ShantanuT01/DACTYL-Pretraining huggingface dataset:
We make a comparative analysis of the various independent methods proposed in the literature for studying the nature of dark energy, using four different mocks of SnIa data. In particular, we explore a generic principal components analysis approach, the genetic algorithms, a series of approximations like Pad\'e power law approximants, and various expansions in orthogonal polynomials, as well as cosmography, and compare them with the usual fit to a model with a constant dark energy equation of state w. We find that, depending on the mock data, some methods are more efficient than others at distinguishing the underlying model, although there is no universally better method.
We present a new high signal-to-noise (S/N) observations of the Diffuse Interstellar Bands (DIBs) in the Local Bubble and its surroundings. We observed 432 sightlines and obtain the equivalent widths of $\lambda$5780 and $\lambda$5797 \AA\ DIBs up to distance of $\sim$ 200 pc. All observations have been carried out by using Intermediate Dispersion Spectrograph (IDS) on 2.5 m Isaac Newton Telescope, during three years, to reach a minimum S/N ratio of $\sim$ 2000. All $\lambda$5780 and $\lambda$5797 absorptions are presented in this paper and the observed values of interstellar parameter; $\lambda$5780, $\lambda$5797, Na I D lines including the uncertainties are tabulated.
This paper is devoted to the study of $\Phi$-moments of sums of independent/freely independent random variables. More precisely, let $(f_k)_{k=1}^n$ be a sequence of positive (symmetrically distributed) independent random variables and let $\Phi$ be an Orlicz function with $\Delta_2$-condition. We provide an equivalent expression for the quantity $\mathbb{E}(\Phi(\sum_{k=1}^n f_k))$ in term of the sum of disjoint copies of the sequence $(f_k)_{k=1}^n.$ We also prove an analogous result in the setting of free probability. Furthermore, we provide an equivalent characterization of $\tau(\Phi(\sup^+_{1\leq k\leq n}x_k))$ for positive freely independent random variables and also present some new results on free Johnson-Schechtman inequalities in the quasi-Banach symmetric operator space.
We present detailed elemental abundances and radial velocities of stars in the metal-poor globular cluster (GC) NGC 2298, based on near-infrared high-resolution ($R\sim$ 22,500) spectra of twelve members obtained during the second phase of the Apache Point Observatory Galactic Evolution Experiment (APOGEE-2) at Las Campanas Observatory as part of the seventeenth Data Release (DR 17) of the Sloan Digital Sky Survey IV (SDSS-IV). We employ the Brussels Automatic Code for Characterizing High accuracy Spectra (\texttt{BACCHUS}) software to investigate abundances for a variety of species including $\alpha$-elements (Mg, Si, and Ca), the odd-Z element Al, and iron-peak elements (Fe and Ni) located in the innermost regions of NGC 2298. We find a mean and median metallicity [Fe/H] $ = -1.76$ and $-1.75$, respectively, with a star-to-star spread of 0.14 dex, compatible with the internal measurement errors. Thus, we find no evidence for an intrinsic Fe abundance spread in NGC 2298. The typical $\alpha-$element enrichment in NGC 2298 is overabundant relative to the Sun, and follows the trend of other metal-poor GCs. We confirm the existence of an Al-enhanced population in this cluster, which is clearly anti-correlated with Mg, indicating the prevalence of the multiple-population phenomenon in NGC 2298.
The problem of one pair of identical nucleons sitting in ${\cal N}$ single particle levels of a potential well and interacting through the pairing force is treated introducing even Grassmann variables. The eigenvectors are analytically expressed solely in terms of these with coefficients fixed by the eigenvalues and the single particle energies. When the latter are those of an harmonic oscillator well an accurate expression is derived for both the collective eigenvalue and for those trapped in between the single particle levels, for any strength of the pairing interaction and for any number of levels. Notably the trapped solutions are labelled through an index upon which they depend parabolically.
In this article we initiate the study of the heat traces and spectral zeta functions for certain p-adic Laplacians. We show that the heat traces are given by p-adic integrals of Laplace type, and that the spectral zeta functions are p-adic integrals of Igusa-type. We find good estimates for the behaviour of the heat traces when the time tends to infinity, and for the asymptotics of the function counting the eigenvalues less than or equal to a given quantity.
The Hubble tension that the standard $\Lambda$CDM model is suffering from can be resolved with pre-recombination early dark energy. We present the first constraint on the tensor-to-scalar ratio $r$ in corresponding Hubble-tension-free cosmologies using the most recent BICEP/Keck cosmic microwave background (CMB) B-mode polarization data. We find, combining BICEP/Keck with Planck18 CMB and baryon acoustic oscillation data, that the models with larger Hubble constant $H_0$ will have tighter upper bound on $r$, and resolution $H_0\sim73$ km/s/Mpc of the Hubble tension tightens the upper bound to $r<0.028\ (95\%\text{C.L.})$, $25\%$ tighter than the $\Lambda$CDM constraint $r<0.036$. We clarify the origin of this tightening bound.
We develop a matrix model for the SO(32) Heterotic string with certain Wilson lines on the lightlike circle. This is done by using appropriate T-dualities. The method works for an infinite number of Wilson lines, but not for all. The matrix model is the theory on the D-string of type I wrapped on a circle with a SO(32) Wilson line on the circle. The radius of the circle depends on the Wilson line. This is a 1+1 dimensional O(N) theory on a circle. N depends not only on the momentum around the lightlike circle but also on the winding and SO(32) quantum numbers of the state. Perspectives for obtaining a matrix model for all Wilson lines are discussed.
Recently it was shown that the Born-Infeld-type modification of the quadratic Yang-Mills action gives rise to classical particle-like solutions in the flat space which have a striking similarity with the Bartnik-McKinnon solutions known in the gravity coupled Yang-Mills theory. We show that both families are continuously related within the framework of the Einstein-Born-Infeld theory through interpolating sequences of parameters. We also investigate an internal structure of the associated black holes. It is found that the Born-Infeld non-linearity leads to a drastic modification of the black hole interior typical for the usual Yang-Mills theory. In the latter case a generic solution exhibits violent metric oscillations near the singularity. In the Born-Infeld case a generic interior solution is smooth, the metric has the standard Schwarzschild type singularity, and we did not observe internal horizons. Such smoothing of the 'violent' EYM singularity may be interpreted as a result of quantum effects.
In this paper we construct a conservative Markov semi-group with generator $L=\Delta+b\cdot\nabla$ on $\mathbb{R}^n$, where $b$ is a divergence-free vector field which belongs to $L^{2}\cap L^{p}$ with $\frac{n}{2}<p$. The research is motivated by the question of understanding the blow-up solutions of the fluid dynamic equations, which attracts a lot of attention in recent years.
The motion of overdamped particles in a one-dimensional spatially-periodic potential is considered. The potential is also randomly-fluctuating in time, due to multiplicative colored noise terms, and has a deterministic tilt. Numerical aimulations show two distinct parameter regimes, corresponding to free-running near-deterministic particles, and particles which are trapped in local minima of the potential with intermittent escape flights. Perturbation and asymptotic methods are developed to understand the drift velocity and diffusion coefficient in each parameter regime.
In this work we study the contribution of the isoscalar tensor coupling to the realization of pseudospin symmetry in nuclei. Using realistic values for the tensor coupling strength, we show that this coupling reduces noticeably the pseudospin splittings, especially for single-particle levels near the Fermi surface. By using an energy decomposition of the pseudospin energy splittings, we show that the changes in these splittings come by mainly through the changes induced in the lower radial wave function for the low-lying pseudospin partners, and by changes in the expectation value of the pseudospin-orbit coupling term for surface partners. This allows us to confirm the conclusion already reached in previous studies, namely that the pseudospin symmetry in nuclei is of a dynamical nature.
We present ab initio GW plus cumulant-expansion calculations for an organic compound (TMTSF)2PF6 and a transition-metal oxide SrVO3. These materials exhibit characteristic low-energy band structures around the Fermi level, which bring about interesting low-energy properties; the low-energy bands near the Fermi level are isolated from the other bands and, in the isolated bands, unusually low-energy plasmon excitations occur. To study the effect of this low-energy-plasmon fluctuation on the electronic structure, we calculate spectral functions and photoemission spectra using the ab initio cumulant expansion of the Green's function based on the GW self-energy. We found that the low-energy plasmon fluctuation leads to an appreciable renormalization of the low-energy bands and a transfer of the spectral weight into the incoherent part, thus resulting in an agreement with experimental photoemission data.
The mismatch between different independent measurements of the expansion rate of the Universe is known as the Hubble constant ($H_0$) tension, and it is a serious and pressing problem in cosmology. We investigate this tension considering the dataset from the Pantheon sample, a collection of 1048 Type Ia Supernovae (SNe Ia) with a redshift range $0<z<2.26$. We perform a binned analysis in redshift to study if the $H_0$ tension also occurs in SNe Ia data. Hence, we build equally populated subsamples in three and four bins, and we estimate $H_{0}$ in each bin considering the $\Lambda$CDM and $w_{0}w_{a}$CDM cosmological models. We perform a statistical analysis via a Markov Chain Monte Carlo (MCMC) method for each bin. We observe that $H_0$ evolves with the redshift, using a fit function $H_{0}(z)=\tilde{H}_{0} (1+z)^{-\alpha}$ with two fitting parameters $\alpha$ and $\tilde{H}_{0}$. Our results show a decreasing behavior of $H_0$ with $\alpha\sim 10^{-2}$ and a consistency with no evolution between 1.2 $\sigma$ and 2.0 $\sigma$. Considering the $H_0$ tension, we extrapolate $H_{0}(z)$ until the redshift of the last scattering surface, $z=1100$, obtaining values of $H_0$ consistent in 1 $\sigma$ with the cosmic microwave background (CMB) measurements by Planck. Finally, we discuss possible $f(R)$ modified gravity models to explain a running Hubble constant with the redshift, and we infer the form of the scalar field potential in the dynamically equivalent Jordan frame.
Early results of JWST observations have delivered bright $z\gtrsim 10$ galaxy candidates in greater numbers than expected, enabling construction of the rest-frame UV luminosity functions (LFs). The LFs contain key information on the galaxy assembly history, star formation activity, and stellar population in the distant universe. Given an upper bound of the total baryonic mass inflow rate to galaxies from their parent halos estimated from abundance matching, we derive a lower bound on the product of the star formation and UV-photon production efficiency in galaxies at each redshift. This stringent constraint requires a high efficiency ($\gtrsim 10-30\%$) converting gas into stars, assuming a normal stellar population with a Salpeter-like mass distribution. The efficiency is substantially higher than those of typical nearby galaxies, but is consistent with those seen in starburst galaxies and super star clusters observed in the nearby universe. Alternatively, the star formation efficiency may be as low as a few percent, which is the average value for the entire galaxy population at $z\simeq 6$, if the stellar population is metal-free and drawn from a top-heavy mass distribution that produces more intense UV radiation. We discuss several other possible scenarios to achieve the constraint, for instance, energetic radiation produced from compact stellar-remnants and quasars, and propose ways to distinguish the scenarios by forthcoming observations.
A class of non-supersymmetric string backgrounds can be constructed using twists that involve space-time fermion parity. We propose a non-perturbative definition of string theory in these backgrounds via gauge theories with supersymmetry softly broken by twisted boundary conditions. The perturbative string spectrum is reproduced, and qualitative effects of the interactions are discussed. Along the way, we find an interesting mechanism for inflation. The end state of closed string tachyon condensation is a highly excited state in the gauge theory which, in all likelihood, does not have a geometric interpretation.
In medical image segmentation, supervised deep networks' success comes at the cost of requiring abundant labeled data. While asking domain experts to annotate only one or a few of the cohort's images is feasible, annotating all available images is impractical. This issue is further exacerbated when pre-trained deep networks are exposed to a new image dataset from an unfamiliar distribution. Using available open-source data for ad-hoc transfer learning or hand-tuned techniques for data augmentation only provides suboptimal solutions. Motivated by atlas-based segmentation, we propose a novel volumetric self-supervised learning for data augmentation capable of synthesizing volumetric image-segmentation pairs via learning transformations from a single labeled atlas to the unlabeled data. Our work's central tenet benefits from a combined view of one-shot generative learning and the proposed self-supervised training strategy that cluster unlabeled volumetric images with similar styles together. Unlike previous methods, our method does not require input volumes at inference time to synthesize new images. Instead, it can generate diversified volumetric image-segmentation pairs from a prior distribution given a single or multi-site dataset. Augmented data generated by our method used to train the segmentation network provide significant improvements over state-of-the-art deep one-shot learning methods on the task of brain MRI segmentation. Ablation studies further exemplified that the proposed appearance model and joint training are crucial to synthesize realistic examples compared to existing medical registration methods. The code, data, and models are available at https://github.com/devavratTomar/SST.
In recent years, the multiple-stage strategy has become a popular trend for visual tracking. This strategy first utilizes a base tracker to coarsely locate the target and then exploits a refinement module to obtain more accurate results. However, existing refinement modules suffer from the limited transferability and precision. In this work, we propose a novel, flexible and accurate refinement module called Alpha-Refine, which exploits a precise pixel-wise correlation layer together with a spatial-aware non-local layer to fuse features and can predict three complementary outputs: bounding box, corners and mask. To wisely choose the most adequate output, we also design a light-weight branch selector module. We apply the proposed Alpha-Refine module to five famous and state-of-the-art base trackers: DiMP, ATOM, SiamRPN++, RTMDNet and ECO. The comprehensive experiments on TrackingNet, LaSOT and VOT2018 benchmarks demonstrate that our approach significantly improves the tracking performance in comparison with other existing refinement methods. The source codes will be available at https://github.com/MasterBin-IIAU/AlphaRefine.
A general class of singular abstract Cauchy problems is considered which naturally arises in applications to certain Free Boundary Problems. Existence of an associated evolution operator characterizing its solutions is established and is subsequently used to derive optimal regularity results. The latter are well known to be important basic tools needed to deal with corresponding nonlinear Cauchy Problems such as those associated to Free Boundary Problems.
Functional determinants for a scalar field with negative mass squared are numerically evaluated on an orbifolded three-sphere, in particular on a lune and on a regular 4--polytope fundamental domain. Graphs are provided of the logdets and some Hartle-Hawking probabilities, on the basis of the dS/CFT correspondence.
We numerically calculate the local density of states (LDOS) of a one-dimensional Mott insulator with open boundaries, which is modelled microscopically by a (extended) Hubbard chain at half filling. In the Fourier transform of the LDOS we identify several dispersing features corresponding to propagating charge and spin degrees of freedom, thus providing a visualisation of the spin-charge separation in the system. We also consider the effect of an additional boundary potential, which, if sufficiently strong, leads to the formation of a boundary bound state which is clearly visible in the LDOS as a non-dispersing feature inside the Mott gap.
The discoveries of high-energy astrophysical neutrinos by IceCube in 2013 and of gravitational waves by LIGO in 2015 have enabled a new era of multi-messenger astronomy. Gravitational waves can identify the merging of compact objects such as neutron stars and black holes. These compact mergers, especially neutron star mergers, are potential neutrino sources. We present an analysis searching for neutrinos from gravitational wave sources reported by the LIGO Virgo Collaboration (LVC). We use a dedicated transient likelihood analysis combining IceCube events with source localizations provided by LVC as spatial priors. We report results for all gravitational wave events from the O1, O2, and O3 observing runs.
We have collected the parameter of 38 neutron stars (NSs) in binary systems with spin periods and measured masses. By adopting the Boot-strap method, we reproduced the procedure of mass calculated for each system separately, to determine the truly mass distribution of the NS that obtained from observation. We also applied the Monte-Carlo simulation and introduce the characteristic spin period 20 ms, in order to distinguish between millisecond pulsars (MSPs) and less recycled pulsars. The mass distributions of MSPs and the less recycled pulsars could be fitted by a Gaussian function as $\rm 1.45\pm0.42 M_{\odot}$ and $\rm 1.31\pm0.17 M_{\odot} (\rm with ~ 1\sigma)$ respectively. As such, the MSP masses are heavier than those in less recycled systems by factor of $\rm \sim 0.13M_{\odot}$, since the accretion effect during the recycling process.
These are lectures notes on rationally connected varieties, written for the "Etats de la Recherche" of the French Mathematical Society held in Strasbourg (May 2008). We focus on geometric aspects. These notes have been written in order that a wide audience can easily read them, except maybe the last section, a bit more technical, where we give the proof of Shokurov rational connectedness conjecture following Hacon and McKernan.   -----   Ce sont les notes d'un mini-cours sur les vari\'et\'es rationnellement connexes, \'ecrit pour les Etats de la Recherche de la Soci\'et\'e Math\'ematique de France (Strasbourg, 2008). On met l'accent sur les aspects g\'eom\'etriques. Ce cours est r\'edig\'e dans l'espoir de s'adresser \`a un public large, \`a l'exception peut-\^etre du \S 7, o\`u nous donnons les grandes lignes de la preuve de la conjecture de connexit\'e rationnelle de Shokurov par Hacon et McKernan, plus technique et o\`u les pr\'erequis sont un peu plus importants.
A new method of abstracting the independent gauge invariances of higher derivative systems, recently introduced in [1], has been applied to higher derivative field theories. This has been discussed taking the extended Maxwell-Chern-Simons model as an example. A new Hamiltonian analysis of the model is provided. This Hamiltonian analysis has been used to construct the independent gauge generator. An exact mapping between the Hamiltonian gauge transformations and the U(1) symmetries of the action has been established.
We theoretically investigate the influence of the fluctuating Overhauser field on the spin of an electron confined to a quantum dot (QD). The fluctuations arise from nuclear angular momentum being exchanged between different nuclei via the nuclear magnetic dipole coupling. We focus on the role of the nuclear electric quadrupole moments (QPMs), which generally cause a reduction in internuclear spin transfer efficiency in the presence of electric field gradients. The effects on the electron spin coherence time are studied by modeling an electron spin echo experiment. We find that the QPMs cause an increase in the electron spin coherence time and that an inhomogeneous distribution of the quadrupolar shift, where different nuclei have different shifts in energy, causes an even larger increase in the electron coherence time than a homogeneous distribution. Furthermore, a partial polarization of the nuclear spin ensemble amplifies the effect of the inhomogeneous quadrupolar shifts, causing an additional increase in electron coherence time, and provides an alternative to the experimentally challenging suggestion of full dynamic nuclear spin polarization.
The elastic property of quantum critical quasicrystal (QC) Yb$_{15}$Al$_{34}$Au$_{51}$ is analyzed theoretically on the basis of the approximant crystal (AC) Yb$_{14}$Al$_{35}$Au$_{51}$. By constructing the realistic effective model in the AC, we evaluate the 4f-5d Coulomb repulsion at Yb as $U_{fd}\approx 1.46$ eV realizing the quantum critical point (QCP) of the Yb-valence transition. The RPA analysis of the QCP shows that softening in elastic constants occurs remarkably for bulk modulus and longitudinal mode at low temperatures. Possible relevance of these results to the QC as well as the pressure-tuned AC is discussed.
We compute the perturbative one-to-three Pomeron vertex in the colour glass condensate using the extended generalized leading logarithmic approximation in high energy QCD. The vertex is shown to be a conformal four-point function in two-dimensional impact parameter space. Our result can be used to compare different theoretical descriptions of the colour glass condensate.