ShantanuT01/DACTYL-Pretraining huggingface dataset:
In the present paper, we consider the coupled Schr\"{o}dinger systems with critical exponent: \begin{equation*} \begin{cases} -\Delta u_i+\lambda_{i}u_i=\sum\limits_{j=1}^{d} \beta_{ij}|u_j|^{3}|u_i|u_i \quad ~\text{ in } \Omega,\\ u_i \in H_0^1(\Omega) ,\quad i= 1,2,...,d. \end{cases} \end{equation*} Here, $\Omega\subset \mathbb{R}^{3}$ is a smooth bounded domain, $d \geq 2$, $\beta_{ii}>0$ for every $i$, and $\beta_{ij}=\beta_{ji}$ for $i \neq j$. We study a Br\'{e}zis-Nirenberg type problem: $-\lambda_{1}(\Omega)<\lambda_{1},\cdots,\lambda_{d}<-\lambda^*(\Omega)$, where $\lambda_{1}(\Omega)$ is the first eigenvalue of $-\Delta$ with Dirichlet boundary conditions and $\lambda^*(\Omega)\in (0, \lambda_1(\Omega))$. We acquire the existence of least energy positive solutions to this system for weakly cooperative case ($\beta_{ij}>0$ small) and for purely competitive case ($\beta_{ij}\leq 0$) by variational arguments. The proof is performed by mathematical induction on the number of equations, and requires more refined energy estimates for this system. Besides, we present a new nonexistence result, revealing some different phenomena comparing with the higher-dimensional case $N\geq 5$. It seems that this is the first paper to give a rather complete picture for the existence of least energy positive solutions to critical Schr\"{o}dinger system in dimension three.
Aims: we propose a gravitational potential method (GPM) as a supercluster finder based on the analysis of the local gravitational potential distribution measured by fast and simple algorithm applied to a spatial distribution of mass tracers. Methodology: the GPM performs a two-step exploratory data analysis: first, it measures the comoving local gravitational potential generated by neighboring mass tracers at the position of a test point-like mass tracer. The computation extended to all mass tracers of the sample provides a detailed map of the negative potential fluctuations. The most negative gravitational potential is provided by the highest mass density or, in other words, the deeper is a potential fluctuations in a certain region of space and denser are the mass tracers in that region. Therefore, from a smoothed potential distribution, the deepest potential well detects unambiguously a high concentration in the mass tracer distribution. Second, applying a density contrast criterion to that mass concentration, a central bound core may be identify and quantify in terms of memberships and total mass. Results: using a complete volume-limited sample of galaxy clusters, a huge concentration of galaxy clusters has been detected. In its central region, 35 clusters seem to form a massive and bound core enclosed in a spherical volume of 51 Mpc radius. Conclusions: the substantial agreement of our findings compared with those obtained by different methodologies, confirms the GPM as a straightforward and powerful as well as fast cluster finder useful for analyzing large datasets.
We prove local and global existence from large, rough initial data for a wave map between 1+1 dimensional Minkowski space and an analytic manifold. Included here is global existence for large data in the scale-invariant norm $\dot L^{1,1}$, and in the Sobolev spaces $H^s$ for $s > 3/4$. This builds on previous work in 1+1 dimensions of Pohlmeyer, Gu, Ginibre-Velo and Shatah.
Possibilities are discussed for determining the top quark mass $m_t$ from observations on the decay processes for top-antitop pairs produced in antiproton-proton collisions, assuming that the $t \to bW^+$ decay channel is dominant and much faster than hadronization. The final states $t \bar{t} \to \bar{b} b \mu^\pm e^\mp$ provide the most striking signal, with little background, but they are rare ($\approx 2/81$). If all candidate events prove to be from $t \bar{t}$, an estimate follows for $P(m_t|rate)$, the probability distribution for $m_t$. The one reported configuration allows an independent estimate for $P(m_t|\mu^\pm e^\mp \,2jets)$. These two distributions are compatible,yielding an estimate of about 122 GeV. Decay events ``1 energetic lepton($l$) + 4jets'' should appear twelve times as often as ``$\mu^\pm e^\mp \,2jets$'' events and can be analysed to give estimates for $P(m_t|l\, 4jets)$. There may be background from non-top events but suitable cuts on the data and our analysis procedure together reduce this to a low level. The rate observed for these events does not appear to be as large as this factor 12. Identification of either or both of the $(b \bar{b})$ jets would be a great step forward. We advocate an energetic approach to the analysis of individual events on an event by event basis, with the hope of finding a subgroup of events with a common mass estimate.
We develop an effective numerical method of studying large-time properties of reversible reaction-diffusion systems of type A + B <-> C with initially separated reactants. Using it we find that there are three types of asymptotic reaction zones. In particular we show that the reaction rate can be locally negative and concentrations of species A and B can be nonmonotonic functions of the space coordinate x, locally significantly exceeding their initial values.
Two rooted locally finite trees are considered equivalent if both can be embedded into each other as topological minors by means of tree-order preserving mappings. By exploiting Nash-William's Theorem, Matthiesen provided a non-constructive proof of the uncountability of such equivalence classes, thus answering a question of van der Holst. As an open problem, Matthiesen asks for a constructive proof of this fact. The purpose of this paper is to provide one such construction; working solely within ZFC we illustrate a collection of !1 many topological types of rooted trees. In particular, we also show that this construction strengthens that of Matthiesen in that it also applies to free (unrooted) trees of degree two.
Soft Collinear Effective Theory (SCET) is an effective field theory which describes the interactions of low invariant mass jets which are highly boosted with respect to one another. In the standard formulation of SCET, the effective Lagrangian for collinear fields is expanded in inverse powers of the energy. At leading order this leads to manifest decoupling of soft and collinear degrees of freedom; however, subleading terms in the effective Lagrangian violate this manifest decoupling. In this paper we point out that the collinear expansion in the SCET Lagrangian is unnecessary, and that the SCET Lagrangian may instead be written as multiple decoupled copies of QCD. The interactions between the sectors in full QCD are reproduced in the effective theory by an external current consisting of QCD fields coupled to Wilson lines. We illustrate this picture with two examples: dijet production and B->X_s + gamma.
We consider simple random walk on Z^d, d bigger or equal to 3. Motivated by the work of A.-S. Sznitman and the author in arXiv:1304.7477 and arXiv:1310.2177, we investigate the asymptotic behaviour of the probability that a large body gets disconnected from infinity by the set of points visited by a simple random walk. We derive asymptotic lower bounds that bring into play random interlacements. Although open at the moment, some of the lower bounds that we obtain possibly match the asymptotic upper bounds obtained in a recent article of A.-S. Sznitman. This potentially yields special significance to the tilted walks that we use in this work, and to the strategy that we employ to implement disconnection.
In this paper we compute the holonomies along curves in the gravitational field of a slowly rotating massive body. We use our results to study the gravitational analogue of Aharanov-Bohm effect in this space-time. We also investigate the behaviour of a scalar quantum particle in this space-time and determine Berry's quantum phase acquired by this particle when transported along a closed curve surrounding the body.
Interferometric observations of two well-known Be stars, gamma Cas and phi Per, were collected and analyzed to determine the spatial characteristics of their circumstellar regions. The observations were obtained using the Navy Prototype Optical Interferometer equipped with custom-made narrowband filters. The filters isolate the H-alpha emission line from the nearby continuum radiation, which results in an increased contrast between the interferometric signature due to the H-alpha-emitting circumstellar region and the central star. Because the narrowband filters do not significantly attenuate the continuum radiation at wavelengths 50 nm or more away from the line, the interferometric signal in the H-alpha channel is calibrated with respect to the continuum channels. The observations used in this study represent the highest spatial resolution measurements of the H-alpha-emitting regions of Be stars obtained to date. These observations allow us to demonstrate for the first time that the intensity distribution in the circumstellar region of a Be star cannot be represented by uniform disk or ring-like structures, whereas a Gaussian intensity distribution appears to be fully consistent with our observations.
Previous radio observations revealed widespread gas-phase methanol (CH$_3$OH) in the Central Molecular Zone (CMZ) at the Galactic center (GC), but its origin remains unclear. Here, we report the discovery of CH$_3$OH ice toward a star in the CMZ, based on a Subaru $3.4$-$4.0\ \mu$m spectrum, aided by NASA/IRTF $L'$ imaging and $2$-$4\ \mu$m spectra. The star lies $\sim8000$ au away in projection from a massive young stellar object (MYSO). Its observed high CH$_3$OH ice abundance ($17\%\pm3\%$ relative to H$_2$O ice) suggests that the $3.535\ \mu$m CH$_3$OH ice absorption likely arises in the MYSO's extended envelope. However, it is also possible that CH$_3$OH ice forms with a higher abundance in dense clouds within the CMZ, compared to within the disk. Either way, our result implies that gas-phase CH$_3$OH in the CMZ can be largely produced by desorption from icy grains. The high solid CH$_3$OH abundance confirms the prominent $15.4\ \mu$m shoulder absorption observed toward GC MYSOs arises from CO$_2$ ice mixed with CH$_3$OH.
We present detailed elemental abundances, radial velocity, and orbital elements for Patchick~125, a recently discovered metal-poor globular cluster (GC) in the direction of the Galactic bulge. Near-infrared high-resolution ($R\sim22,500$) spectra of two members were obtained during the second phase of the Apache Point Observatory Galactic Evolution Experiment at Las Campanas Observatory as part of the sixteenth Data Release (DR 16) of the Sloan Digital Sky Survey. We investigated elemental abundances for four chemical species, including $\alpha$- (Mg, Si), Fe-peak (Fe), and odd-Z (Al) elements. We find a metallicity covering the range from [Fe/H] $= -1.69$ to $-1.72$, suggesting that Patchick~125 likely exhibits a mean metallicity $\langle$[Fe/H]$\rangle \sim -1.7$, which represents a significant increase in metallicity for this cluster compared to previous low-resolution spectroscopic analyses. We also found a mean radial velocity of 95.9 km s$^{-1}$, which is $\sim$21.6 km s$^{-1}$ higher than reported in the literature. The observed stars exhibit an $\alpha$-enrichment ([Mg/Fe]$\lesssim+0.20$, and [Si/Fe]$\lesssim +0.30$) that follows the typical trend of metal-poor GCs. The aluminum abundance ratios for the present two member stars are enhanced in [Al/Fe]$\gtrsim +0.58$, which is a typical enrichment characteristic of the so-called `second-generation' of stars in GCs at similar metallicity. This supports the possible presence of the multiple-population phenomenon in Patchick~125, as well as its genuine GC nature. Further, Patchick~125 shows a low-energy, low-eccentric ($<0.4$) and retrograde orbit captured by the inner Galaxy, near the edge of the bulge. We confirm that Patchick~125 is a genuine metal-poor GC, which is currently trapped in the vicinity of the Milky Way bulge.
In this paper, we employ Machine Learning algorithms on multi-mission observations for the classification of accretion states of outbursting Black hole X-ray binaries for the first time. Archival data from RXTE, Swift, MAXI and AstroSat observatories are used to generate the hardness intensity diagrams (HIDs) for outbursts of the sources XTE J1859+226 (1999 outburst), GX 339-4 (2002, 2004, 2007 and 2010 outbursts), IGR J17091-3624 (2016 outburst), and MAXI J1535-571 (2017 outburst). Based on variation of X-ray flux, hardness ratios, presence of various types of Quasi-periodic Oscillations (QPOs), photon indices and disk temperature, we apply clustering algorithms like K-Means clustering and Hierarchical clustering to classify the accretion states (clusters) of each outburst. As multiple parameters are involved in the classification process, we show that clustering algorithms club together the observations of similar characteristics more efficiently than the `standard' method of classification. We also infer that K-Means clustering provides more reliable results than Hierarchical clustering. We demonstrate the importance of the classification based on machine learning by comparing it with results from `standard' classification.
The reaction dynamics of axisymmetric deformed $^{24}$Mg + $^{24}$Mg collisions have been investigated systematically by an isospin-dependent quantum molecular dynamics (IDQMD) model. It is found that different deformations and orientations result in apparently different properties of reaction dynamics. We revealed that some observables such as nuclear stopping power ($R$), multiplicity of fragments, and elliptic flow are very sensitive to the initial deformations and orientations. There exists an eccentricity scaling of elliptic flow in central body-body collisions with different deformations. In addition, the tip-tip and body-body configurations turn out to be two extreme cases in central reaction dynamical process.
Explicit bases for the spaces of holomorphic cusp forms of all even positive weights and all orders are constructed. The dimensions of these spaces are computed.
In this paper we study the possibility of efficient pair production in a pulsar's magnetosphere. It has been shown that by means of the relativistic centrifugal force the electrostatic field exponentially amplifies. As a result the field approaches the Schwinger limit leading to pair creation process in the light cylinder area where the effects of rotation are very efficient. Analysing the parameters of the normal period ($\sim 1$ sec) pulsars we have found that the process is so efficient that the number density of electron-positron pairs exceeds the Goldreich-Julian density by five orders of magnitude.
To simplify the parameter of the deep learning network, a cascaded compressive sensing model "CSNet" is implemented for image classification. Firstly, we use cascaded compressive sensing network to learn feature from the data. Secondly, CSNet generates the feature by binary hashing and block-wise histograms. Finally, a linear SVM classifier is used to classify these features. The experiments on the MNIST dataset indicate that higher classification accuracy can be obtained by this algorithm.
We propose a novel framework to learn the spatiotemporal variability in longitudinal 3D shape data sets, which contain observations of objects that evolve and deform over time. This problem is challenging since surfaces come with arbitrary parameterizations and thus, they need to be spatially registered. Also, different deforming objects, also called 4D surfaces, evolve at different speeds and thus they need to be temporally aligned. We solve this spatiotemporal registration problem using a Riemannian approach. We treat a 3D surface as a point in a shape space equipped with an elastic Riemannian metric that measures the amount of bending and stretching that the surfaces undergo. A 4D surface can then be seen as a trajectory in this space. With this formulation, the statistical analysis of 4D surfaces can be cast as the problem of analyzing trajectories embedded in a nonlinear Riemannian manifold. However, performing the spatiotemporal registration, and subsequently computing statistics, on such nonlinear spaces is not straightforward as they rely on complex nonlinear optimizations. Our core contribution is the mapping of the surfaces to the space of Square-Root Normal Fields where the L2 metric is equivalent to the partial elastic metric in the space of surfaces. Thus, by solving the spatial registration in the SRNF space, the problem of analyzing 4D surfaces becomes the problem of analyzing trajectories embedded in the SRNF space, which has a Euclidean structure. In this paper, we develop the building blocks that enable such analysis. These include: (1) the spatiotemporal registration of arbitrarily parameterized 4D surfaces in the presence of large elastic deformations and large variations in their execution rates; (2) the computation of geodesics between 4D surfaces; (3) the computation of statistical summaries; and (4) the synthesis of random 4D surfaces.
We construct N = 2 chiral supergravity (SUGRA) which leads to Ashtekar's canonical formulation. The supersymmetry (SUSY) transformation parameters are not constrained at all and auxiliary fields are not required in contrast with the method of the two-form gravity. We also show that our formulation is compatible with the reality condition, and that its real section is reduced to the usual N = 2 SUGRA up to an imaginary boundary term.
Observations of galactic nuclei help us to test General Relativity. Whereas the No-hair Theorem states that classical, isolated black holes eventually settle to a stationary state that can be characterized by a small number of parameters, cosmic black holes are neither isolated nor steady. Instead, they interact with the environment and evolve on vastly different time-scales. Therefore, the astrophysically realistic models require more parameters, and their values likely change in time. New techniques are needed in order to allow us to obtain independent constraints on these additional parameters. In this context, non-electromagnetic messengers have emerged and a variety of novel electromagnetic observations is going to supplement traditional techniques in the near future. In this outline, we summarize several fruitful aspects of electromagnetic signatures from accretion disks in strong-gravity regime in the outlook of upcoming satellite missions and ground-based telescopes. As an interesting example, we mention a purely geometrical effect of polarization angle changes upon light propagation, which occurs near the black hole event horizon. Despite that only numerical simulations can capture the accretion process in a realistic manner, simplified toy-models and semi-analytical estimates are useful to understand complicated effects of strong gravity near the event horizon of a rotating black hole, and especially within the plunging region below the innermost stable circular orbit.
We consider an inert Higgs doublet (IHD) extension of the Standard Model accompanied with three right handed neutrinos and a dark sector, consisting of a singlet fermion and a scalar, in order to provide a common framework for dark matter, leptognesis and neutrino mass. While the Yukawa coupling of the right handed neutrinos with IHD (having mass in the intermediate regime: 80-500 GeV) is responsible for explaining the observed baryon asymmetry through leptogenesis, its coupling with the dark sector explains the dark matter relic density. The presence of IHD also explains the neutrino mass through radiative correction. We find that study of the high scale validity of the model in this context becomes crucial as it restricts the parameter space significantly. It turns out that there exists a small, but non-zero contribution to the relic density of DM from IHD too. Considering all the constraints from dark matter, leptogenesis, neutrino mass and high scale validity of the model, we perform a study to find out the viable parameter space.
We review the results of a timing analysis of the observations for ten bright X-ray pulsars (with fluxes >100 mCrab in the 20-100 keV energy band) that fell within the INTEGRAL field of view from 2003 to 2007. The dependence of the pulse profile on the energy and intrinsic source luminosity has been investigated; particular attention has been paid to searching for changes in the pulse profile near the cyclotron frequency. The dependence of the pulsed fraction for X-ray pulsars on their luminosity and energy band has been studied in detail for the first time.
We have studied the spin-splitting effect in a four-terminal two-dimensional (2D) electron gas system with two potential barriers generated by two surface metal gates and an external perpendicular magnetic field. The calculations show that by tuning the voltage applied on the gates, the injected spin-unpolarized current can be split into different spin currents with a high efficiency. The split currents flow out of the geometry from different output leads separately. The spin freedom of the outputs can be controlled by simply tuning voltage on gates. This phenomenon is a result of the combination of three effects - the potential barriers, Zeeman splitting and edge current. Furthermore, by tuning the voltage on gates, the outflow spin of current in one terminal can be switched. Therefore, these features open up a possibility for making a spin filter or a switcher device by applying the four-terminal 2D electron gas system.
We consider the neutralino as a dominant Dark Matter particle in the galactic halo and investigate some general issues of direct Dark Matter searches via elastic neutralino-nucleus scattering. On the basis of conventional assumptions about the nuclear and nucleon structure we analyse constraints on SUSY model parameter space accessible by the direct Dark Matter searches. This analysis shows that Dark Matter detectors fall into the THREE different categories with respect to their sensitivity to different groups of the SUSY model parameters. We calculate the event rate for various experimentally interesting isotopes within the Minimal Supersymmetric Standard Model (MSSM) taking into account the known accelerator and cosmological constraints on the MSSM parameter space. We investigate the role of nuclear spin in elastic neutralino - nucleus scattering. It is found that the contribution of the spin-dependent interaction to this process is subdominant for nuclei with atomic weights A > 50.
We introduce a simple single-system game inspired by the Clauser-Horne-Shimony-Holt (CHSH) game. For qubit systems subjected to unitary gates and projective measurements, we prove that any strategy in our game can be mapped to a strategy in the CHSH game, which implies that Tsirelson's bound also holds in our setting. More generally, we show that the optimal success probability depends on the reversible or irreversible character of the gates, the quantum or classical nature of the system and the system dimension. We analyse the bounds obtained in light of Landauer's principle, showing the entropic costs of the erasure associated with the game. This shows a connection between the reversibility in fundamental operations embodied by Landauer's principle and Tsirelson's bound, that arises from the restricted physics of a unitarily-evolving single-qubit system.
In bilayers of two-dimensional (2D) semiconductors with stacking arrangements which lack inversion symmetry charge transfer between the layers due to layer-asymmetric interband hybridisation can generate a potential difference between the layers. We analyse bilayers of transition metal dichalcogenides (TMDs) - in particular, WSe$_2$ - for which we find a substantial stacking-dependent charge transfer, and InSe, for which the charge transfer is found to be negligibly small. The information obtained about TMDs is then used to map potentials generated by the interlayer charge transfer across the moir\'e superlattice in twistronic bilayers.