ShantanuT01/DACTYL-Pretraining huggingface dataset:
We report the discovery of a peculiar horizontal branch (HB) in NGC 6440 and NGC 6569, two massive and metal-rich Galactic globular clusters (GGCs) located in the Galactic bulge, within 4 kpc from the Galactic Center. In both clusters, two distinct clumps are detected at the level of the cluster HB, separated by only ~ 0.1 magnitudes in the Ks band. They were detected with IR photometric data collected with the "VISTA Variables in the Via Lactea" (VVV) Survey, and confirmed in independent IR catalogs available in the literature, and HST optical photometry. Our analysis demonstrates that these clumps are real cluster features, not a product of field contamination or interstellar reddening. The observed split HBs could be a signature of two stellar sub-populations with different chemical composition and/or age, as recently found in Terzan 5, but it cannot be excluded that they are caused by evolutionary effects, in particular for NGC 6440. This interpretation, however, requires an anomalously high helium content (Y > 0.30). Our discovery suggests that such a peculiar HB morphology could be a common feature of massive, metal-rich bulge GGCs.
We construct bases of quasi-symmetric functions whose product rule is given by the shuffle of binary words, as for multiple zeta values in their integral representations, and then extend the construction to the algebra of free quasi-symmetric functions colored by positive integers. As a consequence, we show that the fractions introduced in [Guo and Xie, Ramanujan Jour. 25 (2011) 307-317] provide a realization of this algebra by rational moulds extending that of free quasi-symmetric functions given in [Chapoton et al., Int. Math. Res. Not. IMRN 2008, no. 9, Art. ID rnn018].
Given a covering f: X \to Y of projective manifolds, we consider the vector bundle E on Y given as the dual of f_*(\O_X) / \O_Y. This vector bundles often has positivity properties, e.g. E is ample when Y is projective space by a theorem of Lazarsfeld. In general however E will not be ample due to the geometry of Y. We prove various results when E is spanned, nef or generically nef, under some assumptions on the base Y.
This paper is to investigate the spectral properties of sample covariance matrices under a more general population. We consider a class of matrices of the form $\mathbf S_n=\frac1n\mathbf B_n\mathbf X_n\mathbf X_n^*\mathbf B_n^*$, where $\mathbf B_n$ is a $p\times m$ non-random matrix and $\mathbf X_n$ is an $m\times n$ matrix consisting of i.i.d standard complex entries. $p/n\to c\in (0,\infty)$ as $n\to \infty$ while $m$ can be arbitrary. We proved that under some mild assumptions, with probability 1, there will be no eigenvalues in any closed interval contained in an open interval outside the supports of the limiting distribution $F_{c_n,H_n}$, for all sufficiently large $n$. An extension of Bai-Yin law is also obtained.
We present new data from BVRI photometric observations of five PMS stars during the period from April 2013 to July 2014. The stars are located in the field of NGC 7000/IC 5070 ("Gulf of Mexico") - a region with active star formation. The presented paper is a continuation of our long-term photometric investigations of the young stellar objects in this region. The long-term multicolor photometric observations of PMS stars are very important for their exact classification. Our results show that the studied stars exhibit different types of photometric variability in all bands. We tried to classify them using our data from the long-term photometry and data published by other authors.
The early petite unification (PUT) of quarks and leptons at TeV scales with sin^2 theta_W(M^2_Z) used as a constraint, necessitates the introduction of extra quarks and leptons with unconventional electric charges (up to 4/3 for the quarks and 2 for the leptons). This talk, in honor of Paul Frampton's 60th birthday, will be devoted to the motivation and construction of models of early unification and to their implications, including the issues of rare decays and unconventional fermions.
In 1980, Ajtai, Komlos and Szemer{\'e}di defined "groupie": Let $G=(V,E)$ be a simple graph, $|V|=n$, $|E|=e$. For a vertex $v\in V$, let $r(v)$ denote the sum of the degrees of the vertices adjacent to $v$. We say $v\in V$ is a {\it groupie}, if $\frac{r(v)}{\deg(v)}\geq\frac{e}{n}.$ In this paper, we prove that in random graph $B(n,p)$, $0<p<1$, the proportion of groupies converges in probability towards $\Phi(1)\approx0.8413$ as $n$ approaches infinity, where $\Phi(x)$ is the distribution function of standard normal distribution N(0,1). We also discuss the asymptotic behavior of the proportion of groupies in complete bipartite graph $B(n_1,n_2,p)$.
The atomistic structure and energetics of the Sigma 13 (10-14)[1-210] symmetrical tilt grain boundary in alpha-Al2O3 are studied by first-principles calculations based on the local-density-functional theory with a mixed-basis pseudopotential method. Three configurations, stable with respect to intergranular cleavage, are identified: one Al-terminated glide-mirror twin boundary, and two O-terminated twin boundaries, with glide-mirror and two-fold screw-rotation symmetries, respectively. Their relative energetics as a function of axial grain separation are described, and the local electronic structure and bonding are analysed. The Al-terminated variant is predicted to be the most stable one, confirming previous empirical calculations, but in contrast with high-resolution transmission electron microscopy observations on high-purity diffusion-bonded bicrystals, which resulted in an O-terminated structure.   An explanation of this discrepancy is proposed, based on the different relative energetics of the internal interfaces with respect to the free surfaces.
We study the half advanced and half retarded Wheeler Green function and its relation to Feynman propagators. First for massless equation. Then, for Klein-Gordon equations with arbitrary mass parameters; real, imaginary or complex. In all cases the Wheeler propagator lacks an on-shell free propagation. The Wheeler function has support inside the light-cone (whatever the mass). The associated vacuum is symmetric with respect to annihilation and creation operators.   We show with some examples that perturbative unitarity holds, whatever the mass (real or complex). Some possible applications are discussed.
We formulate a linear response theory of the chiral magnetic effect in a finite Weyl semimetal, expressing the electrical current density $j$ induced by a slowly oscillating magnetic field $B$ or chiral chemical potential $\mu$ in terms of the scattering matrix of Weyl fermions at the Fermi level. Surface conduction can be neglected in the infinite-system limit for $\delta j/\delta \mu$, but not for $\delta j/\delta B$: The chirally circulating surface Fermi arcs give a comparable contribution to the bulk Weyl cones no matter how large the system is, because their smaller number is compensated by an increased flux sensitivity. The Fermi arc contribution to $\mu^{-1}\delta j/\delta B$ has the universal value $(e/h)^2$, protected by chirality against impurity scattering --- unlike the bulk contribution of opposite sign.
For a Latt\`es map $\phi:\mathbb P^1 \to \mathbb P^1$ defined over a number field $K$, we prove a conjecture on the integrality of points in the backward orbit of $P\in \mathbb P^1(\overline K)$ under $\phi$.
The breakup of the radioactive 17F nucleus into a proton and 16O is studied for the reaction 17F + 208Pb --> p + 16O + 208Pb at 65 MeV/nucleon. The possibility of using this reaction as a test case for studying dynamical Coulomb reacceleration effects is assessed. It is shown that the reaction is dominated by elastic nuclear breakup (diffraction dissociation).
A kinetic equation which combines the quasiparticle drift of Landau's equation with a dissipation governed by a nonlocal and noninstant scattering integral in the spirit of Snider's equation for gases is derived. Consequent balance equations for the density, momentum and energy include quasiparticle contributions and the second order quantum virial corrections. The medium effects on binary collisions are shown to mediate the latent heat, i.e., an energy conversion between correlation and thermal energy. An implementation to heavy ion collisions is discussed.
In this review we discuss what is known about semiorthogonal decompositions of derived categories of algebraic varieties. We review existing constructions, especially the homological projective duality approach, and discuss some related issues such as categorical resolutions of singularities.
One of the most energetic gamma-ray burst GRB 110731A was observed from optical to GeV energy range. Previous analysis on the prompt phase revealed similarities with the Large Area Telescope (LAT) bursts observed by Fermi: i) a delayed onset of the high-energy emission ($> 100$ MeV), ii) a short-lasting bright peak at later times and iii) a temporally extended component from this phase and lasting hundreds of seconds. Additionally to the prompt phase, multiwavelength observations over different epochs showed that the spectral energy distribution was better fitted by a wind afterglow model. We present a leptonic model based on an early afterglow that evolves in a stellar wind of its progenitor. We apply this model to interpret the temporally extended LAT emission and the brightest LAT peak exhibited by the prompt phase of GRB 110731A. Additionally, using the same set of parameters, we describe the multiwavelength afterglow observations. The origin of the temporally extended LAT, X-ray and optical flux is explained through synchrotron radiation from the forward shock and the brightest LAT peak is described evoking the synchrotron self-Compton emission from the reverse shock. The bulk Lorentz factor required in this model ($\Gamma\simeq520$) lies in the range of values demanded for most LAT-detected gamma-ray bursts. We show that the strength of the magnetic field in the reverse-shock region is $\sim$ 50 times stronger than in the forward-shock region. This result suggests that for GRB 110731A, the central engine is likely entrained with strong magnetic fields.
Low energy interactions between particles are often characterised by elastic scattering. Just as electrons undergo Thomson scattering with photons, dark matter particles may experience an analogous form of momentum exchange with dark energy. We investigate the influence such an interaction has on the formation of linear and nonlinear cosmic structure, by running for the first time a suite of N-body simulations with different dark energy equations of state and scattering cross sections. In models where the linear matter power spectrum is suppressed by the scattering, we find that on nonlinear scales the power spectrum is strongly enhanced. This is due to the friction term increasing the efficiency of gravitational collapse, which also leads to a scale-independent amplification of the concentration and mass functions of halos. The opposite trend is found for models characterised by an increase of the linear matter power spectrum normalisation. More quantitatively, we find that power spectrum deviations at nonlinear scales ($k \approx 10\, h/$Mpc) are roughly ten times larger than their linear counterparts, exceeding $100%$ for the largest value of the scattering cross section considered in the present work. Similarly, the concentration-mass relation and the halo mass function show deviations up to $100%$ and $20%$, respectively, over a wide range of masses. Therefore, we conclude that nonlinear probes of structure formation might provide much tighter constraints on the scattering cross section between dark energy and dark matter as compared to the present bounds based on linear observables.
The game of Antonim is a variant of the game Nim, with the additional rule that heaps are not allowed to be the same size. A winning strategy for three heap Antonim has been solved. We will discuss the solution to three-heap Antonim and generalize this theory to an arbitrary number of heaps.
The mapping of topologically nontrivial gauge transformations in noncommutative gauge theory to corresponding commutative ones is investigated via the operator form of the Seiberg-Witten map. The role of the gauge transformation part of the map is analyzed. Chern-Simons actions are examined and the correspondence to their commutative counterparts is clarified.
Deep learning models generally learn the biases present in the training data. Researchers have proposed several approaches to mitigate such biases and make the model fair. Bias mitigation techniques assume that a sufficiently large number of training examples are present. However, we observe that if the training data is limited, then the effectiveness of bias mitigation methods is severely degraded. In this paper, we propose a novel approach to address this problem. Specifically, we adapt self-supervision and self-distillation to reduce the impact of biases on the model in this setting. Self-supervision and self-distillation are not used for bias mitigation. However, through this work, we demonstrate for the first time that these techniques are very effective in bias mitigation. We empirically show that our approach can significantly reduce the biases learned by the model. Further, we experimentally demonstrate that our approach is complementary to other bias mitigation strategies. Our approach significantly improves their performance and further reduces the model biases in the limited data regime. Specifically, on the L-CIFAR-10S skewed dataset, our approach significantly reduces the bias score of the baseline model by 78.22% and outperforms it in terms of accuracy by a significant absolute margin of 8.89%. It also significantly reduces the bias score for the state-of-the-art domain independent bias mitigation method by 59.26% and improves its performance by a significant absolute margin of 7.08%.
A set of equations is derived from the Boltzmann kinetic equation describing charge transport in semiconductors. The unknowns of these equations depend on the space-time coordinates and the electron energy. The non-parabolic and parabolic band approximation are treated in detail. In these cases, the set of equations is equivalent to those obtained in the spherical-harmonics expansion. Stationary and homogeneous solutions are explicitly treated. In order to solve numerically the equations, a cut in the energy range is introduced. The modified model maintains the physical characteristics of the original equations. The solution of an asymptotic equation is found and compared to the numerical solutions.
The search for the Higgs boson and for physics beyond the Standard Model are the major motivations behind the LHC experiment. In many scenarios the success of the experiment depends on the knowledge of signal and background event rates at least at one-loop precision. We present the approach of the \texttt{GOLEM} collaboration to build a highly automated framework for the calculation of matrix elements at the one-loop level, which is based on the evaluation of Feynman diagrams. Part of this effort is an open-source library for the numerical evaluation of tensor integrals. As an application, some results for the process $pp\to b\bar{b}b\bar{b}$ calculated with this method are presented.
Magnetic susceptibility and muon spin relaxation (muSR) experiments have been carried out on the quasi-2D triangular-lattice spin S = 2 antiferromagnet FeGa2S4. The muSR data indicate a sharp onset of a frozen or nearly-frozen spin state at T* = 31(2) K, twice the spin-glass-like freezing temperature T_f = 16(1) K. The susceptibility becomes field dependent below T*, but no sharp anomaly is observed in any bulk property. A similar transition is observed in muSR data from the spin-1 isomorph NiGa2S4. In both compounds the dynamic muon spin relaxation rate lambda_d(T) above T* agrees well with a calculation of spin-lattice relaxation by Chubukov, Sachdev, and Senthil in the renormalized classical regime of a 2D frustrated quantum antiferromagnet. There is no firm evidence for other mechanisms. At low temperatures lambda_d(T) becomes temperature independent in both compounds, indicating persistence of spin dynamics. Scaling of lambda_d(T) between the two compounds is observed from ~T_f to ~1.5T*. Although the muSR data by themselves cannot exclude a truly static spin component below T*, together with the susceptibility data they are consistent with a slowly-fluctuating "spin gel" regime between T_f and T*. Such a regime and the absence of a divergence in lambda_d(T) at T* are features of two unconventional mechanisms: (1) binding/unbinding of Z_2 vortex excitations, and (2) impurity spins in a nonmagnetic spin-nematic ground state. The absence of a sharp anomaly or history dependence at T* in the susceptibility of FeGa2S4, and the weakness of such phenomena in NiGa2S4, strongly suggest transitions to low-temperature phases with unconventional dynamics.
Schauder's fixed point theorem is used to derive the existence of solutions to a semilinear heat equation. The equation features a nonlinear term that depends on the time-integral of the unknown on the whole, a priori given, interval of existence.
We prove a selection of results from different areas of extremal combinatorics, including complete or partial solutions to a number of open problems. These results, coming mainly from extremal graph theory and Ramsey theory, have been collected together because in each case the relevant proofs are reasonably short.
We considered the interaction of semiconductor quantum register with noisy environment leading to various types of qubit errors. We analysed both phase and amplitude decays during the process of electron-phonon interaction. The performance of quantum error correction codes (QECC) which will be inevitably used in full scale quantum information processors was studied in realistic conditions in semiconductor nanostructures. As a hardware basis for quantum bit we chose the quantum spatial states of single electron in semiconductor coupled double quantum dot system. The modified 5- and 9-qubit quantum error correction (QEC) algorithms by Shor and DiVincenzo without error syndrome extraction were applied to quantum register. 5-qubit error correction procedures were implemented for Si charge double dot qubits in the presence of acoustic phonon environment. Chi-matrix, Choi-Jamiolkowski state and measure of decoherence techniques were used to quantify qubit fault-tolerance. Our results showed that the introduction of above quantum error correction techniques at small phonon noise levels provided quadratic improvement of output error rates. The efficiency of 5-qubits quantum error correction algorithm in semiconductor quantum information processors was demonstrated.
The relationship between the X-ray determined temperature $T$ of the intracluster gas and the optical measured velocity dispersion $\sigma$ of the cluster galaxies is often believed to be not only a straightforward but also robust test for the dynamical properties of galaxy clusters. Here, we present the $\sigma$-$T$ relationship using the 94 clusters drawn from the largest sample of 149 clusters in literature, for which both $\sigma$ and $T$ are observationally determined. Employment of the doubly weighted orthogonal distance regression to our sample yields $\sigma=10^{2.47\pm0.06}T^{0.67\pm0.09}$, indicating an apparent deviation of dynamical state from that predicted by the isothermal and hydrostatic equilibrium model for galaxy clusters, though the average ratio $\beta_{spec}$ of specific energy in galaxies to that in gas is found to be in excellent agreement with unity. It shows that a nonisothermal gas distribution with a mean polytropic index of $\gamma=1.3$ can account for the reported $\sigma$-$T$ relationship, while overall clusters can still be regarded as dynamically-relaxed systems.
We examine GRBs with both Fermi-LAT and X-ray afterglow data. Assuming that the 100MeV (LAT) emission is radiation from cooled electrons accelerated by external shocks, we show that the kinetic energy of the blast wave estimated from the 100MeV flux is 50 times larger than the one estimated from the X-ray flux. This can be explained if either: i) electrons radiating at X-rays are significantly cooled by SSC (suppressing the synchrotron flux above the cooling frequency) or ii) if the X-ray emitting electrons, unlike those emitting at 100MeV energies, are in the slow cooling regime. In both cases the X-ray flux is no longer an immediate proxy of the blast wave kinetic energy. We model the LAT, X-ray and optical data and show that in general these possibilities are consistent with the data, and explain the apparent disagreement between X-ray and LAT observations. All possible solutions require weak magnetic fields: $10^{-6}< \epsilon_B < 10^{-3}$ (where $\epsilon_B$ is the fraction of shocked plasma energy in magnetic fields). Using the LAT emission as a proxy for the blast wave kinetic energy we find that the derived prompt efficiencies are of order 15%. This is considerably lower compared with previous estimates (87% and higher for the same bursts). This provides at least a partial solution to the "prompt high efficiency paradox".
Previous work on color transparency is reviewed briefly with an emphasis on aspects related to an upgrade of CEBAF.
Due to abundance of data from multiple modalities, cross-modal retrieval tasks with image-text, audio-image, etc. are gaining increasing importance. Of the different approaches proposed, supervised methods usually give significant improvement over their unsupervised counterparts at the additional cost of labeling or annotation of the training data. Semi-supervised methods are recently becoming popular as they provide an elegant framework to balance the conflicting requirement of labeling cost and accuracy. In this work, we propose a novel deep semi-supervised framework which can seamlessly handle both labeled as well as unlabeled data. The network has two important components: (a) the label prediction component predicts the labels for the unlabeled portion of the data and then (b) a common modality-invariant representation is learned for cross-modal retrieval. The two parts of the network are trained sequentially one after the other. Extensive experiments on three standard benchmark datasets, Wiki, Pascal VOC and NUS-WIDE demonstrate that the proposed framework outperforms the state-of-the-art for both supervised and semi-supervised settings.
This paper is concerned with ground states of attractive Bose gases confined in an anharmonic trap $V(x)=\omega(|x|^2+k|x|^4)$ rotating at the velocity $\Omega>0$, where $\omega>0$ denotes the trapping frequency, and $k>0$ represents the strength of the quartic term. It is known that for any $\Omega>0$, ground states exist in such traps if and only if $0<a<a^*$, where $a^*:=\|Q\|^{2}_{2}$ and $Q>0$ is the unique positive solution of $\Delta Q-Q+Q^{3}=0$ in $\mathbb{R}^2$. By analyzing the refined energies and expansions of ground states, we prove that there exists a constant $C>0$, independent of $0<a<a^*$, such that ground states do not have any vortex in the region $R(a):=\big\{x\in\mathbb{R}^2:\, |x|\leq C(a^*-a)^{-\frac{1-6\beta}{20}}\big\}$ as $a\nearrow a^*$, for the case where $\omega=\frac{3\Omega^2}{4}$, $k=\frac{1}{6}$, and $\Omega=C_0(a^*-a)^{-\beta}$ varies for some $\beta\in [0,\frac{1}{6})$ and $C_0>0$.