ShantanuT01/DACTYL-Pretraining huggingface dataset:
We report optical photometric and spectroscopic observations of the M33 star B416, establishing it as the fifth identified LBV in that galaxy. The B magnitude of the star varies with a period of 8.26 day and an amplitude of 0.03 magnitude. The red end of the optical spectrum does not seem to partake in these oscillations, which we identify as the microvariations, known to persist in LBV stars. B416 is the first LBV with such oscillations that are strictly periodic and coherent over at least 10 years. The brightness of the star is also varying on a longer (years) time scale, again mainly in its blue light. The spectrum has most of the characteristics of an LBV in quiescence, showing Balmer, He I, Fe II and [Fe II] emission lines. The flux and profile of some of these lines are varying but the scarcity of the observations prevents us from establishing their characteristic time scale. B416 is at the centre of an H II region, another indication of the relatively young age of this stellar system.
In this paper we prove that the property of being scattered for a $\mathbb{F}_q$-linearized polynomial of small $q$-degree over a finite field $\mathbb{F}_{q^n}$ is unstable, in the sense that, whenever the corresponding linear set has at least one point of weight larger than one, the polynomial is far from being scattered. To this aim, we define and investigate $r$-fat polynomials, a natural generalization of scattered polynomials. An $r$-fat $\mathbb{F}_q$-linearized polynomial defines a linear set of rank $n$ in the projective line of order $q^n$ with $r$ points of weight larger than one. When $r$ equals $1$, the corresponding linear sets are called clubs, and they are related with a number of remarkable mathematical objects like KM-arcs, group divisible designs and rank metric codes. Using techniques on algebraic curves and global function fields, we obtain numerical bounds for $r$ and the non-existence of exceptional $r$-fat polynomials with $r>0$. In the case $n\leq 4$, we completely determine the spectrum of values of $r$ for which an $r$-fat polynomial exists. In the case $n=5$, we provide a new family of $1$-fat polynomials. Furthermore, we determine the values of $r$ for which the so-called LP-polynomials are $r$-fat.
Human pose and shape estimation from RGB images is a highly sought after alternative to marker-based motion capture, which is laborious, requires expensive equipment, and constrains capture to laboratory environments. Monocular vision-based algorithms, however, still suffer from rotational ambiguities and are not ready for translation in healthcare applications, where high accuracy is paramount. While fusion of data from multiple viewpoints could overcome these challenges, current algorithms require further improvement to obtain clinically acceptable accuracies. In this paper, we propose a learnable volumetric aggregation approach to reconstruct 3D human body pose and shape from calibrated multi-view images. We use a parametric representation of the human body, which makes our approach directly applicable to medical applications. Compared to previous approaches, our framework shows higher accuracy and greater promise for real-time prediction, given its cost efficiency.
This work focuses on learning deep visual representation models for retrieval by exploring the interplay between a new loss function, the batch size, and a new regularization approach. Direct optimization, by gradient descent, of an evaluation metric, is not possible when it is non-differentiable, which is the case for recall in retrieval. A differentiable surrogate loss for the recall is proposed in this work. Using an implementation that sidesteps the hardware constraints of the GPU memory, the method trains with a very large batch size, which is essential for metrics computed on the entire retrieval database. It is assisted by an efficient mixup regularization approach that operates on pairwise scalar similarities and virtually increases the batch size further. The suggested method achieves state-of-the-art performance in several image retrieval benchmarks when used for deep metric learning. For instance-level recognition, the method outperforms similar approaches that train using an approximation of average precision.
We investigate the zonal polynomials, a family of symmetric polynomials that appear in many mathematical contexts, such as multivariate statistics, differential geometry, representation theory, and combinatorics. We present two computer algebra packages, in SageMath and in Mathematica, for their computation. With the help of these software packages, we carry out an experimental mathematics study of some properties of zonal polynomials. Moreover, we derive and prove closed forms for several infinite families of zonal polynomial coefficients.
We use a semianalytical approach and a CDM cosmological model to study the gravitational collapse and virialization, the structure, as well as the global and statistical properties of isolated dark matter galactic halos which emerge from primordial Gaussian fluctuations. From the statistical properties of the density fluctuation field the possible mass aggregation histories (MAHs) are generated, and these histories are used as the initial conditions of the gravitational collapse. To calculate the structure of the virialized systems we have generalized the secondary infall model. Although a range of halo structures is obtained, the average density profiles agree with the profile derived as a fitting formula to results of N-body cosmological simulations. The comparison of the density profiles with the observational data is disscused, and some possible solutions to the disagreement found in the inner regions are discussed. The results of our approach, after considering the gravitational dragging of the baryon matter that forms a central disk in centrifugal equilibrium, show that the Tully-Fisher relation and its scatter can be explained through the initial cosmological conditions. The sigma8=1 SCDM model produces galaxies with high velocities when compared to observations, but when the SCDM power spectrum is normalized to sigma8=0.57 an excellent agreement with the observable TF relation is found, suggesting that this relation is the natural extension to galactic scales of the observed galaxy distribution power spectrum. The theoretical TF scatter is close to the measured one. The slope of the TF relation is practically invariant with respect to the spin parameter lambda.
We introduce a stochastic lattice model to investigate the effects of pore formation in a passive layer grown with products of metal corrosion. It considers that an anionic species diffuses across that layer and reacts at the corrosion front (metal-oxide interface), producing a random distribution of compact regions and large pores, respectively represented by O (oxide) and P (pore) sites. O sites are assumed to have very small pores, so that the fraction $\Phi$ of P sites is an estimate of the porosity, and the ratio between anion diffusion coefficients in those regions is $D_{\text r}<1$. Simulation results without the large pores ($\Phi =0$) are similar to those of a formerly studied model of corrosion and passivation and are explained by a scaling approach. If $\Phi >0$ and $D_{\text r}\ll 1$, significant changes are observed in passive layer growth and corrosion front roughness. For small $\Phi$, a slowdown of the growth rate is observed, which is interpreted as a consequence of the confinement of anions in isolated pores for long times. However, the presence of large pores near the corrosion front increases the frequency of reactions at those regions, which leads to an increase in the roughness of that front. This model may be a first step to represent defects in a passive layer which favor pitting corrosion.
We study the diffusion of tagged hard core interacting particles under the influence of an external force field. Using the Jepsen line we map this many particle problem onto a single particle one. We obtain general equations for the distribution and the mean square displacement $<(x_T)^2>$ of the tagged center particle valid for rather general external force fields and initial conditions. A wide range of physical behaviors emerge which are very different than the classical single file sub-diffusion $<(x_T)^2 > \sim t^{1/2}$ found for uniformly distributed particles in an infinite space and in the absence of force fields. For symmetric initial conditions and potential fields we find $<(x_T)^2 > = {{\cal R} (1 - {\cal R})\over 2 N {\it r} ^2} $ where $2 N$ is the (large) number of particles in the system, ${\cal R}$ is a single particle reflection coefficient obtained from the single particle Green function and initial conditions, and $r$ its derivative. We show that this equation is related to the mathematical theory of order statistics and it can be used to find $<(x_T)^2>$ even when the motion between collision events is not Brownian (e.g. it might be ballistic, or anomalous diffusion). As an example we derive the Percus relation for non Gaussian diffusion.
Explicit relations between the effective-range expansion and the nuclear vertex constant or asymptotic normalization coefficient (ANC) for the virtual decay $B\to A+a$ are derived for an arbitrary orbital momentum together with the corresponding location condition for the ($A+a$) bound-state energy. They are valid both for the charged case and for the neutral case. Combining these relations with the standard effective-range function up to order six makes it possible to reduce to two the number of free effective-range parameters if an ANC value is known from experiment. Values for the scattering length, effective range, and form parameter are determined in this way for the $^{16}$O+$p$, $\alpha+t$ and $\alpha+^3$He collisions in partial waves where a bound state exists by using available ANCs deduced from experiments. The resulting effective-range expansions for these collisions are valid up to energies larger 5 MeV.
The availability of large labeled datasets is the key component for the success of deep learning. However, annotating labels on large datasets is generally time-consuming and expensive. Active learning is a research area that addresses the issues of expensive labeling by selecting the most important samples for labeling. Diversity-based sampling algorithms are known as integral components of representation-based approaches for active learning. In this paper, we introduce a new diversity-based initial dataset selection algorithm to select the most informative set of samples for initial labeling in the active learning setting. Self-supervised representation learning is used to consider the diversity of samples in the initial dataset selection algorithm. Also, we propose a novel active learning query strategy, which uses diversity-based sampling on consistency-based embeddings. By considering the consistency information with the diversity in the consistency-based embedding scheme, the proposed method could select more informative samples for labeling in the semi-supervised learning setting. Comparative experiments show that the proposed method achieves compelling results on CIFAR-10 and Caltech-101 datasets compared with previous active learning approaches by utilizing the diversity of unlabeled data.
The problem of constructing a guaranteed convergent sequence of corrections to the Hartree--Fock ground state energy of a molecule without storing the many-electron wave function is considered. Several methods based on cumulants are considered and it is shown that such a sequence is obtained by Lanczos tridiagonalization, in which the elements of the tridiagonal matrix are calculated through cumulants.
Motivated by the absence of Misner string in the Euclidean Taub-Bolt/NUT solutions with flat horizons, we present a new treatment for studying the thermodynamics of these spactimes. This treatment is based on introducing a new charge, $N=\sigma \, n$ (where $n$ is the nut charge and $\sigma$ is some constant) and its conjugate thermodynamic potential $\Phi_N$. Upon identifying one of the spatial coordinates, the boundary of these solutions contains two annulus-like surfaces in addition to the constant-r surface. For these solutions, we show that these annuli surfaces receive electric, magnetic and mass/energy fluxes, therefore, they have nontrivial contributions to these conserved charges. Calculating these conserved charges we find, $Q_e = Q^{\infty}_e-2N\Phi_m$, $Q_m =Q^{\infty}_m+2N\Phi_e$ and $\mathfrak{M} =M-2N\Phi_N$, where $Q^{\infty}_e$, $Q^{\infty}_m$, $M$ are electric charge, magnetic charge and mass in the $n=0$ case, while $\Phi_e$ and $\Phi_m$ are the electric and magnetic potentials. The calculated thermodynamic quantities obey the first law of thermodynamics while the entropy is the area of the horizon. Furthermore, all these quantities obey Smarr's relation. We show the consistency of these results through calculating the Hamiltonian and its variation which reproduces the first law.
We describe the basic assumptions and key results of loop quantum gravity, which is a background independent approach to quantum gravity. The emphasis is on the basic physical principles and how one deduces predictions from them, at a level suitable for physicsts in other areas such as string theory, cosmology, particle physics, astrophysics and condensed matter physics. No details are given, but references are provided to guide the interested reader to the literature. The present state of knowledge is summarized in a list of 35 key results on topics including the hamiltonian and path integral quantizations, coupling to matter, extensions to supergravity and higher dimensional theories, as well as applications to black holes, cosmology and Plank scale phenomenology. We describe the near term prospects for observational tests of quantum theories of gravity and the expectations that loop quantum gravity may provide predictions for their outcomes. Finally, we provide answers to frequently asked questions and a list of key open problems.
With appropriate hypotheses on the nonlinearity $f$, we prove the existence of a ground state solution $u$ for the problem \[(-\Delta+m^2)^\sigma u+Vu=\left(W*F(u)\right)f(u)\ \ \text{in }\ \mathbb{R}^{N},\] where $0<\sigma<1$, $V$ is a bounded continuous potential and $F$ the primitive of $f$. We also show results about the regularity of any solution of this problem.
String theory builds on the great legacy of Yukawa and Tomonaga: New degrees of freedom and control of the UV are two important themes. This talk will give an overview of some of the progress and some of the unsolved problems that characterize string theory today. It is divided into two parts: (1) Connecting String Theory to the Real World; (2) Gauge Theory/String Theory Duality. Two other major subjects, which I will omit, are Black Holes in String Theory and The Impact of String Theory on Mathematics.
We describe the first-principles design and subsequent synthesis of a new material with the specific functionalities required for a solid-state-based search for the permanent electric dipole moment of the electron. We show computationally that perovskite-structure europium barium titanate should exhibit the required large and pressure-dependent ferroelectric polarization, local magnetic moments, and absence of magnetic ordering even at liquid helium temperature. Subsequent synthesis and characterization of Eu$_{0.5}$Ba$_{0.5}$TiO$_3$ ceramics confirm the predicted desirable properties.
Let $H_{n,(p_m)_{m=2,\ldots,M}}$ be a random non-uniform hypergraph of dimension $M$ on $2n$ vertices, where the vertices are split into two disjoint sets of size $n$, and colored by two distinct colors. Each non-monochromatic edge of size $m=2,\ldots,M$ is independently added with probability $p_m$. We show that if $p_2,\ldots,p_M$ are such that the expected number of edges in the hypergraph is at least $dn\ln n$, for some $d>0$ sufficiently large, then with probability $(1-o(1))$, one can find a proper 2-coloring of $H_{n,(p_m)_{m=2,\ldots,M}}$ in polynomial time. We present a polynomial time algorithm for hypergraph 2-coloring, and provide discussions on extension of the approach for $k$-coloring of non-uniform hypergraphs.
A review is presented of the development and current status of nuclear shell-model calculations in which the two-body effective interaction is derived from the free nucleon-nucleon potential. The significant progress made in this field within the last decade is emphasized, in particular as regards the so-called V-low-k approach to the renormalization of the bare nucleon-nucleon interaction. In the last part of the review we first give a survey of realistic shell-model calculations from early to present days. Then, we report recent results for neutron-rich nuclei near doubly magic 132Sn and for the whole even-mass N=82 isotonic chain. These illustrate how shell-model effective interactions derived from modern nucleon-nucleon potentials are able to provide an accurate description of nuclear structure properties.
We outline to the community the value of a Magellanic Clouds Survey that consists of three components: I) a complete-area, high resolution, multi-band UV-near-IR broadband survey; II) a narrowband survey in 7 key nebular filters to cover a statistically significant sample of representative HII regions and a large-area, contiguous survey of the diffuse, warm ISM; and III) a comprehensive FUV spectroscopic survey of 1300 early-type stars. The science areas enabled by such a dataset are as follows: A) assessment of massive star feedback in both HII regions and the diffuse, warm ISM; B) completion of a comprehensive study of the 30 Doradus giant extragalactic HII region (GEHR); C) development and quantitative parameterization of stellar clustering properties; D) extensive FUV studies of early-type stellar atmospheres and their energy distributions; and E) similarly extensive FUV absorption-line studies of molecular cloud structure and ISM extinction properties. These data will also allow a number of additional studies relating to the underlying stellar populations.
Recent works have indicated that the $^{56}$Ni masses estimated for Stripped Envelope SNe (SESNe) are systematically higher than those estimated for SNe II. Although this may suggest a distinct progenitor structure between these types of SNe, the possibility remains that this may be caused by observational bias. One important possible bias is that SESNe with low $^{56}$Ni mass are dim, and therefore they are more likely to escape detection. By investigating the distributions of the $^{56}$Ni mass and distance for the samples collected from the literature, we find that the current literature SESN sample indeed suffers from a significant observational bias, i.e., objects with low $^{56}$Ni mass - if they exist - will be missed, especially at larger distances. Note, however, that those distant objects in our sample are mostly SNe Ic-BL. We also conducted mock observations assuming that the $^{56}$Ni mass distribution for SESNe is intrinsically the same with that for SNe II. We find that the $^{56}$Ni mass distribution of the detected SESNe samples moves toward higher mass than the assumed intrinsic distribution, because of the difficulty in detecting the low-$^{56}$Ni mass SESNe. These results could explain the general trend of the higher $^{56}$Ni mass distribution (than SNe II) of SESNe found thus far in the literature. However, further finding clear examples of low-$^{56}$Ni mass SESNe ($\leq 0.01M_{\odot}$) is required to add weight to this hypothesis. Also, the objects with high $^{56}$Ni mass ($\gtrsim 0.2 M_{\odot}$) are not explained by our model, which may require an additional explanation.
Let $(X,o)$ be a complex analytic normal surface singularity and let ${\mathcal O}_{X,o}$ be its local ring. We investigate the normal reduction number of ${\mathcal O}_{X,o}$ and related numerical analytical invariants via resolutions $\widetilde{X}\to X$ of $(X,o)$ and cohomology groups of different line bundles ${\mathcal L}\in {\rm Pic}(\widetilde{X})$. The normal reduction number is the universal optimal bound from which powers of certain ideals have stabilization properties. Here we combine this with stability properties of the iterated Abel maps. Some of the main results provide topological upper bounds for both stabilization properties.
Using the relativistic electrodynamics of continuous media formalism and main relativistic quantum field theory principles the covariant Lagrangian of electromagnetic field interaction with polarizable 1/2-spin particles have been obtained. This Lagrangian let us to determine canonical and metric energy-momentum tensors as well as low-energy Compton scattering amplitude. The application of this Lagrangian for the calculation of the radiative correction to the imaginary part of double virtual Compton scattering is demonstrated.
In this paper, we prove a sharp and strong non-uniqueness for a class of weak solutions to the three-dimensional magneto-hydrodynamic (MHD) system. More precisely, we show that any weak solution $(v,b)\in L^p_tL^{\infty}_x$ is non-unique in $L^p_tL^{\infty}_x$ with $1\le p<2$, which reveals the strong non-uniqueness, and the sharpness in terms of the classical Ladyzhenskaya-Prodi-Serrin criteria at endpoint $(2, \infty)$. Moreover, for any $1\le p<2$ and $\epsilon>0$, we construct non-Leray-Hopf weak solutions in $L^p_tL^{\infty}_x\cap L^1_tC^{1-\epsilon}$. The results of Navier-Stokes equations in \cite{1Cheskidov} imply the sharp non-uniqueness of MHD system with trivial magnetic field $b$. Our result shows the non-uniqueness for any weak solution $(v,b)$ including non-trivial magnetic field $b$.
This paper generalizes the easy addition formula. Given a normal variety $X$ with an invertible sheaf $L$, inequalities are found bounding $\ka(X,L)$ from above based on the behavior of $L$ restricted to a subvariety or to a pair of "positive" intersecting subvarieties.
Motivated by the classification of non-equilibrium steady states suggested by R.K.P. Zia and B. Schmittmann in J. Stat. Mech. P07012 (2007), we propose to measure the violation of the 'detailed balance' criterion by the $p$-norm ($||K||_p$) of the matrix formed by the probability currents. Its asymptotic analysis, for the totally asymmetric exclusion process, motivates the definition of a 'distance' from equilibrium $K^*$ obtained for $p=1$. In addition, we show that the latter quantity and the average activity $A^*$ are both related to the probability distribution of the entropy production. Finally, considering the open-ASEP and open-ZRP, we show that the current of particles gives an exact measure of the violation of 'detailed balance'.
We present our study of effect of substrate induced strain on the La5/8-yPryCa3/8MnO3 (y=0.45), thin films grown on LaAlO3, NdGaO3 and SrTiO3 susbtrates that show large scale phase separation. It is observed that unstrained films grown on NdGaO3 behave quite similar to bulk material but the strained film grown on SrTiO3 show melting of insulating phase to metallic phase at low temperatures. However, the large scale phase separation and metastable glass-like state is observed in all the films despite difference in substrate induced strain. The measurements of resistivity as a function of temperature under cooling and heating in unequal field (CHUF) protocol elucidates the presence of glass-like meta-stable phase generated due to kinetic arrest of first order transformation in all the films. Like structural glasses, these magnetic glass-like phase shows evidence of devitrification of the arrested charge order-antiferromagnetic insulator (CO-AFI) phase to equilibrium ferromagnetic metallic (FMM) phase with isothermal increase of magnetic field and/or iso-field warming. These measurements also clearly brought out the equilibrium ground state of this system to be FMM and metastable glass-like phase to be AFI phase.