrated 3D-TCAD simulation results validate characteristics and functionalities of the configurable FET, and showed good consistency with the static conventional MOSFET (or TFET).
Feedback, in particular from active galactic nuclei (AGN), is believed to play a crucial role in the evolution of galaxies. In the local Universe, many galaxies with an AGN are indeed observed to reside in the so-called green valley, usually interpreted as a transition phase from a blue star-forming to a red quenched state. We use data from the Sloan Digital Sky Survey to show that such an interpretation requires substantial revision. Optically-selected nearby AGN galaxies follow exponentially declining star formation histories, as normal galaxies of similar stellar and dark matter halo mass, reaching in the recent past ($\sim$0.1 Gyr ago) star formation rate levels consistent with a quiescent population. However, we find that local AGN galaxies have experienced a sudden increase in their star formation rate, unfolding on timescales similar to those typical of AGN activity, suggesting that both star formation and AGN activity were triggered simultaneously. We find that this quenching followed by an enhancement in the star formation rate is common to AGN galaxies and more pronounced in early type galaxies. Our results demonstrate that local AGN galaxies are not just a simple transition type between star-forming and quiescent galaxies as previously postulated.
This paper is devoted to the study of the emptiness formation probability $\tau\pa{m}$ of the open XXZ chain. We derive a closed form for $\tau\pa{m}$ at $\Delta=\tf{1}{2}$ when the boundary field vanishes. Moreover we obtain its leading asymptotics for an arbitrary boundary field at the free fermion point. Finally, we compute the first term of the asymptotics of $\ln\pa{\tau\pa{m}}$ in the whole massless regime $-1<\Delta<1$.
Transition charge density (TCD) for $ 0^+\to 2_1^+ $ excitation have been calculated for $\rm ^{70,72,74,76}Ge$ nuclei within microscopic variational framework employing $2p_{3/2}, 1f_{5/2}, 2p_{1/2}$ and $1g_{9/2}$ valence space. The calculated TCDs for different monopole variants of Kuo interaction are compared with available experimental results. Other systematics like reduced transition probabilities B(E2) and static quadrupole moments Q(2) are also presented. It is observed that the transition density study acts as a sensitive probe for discriminating the response of different parts of effective interactions.
We study here the crepant resolution correspondence for the torus equivariant descendent Gromov-Witten theories of Hilb(C2) and Sym(C2).The descendent correspondence is obtained from our previous matching of the associated CohFTs by applying Givental's quantization formula to a specific symplectic transformation K. The first result of the paper is an explicit computation of K. Our main result then establishes a fundamental relationship between the Fourier-Mukai equivalence of the associated derived categories (by Bridgeland, King, and Reid) and the symplectic transformation K via Iritani's integral structure. The results use Haiman's Fourier-Mukai calculations and are exactly aligned with Iritani's point of view on crepant resolution.
Semi-supervised learning (SSL) is an effective means to leverage unlabeled data to improve a model's performance. Typical SSL methods like FixMatch assume that labeled and unlabeled data share the same label space. However, in practice, unlabeled data can contain categories unseen in the labeled set, i.e., outliers, which can significantly harm the performance of SSL algorithms. To address this problem, we propose a novel Open-set Semi-Supervised Learning (OSSL) approach called OpenMatch. Learning representations of inliers while rejecting outliers is essential for the success of OSSL. To this end, OpenMatch unifies FixMatch with novelty detection based on one-vs-all (OVA) classifiers. The OVA-classifier outputs the confidence score of a sample being an inlier, providing a threshold to detect outliers. Another key contribution is an open-set soft-consistency regularization loss, which enhances the smoothness of the OVA-classifier with respect to input transformations and greatly improves outlier detection. OpenMatch achieves state-of-the-art performance on three datasets, and even outperforms a fully supervised model in detecting outliers unseen in unlabeled data on CIFAR10.
We used two XMM-Newton and six Neutron Star Interior Composition Explorer (NICER) observations to investigate the fractional rms amplitude of the millihertz quasi-periodic oscillations (mHz QPOs) in the neutron-star low-mass X-ray binary 4U 1636-53. We studied, for the first time, the fractional rms amplitude of the mHz QPOs vs. energy in 4U 1636-53 down to 0.2 keV. We find that, as the energy increases from 0.2 keV to 3 keV, the rms amplitude of the mHz QPOs increases, different from the decreasing trend that has been previously observed above 3 keV. This finding has not yet been predicted by any current theoretical model, however, it provides an important observational feature to speculate whether a newly discovered mHz oscillation originates from the marginally stable nuclear burning process on the neutron star surface.
Quantum simulation methods based on density-functional theory are currently deemed unfit to cope with atomic heat transport within the Green-Kubo formalism, because quantum-mechanical energy densities and currents are inherently ill-defined at the atomic scale. We show that, while this difficulty would also affect classical simulations, thermal conductivity is indeed insensitive to such ill-definedness by virtue of a sort of gauge invariance resulting from energy extensivity and conservation. Based on these findings, we derive an expression for the adiabatic energy flux from density-functional theory, which allows heat transport to be simulated using ab-initio equilibrium molecular dynamics. Our methodology is demonstrated by comparing its predictions with those of classical equilibrium and ab-initio non-equilibrium (M\"uller-Plathe) simulations for a liquid-Argon model, and finally applied to heavy water at ambient conditions.
Today deep convolutional neural networks (CNNs) push the limits for most computer vision problems, define trends, and set state-of-the-art results. In remote sensing tasks such as object detection and semantic segmentation, CNNs reach the SotA performance. However, for precise performance, CNNs require much high-quality training data. Rare objects and the variability of environmental conditions strongly affect prediction stability and accuracy. To overcome these data restrictions, it is common to consider various approaches including data augmentation techniques. This study focuses on the development and testing of object-based augmentation. The practical usefulness of the developed augmentation technique is shown in the remote sensing domain, being one of the most demanded ineffective augmentation techniques. We propose a novel pipeline for georeferenced image augmentation that enables a significant increase in the number of training samples. The presented pipeline is called object-based augmentation (OBA) and exploits objects' segmentation masks to produce new realistic training scenes using target objects and various label-free backgrounds. We test the approach on the buildings segmentation dataset with six different CNN architectures and show that the proposed method benefits for all the tested models. We also show that further augmentation strategy optimization can improve the results. The proposed method leads to the meaningful improvement of U-Net model predictions from 0.78 to 0.83 F1-score.