ShantanuT01/DACTYL-Pretraining huggingface dataset:
For a $k$-uniform hypergraph $H$, we obtain some trace formulas for the Laplacian tensor of $H$, which imply that $\sum_{i=1}^nd_i^s$ ($s=1,\ldots,k$) is determined by the Laplacian spectrum of $H$, where $d_1,\ldots,d_n$ is the degree sequence of $H$. Using trace formulas for the Laplacian tensor, we obtain expressions for some coefficients of the Laplacian polynomial of a regular hypergraph. We give some spectral characterizations of odd-bipartite hypergraphs, and give a partial answer to a question posed by Shao et al \cite{ShaoShanWu}. We also give some spectral properties of power hypergraphs, and show that a conjecture posed by Hu et al \cite{HuQiShao} holds under certain conditons.
We describe a first-principles statistical mechanics approach enabling us to simulate the steady-state situation of heterogeneous catalysis. In a first step density-functional theory together with transition-state theory is employed to obtain the energetics of all relevant elementary processes. Subsequently the statistical mechanics problem is solved by the kinetic Monte Carlo method, which fully accounts for the correlations, fluctuations, and spatial distributions of the chemicals at the surface of the catalyst under steady-state conditions. Applying this approach to the catalytic oxidation of CO at RuO2(110), we determine the surface atomic structure and composition in reactive environments ranging from ultra-high vacuum (UHV) to technologically relevant conditions, i.e. up to pressures of several atmospheres and elevated temperatures. We also compute the CO2 formation rates (turnover frequencies). The results are in quantitative agreement with all existing experimental data. We find that the high catalytic activity of this system is intimately connected with a disordered, dynamic surface ``phase'' with significant compositional fluctuations. In this active state the catalytic function results from a self-regulating interplay of several elementary processes.
Intrinsic time-dependent invariants are constructed for classical, flat, homogeneous, anisotropic cosmology with a massless scalar material source. Invariance under the time reparameterization-induced canonical symmetry group is displayed explicitly.
We study the regularity of minimizers of a two-phase free boundary problem. For a class of n-dimensional convex domains, we establish the Lipschitz continuity of the minimizer up to the fixed boundary under Neumann boundary conditions. Our proof uses an almost monotonicity formula for the Alt-Caffarelli-Friedman functional restricted to the convex domain. This requires a variant of the classical Friedland-Hayman inequality for geodesically convex subsets of the sphere with Neumann boundary conditions. To apply this inequality, in addition to convexity, we require a Dini condition governing the rate at which the fixed boundary converges to its limit cone at each boundary point.
Recent observations of high energy (> 20 keV) X-ray emission in a few clusters of galaxies broaden our knowledge of physical phenomena in the intracluster space. This emission is likely to be nonthermal, probably resulting from Compton scattering of relativistic electrons by the cosmic microwave background (CMB) radiation. Direct evidence for the presence of relativistic electrons in some 50 clusters comes from measurements of extended radio emission in their central regions. We briefly review the main results from observations of extended regions of radio emission, and Faraday rotation measurements of background and cluster radio sources. The main focus of the review are searches for nonthermal X-ray emission conducted with past and currently operating satellites, which yielded appreciable evidence for nonthermal emission components in the spectra of a few clusters. This evidence is clearly not unequivocal, due to substantial observational and systematic uncertainties, in addition to virtually complete lack of spatial information. If indeed the emission has its origin in Compton scattering of relativistic electrons by the CMB, then the mean magnetic field strength and density of relativistic electrons in the cluster can be directly determined. Knowledge of these basic nonthermal quantities is valuable for the detailed description of processes in intracluster gas and for the origin of magnetic fields.
Context: We present results of an extensive world-wide observing campaign of MN Draconis.   Aims: MN Draconis is a poorly known active dwarf nova in the period gap and is one of the only two known cases of period gap SU UMa objects showing the negative superhumps. Photometric behaviour of MN Draconis poses a challenge for existing models of the superhump and superoutburst mechanisms. Therefore, thorough investigation of peculiar systems, such as MN Draconis, is crucial for our understanding of evolution of the close binary stars.   Methods: To measure fundamental parameters of the system, we collected photometric data in October 2009, June-September 2013 and June-December 2015. Analysis of the light curves, $O-C$ diagrams and power spectra was carried out.   Results: During our three observational seasons we detected four superoutburts and several normal outbursts. Based on the two consecutive superoutbursts detected in 2015, the supercycle length was derived P_sc = 74 +/- 0.5 days and it has been increasing with a rate of P_dot = 3.3 x 10^(-3) during last twelve years. Based on the positive and negative superhumps we calculated the period excess epsilon = 5.6% +/- 0.1%, the period deficit epsilon_ = 2.5% +/- 0.6%, and in result, the orbital period P_orb = 0.0994(1) days (143.126 +/- 0.144 min). We updated the basic light curve parameters of MN Draconis.   Conclusions: MN Draconis is the first discovered SU UMa system in the period gap with increasing supercycle length.
Upcoming large-scale ground- and space- based supernova surveys will face a challenge identifying supernova candidates largely without the use of spectroscopy. Over the past several years, a number of supernova identification schemes have been proposed that rely on photometric information only. Some of these schemes use color-color or color-magnitude diagrams; others simply fit supernova data to models. Both of these approaches suffer a number of drawbacks partially addressed in the so-called Bayesian-based supernova classification techniques. However, Bayesian techniques are also problematic in that they typically require that the supernova candidate be one of a known set of supernova types. This presents a number of problems, the most obvious of which is that there are bound to be objects that do not conform to any presently known model in large supernova candidate samples. We propose a new photometric classification scheme that uses a Bayes factor based on color in order to identify supernovae by type. This method does not require knowledge of the complete set of possible astronomical objects that could mimic a supernova signal. Further, as a Bayesian approach, it accounts for all systematic and statistical uncertainties of the measurements in a single step. To illustrate the use of the technique, we apply it to a simulated dataset for a possible future large-scale space-based Joint Dark Energy Mission and demonstrate how it could be used to identify Type Ia supernovae. The method's utility in pre-selecting and ranking supernova candidates for possible spectroscopic follow-up -- i.e., its usage as a supernova trigger -- will be briefly discussed.
We present spectroscopic analysis of the low mass binary star system GJ 660.1AB, a pair of nearby M dwarfs for which we have obtained separated near-infrared spectra (0.9-2.5 $\mu$m) with the SpeX spectrograph. The spectrum of GJ 660.1B is distinctly peculiar, with a triangular-shaped 1.7 $\mu$m peak that initially suggests it to be a low surface gravity, young brown dwarf. However, we rule out this hypothesis and determine instead that this companion is a mild subdwarf (d/sdM7) based on the subsolar metallicity of the primary, [Fe/H] = $-$0.63$\pm$0.06. Comparison of the near-infrared spectrum of GJ 660.1B to two sets of spectral models yields conflicting results, with a common effective temperature T$_{eff}$ = 2550-2650 K, but alternately low surface gravity ($\log{g}$ = 4.4$\pm$0.5 cgs) and very low metallicity ([M/H] = $-$0.96$^{+0.19}_{-0.24}$), or high surface gravity ($\log{g}$ = 5.0-5.5) and slightly subsolar metallicity ([M/H] =$-$0.20$^{+0.13}_{-0.19}$). We conjecture that insufficient condensate opacity and excessive collision induced H$_2$ absorption in the models bias them toward low surface gravities and a metallicity inconsistent with the primary, and points toward improvements needed in the spectral modeling of metal-poor, very-low mass dwarfs. The peculiar spectral characteristics of GJ 660.1B emphasize that care is needed when interpreting surface gravity features in the spectra of ultracool dwarfs.
We study the $P-V/r_{+}$ criticality and phase transition of quantum-corrected black hole in asymptotic safety (AS) gravity in the extended phase space. For the black hole, the cosmological constant is dependent on the momentum cutoff or energy scale, therefore one can naturally treat it as a variable and connect it with the thermodynamic pressure. We find that for the quantum-corrected black hole there is a similar first-order phase transition to that of the van der Waals liquid/gas system. We also analyze the types of the phase transition at the critical points according to Ehrenfest's classification. It is shown that they are second-order phase transition.
Multi-view clustering attracts much attention recently, which aims to take advantage of multi-view information to improve the performance of clustering. However, most recent work mainly focus on self-representation based subspace clustering, which is of high computation complexity. In this paper, we focus on the Markov chain based spectral clustering method and propose a novel essential tensor learning method to explore the high order correlations for multi-view representation. We first construct a tensor based on multi-view transition probability matrices of the Markov chain. By incorporating the idea from robust principle component analysis, tensor singular value decomposition (t-SVD) based tensor nuclear norm is imposed to preserve the low-rank property of the essential tensor, which can well capture the principle information from multiple views. We also employ the tensor rotation operator for this task to better investigate the relationship among views as well as reduce the computation complexity. The proposed method can be efficiently optimized by the alternating direction method of multipliers~(ADMM). Extensive experiments on six real world datasets corresponding to five different applications show that our method achieves superior performance over other state-of-the-art methods.
We present a class of exact ground states of a three-dimensional periodic Anderson model at 3/4 filling. Hopping and hybridization of d and f electrons extend over the unit cell of a general Bravais lattice. Employing novel composite operators combined with 55 matching conditions the Hamiltonian is cast into positive semidefinite form. A product wave function in position space allows one to identify stability regions of an insulating and a conducting ground state. The metallic phase is a non-Fermi liquid with one dispersing and one flat band.
The point-form version of the Bakamjian-Thomas construction is applied to the description of several semileptonic decays of mesons. Weak form factors are extracted without ambiguity for pseudoscalar-to-pseudoscalar as well as for pseudoscalar-to-vector transitions of mesons from the most general covariant decomposition of the weak current. No manifestation of cluster-separability violation appears in the form of non-physical contributions to the structure of such a current, in contrast to what happens in the electromagnetic case. Moreover, no frame dependence is observed when we extract the form factors from the most general covariant decomposition of the current, which contrasts with analogous front-form calculations that involve vector mesons in the transition. We present our results for heavy-light meson decays, i.e. $B\to D$, as well as for $B$ and $D$ mesons decaying into $\pi$, $\rho$ and $K^{(*)}$ and perform a numerical comparison with the analogous front-form approach. Differences between point and front forms that are not seen in the heavy-quark limit of $q\bar Q$-systems appear. These differences are attributed to the different role that the non-valence contributions play in the description of hadronic reactions in each form. It is argued how contributions from missing $Z$-graphs can be estimated.
We study the occurrence of spectroscopic binaries in young star-forming regions using the INfrared Spectroscopy of Young Nebulous Clusters(IN-SYNC) survey, carried out in SDSS-III with the APOGEE spectrograph. Multi-epoch observations of thousands of low-mass stars in Orion A, NGC 2264, NGC 1333, IC 348, and the Pleiades have been carried out, yielding H-band spectra with a nominal resolution of R=22,500 for sources with H $\le$ 12 mag. Radial velocity precisions of $\sim$0.3 $km\:s^{-1}$ were achieved, which we use to identify radial velocity variations indicative of undetected companions. We use Monte Carlo simulations to assess the types of spectroscopic binaries to which we are sensitive, finding sensitivity to binaries with orbital periods $< 10^{4}$ d, for stars with $2500 {\rm K} \le T_\mathrm{eff} \le 6000 {\rm K}$ and $\it{v} \sin \it{i}$ $\le$ 100 $km\:s^{-1}$. Using Bayesian inference, we find evidence for a decline in the spectroscopic binary fraction, by a factor of 3-4 from the age of our pre-main-sequence sample to the Pleiades age . The significance of this decline is weakened if spot-induced radial-velocity jitter is strong in the sample, and is only marginally significant when comparing any one of the pre-main-sequence clusters against the Pleiades. However, the same decline in both sense and magnitude is found for each of the five pre-main-sequence clusters, and the decline reaches statistical significance of greater than 95% confidence when considering the pre-main-sequence clusters jointly. Our results suggest that dynamical processes disrupt the widest spectroscopic binaries ($P_{\rm orb} \approx 10^3 - 10^4$ d) as clusters age, indicating that this occurs early in the stars' evolution, while they still reside within their nascent clusters.
Pedestrian Attribute Recognition (PAR) is a challenging task in intelligent video surveillance. Two key challenges in PAR include complex alignment relations between images and attributes, and imbalanced data distribution. Existing approaches usually formulate PAR as a recognition task. Different from them, this paper addresses it as a decision-making task via a reinforcement learning framework. Specifically, PAR is formulated as a Markov decision process (MDP) by designing ingenious states, action space, reward function and state transition. To alleviate the inter-attribute imbalance problem, we apply an Attribute Grouping Strategy (AGS) by dividing all attributes into subgroups according to their region and category information. Then we employ an agent to recognize each group of attributes, which is trained with Deep Q-learning algorithm. We also propose a Group Optimization Reward (GOR) function to alleviate the intra-attribute imbalance problem. Experimental results on the three benchmark datasets of PETA, RAP and PA100K illustrate the effectiveness and competitiveness of the proposed approach and demonstrate that the application of reinforcement learning to PAR is a valuable research direction.
We study the narrow emission line properties and stellar populations of a sample of 1385 AGN selected to have strong excess emission at mid-infrared wavelengths based on comparing Wide-field Infrared Survey Explorer W1-W2 band colours with optical stellar absorption line indicators. Our goal is to understand whether the physical conditions in the interstellar medium of these objects differ from those of local AGN selected by their optical emission line ratios. To enable this comparison, we construct a control sample of 50,000 optically-selected AGN with the same redshifts that do not have strong mid-IR excess emission. The mid-IR excess and control samples differ strongly in [OIII] line luminosity, ionized gas excitation mechanism, ionization state and electron density. We show that the radio-detected, mid-IR excess AGN constitute the most luminous and highly ionized AGN in the local Universe and they contribute primarily to the growth of black holes in the most massive galaxies. At least half of this black hole growth is occurring in galaxies with recent starbursts. The morphologies of these systems indicate that the starbursts have probably been triggered by galaxy-galaxy mergers and interactions. The most luminous AGN in our mid-IR excess sample have properties that are similar to the Type II quasars studied at higher redshifts. In contrast, the control sample constitute a class of lower ionization, less luminous AGN in more quiescent galaxies that contribute primarily to the growth of low mass black holes.
We revisit a result by Cuccagna, Kirr and Pelinovsky about the cubic nonlinear Schr\" odinger equation (NLS) with an attractive localized potential and a time-dependent factor in the nonlinearity. We show that, under generic hypotheses on the linearization at 0 of the equation, small energy solutions are asymptotically free. This is yet a new application of the hamiltonian structure, continuing a program initiated in a paper by Bambusi and Cuccagna.
An example of the macroscopic game of two partners consisting of two classical games played simultaneously with special dependence of strategies is considered. The average profit of each partner is equal to the average profit obtained in the quantum game with two noncommuting operators for the spin one half system with strategies defined by the wave function. Nash equilibria in the macroscopic game coincide with Nash equilibria of the quantum game.
The guest star of AD 1181 is the only historical supernova of the last millennium that is without a definite counterpart. The previously proposed association with supernova remnant 3C58 is in strong doubt because of the inferred age of this remnant. Here we report a new identification of SN 1181 with our codiscovery of the hottest known Wolf Rayet star of the Oxygen sequence (dubbed Parkers star) and its surrounding nebula Pa 30. Our spectroscopy of the nebula shows a fast shock with extreme velocities of approx. 1,100kms. The derived expansion age of the nebula implies an explosive event approx 1,000 years ago which agrees with the 1181 AD event. The on sky location also fits the historical Chinese and Japanese reports of SN 1181 to 3.5degrees. Pa 30 and Parkers star have previously been proposed to be the result of a double-degenerate merger, leading to a rare Type Iax supernova. The likely historical magnitude and the distance suggest the event was subluminous for normal supernova. This agrees with the proposed Type Iax association which would also be the first of its kind in the Galaxy. Taken together, the age, location, event magnitude and duration elevate Pa 30 to prime position as the counterpart of SN 1181. This source is the only Type Iax supernova where detailed studies of the remnant star and nebula are possible. It provides strong observational support for the double degenerate merger scenario for Type Iax supernovae.
The use of roman numerals for stellar populations represents a classification approach to galaxy formation which is now well behind us. Nevertheless, the concept of a pristine generation of stars, followed by a protogalactic era, and finally the mainstream stellar population is a plausible starting point for testing our physical understanding of early star formation. This will be observationally driven as never before in the coming decade. In this paper, we search out observational tests of an idealized coeval and homogeneous distribution of population II stars. We examine the spatial distribution of quasars, globular clusters, and the integrated free electron density of the intergalactic medium, in order to test the assumption of homogeneity. Any $real$ inhomogeneity implies a population II that is not coeval.
We analyze the extraction of weak phases from CP violation in $B\to\pi^+\pi^-$ decays. We propose to determine the unitarity triangle $(\bar\rho,\bar\eta)$ by combining the information on mixing induced CP violation in $B\to\pi^+\pi^-$, $S$, with the precision observable $\sin 2\beta$ obtained from the CP asymmetry in $B\to\psi K_S$. It is then possible to write down exact analytical expressions for $\bar\rho$ and $\bar\eta$ as simple functions of the observables $S$ and $\sin 2\beta$, and of the penguin parameters $r$ and $\phi$. As an application clean lower bounds on $\bar\eta$ and $1-\bar\rho$ can be derived as functions of $S$ and $\sin 2\beta$, essentially without hadronic uncertainty. Computing $r$ and $\phi$ within QCD factorization yields precise determinations of $\bar\rho$ and $\bar\eta$ since the dependence on $r$ and $\phi$ is rather weak. It is emphasized that the sensitivity to the phase $\phi$ enters only at second order and is extremely small for moderate values of this phase, predicted in the heavy-quark limit. Transparent analytical formulas are further given and discussed for the parameter $C$ of direct CP violation in $B\to\pi^+\pi^-$. We also discuss alternative ways to analyze $S$ and $C$ that can be useful if new physics affects $B_d$--$\bar B_d$ mixing. Predictions and uncertainties for $r$ and $\phi$ in QCD factorization are examined in detail. It is pointed out that a simultaneous expansion in $1/m_b$ and 1/N leads to interesting simplifications. At first order infrared divergences are absent, while the most important effects are retained. Independent experimental tests of the factorization framework are briefly discussed.
The higher order corrections of SU(3) rotating excited states to the Gell-Mann-Okubo Relations (or GOR) are presented in the standard SU(3) Skyrme model.The Improved GOR (or IGOR) are obtained. The results show the IGOR for decuplet up to the third order and for octet up to the second order are much compatible with the experimental data. But things becomes quite inadequate for the octet to the third order. In order to overcome the inadequacy, a heuristic discussion is presented. The properties of SU(3) rotating excited states 27-let(with spin 1/2 or 3/2),10$^*$-let (with spin 1/2) and 35-let (with spin 3/2) are also discussed.
We obtain a necessary and sufficient condition in order that a semi-plane of the form $\Re(s)>r$, $r\in \mathbb{R}$, is free of zeros of a given Dirichlet polynomial. The result may be considered a natural generalization of a well-known criterion for the truth of the Riemann hypothesis due to B\'aez-Duarte. An analog for the case of Dirichlet polynomials of a result of Burnol which is closely related to B\'aez-Duarte's one is also established.
In this paper we prove that for a certain class of initial data, smooth solutions of the hydrostatic Euler equations blow up in finite time.
The continued-fraction method was developed systematically by Risken and co-workers to solve problems of arbitrary fluctuations in nonlinear systems. However, this efficient technique is limited to problems with a few variables, which in practice means systems of noninteracting entities (particles, spins, etc.) We illustrate how to extend the continued-fraction method to weakly coupled systems with the problem of relaxation in classical spins.
With the experimental data from STAR and PHENIX on the centrality dependence of the $p_T$ spectra of protons and anti-protons produced at mid-rapidity in Au+Au collisions at 200 GeV, we show that for protons and anti-protons there exists a scaling distribution independent of the colliding centrality. The scaling functions can also describe data from BRAHMS for both proton and anti-proton spectra at $y=2.2$ and 3.2. The scaling behaviors are shown to be incompatible with the usual string fragmentation scenario for particle production.